To assess how sensitive connectivity estimates are to the completeness level of the tracing, we compared both the pre- and postsynaptic connectivity of a selection of neurons (see Materials and methods) arborizing in a specific brain structure, the EB, before and after it was subjected to focused proofreading (Figure 3A). Proofreading increased the number of pre- and postsynapses for which the synaptic partner could now be identified (Figure 3B), mainly by merging small dendritic fragments onto known neurons. However, the relative synaptic contributions that each neuron received from its various partners remained largely the same before and after dense proofreading (example fit for the EPG neuron of Figure 3A is shown in Figure 3C, the slopes from regression analyses of all neurons are shown in Figure 3D). Indeed, with the exception of some FB neurons with minor projections in the EB (green points in Figure 3D, right), the input and output connectivity of most neurons did not significantly change when expressed as relative weights (Figure 3D, see also Figure 3—figure supplement 1).

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In addition to comparing connectivity for the same neurons at different completion levels, we also examined connectivity in different subregions that were proofread to differing levels of completeness. Parts of the PB (glomeruli L4 and R3) and FB (the third column) were intentionally proofread to a denser level of completeness than other areas within those structures. In addition, although we did not perform an analysis of these differences, the right NO was more densely proofread than the left NO (Scheffer et al., 2020). These differences in level of completeness must be kept in mind when interpreting synapse counts in these regions.

In the PB, we compared connectivity within the densely proofread R3 and L4 glomeruli to their less densely proofread mirror-symmetric glomeruli, L3 and R4, respectively. For a meaningful comparison, we focused our connectivity analysis on neurons with arbors restricted to single PB glomeruli (Figure 4Ai, e.g., shows examples of PFNa neurons that innervate L3 and R3, respectively). The impact of dense proofreading in the PB was evident in the increased percentage of synapses from or to identified partners of neurons of the same type in the densely proofread glomeruli, L4 and R3 (Figure 4Aii, for presynaptic partners, left, and postsynaptic partners, right). However, as with the EB comparison before and after dense proofreading (Figure 3), we found that the relative contributions of different identified partners onto the selected types remained nearly unchanged across the two glomeruli (see Figure 4Aiii and Aiv for an example regression), both for inputs and outputs. As a control, we also performed the same analyses on two additional pairs of mirror-symmetric PB glomeruli, L5 and R5, and L6 and R6 (Figure 4—figure supplement 1), finding no more differences in relative contributions than we found when comparing the L3-R3 and L4-R4 pairs.

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Finally, we also selected a columnar region within the medial part of the FB (‘C3’) for focused proofreading (Figure 4Bi). As with the EB and PB, this process led to an increase in the percentage of synapses with identified partners (Figure 4Bii) without significant changes in relative connectivity when compared to other columns of the FB (Figure 4Biv). Note that correlations in connectivity in the FB are lower than those observed in the PB (compare Figure 4Aiv with Figure 4Biv). We believe this to be the result of both the lack of clear columnar definition in the FB and of true inhomogeneities across vertical sections of the FB, as we discuss further in the FB section.

The anterior visual pathway brings visual information from the medulla into the small subunit of the AOTU (AOTUsu, also called ‘lower unit of the AOTU’ in other insects), and thence to the BU’s ring neurons (Hanesch et al., 1989), which deliver highly processed information to the EB (Omoto et al., 2017; Timaeus et al., 2020; Figure 6A and B, Video 1, Video 2). The ring neurons, which are called TL neurons in other insects (Homberg et al., 1999; Muller et al., 1997), are fed by multiple, developmentally distinguishable types of visually responsive neurons from the AOTUsu. Together, these tuberculo-bulbar or TuBu neurons compose the first part of the anterior visual pathway that is covered by the hemibrain volume. The full pathway comprises neurons that project from the photoreceptors to the medulla, the medulla to the AOTUsu, the AOTUsu to the BU, and the BU to the EB (Figure 6A and B; Homberg et al., 2003; Omoto et al., 2017; Sun et al., 2017). Across insects, some types of TuBu neurons (also called TuLAL1 neurons in some insects) are known to be tuned to polarized light e-vector orientations, spectral cues, and visual features (el Jundi et al., 2014; Heinze et al., 2009; Heinze and Reppert, 2011; Omoto et al., 2017; Pfeiffer et al., 2005; Sun et al., 2017), properties that they likely inherit from their inputs in the AOTU (Hardcastle et al., 2020; Omoto et al., 2017; Sun et al., 2017). In the fly, some TuBu neurons are known to respond strongly to bright stimuli on dark backgrounds (Omoto et al., 2017) or to the orientation of polarized light e-vectors (Hardcastle et al., 2020), consistent with the idea that these neurons may be part of a sky compass pathway, as in other insects (el Jundi et al., 2018; Homberg et al., 2011).

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The hemibrain volume (light blue shaded region in Figure 6A) does not include areas of the optic lobe that would permit an unambiguous identification of AOTU inputs from the medulla (together called the anterior optic tract), thus only two broad subclasses of medulla columnar neurons can be distinguished. MC64 and MC61 (Figure 6C). However, following the schema employed in recent studies, we used the innervation patterns of different medulla columnar neuron types to delineate two distinct zones in the AOTUsu (Figure 6Di). These zones are consistent with previously characterized, finer-grained regions that receive input from different types of medulla columnar neurons (Omoto et al., 2017; Timaeus et al., 2020).

In other insects, some AOTU-projecting medulla columnar neurons (MeTus) are thought to be tuned to polarized light e-vector orientations (Heinze, 2014), and such information is known to be present in the Drosophila medulla as well (Weir et al., 2016). A more recent study has confirmed that some classes of fly AOTU neurons, as well as their downstream partners, respond to polarized light stimuli much like in other insects (Hardcastle et al., 2020). We believe that TuBu01 and TuBu06 neuron types are tuned to polarized light based on both their connectivity to ring neurons in the BU and their arborization patterns in the AOTU. TuBu01 is the only TuBu neuron that projects to the anterior BU and feeds the ER4m neuron type, which shows strong polarization tuning (Hardcastle et al., 2020), and TuBu06 appears to get input from the same population of MeTu neurons as TuBu01 in the AOTU (Figure 6C and Dii, top row, Figure 7D). However, a recent study reported that glomeruli in the dorsal part of the BUs were also polarization tuned (Hardcastle et al., 2020), suggesting that other TuBu types may also carry information about e-vector orientation.

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TuBu neuron types arborize in subregions of the AOTU that respect the boundaries defined by medulla columnar inputs, and TuBu neurons form columns along the dorsoventral axis of their respective AOTUsu subregion (Figure 6Dii; Omoto et al., 2017; Timaeus et al., 2020). Both the medulla columnar neurons and the TuBu neurons tile each AOTUsu zone (Figure 6Bi, E), consistent with the TuBu neurons preserving a retinotopic organization from their columnar inputs (Timaeus et al., 2020). On average, there is a 40:1 convergence from medulla columnar neurons onto TuBu neurons (Figure 6—figure supplement 1), potentially increasing the size of the receptive fields of TuBu neurons compared to MeTu neurons. Although this tiling is well-organized for TuBu neurons that receive inputs from MC61 medulla neurons (Figure 6Ei), it becomes more diffuse for TuBu neurons that receive inputs from MC64 medulla neurons (Figure 6Eii), consistent with LM-based anatomical analysis (Timaeus et al., 2020). This differentiation of TuBu neuron types is also maintained in their downstream projections to the BU (next section). Note, however, that multiple TuBu neuron types can also receive their inputs from the same AOTUsu zone, for example, TuBu01 and TuBu06 (Figure 6Dii). It is possible that these different TuBu neuron types receive different medullary inputs in the same zone of the AOTU, but they are, regardless, easily distinguished both by the additional inputs they receive in the BU, as well as by their downstream partners in that structure (discussed below).

The BU is primarily an input structure for the CX. Nearly every neuron type that receives most of its input in the BU has presynaptic specializations within one or more core CX structures (Figure 7A). The majority of cells in the BU are part of the anterior visual pathway. This pathway includes the TuBu neurons and their postsynaptic partners, the ring neurons (ER), which bring visual information to the EB (Table 5). Most neurons innervating the BU (e.g., the TuBu neuron types and the ring neurons [except ER6]) have spatially restricted, glomerular arborizations (Trager et al., 2008). Other neuron types arborize widely within the structure, such as the AOTU046 and extrinsic ring (ExR) neurons (Figure 7B). A recent study combining lineage-based anatomy and functional imaging has suggested that the BU may be organized into zones with similarly tuned TuBu neurons (Omoto et al., 2017). We used synapse locations of different types of TuBu neurons and their downstream partners, the ring neurons, to partition the BU into different zones (Figure 7B and C), each with numerous microglomeruli where TuBu neurons make synapses onto ring neurons (Trager et al., 2008). Each microglomerulus is formed by small arbors of up to five TuBu neurons from one type and their downstream ring neuron partners (see below and Figure 7—figure supplement 1A and B). Consistent with the functional and anatomical segregation suggested by Omoto et al., 2017, TuBu neurons originating from different parts of the AOTU do indeed segregate into different zones within the BU (superior, inferior, and anterior BU, Figure 7Ci), with MC61-fed TuBu neurons innervating the superior BU and MC64-fed TuBu neurons targeting the inferior BU (Figure 6C). The only exception is the polarization-tuned TuBu01, which arborizes in its own compartment, the anterior BU (Figure 7Ci). MC61-fed superior and anterior TuBu share a developmental origin, DALcl1, while the MC64-fed inferior TuBu neurons originate from DALcl2 (Omoto et al., 2017). Glomeruli in the superior BU tend to be smaller and more defined than glomeruli in the inferior BU. Except for ER6, an atypical ring neuron, ring neurons that receive their input in the BU also send their dendrites into a single zone of the BU, thereby maintaining some separation of visual pathways from the AOTU (Figure 7Cii).

The type-to-type mapping from TuBu neurons to ring neurons is largely one-to-one, with most ring neuron types receiving synaptic inputs from only a single TuBu type each, for example, TuBu01 to ER4m and TuBu06 to ER5 (Figure 7D, see yellow and blue-framed boxes). However, some TuBu types feed multiple ring neuron types, for example, most TuBu02 neurons project to both ER3a_a and ER3a_d ring neurons, and also to ER3m ring neurons (Figure 7D). Although the segregation of TuBu types is largely maintained at the type-to-type level, there is significant mixing at the level of individual TuBu to ring neuron connections. Most TuBu neurons feed several ring neurons of a given type, but the level of divergence varies between TuBu types (Figure 7D, Figure 7—figure supplement 1B). TuBu02 neurons, for example, make synapses onto multiple ER3a_a, ER3a_d and ER3m neurons (Figure 7, Figure 7—figure supplement 1B). There is also significant convergence, with many ring neurons receiving inputs from multiple TuBu neurons of the same type (Figure 7D, Figure 7—figure supplement 1A).

A particularly strong contrast can be observed between the mapping of TuBu01 to ER4m, which is strictly one-to-one, preserving receptive fields (but not polarotopy; Hardcastle et al., 2020), and TuBu06 to ER5, where multiple TuBu06 neurons contact a single ER5 neuron and single TuBu06 neurons project to multiple ER5 neurons (Figure 7D and E, Figure 7—figure supplement 1B and C). This is noteworthy as TuBu01 and TuBu06 receive input in the same region of the AOTU, but their downstream partners, ER4m and ER5 neurons, are known to have different functions. ER4m is tuned to polarized light (Hardcastle et al., 2020) and is likely involved in visual orientation, whereas ER5 neurons are involved in sleep (Liu et al., 2016). Both will be discussed in more detail in later sections.

Overall, this combination of divergence from individual TuBu neurons to multiple ring neurons and convergence from multiple TuBu neurons to individual ring neurons strongly suggests that we should expect receptive fields in the anterior visual pathway to expand, and sensory tuning to potentially become more complex from TuBu to ring neurons. Finally, it is important to note that there are several neuron types with wide arborizations within the BU that likely also influence processing in the structure. These include a subset of ExR neuron types (ExR1, ExR2, ExR3, and ExR5) and the AOTU046 neurons, which are discussed below.

Thus far, we have characterized the anterior visual pathway as a largely feedforward pathway of neurons with spatially localized arbors projecting from the early visual system to the AOTU and on to the BU. Indeed, many TuBu neuron types in the superior BU are known to display prominent ipsilateral visual receptive fields consistent with ipsilateral inputs in the AOTU (Omoto et al., 2017; Seelig and Jayaraman, 2013; Sun et al., 2017). However, the connectome suggests that other, widely arborizing neuron types influence responses of neurons at different stages of the pathway (Figure 8A and B).

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There is functional evidence that many of these neurons also receive large-field inhibitory input from the contralateral hemisphere, creating the potential for stimulus competition across the left and right visual fields (Omoto et al., 2017; Sun et al., 2017). The interhemispheric TuTuB_a neurons connect the right and left AOTU (Figure 8Ai). These neurons pool medullary input from the visual field of one hemisphere and synapse onto a subset of TuBu neurons on the contralateral side. Note that at least one of these TuTuB neurons is known to be tuned to polarized light e-vector orientation (Hardcastle et al., 2020). The interhemispheric AOTU046 neurons receive input from multiple brain regions including both AOTUs, the BU (although they primarily send outputs there), the FB, and the ipsilateral (to their soma) IB and superior posterior slope (SPS) (Figure 8Aii,Ci, Di, and E). AOTU046 and TuTu neurons are well positioned to mediate contralateral inhibition since both neuron types receive input from large areas of the contralateral AOTU (Figure 8C). Indeed, AOTU046 targets ring neuron types in the BU that show strong signatures of contralateral inhibition (Sun et al., 2017). Curiously, AOTU046 provides input to TuBu neurons in both the AOTU and BU, targeting somewhat different subsets (Figure 8—figure supplement 1A).

We did not find any obvious candidates that could provide TuBu neurons of the inferior BU with small-object-sized receptive fields in the contralateral hemisphere as has recently been suggested for a subset of these neurons (Omoto et al., 2017; Shiozaki and Kazama, 2017). Based on the connectome, one possibility is that these reported responses were not caused by small-field feature detectors related to the AOTU or BU, but rather by input from the ExR3 neurons (Figure 8Aiii and Dii, Figure 8—figure supplement 1B). The ExR3 neurons receive synaptic input from a variety of neurons in areas that are known to respond to optic flow and the fly’s own movements (Figure 8F, note that inputs are mixed with outputs; see also later section on ExR neurons), both of which may have contributed to the reported response properties. A second possibility is that these responses were observed in the subset of ring neurons that form glomeruli in the BU, but also receive additional inputs in the LAL (ER3a_a and ER3a_d, Figure 7A, Figure 10—figure supplement 5). Finally, contralateral visual information may also reach these neurons from inter-medullary connections, a possibility that we could not investigate in the hemibrain dataset.

The widely arborizing neurons – ExR1, ExR2, ExR3, ExR5, and AOTU046 (Figure 8A) – have somewhat overlapping arbors in the BU (Figure 8D) but are selectively interconnected in the region (Figure 8B). The bilaterally projecting AOTU046 neurons receive ipsilateral inputs from ExR2 and ExR5 neurons and contralateral input from the ExR3 neurons (Figure 8B, the right AOTU046 receives input from ExR2 and ExR5, the left one from ExR3), and then provide input to ExR1 neurons in the same hemisphere (Figure 8B). The ExR3 neurons appear to be recurrently connected to TuBu02, TuBu03, and TuBu04 neuron types (Figure 8B, Figure 8—figure supplement 1B). The function of these external inputs is not yet known.

In contrast to all the ring neuron types described above, most of which have been considered as bringing visual input into the EB, we note that the ER5 neurons have been primarily associated with conveying a signal related to sleep homeostasis and are thought to not be responsive to visual stimuli (Donlea et al., 2018; Liu et al., 2019; Liu et al., 2016; Raccuglia et al., 2019). These neurons are known to receive input from TuBu neurons (Guo et al., 2018; Lamaze et al., 2018; Liang et al., 2019; Raccuglia et al., 2019). The connectome allowed us to identify these neurons as TuBu06 (Figures 7D and E and 8B). TuBu06 neurons, in turn, receive input from the bilateral TuTuB_b neurons that receive clock circuit input through the DN1pB neurons (Guo et al., 2018; Lamaze et al., 2018; Liang et al., 2019; Figure 6C). These connections provide a link between sleep and circadian circuits within the CX, which we discuss in more detail in a later section. Circadian input from DN1pB neurons to ER4m via TuBu01 neurons (Figure 6C) may also affect neural responses in the polarized light e-vector pathway, consistent with findings in other insects; this could allow for polarized light responses to be adjusted based on the time of day to compensate for changes in the polarization pattern as the sun moves across the sky (Heinze and Reppert, 2011; Pfeiffer and Homberg, 2007; Sauman et al., 2005).

In addition to the visual inputs described above, the EB also receives mechanosensory input, as demonstrated by intracellular recordings of wind-sensitive activity in the locust (Homberg, 1994) and by extracellular recordings in the cockroach CX demonstrating directionally tuned activity in response to mechanical stimulation of the antennae (Bender et al., 2010; Guo and Ritzmann, 2013; Ritzmann et al., 2008). In the fly, recent work has shown that mechanosensory information is carried by ER1 and a subset of ER3a ring neurons (Okubo et al., 2020). Unlike the majority of ring neurons that bring sensory information to the EB and receive visual input in the BU, these ring neurons gather much of their input from the LAL and WED (Figure 9A and B), a structure known to receive significant mechanosensory input from the antennal Johnston’s organ (Patella and Wilson, 2018; Suver et al., 2019). ER1 neurons differ from ER3a cells most prominently in their arborizations in the EB, which we will cover in more detail in the next section. The CX connectome revealed that both of these neuron populations consist of multiple types. There are two ER1 types, ER1_a and ER1_b, and four ER3a types (Figure 10—figure supplement 5). Of the four ER3a types, ER3a_a and ER3a_d primarily receive inputs in the BU, whereas ER3a_b and ER3a_c receive inputs in the LAL (Figure 10—figure supplement 5). We found that only ER3a_b and ER1_b neurons are postsynaptic to neurons that we believe to be WPN neurons (Figure 9A–C) – neurons that have been characterized as being wind-direction-sensitive (Suver et al., 2019). These putative WPN neurons are themselves downstream of APN neurons (Figure 9A and C), which are known to be mechanosensory (Patella and Wilson, 2018; Suver et al., 2019). The ER1_b neurons also receive input in the LAL from the LAL138 (previously known as WL-L) neurons (Franconville et al., 2018; Okubo et al., 2020), which, recent work has suggested, tonically inhibit the ER1_b neurons (Okubo et al., 2020). We note that this study also showed evidence for WL-L neurons being gap-junction-coupled to ER1_b neurons. The hemibrain volume lacks the resolution to confirm this observation. In contrast to the ER1_a neurons, whose processes are uniformly distributed along the dorsal-ventral axis of the LAL (Figure 9Di and Ei), the ER1_b neurons receive inputs, especially from ExR7 neurons (discussed in later sections) in relatively distinct clusters arranged along the dorsal-ventral axis (Figure 9Dii and Eii). The latter spatial segregation is consistent with physiological reports of their distinct but overlapping tuning to wind direction (Okubo et al., 2020). Our analysis suggests that directional information from wind stimuli is conveyed to the EB by ER1_b and ER3a_b neurons. Functional properties of major inputs to the other LAL ring neurons have not been characterized, and it is therefore unknown what information is conveyed by these types. Because ER1_a, ER1_b, and ER3a_b neurons receive the majority of their input from unidentified neurons in the LAL, WED, and CRE (Figure 9B), the directional mechanosensory information that they receive may well be combined with other sensorimotor information from other presynaptic partners (Figure 9—figure supplement 1).

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Each ring neuron sends its processes around the entire circumference of the EB, forming a ring-shaped arbor. Different types occupy rings at specific depths within the anterior-posterior axis (Hanesch et al., 1989; Lin et al., 2013; Omoto et al., 2018; Young and Armstrong, 2010b) and make synapses within type-specific annuli along the radial axis (Video 2). Figure 10B, for example, shows the locations of ER4m synapses for three different projections (see Figure 10—figure supplements 1–3 for synapse locations of other ring, columnar, and ExR neuron types, respectively). Ring neuron types also vary in the spatial extent of their arbors and the degree to which they overlap with the arbors of other ring neuron types. Figure 10Ci displays this overlap through the location of synapses in the anterior-radial plane (see Figure 10—figure supplement 4A for anterior-radial cross-sections along different parts of the EB). When neuron types are grouped by the subregions of structures outside the EB where they receive their inputs, synapses of different ring neuron classes appear to tile the anterior-radial cross-section of the EB (sample cross-section shown in Figure 10Cii). The only significant overlap between different ring neuron classes occurs between the BUs and BUa ring neurons, which receive inputs in similar parts of the AOTUsu (see previous section). Most columnar neurons, which are so named because they each only innervate single glomeruli in the PB and single sectors (‘tiles’ and ‘wedges’ [Wolff et al., 2015]) of the EB torus, spread their synapses across fairly large fractions of the anterior-radial cross-section of the structure (Figure 10D, Figure 10—figure supplement 4B, see Figure 10—figure supplement 2C for synapse locations of individual EB columnar types). In particular, the population of EPG and EL neurons makes synapses across most of the EB (Figure 10—figure supplement 2). EL neurons (called EB.w.AMP.s-Dga-s.b in Wolff et al., 2015) have never been characterized physiologically. The ExR neuron types are similar to ring neurons in arborizing across the entire circumference of the EB. However, in contrast to most ring neurons, they make synapses across fairly large fractions of the anterior-radial cross-section of the EB (Figure 10E, Figure 10—figure supplement 3C, Figure 10—figure supplement 4C). The networks created by connections between these different neuron types in the EB are thought to be involved in generating neural dynamics that maintain the fly’s head direction representation and control sleep (Figure 10F).

Most ring neurons are thought to be GABAergic (Hanesch et al., 1989; Homberg et al., 2018; Homberg et al., 1999; Isaacman-Beck et al., 2019; Turner-Evans et al., 2020) and therefore inhibitory. They bring diverse sensory information into the EB (see Table 5, morphological renderings in Figure 10—figure supplement 5). Visually tuned ring neurons with ipsilateral receptive fields (ER2a-d, ER4d) and ring neurons tuned to polarized light (ER4m) are well-characterized and the fly’s head direction system is known to tether to such cues (Fisher et al., 2019; Hardcastle et al., 2020; Kim et al., 2019). ER1_b and ER3a_b are tuned to wind direction, but only ER1_b appears to directly influence the head direction representation (Okubo et al., 2020). Less is known about the tuning and function of other ER3 neuron types. Pan-neuronal imaging has suggested that a subset of ER3 neurons in the aBUi responds to contralateral visual information and motor actions (potentially the ER3a neurons, based on their anatomical position in the BU and their inputs in the LAL), but many ER3 neurons have been reported to be unresponsive to visual stimuli (Omoto et al., 2017; Shiozaki and Kazama, 2017). Based on their connectivity with ExR3 and ExR1, we hypothesize that ER3d ring neurons are involved in sleep-wake control (see section on sleep for details). One other ring neuron type, ER5, has been explicitly linked to tracking sleep need (discussed further in a later section). Finally, the unusual ring neuron type – the ER6 – receives most of its non-EB input in the GA (discussed in more detail in a later section), where it contacts EPG and PEG neurons.

The fly’s compass system can tether to directional sensory cues carried by a variety of ring neuron types, forming an internal representation of head direction in a world-centered (i.e., allocentric) reference frame. Using the complete EB connectivity information of the hemibrain connectome, we found that most – but not all – ring neuron types from both hemispheres make direct synaptic contacts with EPG neurons from both sides of the brain (Figure 11A, third and fourth columns of the connectivity matrix, Video 3; Video 4; see also Turner-Evans et al., 2020). In the analyses that follow, we will consider the number and location of synapses that various visual and mechanosensory ring neurons make onto EPG neurons as a proxy for the influence that these different sensory cues exert on the EPG compass. For example, the physiological observation that ER3a_b neurons, which respond to wind direction, do not directly impact EPG dynamics (Okubo et al., 2020) is well accounted for by their lack of direct synaptic connections to EPG neurons (Figure 11A). The other ER3a neurons also make few connections to EPG neurons. Note that although the unusual ER6 neuron type does not synaptically contact EPG neurons in the EB (top two row blocks in Figure 11A), these neurons – and most of the ER3a as well as ER5 neurons – do make strong contacts with the EL columnar neuron types (first and second columns in the connectivity matrix in Figure 11A, morphological rendering in Figure 11B). The functional significance of EL neurons and of these connections is unknown. The stimulation of ER6 neurons triggers an inhibitory response in EPG neurons (Franconville et al., 2018), which might be mediated through their connections in the gall (see Figure 56) or indirectly through other columnar neurons (see below).

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The diversity of sensory cues that the head direction representation tethers to indicates that the fly compass is flexible enough to function in a variety of multisensory settings. This flexibility of tethering the EPG compass to different cues is thought to be achieved by experience-dependent plasticity acting on the synaptic weights between ring neurons and EPG neurons (Fisher et al., 2019; Kim et al., 2019). These studies suggested that the strength of a visual ring neuron’s synapses onto EPG neurons would, through sculpted inhibition, localize EPG activity to a specific sector of the EB for a given head direction in a specific visual setting (schematized in Figure 11C). Considering the strong correlation between synapse counts and the area of synaptic contact between neuron pairs in at least larval Drosophila (Barnes et al., 2020), and assuming that the functional strength of synapses depends on synaptic surface area (Holler-Rickauer et al., 2019), we asked whether we could detect any signatures of such plasticity-based sculpting in synapse counts between ring and EPG neurons (note that a change in synapse counts is only one of many potential signatures of plasticity-related changes in synaptic strength). Specifically, we examined the connectivity matrix between a variety of ring neurons – ER1_a, ER1_b, ER2_a-d, ER4d, and ER4m – and EPG neurons for any consistent nonuniformities. We conjectured that if synapse counts or relative weights reflect functional synaptic strengths, we should see specific patterns in the connectivity between ring neurons and EPG neurons. For example, we might expect that the ring neuron synaptic profiles onto multiple EPG neurons within a wedge (i.e., EPG neurons that share the same head direction tuning) would be more similar than their synaptic profiles onto EPG neurons with very different tuning (i.e., those from angularly distant parts of the EB) (see Figure 11C). We found no such correlations or modularity for most ring neuron types (Figure 11—figure supplement 1; Table 6). There were two exceptions: the polarization-tuned ER4m neurons (Figure 11A and D, Figure 11—figure supplement 1Cviii), and, to a lesser extent, the ER1_a neurons (Figure 11—figure supplement 1Ci). Thus, if synaptic weights from sensory ring neurons onto EPG neurons vary in consistent patterns as a result of a fly’s experience, as we expect they must, this is not reflected in synapse counts for the vast majority of ring neuron types (note, however, that we know little of the sensory experience of this fly; see Materials and methods). The absence of obvious structural signatures of synaptic strength is perhaps unsurprising in the context of plasticity that acts at a timescale of tens of seconds to a few minutes, as is the case here (Fisher et al., 2019; Kim et al., 2019). In the case of the polarization-tuned ER4m neurons, we observed that synapse counts to EPG neurons varied smoothly along the circumference of the EB, but with mirror-symmetric profiles for ER4m neurons from the left and right hemisphere, respectively (Figure 11D), resulting in stronger connections from the left hemisphere for EB wedges on the right half of the EB and stronger connections from the right hemisphere to the left half of the EB. Given the mirror symmetry of the represented axis of polarization (Hardcastle et al., 2020), this connectivity pattern may allow the fly to generate a complete, 360° head direction representation from twofold symmetric polarized light input, an idea that we return to in ‘Discussion.’ Although a recent study reported wind-direction-tuned responses in ER1 neurons (Okubo et al., 2020), we believe that the neurons characterized in that study to be only ER1_b neurons – whether the ER1_a neuron type is also mechanosensory is as yet unknown.

The same plasticity in the EB that enables the fly’s internal compass to tether to visual cues in the animal’s surroundings (Fisher et al., 2019; Kim et al., 2019) likely also enables the flexible tethering of the head direction representation to other sensory cues. What if the different sensory streams do not provide a consistent estimate of head direction? This kind of conflict can, for example, arise during translational movement when local visual landmarks provide a less stable estimate of head direction than global cues like wind direction and the polarization pattern of the sky. We asked if the spatial connectivity pattern of ring neurons onto EPG neurons holds any clues about how such conflicts are resolved. Specifically, we considered the electrotonic distances of synapses to the spike initiation zone of a neuron, which is often correlated with the influence that the input can exert on the neuron’s ability to fire (or not fire) a spike. We asked if we could extract an expected weighting of head direction-tethering cues conveyed by ring neurons based on the electrotonic distance of their synapses to the estimated spike initiation zone of their EPG neuron targets.

Although little is known about spike initiation zones in fly neurons, the best estimates thus far have come from studies in olfactory PNs (Gouwens and Wilson, 2009). In these multipolar neurons, spikes are thought to be initiated near the base of their major input arbors in the AL. These results are also consistent with the subcellular localization of voltage-gated sodium channels in a broader class of central brain neurons (Ravenscroft et al., 2020). We thus made the assumption that spikes in the EPG neurons are initiated at the root of their arbors in the EB, near the intersection of these processes with processes that travel to the GA and PB (Figure 12A). We found that these putative spike initiation points (yellow circles in Figure 12A and C, left) tend to cluster at a certain depth and radial position of the EB. Specifically, EPG neurons tend to enter the EB near a central annulus and from the posterior side. We expected some systematic variation in ring neuron synapse locations by type because different ring neuron types arborize at different depths and radial positions in the EB (Figure 10—figure supplement 1C). By grouping the ring neuron types according to their sensory modality, inspired by their overall connectivity in the EB and their known sensory tuning (Figures 10F and 12B), we found that the locations of synapses from the ring neurons to the EPG neurons tend to cluster by modality group (Figure 12C, right, Figure 12—figure supplement 1A, compare also to Figure 10Cii). Further, an analysis of the synapses of the ring neurons in these different sensory modality groups onto the EPG neurons revealed a clear trend in their relative electrotonic distances to the root node (Figure 12D and E). Broadly, as seen in the cumulative distribution function (CDF) of an example EPG (Figure 12D), the electrotonic distance between different ring neuron types and the root of each of their postsynaptic EPG neurons suggests an ordering in expected influence on EPG activity, with the mechanosensory neuron synapses being the closest, the different visual neurons being next, and the sleep-related ring neurons potentially exerting the least impact on the EPG neuron’s ability to fire a spike. We then compared the locations of ring neuron synapses to those of PEN synapses (labeled ‘motor’ in Figure 12B–E). These self-motion inputs to the fly’s head direction system (discussed in later sections) were electrotonically closer to the root of the EPG arbors in the EB than any of the ring neuron inputs (compare left plot with purple region in right plot in Figure 12C, Figure 12—figure supplement 1A). While there is some variability, these broad trends are consistent across neuron types within the different modality groups (Figure 12—figure supplement 2). The rank ordering is fairly consistent across EPG neurons, as can be seen by comparing the medians of the distributions of the synapse locations of ring neurons from each modality group (Figure 12E, Figure 12—figure supplement 1B, C; see Materials and methods). These same trends were also observed when analyzing the physical distance along the arbor between synapses and the postsynaptic EPG root (Figure 12—figure supplement 1D, E). Most synapses were found to occur within 50 µm of the root (Figure 12—figure supplement 1F). A similar picture emerged for the EL neuron type, the second columnar neuron type that receives inputs from many ring neurons (Figure 12—figure supplement 3; the higher variability across individual ELs is likely due to a greater variation in arbor shape along the circumference of the EB relative to the EPG neurons as seen in Figure 10—figure supplement 4B). In summary, our analysis of the electrotonic distances of synapses from different ring neuron types to EPG neurons in the EB suggests a consistent prioritization of sensory inputs to EPG neurons that may reflect the relative importance of different sensory stimuli in driving the fly’s head direction estimate. Sculpted inhibition from different sensory ring neurons appears largely focused on the intermediate arbors of the EPG neurons, and excitatory self-motion inputs that update the head direction representation during turns are closer to the root of the EPG neuron arbors in the EB.

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Past studies have classified ring neurons based on their morphology and their developmental origins (Hanesch et al., 1989; Omoto et al., 2017; Omoto et al., 2018; Renn et al., 1999; Young and Armstrong, 2010a). The connectome permitted us to refine the classification of ring neurons based on their pre- and postsynaptic connectivity patterns in different brain regions (Scheffer et al., 2020). In this connectivity-based classification of ring neurons into types, a key distinguishing feature was their dense ‘within-type’ connectivity. Ring neurons are strongly and consistently connected to other ring neurons of the same type. A recent study combined optogenetics with electrophysiology to show that ring neurons inhibit other ring neurons of the same type (Isaacman-Beck et al., 2019). Although these data were collected in a single-ring neuron type, the connectome suggests that all-to-all inhibition among cells of a single type is likely a feature of nearly all ring neuron types (blocks around the diagonal in Figure 13A). As we outline in ‘Discussion,’ such all-to-all inhibition may help to minimize the influence of noise on the compass system and effectively enhance the influence of the most prominent sensory cues on the angular position of the EPG bump in the EB.

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Notably, some ring neuron types show all-to-all connectivity not just to neurons of their type, but also to neurons of other types. Examples of types that show all-to-all connections include the ER4m, ER2a-d, and ER3w types (off-diagonal blocks in Figure 13A). A different heavily connected set includes the ER3_m and all ER3a neurons. In both cases, most – but not all – type-to-type connections are reciprocal. While the first set of ring neuron types synapse directly onto EPG neurons (Figures 11A and 13B), the second set mostly interact with EPG neurons indirectly – in the case of the ER3a neurons, through their impact on ER3m neurons (Figures 11A and 13A) and EL neurons (Figure 13B). To assess the potential impact of across-type connections between ring neurons, we generated a graph for connections between ring neurons, which showed that ring neuron types with similar tuning formed highly interconnected clusters (Figure 13C, Table 5). We ranked individual types by the numbers of synapses that they make onto EPG neurons – presumably contributing to the generation and maintenance of the head direction signal (Fisher et al., 2019; Kim et al., 2019; Figure 13C, see Materials and methods). For groups of ring neuron types that provide strong input to the EPG neurons, this revealed a second, implicit hierarchy between different ring neuron types (Figures 11A and 13B). Prominent among these ring neuron types are those that – based on their TuBu inputs and recent neurophysiological evidence (Hardcastle et al., 2020) – we believe to be associated with the sky compass pathway. ER4m, ER2_a-d, and possibly ER3w. All of these types are part of a highly interconnected cluster. Within this cluster, connections between inhibitory ring neurons define a suppression hierarchy. For example, the ER4m neurons, which are most strongly tuned to polarized light e-vector orientation (Hardcastle et al., 2020), make a significant number of synapses onto all other neuron types in the cluster (Figure 13A and C), and do not receive nearly as many in return (as indicated by the size of the dot representing the neuron type), placing this neuron type at the top of the hierarchy within this cluster. The ER2_c type appears next, inhibiting ER2_a and ER2_d neuron types. ER4d neurons, which likely convey information about a broader range of visual features (Seelig and Jayaraman, 2013), are not inhibited by any of the other ring neuron types and make a large number of synapses onto EPG neurons themselves (Figure 13C). Other high-ranking ring neuron types include the ER3p_a, which is one of the primary target types of the EL neurons in the EB (Figure 13B, Figure 13—figure supplement 1B), and the ER1_a and ER1_b neurons (Figure 12B), at least one of which is mechanosensory and brings information about wind direction to the EB (likely ER1_b, Figure 9; Okubo et al., 2020). Figure 13B shows the relative contributions of all ring neuron types to tethering the EPG compass in terms of the relative strength of the respective ring neuron inputs to EPG neurons. On top of this, the suppression hierarchy circuit motif could help with selecting a single-ring neuron type for updating the compass when multiple-ring neuron populations are activated, thus effectively establishing a preference for certain sensory compass cues over others.

A few ring neuron types appear to be privileged in also receiving feedback from the EPG neurons (Figure 13—figure supplement 1B). This privileged set of ring neuron types includes, once again, the ER4m neurons, which carry polarized light e-vector information. This feedback may serve to amplify their impact on tethering the head direction representation to sensory input, while potentially reducing the influence of ring neurons that carry other types of sensory information.

In summary, we found evidence for several mechanisms by which different sensory inputs to EPG neurons could be integrated, and potential conflicts between cues resolved. First, the strength of connections from various ring neurons onto EPG neurons, as measured by relative weight, varies between types. Polarization-sensitive ER4m neurons provide the strongest input to EPG neurons and are also privileged in receiving feedback from EPG neurons. Consistent, but weaker, ring neuron-to-EPG connections are made by other visually tuned ring neurons and those that bring in mechanosensory information (Figures 11A and 13B). Second, the position of ring neuron synapses along EPG neuron arbors varies systematically, not only with ring neuron type but more generally with the type of sensory information carried by different types (Figure 12E). This is also reflected in the organization of ring neuron arbors in the EB (Figure 10Cii). Based on the electrotonic distance of synapses from the putative spike initiation zone of EPG neurons, self-motion signals from PEN neurons are in a privileged position to excite the compass neurons, while ring neurons carrying mechanosensory, ipsilateral visual, and polarization e-vector cues provide the strongest inhibitory influences (Figure 12E). However, the ordering of ring neuron influence on the EPG compass based on synapse location differs slightly from the ranking based on relative connection weights for mechanosensory ER1 neurons and the likely polarization-sensitive ER4m, ER2c, and ER3w neurons (compare Figure 12E to Figure 13C). Finally, within modality groups, inhibitory ring neurons form suppression hierarchies that may help to select strong guidance signals when multiple sensory cues are present. These suppression hierarchies occur between types that carry potentially related compass information such as the position of the sun (potentially ER2 types) and the celestial polarization pattern (likely ER4m) (Figure 13C). Taken together, these circuit motifs may help to resolve guidance cue conflicts and ensure a stable head direction representation.

Some ring neuron types synapse onto some of the other columnar neuron types in the EB. These connections are summarized in Figure 13—figure supplement 1. The strongest connections are made by ER6 neurons (already noted above as contacting EL rather than EPG neurons in the EB, Figure 11A), which also make a large number of synapses onto PEG and PEN_b (formerly called PEN2) (Figure 13—figure supplement 1A). In addition, ER1_a and ER1_b neurons contact PEN_a (formerly PEN1) neurons from both sides of the brain although those connections are rather weak (Figure 13—figure supplement 1A). Some ring neuron types receive presynaptic input in the EB from columnar neurons (Figure 13—figure supplement 1B). Most of the columnar-to-ring-neuron connections are weak or inconsistent across neurons of the same type (e.g., inputs from PEN_a to ER1_a and ER1_b neurons, or inputs from EPG and PEN_b neurons to ER4m). A notable exception is the strong PEG-to-ER6 neuron connectivity. Most columnar feedback to ring neurons comes from EL neurons, which themselves receive input from several ER neuron types. The EL neurons make synaptic contacts onto most ring neuron types, most strongly to ER3p neurons. We do not yet know the function of these columnar-to-ER connections.

In contrast to mammals, the function of the fly compass has not yet been monitored in head-free animals (Hulse and Jayaraman, 2019; Rubin et al., 2014; Taube et al., 1990a; Taube et al., 1990b). This motivated us and others to refer to the representation as being of ‘heading direction’ rather than ‘head direction’ until the issue can be conclusively resolved with direct evidence. However, considering that diverse sensory cues are all communicated to the EB in head-centered coordinates, we will now employ the term ‘head direction’ to refer to the EPG population representation. Note that this is consistent with the terminology that has long been used in studies of the CX in many other insects (Homberg, 2004; Varga and Ritzmann, 2016), but awaits experimental confirmation in those animals as well.

In addition to the ring neuron types, which bring information from outside the CX to the EB, another class of neurons termed ‘extrinsic ring’ (ExR) neurons also form ring-shaped arbors along the circumference of the EB (Hanesch et al., 1989). In contrast to most of the ring neurons, ExR neurons are comprised of only one or two neurons per hemisphere and arborize in multiple regions outside the CX (Figure 14A). Only a subset of the ExR neurons have been described before and little is known about their function. We identified eight types of ExR neurons, each type targeting distinct sets of brain regions (Figure 14A, Figure 14—figure supplement 1, Figure 14—figure supplement 2). Consistent with their diverse morphologies and projection patterns outside the CX, the inputs and outputs of different ExR types are largely distinct (Figure 14B, Figure 14—figure supplement 3A). While all ring neurons serve as inputs to the CX, only a subset of the ExR neurons appear to be inputs. Most ExR neuron types have mixed polarity in the EB, and two ExR neuron types are CX output neurons (Figure 14A, bottom). The CX input neurons are ExR1 and ExR4, which convey information primarily from the BU, LAL, and GA (Figure 14A, Figure 14—figure supplement 3B). For a more detailed descriptions of ExR connectivity in the BU, see also Figure 7B. The CX output neurons, ExR7 and ExR8, will be discussed in more detail in the output section. The remaining ExR neurons – ExR2, ExR3, ExR5, and ExR6 – have both inputs and outputs outside of the EB, although some do have clear input or output regions (e.g., ExR5, Figure 14A).

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In the EB, ExR neurons make connections with three groups of neuron types: ring neurons, columnar neurons, and other ExR neurons (Figure 10F, Figure 14—figure supplement 3B). Most ExR neurons arborize in the posterior part of the EB, with the exception of ExR1 and ExR3, which target more anterior shells of the EB and form a connectivity cluster with sleep-related ring neurons (Figure 10E and F, Figure 14—figure supplement 1, Figure 14—figure supplement 2). Indeed, ExR1 neurons, also called Helicon cells, have been linked to the control of sleep homeostasis (Donlea et al., 2018). We will cover ExR1 and ExR3 neurons in more detail in the sleep section. Besides ExR1 and ExR3, ExR5 also receives a large fraction of its EB inputs from ring neurons, specifically from the ipsilateral visual ER4d neurons (Figure 14—figure supplement 3B, Figure 10F). All ExR neurons make connections to columnar EL and EPG neurons, suggesting a role in modulating the function of the fly’s head direction representation (Figure 14Ci, Figure 14—figure supplement 4A). Connectivity with EPGt, PEG, and PEN neurons is sparser, with ExR4 providing strong input to PEG and both PEN neuron types, and ExR6 selectively contacting PEN_a and EPGt neuron types (Figure 14Ci, Figure 14—figure supplement 4A). Columnar neurons also feedback onto ExR neurons (Figure 14Cii, Figure 14—figure supplement 4B).

Many ExR neurons make direct and indirect connections to the same partner types in multiple brain regions, suggesting that they do more than just act as input and output pathways for the EB. We analyzed these different connectivity motifs by comparing ExR connections within the EB to their direct and indirect connections in other regions (Figure 15A). We restricted our analysis to downstream partners of ExRs and focused on three specific connectivity motifs: ‘parallel connections,’ ‘canonical feedback,’ and ‘linked targets’ (see schematic in Figure 15A). ‘Parallel connections’ describe a motif in which ExR neurons make direct or indirect connections outside the EB to the same neuron type that they also contact in the EB (red arrow in Figure 15A, left). The ‘canonical feedback’ motif covers cases in which ExR neurons directly or indirectly connect outside the EB to neurons that feed back onto ExR neurons in the EB (yellow arrow in Figure 15A, middle). The third motif captures cases where downstream partners of ExR neurons are themselves connected in the EB, making them ‘linked targets’ (green arrow in Figure 15A, right). Not all ExR neuron types engage in these motifs. ExR1 and ExR4, because they are primarily input neurons to the EB, and ExR8, because it is purely an output neuron of the EB. Among the others, the linked targets motif is most commonly observed, potentially allowing these ExR neurons to link the activity of related circuitry in multiple brain regions (Figure 15B). The majority of motifs are formed through ring neurons (Figure 15C), suggesting that ExR neurons form a feedback loop onto one of the primary input pathways to the EB.

Figure 15

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We took a closer look at the two large ExR neurons that participate in the strongest out-of-EB connection motifs: ExR2 and ExR3 (Figure 15D). ExR2 are DANs of the PPM3 cluster and have been linked to ethanol-induced hyperactivity and the control of circadian activity peaks (Kong et al., 2010; Liang et al., 2019; Nässel and Elekes, 1992; Omoto et al., 2018). Outside of the EB, ExR2 neurons receive input in the LAL and EB and send outputs primarily to the BU (Figure 14A, Figure 14—figure supplement 3B). Through these BU connections, ExR2 neurons directly and indirectly target many of the same ring neurons that they also contact in the EB, specifically ER neurons from the ipsilateral visually-responsive cluster (Figure 15Ei and Fi, Figure 8B). Thus, ExR2 neurons may modulate the fly’s motor activity by regulating visual inputs to the fly’s head direction system. The putatively serotonergic ExR3 neurons form parallel connections and feedback connections with three sets of highly interconnected ring neuron populations (Figure 15C and Eii). One group of ring neuron partners is the ipsilateral visually tuned cluster of ring neurons, which is also targeted by ExR2. A second group is the ER3a/ER3m cluster, with which ExR3 forms parallel and a few feedback connections in the EB. The third and final group is the ER3d cluster, which may play a role in sleep-wake control (see Figure 53). ExR3 neurons contact ER3d neurons directly in both the EB and the BU, and indirectly through TuBu neurons, forming parallel and feedback connections with each ER3d neuron in the EB (Figure 15Eii and Fii, Figure 8B).

Taken together, our analysis suggests that ExR neurons are highly diverse but can be broadly grouped into types that primarily provide input to the EB, those that serve as output pathways from the EB and those that appear to be mixed input and output neurons; ExR neurons in the last group modulate input pathways to the EB through connections both inside and outside the EB.

The activity in the EPG neurons represents the fly’s head direction. As shown in Figure 16A, each EPG neuron connects an EB wedge with a single glomerulus in the PB, while also innervating the GA (discussed in later sections). The PB is mirror symmetric in appearance, with a left half and a right half. The 16 EPG wedges in the EB alternate so that half go to the right PB while half go to the left. In this way, the EPG neurons map the different locations around the ring of the EB to both the right and the left PB (Figure 16B). The EPG neurons bring the head direction signal to the PB from the EB. A bump of activity in the EPG neurons in the EB will therefore manifest as two bumps in the PB, with one on either side. Due to the alternating left and right projections of EB wedges to either the right or the left PB, the bump on the right side will be shifted 22.5° (360°/16 wedges) with respect to the bump on the left (Wolff et al., 2015), as has been observed experimentally (Lyu et al., 2020).

Figure 16

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The remaining three types of columnar neurons linking the EB and PB – the PEN_a, PEN_b, and PEG neurons – are mainly postsynaptic in the PB and complete direct and indirect recurrent loops with the EPG neurons in the EB. These loops update and maintain the head direction representation, as will be described in more detail in the following section (Green et al., 2017; Green and Maimon, 2018; Hulse and Jayaraman, 2019; Turner-Evans et al., 2017; Turner-Evans et al., 2020). As noted above, the hemibrain dataset does not contain the previously identified ‘canal’ cell (Wolff and Rubin, 2018).

We recently used EM reconstruction to identify the network motifs underlying the interaction of the PB-EB columnar neurons (Turner-Evans et al., 2020). However, this study, which was based primarily on the Full Adult Fly Brain (FAFB) dataset (Zheng et al., 2018), relied on manual reconstruction of only a fraction of the circuit. The completeness of the hemibrain connectome has now allowed us to more thoroughly examine the compass subnetwork and exposed additional structure-function relationships within the compass circuit, which we discuss below.

The EPG activity bump moves around the EB either clockwise (CW) or counterclockwise (CCW), depending on which direction the fly turns (head movements are also likely to update the EPG bump, but this has yet to be established). The angular velocity input that moves the bump in the EB is thought to primarily come from the PEN neurons (Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020). There are two types of PEN neurons, PEN_a and PEN_b, both of which are synaptically connected in recurrent loops with EPG neurons (Turner-Evans et al., 2020), are conjunctively tuned to head direction and angular velocity (Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020), and likely receive angular velocity inputs in the NO (discussed in a later section). These recurrent loops have either a CW or CCW shift in their projection patterns. Considering that the EPG head direction representation spans 360° of angular space, we can describe these projection patterns as ‘anatomical phase shifts’ relative to the EPG population (Figure 17A, schematized in Figure 17B). That is, PEN neurons receive their head direction inputs from a given EPG neuron in the PB. They then send their projections to an EB tile that is shifted CW or CCW from the EB wedge innervated by the presynaptic EPG neuron. The functional consequence of this phase shift is that the phase (angle) of the PEN activity bump is likely to be shifted relative to the phase (angle) of the EPG activity bump. This phase shift is in opposite directions for PEN neurons with arbors in the right vs. left side of the PB (see sample images of EPG and PEN_a neurons in Figures 16A and 17A; connectivity matrices in Figure 17C and D). As discussed in later sections, PB-FB neurons also have anatomical phase shifts.

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A key assumption behind fly compass models is that recurrent loops involving EPG and PEN neurons allow activity to propagate all the way around the EB and in either direction. Consistent with these models, we found that PEN neurons from each PB glomerulus contact EPG neurons in every wedge of the EB (Figure 17C). EPG neurons then complete the loop by synapsing onto PEN neurons in all but the most lateral glomeruli on each side of the PB. The apparent disconnect in connectivity at the edges of the PB is likely addressed by an additional cell type, as discussed below. Importantly, even without this bridging cell type, EPG and PEN_a neurons are so densely interconnected within the EB that a network graph of their subnetwork forms a ring (Figure 17E; see Materials and methods). The PEN_b neurons’ connectivity to the EPG neurons looks much like the PEN_a neurons’ connectivity to the EPG neurons in both the EB and PB. This similarity in connectivity does not extend to all partners of the PENs, however. Indeed, each type has unique partners in both brain regions (Figure 17—figure supplement 1).

The PEN neurons in the outermost (ninth) glomeruli do not receive any EPG input from the EPG neurons that project to the eighth glomerulus. Instead, a key neuron type, EPGt, arborizes in that outer glomerulus and appears to fill the ‘gap’ (Wolff et al., 2015; Figure 18A). While the EPGt neurons have very similar connectivity to the EPG neurons in the PB (Figure 18B), they receive far fewer synaptic inputs in the EB (Figure 18C), with a striking sparsity of ring neuron inputs (Figure 18D). However, EPGt neurons do receive PEN input in the EB. The wedges at the bottom of the EB are innervated by both the EPGt neurons from glomerulus nine and by the EPG neurons that project to glomerulus 1, potentially completing the loop (Figure 18E).

Figure 18

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The PEG neurons also appear to map the nine glomeruli of the PB to eight tiles in the EB though they do so without a phase shift. The PEG neurons form a recurrent loop with the EPG neurons, as reported previously (Turner-Evans et al., 2020). Briefly, they receive input from the EPG neurons in the PB (Figure 17D, right columns) and synapse onto the PEN_b neurons in the EB (Figure 17C, top rows, second group of columns to the right). The PEN_b neurons synapse onto the EPG neurons in the EB, thereby completing the loop (Figure 17C, second group of rows from the top, first group of columns). Although some PEG neurons do synapse directly onto EPG neurons in the EB, these connections are sparse and feature only a few synapses. By contrast, the PEG-to-PEN_b and PEN_b-to-EPG connections are both strong and consistent around the ring. There are nine PEG neurons on each side of the PB, one for each glomerulus. Each connects to one of the eight PEN_b neurons in the EB, with PEG neurons from both glomerulus 1 and glomerulus 9 connecting to PEN_b neurons from PB glomerulus 2. This connectivity pattern matches the connectivity of EPG neurons from glomerulus 1 and EPGt neurons from glomerulus 9 to PEN_b neurons from glomerulus 2.

The direct connection from EPG neurons to PEN neurons in the PB forms a key part of the EB-PB recurrent loop, which updates the fly’s head direction representation with self-motion input. However, this EPG input is also transformed by a population of multi-glomerular interneurons, the glutamatergic Δ7 neurons (Figure 20A; Daniels et al., 2008; Turner-Evans et al., 2020). The Δ7 neurons provide a strong, albeit indirect, link from EPG neurons to all other columnar neurons.

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The PB-spanning Δ7 neurons and their homologs in other insects have long been believed to play a role in navigational computations. Their responses to polarized light e-vector stimuli suggested that they were organized in map-like, polarotopic fashion in the locust brain (Heinze and Homberg, 2007). More recently, imaging and perturbation experiments in the fly have confirmed the importance of these glutamatergic neurons to the function of the fly compass circuit (Turner-Evans et al., 2020). Although this recent work also used EM to identify synaptic connections between Δ7 neurons and EPG, PEG, PEN_a, and PEN_b neurons, it reconstructed only a subset of the processes in a few Δ7 neurons. The hemibrain connectome allowed us to identify the complete set of inputs and outputs of Δ7 neurons across the entire PB. The picture that emerges from this analysis is of a neuron type that is the central hub of the PB. all neurons downstream of EPG neurons receive head direction input that is also processed by theΔ7 neurons (Figure 20B, Figure 20—figure supplements 1 and 2).

A key question raised by the hub-like connectivity of the Δ7 neurons is how these neurons pass on the EPG head direction signal. Many navigational algorithms combine head direction signals with information about the animal’s movements to compute a vector representation of the animal’s position. In these models, the vector representation is stored in sinusoidal activity patterns, where the phase of the sine wave encodes the angle of the vector and the amplitude of the sine wave represents its length (Pisokas et al., 2020; Stone et al., 2017; Touretzky et al., 1993; Wittmann and Schwegler, 1995).

We therefore asked if the Δ7 neurons transform the local EPG head direction signal into sinusoidal activity patterns in the Δ7 neurons’ downstream partners. Each Δ7 neuron receives smoothly varying input from EPG neurons across the PB (Figure 20C, upper-left quadrant). Aligning and averaging these input profiles across all Δ7 neurons revealed that the EPG input to Δ7 neurons was in fact well fit by a cosine (Figure 20D, see Materials and methods) (similar observations are made by a parallel study [Lyu et al., 2020]). Each Δ7 neuron sends output to specific PB glomeruli that are seven glomeruli apart (Figure 20A and C, lower-right quadrant). Since the output is highly targeted and the Δ7 neurons as a population continuously cover the entire PB, the sinusoidal input profile is unlikely to be further shaped by the Δ7 neurons’ outputs.

To further test if any input from the EPG population will be reformatted into a sinusoid, we simulated EPG activity propagating through the Δ7 neurons to their outputs. We began by assuming that the EPG neurons have an activity bump, similar to that observed experimentally (Seelig and Jayaraman, 2015). We also assumed that the EPG to Δ7 and Δ7 to EPG connection weights are approximately proportional to their synaptic counts. Our simulations revealed that propagating this activity across the neuron types led to an activity profile that could be even better fit by a sinusoid than the synaptic connectivity profile alone (Figure 20E). Since the EPG to Δ7 connectivity profile is already sinusoidal, this result is relatively independent of the shape of the input activity. For example, if we assumed an impulse (delta) function input from the EPG neurons to one PB glomerulus, the resulting signal was still shaped like a sinusoid (Figure 20F). We note, however, that these calculations ignore any nonlinearities, as well as the large number of synapses between individual Δ7 neurons. Considering that the Δ7 neurons synapse onto nearly all PB neurons in their specific output glomeruli (Figure 20C, Figure 20—figure supplements 1 and 2), we would expect this transformation of the bump to apply to those neurons as well. By similarly multiplying the EPG-Δ7 synaptic profile with the output profile from the Δ7 neurons onto each of the other neuron types, we found that the sinusoidal reshaping applied to nearly all columnar neurons (Figure 20G). The unique spacing of the Δ7 neurons’ inputs and outputs further suggests that this sinusoidal profile will be passed most strongly to glomeruli that represent head direction angles that are 180° shifted from the glomeruli where the EPG activity is strongest (Figure 20—figure supplement 3).

Note that just as the EPGt neuron type may expand the influence of the head direction signal to the outermost PB glomerulus (discussed in an earlier section), the P6-8P9 neuron type may extend the sinusoidal shaping of the signal to the entire PB. The P6-8P9 neurons have a similar morphology to the Δ7 neurons, receiving input across multiple PB glomeruli while outputting in only one glomerulus (Figure 21A). The P6-8P9 neurons also have similar input partners to the Δ7 neurons across glomeruli 6–9 (Figure 21B), and similar output partners in glomerulus 9 (Figure 21C), though the number of input and output synapses per glomerulus differs across the two cell types. Overall, the similarities between the P6-89 and the Δ7 neurons suggest that the P6-8P9 neurons perform a similar, albeit far more localized, function as the Δ7 neurons.

Figure 21

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Although the Δ7 neurons shape the activity profile of columnar PB neurons, the amplitude of this activity is likely influenced by inputs to the PB (Figure 22A). External (non-CX) input comes from the IB and SPS through the IbSpsP neurons and SpsP neurons (Figure 22B; Wolff et al., 2015). The IbSpsP neurons are columnar, projecting to one, two, or three often-adjacent glomeruli. They target a broad range of other columnar neurons including the PEN and PFN supertypes (Figure 22C). The pair of SpsP neurons, which are easily recognized by arbors that span exactly one half of the PB each, are very selective and target only the PFNd neurons (Figure 22C). The SPS is known to be innervated by DNs (Schnell et al., 2017) and can thus provisionally be considered a premotor area, but less is known about the IB (though a number of CX outputs project to the IB, as discussed later). We speculate in a later section about the potential navigational role of these PB input neurons. The IbSpsPs inputs are varied and largely unknown (Figure 22D, Figure 22—figure supplement 1). The SpsP neurons are incomplete in the hemibrain, and thus their inputs in the SPS are at present unknown. The PB also receives columnar, glomerulus-specific input from the PFNv neurons, which have recently been characterized physiologically (Figure 22C; Lu et al., 2020b; Lyu et al., 2020). These neurons receive relatively uniform input in the NO and FB (Figure 22E).

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The PB receives neuromodulatory input from both DANs (LPsP, Figure 19C) and octopaminergic neurons (P1-9, Figure 23A). The dopaminergic LPsP neurons receive PB input from the Δ7 neurons and the EPG neurons (Figure 20B). They also make synaptic contact with a wide range of other neurons, including the octopaminergic P1-9 neurons (Busch et al., 2009; Wolff and Rubin, 2018; Figure 23A), from which they also receive input (Figure 23B). Unfortunately, the processes of both the P1-9 and the LPsP neurons are cut off outside the PB, where they putatively receive most of their input (Wolff et al., 2015). The P1-9 neurons project throughout the brain while the LPsP neurons get input in the LAL, the SPS, and the IPS. The function of these two types is unknown, though they may control plasticity in the PB. Plasticity in the PB has been implicated in the fly’s ability to estimate the size of gaps that it can safely cross based on its own body size (Krause et al., 2019).

Figure 23

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A representational system for a circular variable, like head direction, might be expected to have the same number of elements to represent each angle. Thus, we might expect each columnar neuron type to have the same number of neurons in each PB glomerulus. In addition to the columnar PB-EB neurons, this would also include the many types of PB-FB columnar neurons that receive input from the EPG and Δ7 neurons (Figure 20B). While the PEG, PFGs, and PFL1 neurons have one neuron in each glomerulus in their PB domain (Figure 24A and B, blue bars), these uniform distributions are the exception rather than the rule. Deviations from uniformity tend to be mirror symmetric across the right and left PB, suggesting that they are not just the result of developmental variability. The EPG neurons, for example, have three neurons in glomeruli R/L 3–7, four neurons in glomeruli R/L 8, and two neurons in glomeruli R/L 1 and 2 (Figure 24A, purple bars). In contrast, the PEN neurons and PFN neurons each have roughly double the number of neurons in glomeruli 4 and 6 as they have in the other glomeruli; for example, PEN_a neurons have two neurons in R4, R6, L4, and L6, but one in each of the other glomeruli where they arborize (Figure 24A and C, magenta bars). Finally, the PFL and PFR neurons each have their own unique distributions of neuron numbers across the PB (Figure 24B). We outline some potential origins and roles for such numeric differences in ‘Discussion.’ We also note that neurons with more instances in a given glomerulus often have fewer total input and output synapses across the different regions in which they arborize (Figure 24—figure supplement 1). These connectivity differences may compensate for the differences in the number of neurons per glomerulus, potentially allowing the net activity in different PB glomeruli to be similar even if those glomeruli have a different number of neurons.

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The FB is coarsely divided into columns along its medial-lateral axis by four large classes of columnar neurons: PB-FB-*, FX, vΔ, and hΔ (Figure 28A and B), where ‘*’ and ‘X’ refer to accessory regions of the CX. In addition to these ~60 columnar neuron types, ~150 types of FB tangential neurons divide the FB into nine layers along the dorsal-ventral axis (Figure 28A and C). Each class of columnar neuron contains many distinct neuron types. Within each type, individual columnar neurons form spatially restricted arbors that innervate type-specific FB layers and, as a population, tile FB columns (Figure 28B and D, Figure 28—figure supplement 1). Compared to the PB, with its spatially segregated glomeruli (nine in each hemisphere), FB columns are not as clearly defined, nor are they clearly visible in light-level images. Instead, FB columnar neurons form a type-specific number of columns (from 6 to 12) and there is considerable variability in how evenly each type tiles the FB. Similarly, FB layers lack clear boundaries, much like the EB’s annuli (i.e., along the radial axis).

Columnar and tangential neurons also project to regions outside the FB, providing pathways for information exchange with accessory neuropils such as the NO, LAL, CRE, and SMP/SIP/SLP (Figure 28A). Based on their input from the EPG neurons and the polarity of their arbors, PB-FB-* neurons likely convey head-direction-related information from the PB to the FB (PFN, PFR, and PFGs types; Shiozaki et al., 2020), and also from the FB to the LAL (PFL types; Rayshubskiy et al., 2020). Two classes of interneurons, the vΔ and hΔ types, are composed of neurons whose arbors are largely confined to the FB, relaying information across layers and columns (Figure 28B and D). FX neurons are a heterogeneous columnar neuron class whose types primarily arborize in the FB and either the CRE or SMP/SIP/SLP. Similar to FX types, FB tangential neurons heavily innervate the CRE, SMP/SIP/SLP, and LAL (Figure 28C and D), but often contain additional arbors in type-specific neuropils, such as the NO, EB, or BU, which we detail in later sections.

Most PB-FB-* columnar types divide the FB into approximately nine columns (Figure 29, Video 5), thereby linking the nine glomeruli in the left and right PB to corresponding regions the FB. PFN neurons that innervate layer 1, such as PFNp_a, project to one of nine distinct tooth-shaped structures (Figure 29A). This is consistent with previous light-level anatomy, which described the ventral margin of layer one as being composed of seven distinct teeth plus two ‘cryptic teeth’ (Wolff et al., 2015), together accounting for the nine clusters observed here. Columnar types with arbors in intermediate FB layers, such as the PFNa neurons, are less well clustered, and instead show a more continuous tiling of the FB, but their innervation pattern is also consistent with the existence of approximately nine columns (Figure 29A). One type, the PFGs neurons, has 18 neurons in total, which fairly evenly tile the FB, dividing it into 9 columns or approximately 18 ‘demi-columns,’ roughly 1 demi-column per neuron (Figure 29B; see legend for exceptions to this pattern). Moreover, individual PB-FB-* neurons have neuronal arbors whose width is slightly less than 1/9th of the layer’s width (Figure 29D), and the distance between neurons in adjacent columns is 1/9th the layer width on average (Figure 29E). One notable exception to this pattern is the PFNd type, which clearly forms eight columns. Figure 29—figure supplement 1 shows morphological renderings and mean column locations for all PB-FB-* types, with the exception of PFL neurons, which we cover in later sections. Overall, the FB innervation of most PB-FB types is consistent with there being approximately nine columns, but there is considerable variability in how evenly each type tiles the FB. Variation in arbor width and spacing determines how much adjacent columns overlap.

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Video 5

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As described in previous sections (Figure 16), EPG neurons project from wedges in the EB to corresponding glomeruli in the left and right PB. This anatomical mapping conveys the activity bump in the EB to both the left and right PB, generating two bumps that get inherited by CX columnar neurons (Green et al., 2017; Turner-Evans et al., 2017). From this mapping, each PB glomerulus can be assigned an approximate ‘anatomical phase’ that indicates its preferred directional tuning, as defined by its EPG input. PB-FB neurons connect glomeruli in the left and right PB to columnar regions of the FB. However, their projection patterns have not been systematically characterized. Here we take a discrete view of this projection pattern and describe the various ways in which PB-FB types link PB glomeruli to FB columns.

The projection pattern of two EB columnar types – PEG and PEN – provides a framework for identifying similar patterns in PB-FB columnar neuron projections. First described at the light level (Wolff et al., 2015), PEG neurons project from PB glomeruli back to the same regions of the EB that provided their input, establishing a ‘default pattern’ where activity bumps from the left and right PB will approximately overlap in the EB. In contrast, PEN neurons project from PB glomeruli back to EB tiles with an ‘anatomical phase shift’ (Figure 17). This phase shift conveys the activity bumps from the left and right PB to regions approximately ±45° from the EPG bump, a motif that is responsible for updating the EPG bump position (Green et al., 2017; Turner-Evans et al., 2017).

To investigate the mappings from PB glomeruli to FB columns, we first focused on neurons innervating glomeruli R5 and L5. These glomeruli receive input from adjacent wedges in the EB and, therefore, have similar allocentric head direction tuning (22.5° difference; Figure 16), ensuring that when a bump is centered at L5 in the left PB there will be a second bump centered between R5/R4 in the right PB (Figure 30Ai; Green et al., 2017; Lyu et al., 2020; Turner-Evans et al., 2017). Next, we compared the columnar position of the R5 and L5 projections in the FB (Figure 30Ai and Aii). Two neuron types – PFGs and PFR_a – were found to map R5 and L5 to the same FB column, C5, consistent with the absence of any phase shift since these similarly tuned neurons project to overlapping regions in the FB. When we extended the PB-FB mapping to the other neurons in these types, we found that this projection pattern was circularly symmetric, leading to a consistent, approximately 0° phase shift across the populations (Figure 30Aiii, Video 6). Thus, for PFGs and PFR_a neuron types, we would expect activity bumps carried by the left and right PB populations to overlap in the FB (see bottom of Figure 30Ai), regardless of bump location (Figure 30Aiii). As described previously (Figure 19E), each PB-FB type innervates a variable number of PB glomeruli across the population. PFGs innervate all nine glomeruli in the left and right PB, and their 0° phase shift provides one means of assigning an approximate phase to each FB column. Importantly, PFGs map glomeruli R1/R9 and L1/L9 to columns C1 and C9, respectively, suggesting that these outer FB columns share a similar anatomical phase (as shown in Figure 30Ai and Aii, Bi and Bii), consistent with a circular representation. The projection pattern of PFR_a neurons (Figure 30Aiii), which only innervate the medial eight glomeruli in the left and right PB, also supports this notion.

Figure 30

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Video 6

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Unlike the PFGs and PFR_a types, all PFN neuron types have nonzero, contralateral phase shifts between their PB glomeruli and FB columns, much like PEN neurons in the PB-EB network. Specifically, as exemplified by the PFNp_a and PFNa types in Figure 30B, PFN neurons that innervate R5 project to C6 and neurons that innervate L5 project to C4. That is, PFN neurons connect PB glomeruli to FB regions using a one-column contralateral phase shift. This phase shift implies that PFN populations from the left and right PB would generate spatially shifted activity bumps in the FB that will be separated by ~90° (see bottom of Figure 30Bi). Plotting the full PB-FB mapping revealed that these one-column contralateral phase shifts are largely consistent across all PB glomeruli for these PFN neuron types (Figure 30Biii, Video 7). Notably, one distinct neuron type, the PFR_b, has a one-column ipsilateral phase shift.

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Here we have provided a discrete view on PB-FB-* phase shifts, a useful description given the CX’s strong topographic organization. However, these phase shifts are also apparent when viewed continuously in anatomical space (Videos 6 and 7). As quantified further below (Figure 34), the precise magnitude of PB-FB phase shifts and FB column phase is also continuous and can be estimated using PB-FB connectivity since these phase shifts will depend on how postsynaptic neurons in the FB sample from their PB-FB inputs. As with the PEN neurons, whose phase shifts appear strongly linked to their function of shifting the EPG bump in the EB (Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020), we believe that the PB-FB phase shifts offer insights as to the likely navigational function of each of these neuron types (outlined in ‘Discussion’). Next, we describe the columnar structure of hΔ and vΔ types, which are the main downstream target of FB columnar types in the FB.

Previously referred to as ‘pontine neurons’ (Hanesch et al., 1989; Heinze et al., 2013; Heinze and Homberg, 2008; Hensgen et al., 2021; Homberg, 1985; Siegl et al., 2009; Stone et al., 2017), the FB’s many interneuron types create an intricately structured scaffold for intercolumnar and interlayer communication within the FB. We renamed these neurons vΔ and hΔ. vΔ refers to the predominantly ‘vertical,’ layer-skipping morphology of the constituent neurons (Figure 31A). hΔ refers to the predominantly ‘horizontal,’ column-skipping morphology of the constituent neurons (Figure 31B).

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Two of these pontine neuron types are not FB interneurons, but rather are neurons that bring information into the FB from other CX structures. The vΔA_a neurons (Figure 31Ai) have mainly postsynaptic specializations in the AB, a mysterious structure at the base of the FB (Jenett et al., 2012; Pascual et al., 2004; Wolff and Rubin, 2018) that we discuss later, and send arbors up throughout the dorsal most layers of the FB. The hΔK neurons (Figures 31Bi and 10F), by contrast, each innervate wedge-shaped regions of the EB, which vary in size and coverage, and columns in intermediate FB layers before projecting to more dorsal layers of the FB. These neurons could carry head direction information directly from the EB to the FB, bypassing the PB, but their connectivity in the FB suggests that they may also be related to behavioral state, a topic we return to in a section focused on sleep circuits (Figure 53). With the exception of the vΔA_a, a subset of vΔA_b that innervates the AB, and hΔK neurons, all other vΔ and hΔ neuron types are interneurons whose arbors are restricted to the FB.

There are many different types of vΔ neurons, each distinguished by the layer(s) that they innervate, by the vertical distance between their multiple (usually two) arbors, and by the spread of each arbor. These different vΔ types are shown in Figure 31—figure supplement 1 and Video 8. Note that although some neuron types, such as the vΔH, form nine FB columns, most types vary in how cleanly, as a population, they tile each layer that they innervate. Similar to PB-FB columnar neurons, even types with a disorganized columnar structure can be assigned to the discrete nine-column scheme based on the average location of their arbor (see Materials and methods), which provides a convenient means to assess their relative columnar positions. Interestingly, all vΔ types also contain one or more individual neurons that project bilaterally to both C1 and C9, which we refer to as ‘C0’ (see Figure 31Ai). These neurons provide further support that columns C1 and C9 correspond to similar anatomical phases since they receive shared into from individual C0 neurons.

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All hΔ neurons have two horizontally separated arbors within the FB, one of which is predominantly presynaptic (Figure 31B). Each hΔ type has matching left- and right-projecting neuron pairs whose two arbors largely overlap. As a population, both the right- and left-projecting populations tile all FB columns. The many hΔ types are distinguished by the layer(s) that they innervate and by the horizontal spread of their arbors. These different types are shown in detail in Figure 31—figure supplement 2 and Video 9. By contrast with the nine-column tiling of the vΔ neurons, some hΔ types divide the layers they innervate into 12 columns, such as the hΔA and hΔL neurons, others into 8 columns, such as the hΔD and hΔH neurons, and one, the hΔF, into just 6 columns (Figure 31—figure supplement 2). In most cases, the population of neurons within each type neatly tile the layers that they innervate (see, e.g., the hΔH and hΔM neurons). Overall, the structure of the hΔ and vΔ backbone provides an avenue to determine the direction of information flow through the intra-FB columnar network, which we discuss in a later section (Figure 37).

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In addition to the PB-FB-*, vΔ, and vΔ columnar classes described above, the connectome revealed ~20 columnar types – including many novel types – belonging to the FX class, which innervate either the round body (ROB), SMP/SIP/SLP, or CRE (Figure 32). These types do not have arbors in the PB. Each type is composed of individual neurons that collectively tile all columns of the FB (Figure 32—figure supplements 1–2, Video 10), and the various types can be distinguished by the layer(s) of the FB they innervate, their overall columnar structure, and the extra-FB region that they project to. FR types send projections to the ROB; FS types send projections to the SMP/SIP/SLP regions; and FC types send projections to the CRE. With few exceptions, FR and FS types have primarily postsynaptic arbors in the FB and presynaptic specializations in their extra-FB neuropil (Figure 28—figure supplement 1), potentially forming additional columnar output pathways, as discussed in the CX outputs sections. FC types have mixed arbors both within and outside the FB (Figure 28—figure supplement 1), perhaps providing bidirectional communication between the FB and CRE.

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In the sections above, we described the major FB neuron types, with a particular focus on their morphology, columnar structure, and extra-FB innervations. We now turn our focus to connectivity within the intra-FB network and describe how columnar information may flow from PB-FB inputs to columnar outputs.

Much of the FB’s columnar input comes from the PFN neurons (Figure 33A, Figure 33—figure supplement 1, see also 19,25,26Figures 19 and 25–26), which have postsynaptic specializations in both the PB and NO. Some of the PFN types also make synapses within their type in the FB columns that they innervate – much like the PEN neurons in the EB. Though there are direct connections between PFN neurons and columnar FB output neurons in the FB, the majority of PFN synapses are to vΔ, hΔ, and FC neurons (Figure 33A, Figure 33—figure supplement 1). Thus, much of the input to the FB passes into a multilayer, multicolumn intra-FB network. To gauge the ‘depth’ of the intra-FB network, we quantified the different ‘path lengths’ from PFN inputs to columnar FB output neurons (Figure 33Bi) (see Materials and methods). For example, PFNa neurons have direct connections to PFL1 neurons. This is a path length of 1. PFNa neurons also have indirect connections to PFL2 neurons through first hΔJ and then hΔH neurons (Figure 33Bi and Bii). This is a path length of 3. We found that direct connections from PFN neurons to output neurons are relatively sparse, while many more two- or three-step pathways can be traced through hΔ and/or vΔ neurons (Figure 33Bii). While highly recurrent, the intra-FB network can therefore roughly be thought of as being 3–4 layers deep, though we note that this analysis does not include the FB tangential neurons.

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We next sought to characterize the structure of the intra-FB network connectivity. The connectivity shows clear indications of preferred pathways and subnetworks. For example, the PFNa/FC1/PFL1 types are primarily connected to one another, with only sparse connections to other FB neuron types. These types therefore form their own subnetwork within the FB (below the line in Figure 33A, Figure 33—figure supplement 1). Examining this subnetwork at the individual neuron level (Figure 33C), we found that the connectivity patterns in the subnetwork largely matched the columnar overlap of the different constituent neurons. However, we found that direct connections from individual PFNa neurons to PFL1 neurons were not as strong or as consistent across neurons as direct connections from PFNa neurons to FC1 neurons. FC1 neurons themselves send their outputs to a putative motor area (CRE), to PFL1 neurons within their column, and to other FC neurons. Thus, the indirect pathways from PFNa to FC1 to PFL1 may contribute more to PFL1 activity than the direct PFNa to PFL1 connections. These indirect pathways point to the importance of depth in FB networks.

To parse additional subnetworks in the FB, we next grouped neuron types based on common connectivity patterns – specifically, their upstream and downstream partners (Figure 33—figure supplement 2, and Materials and methods). We expected that types within a subnetwork would share common upstream and downstream partners. Indeed, the FC1 neurons clustered together based on both their inputs and outputs, a clear signature of the PFNa/FC1/PFL1 subnetwork. The vΔF, vΔG, vΔH, and vΔI neurons also clustered together (Figure 33—figure supplement 2, Figure 33—figure supplement 3). However, most neuron types that share an upstream cluster split into multiple downstream clusters (and vice versa). This splitting suggests that the intra-FB network cannot, through columnar connectivity alone, be cleanly split into multiple subnetworks. Instead, information is propagated throughout the FB, across layers and columns. However, we note that FB tangential neurons may ‘gate’ some of these pathways, allowing for a clean functional separation of subnetworks. We return to this topic in the ‘Discussion.’

The anatomical projection pattern of PB-FB neuron types suggests that they convey activity bumps from the left and right PB to the FB, but with type-specific phase shifts, as described above (Figure 30). In particular, the projection pattern of PFGs and PFR_a types suggests that they convey the activity bumps from the left and right PB to overlapping columnar locations in the FB, establishing a ‘default’ mapping between PB glomeruli and FB columns. In contrast, all PFN types have a one-column contralateral phase shift, predicting that the left and right activity bumps will end up ~90° apart in the FB (Figure 34A). Consistent with this notion, these anatomical phase shifts impact PB-FB neurons’ connectivity with their downstream targets in the FB (Figure 34B, C). For example, PFNa neurons that innervate glomerulus R5 synapse onto FC1B neurons in C6, and L5 neurons synapse onto FC1B neurons in C4, consistent with their anatomical projection pattern (top panel, Figure 34C). More nuanced morphological characteristics also affect connectivity. For example, PFNp_a neurons, which arborize in spatially restricted regions of the FB (Figure 29), primarily connect single PB glomeruli to single FB columns, while PFNa neurons, which have slightly wider FB arbors, connect single PB glomeruli to several adjacent FB columns (Figure 34C). Thus, PB-FB phase shifts structure columnar input to the FB network.

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The above analysis views PB-FB projections as connecting individual glomeruli in the PB to discrete columns in the FB. However, as noted above (Figures 29, 31 and 32), FB columnar neurons form a type-specific number of columns and there is a large variability in how evenly each type tiles the FB. This raises the possibility that the directional tuning of FB neurons may vary continuously according to their medial-lateral position in the FB. To assess this possibility, we used connectivity to infer the directional tuning of FB neurons by taking circular means of the phases that FB neurons inherit from their presynaptic PB-FB inputs (Lyu et al., 2020; Figure 34—figure supplement 1). This analysis revealed a strong correlation between FB neurons’ medial-lateral position and their estimated directional tuning (Figure 34D). Consistent with the notion that the FB inherits a sinusoidal activity bump from the PB, the medial and lateral borders are tuned to similar phases, as expected for a circular representation. In addition, FB neurons’ directional tuning is quite evenly distributed, suggesting that, rather than forming discrete columns that are consistent across neuron types, FB neurons can take on a range of angles that is largely determined by their medial-lateral position and, therefore, the subset of PB-FB inputs that they sample from.

This approach (Lyu et al., 2020) also allowed us to estimate the magnitude of the PB-FB phase shift for PB-FB neuron types (Figure 34E). In agreement with our projection-based analysis (Figure 30), PFGs and PFR_a were found to have anatomical phase shifts close to 0°. In contrast, all PFN neuron types have an ~90° phase shift, with some variability across neuron type. To investigate the source of PFN phase shift variability, we analyzed how individual FB neurons sample from the left and right PB-FB populations (Figure 34F and Figure 34—figure supplement 1). Consistent with our angular assignments in the PB, FB neurons that sample from just two distinct angles – one from the left PFN population and one from the right PFN population – have phase shifts that are usually 67.5 or 112.5° (Figure 34F). This is because no left-right pair of glomeruli is separated by 90° (Figure 34—figure supplement 1B). Instead, neurons with a 90° phase shift sampled from at least three PB glomeruli. This effect explains some of the type-to-type variability in PFN phase shifts. For example, FB neurons that receive input from PFNa neurons have phase shifts very close to 90° since they mostly sample from at least three glomeruli (Figure 34—figure supplement 1C), likely due to PFNa neurons’ wide FB arbors, as mentioned above. In contrast, neurons that receive input from PFNp types often sample from just two glomeruli that are 112.5° apart. This may be because PFNp types form spatially clustered arbors in the ventral FB, which favors a more restricted connectivity pattern, as mentioned above. Since this effect reflects the diverse ways in which FB neurons sample from the left and right PB populations, it is unlikely to be due to the precise angles assigned to PB glomeruli. We return to the potential functional role of PB-FB phase shifts in the context of vector navigation in ‘Discussion.’

These PB-FB projection patterns raises the possibility that the bumps conveyed from the left and right PB could propagate independently through the FB network, a scenario we refer to as ‘functional lateralization.’ Does the FB network’s connectivity support such a scenario? One signature of lateralization would be that PFN neurons from different sides of the PB might project to different neuron types in the same FB columns (Figure 35A). However, we found no systematic differences in left versus right PFN inputs to different downstream FB neuron types (Figure 35B). A second signature of lateralization might be PFN neurons from different sides of the PB projecting to distinct neurons within a downstream type, perhaps organized by demi-columns (Figure 35C). However, we found that the input contributions of left and right PB neurons were very similar for most downstream neurons (Figure 35D). Although there are some exceptions to this rule, these exceptions are almost all neurons with both weak and inconsistent connections at the population level (small dots to the top left of the plot in Figure 35E and an absence of large dots at the top right). Note that the PFNd neurons do preferentially and consistently make lateralized connections with other PFNd neurons. That is, within the FB, PFNd neurons from the left PB synapse onto PFNd neurons from the right PB, and those from the right PB onto those from the left PB, but neither population makes synapses with other PFNd neurons from the same side of the bridge (see arrow in Figure 35E). Thus, consistent with physiological reports from some PB-FB neuron types (Shiozaki et al., 2020), the bumps from the left and right PB are likely to be summed by each downstream FB neuron type, rather than multiple bumps that might then be processed independently within the FB. Note, however, that this does not rule out the possibility of multiple activity bumps arising from different PFN types, the navigational implications of which we explore in ‘Discussion.’ Note also that although there appears to be no lateralization in the context of FB bump dynamics, there is considerable asymmetry in how some FB neurons from the left and right halves of the structure project to the AB.

Figure 35

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The AB, which sits at the base of the FB (Figure 36A), is now considered a core structure of the CX (Wolff and Rubin, 2018). As suggested by its name, the structure is notable for having distinctly different sizes on either side of the midline, with the right side typically being larger than the left (Jenett et al., 2012; Pascual et al., 2004; Wolff and Rubin, 2018). There is some evidence suggesting that flies with an AB that is roughly equal in size in both the right and left hemisphere have reduced long-term memories of shock-associated odors as compared to their more asymmetric conspecifics, though their short-term memories are unaffected (Pascual et al., 2004). Neurons in the AB have also been associated with fructose feeding preference (Musso et al., 2021). The AB may therefore serve multiple functional roles. Indeed, the AB receives inputs from many different brain regions, including the SMP, SIP, ATL, and CRE, and sends its outputs primarily to the dorsal and ventral layers of the FB (Figure 36B). Pathways upstream from the AB inputs primarily originate in the LH, though clock neurons, the AL, vPNs, and other sources also appear (Figure 36—figure supplement 1A). Many of the AB neuron types that innervate the FB have been described previously (Wolff and Rubin, 2018), but we identified two new types that primarily get input in the AB: the FS4A and FS4B neurons (Figure 36C). FS4A and FS4B also receive input throughout the FB and output in the SMP/SIP/SLP.

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The asymmetry of the two sides of the AB is clearly reflected in the connectivity of the neuron types that arborize there. The left AB primarily connects the vΔA_a neurons with the SA3 neurons, while the right AB connects many more types of AB neurons (Figure 36D). Another notable feature is that FB-AB columnar neurons that arborize in the right half and center of the FB send processes to the right AB, while neurons that arborize in the left FB send processes to the left AB (Figure 36E, Figure 36—figure supplement 1B). This is in stark contrast with the NO, whose left and right halves both receive PFN projections from all FB columns. The FB targets of AB-FB neurons are varied, including tangential, vΔ, and hΔ neurons (Figure 36F, Figure 36—figure supplement 1C). The role of the asymmetry introduced by the AB is not currently understood.

Unlike the EB network, whose columnar neurons form recurrent EB-PB loops, FB columnar neurons mainly receive input in the PB and provide output to the FB, suggesting a primarily feedforward pathway (Figure 22). Even PFNv neurons, which have presynaptic sites within the PB, do not receive much columnar input in the FB, making recurrent columnar loops unlikely. This suggests that the FB acts as a way station along a feedforward pathway, receiving a PB bump – modified by input from accessory structures like the NO – before initiating actions by transmitting commands to premotor centers. However, also in contrast to the EB, the FB is characterized by dense and highly specific intercolumnar and interlayer recurrent connections between different neuron types. This connection matrix likely strongly influences bump dynamics and enables recurrent network dynamics within the structure. We now focus on describing the most prominent motifs in this network.

As described in a previous section (Figure 31), the backbone of the FB’s recurrent network is a 2D grid formed by the hΔ and vΔ neurons. More generally, all FB columnar types can be divided into two broad categories based on the morphology of their neurons (Figure 37A). The processes of ‘vertical’ neuron types are largely confined to a single column and include all PB-FB-*, FX, and vΔ types. ‘Horizontal’ hΔ neuron types, by contrast, have processes in two distinct columns. As depicted in Figure 37A, these vertical and horizontal neuron types connect to each other in several different ways. Importantly, however, the connectivity between different vertical and horizontal types closely respects some simple rules. We found that connections were typically either localized to the same column (Figure 37Bi), jumped half the width of the FB (Figure 37Bii), or did both (Figure 37Biii). In this last case, a presynaptic neuron in one FB column synapses onto postsynaptic hΔ neurons, some with primarily dendritic arbors in the column and some with primarily axonal arbors in the column. Because hΔ neurons are assigned to columns based on the location of their dendritic arbor, this connectivity motif produces two diagonal bands in the column-to-column connectivity matrix (bottom panel of Figure 37Biii).

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It is as yet unknown whether these connections are excitatory or inhibitory, something that – much as is the case with the Δ7 neurons in the PB – would impact how activity is propagated across these connections. For example, a column-matched excitatory connection (Figure 37Bi) would preserve the phase of the bump, but if that connection were inhibitory, it would shift the bump by half the width of the FB (roughly 180° in azimuth). Similarly, a connection across half the FB’s width might shift the bump by 180°, if it happens to be excitatory, or keep it in place (0°) if it were inhibitory (Figure 37ii). We analyzed the complete set of connectivity matrices (see, e.g., the bottom row of Figure 37Bi–iii) between all vertical and horizontal types using principal components analysis (PCA) and found that the three broad intercolumnar motifs that we identified accounted for most of the variance across the entire set (Figure 37C and Figure 37—figure supplements 1 and 2, see Materials and methods). Not knowing the neurotransmitters and receptors involved in these motifs, we cannot exactly say how the activity bump from the PB is modified by the FB network. However, the connectivity strongly suggests that azimuthal comparisons and transformations of activity bumps are a key function of much of the FB’s recurrent circuitry. We describe the potential significance of these specific motifs for bump-driven navigational computations in ‘Discussion.’

We now turn to the other axis of information flow in the FB, the vertical axis. As noted in a previous section, the PFN neurons provide the FB with most of its columnar input. These neurons target the ventral layers of the FB (Figure 38A) – in fact, most PFN neurons target layers 1 and 2, while PFNa, PFNd, and PFNv types target layers 3 and 4 (Figure 28—figure supplement 1). The PFR and PFGs types are the exception to this rule, with presynaptic specializations up to layer 6 (Figure 28—figure supplement 1). When we examined the 2D grid of neuron types formed by the FB’s interneurons, we found a discernable vertical direction to information flow within the structure. Specifically, most of the intra-FB columnar neurons transfer information from the ventral layers of the FB to the dorsal layers, as can be seen from the distribution of their postsynaptic and presynaptic specializations (Figure 38B and C). Both the hΔ and vΔ types receive most of their extra-FB columnar input in their ventral arbors and provide output in their dorsal arbors (as denoted by the dark circles being consistently higher than light circles in Figure 38D). The FB output neurons do not appear to selectively get input from the lower FB layers (Figure 28), suggesting that the dorsal flow of information in the FB is primarily used in intra-FB computations.

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As discussed above (Figures 30 and 34), the primary PB-FB columnar inputs to the FB enter the structure with type-specific anatomical phase shifts, which we believe to subserve specific vector computations required for navigation (see ‘Discussion’). The previously identified output neurons, three types of PFL neurons (Lin et al., 2013), also display type-specific phase shifts (Figure 39, Figure 39—figure supplement 1). These PFL phase shifts position them well to modulate or control directed actions, an idea developed further in ‘Discussion.’

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The PFL2 neurons are distinguished from all other PB-FB columnar neurons based on their coverage of PB glomeruli. In contrast with the other columnar neurons, these neurons only receive inputs from the inner five PB glomeruli on each side (Figure 39Ai–iii). Thus, these neurons only inherit a single bump in the PB since they effectively sample from a 360° space that is split between the left and right halves of the PB (by contrast, most other PB types sample from 360° space in both the left and right PB). The PFL2 neurons are also distinguished by their four-column phase shift, giving them an ~180° phase shift in their FB innervation relative to their input PB glomerulus or glomeruli (since individual PFL2s sometimes arborize in two neighboring glomeruli) (Figure 39Aii–iv, Video 11). Notably, these neurons send projections to both sides of the LAL, a pattern of connectivity whose potential navigational function for forward locomotion we explore in a later section on output pathways of the CX, and revisit in ‘Discussion.’

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By contrast, almost all PFL1 neurons have a single column (~45°) ipsilateral phase shift and project to the contralateral LAL (Figure 39Bi–iv). The exceptions to this rule are, first, the innermost PFL1 neurons. These neurons, which originate in PB glomeruli L1 and R1, send their outputs to the LAL on the same side. Second, the PFL1 neurons in L7 and R7 are not phase shifted as expected, but project to C1 instead of C2 and C9 instead of C8 in the FB, respectively.

Finally, the PFL3 neurons display a two-column (~90°) ipsilateral phase shift and also project to the contralateral LAL (Figure 39Ci–iv, Video 12). Exceptions to this rule are described in the figure legend. Just as the 180° phase shift of the PFL2 neurons and their projection to both sides of the LAL suggest a role in directing forward locomotion, this 90° phase shift suggests a potential role for PFL3 neurons in directing turns towards an FB-specified goal, an idea that we develop in the section on CX output pathways and in ‘Discussion.’

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Overall, the PFL neurons, along with the other FB columnar outputs, appear to constitute dedicated circuits for a variety of bump-dependent navigational behaviors. How does the fly set directional goals based on internal state and context and then select the behavioral programs to achieve those goals? The large set of tangential inputs into the FB are obvious candidates to play a leading role in this process, which we turn to next.

In earlier sections, we described the ring and ExR neurons that bring tangential input to the EB. Most ring neurons bring information about directional sensory cues to the EB-PB compass network, tethering the fly’s internal compass to its surroundings, while several of the ExR neurons likely provide modulatory input. In contrast to the ring neurons, the FB’s many tangential inputs are less well understood.

The FB has nine different layers of varying widths. Layers 4 and 5 are the widest, while layers 1 and 9 are the smallest (Figure 40A, Video 13). All FB tangential (FBt) neurons have presynaptic specializations in characteristic FB layers and most bring input from accessory structures of the CX, such as the CRE, SMP/SIP/SLP, and LAL, as well as from the NO (Figure 40A, Figure 40—figure supplement 1A). The FB4O neurons, for example, receive input in the CRE and SMP/SIP/SLP and send their outputs solely to layer 4 in the FB (Figure 40Aii).

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Like the ExR neuron types, there is considerable variability in neuronal morphology across the different FB tangential neuron types (Figure 40B). While most types target one FB layer, some, such as FB1I, target multiple layers (Figure 40Bi). Separately, while most types have processes external to the CX, some, such as FB4Z, are intrinsic FB interneurons, with no external processes (Figure 40Bii). Notably, not all FB tangential neurons uniformly fill their layer. FB4Z, for example, sends out selective processes to target specific partners within layer 4 (Figure 40—figure supplement 1B). There is also considerable variability in where the FB tangential neurons arborize outside of the CX. For example, the FB tangential neurons in layers 3–5 preferentially send processes to the LAL and CRE, while the upper layers tend to target the SMP/SIP/SLP (Figure 40C, Figure 40—figure supplement 2). Finally, in stark contrast with EB ring neurons, most FB tangential neurons consist of only one or two neurons per side (Figure 40D). We found no clear evidence of side preference for neurons originating on the right or left within a given type. Neurons from both sides target PB-FB columnar neurons from both sides of the PB. The small number of neurons per type suggests that they convey specific, uniform information to their targeted layer(s).

The number of different FB tangential neurons that provide output to any given FB layer and the diversity of brain regions from which they draw their inputs suggests that every computation that the FB participates in is likely modulated by context. Precisely what these modulatory influences are is largely unknown. They could be purely sensory, for example, or they could convey the state of the animal. However, some hints may come from the upstream partners of the different FB tangential neurons (Figure 40E). For example, MB output neurons preferentially target layer 4 (which will be discussed in the next section). The LH, which receives direct olfactory, thermosensory, and hygrosensory input and multisensory inputs from the visual, mechanosensory, and gustatory systems as well (Dolan et al., 2019; Schlegel et al., 2020), is part of input pathways that project to most FB layers. vPNs, AL neurons, and the courtship-associated Fru neurons are also upstream of many FB tangential types. This diverse array of upstream partners could convey a range of contextual cues to layers throughout the FB.

Although little is known about most of the FB’s tangential neurons, there are some exceptions. Most notably, dorsal FB tangential types are known to be involved in sleep-wake control (reviewed in Artiushin and Sehgal, 2017; Donlea, 2017; Dubowy and Sehgal, 2017; Helfrich-Forster, 2018), a topic we return to below (Figures 48–53). In addition, a recent study focused on the LH identified an FB tangential neuron type they called PV5k1, which, when optogenetically stimulated under closed-loop visual conditions, leads to a reduction in the fly’s wingbeat frequency (Dolan et al., 2019). The neurons targeted by the GAL4 lines used in that study likely correspond to FB2H_a, FB2H_b, and/or FB2I_b, neuron types that target some hΔ neuron types and also the PFL2 and PFL3 neuron types, consistent with the direct influence on the fly’s behavioral patterns (see later sections on PFL neurons). Another recent study found that FB tangential neurons that target layer 6 encode food choice (Sareen et al., 2020). Inhibiting these neurons made hungry flies more likely to eat bittersweet food with 500 mM sucrose instead of purely sweet food with 50 mM sucrose. The activity of these neurons was also shown to encode the food choice.

The ExFl1 neurons (Liu et al., 2006; Weir et al., 2014; Young and Armstrong, 2010b), which are likely the FB2B_a and/or FB2B_b neurons (Figure 41A), have also been characterized. These neurons respond to progressive optic flow and are strongly modulated by whether or not the fly is flying (Weir et al., 2014), providing a potential indication the motor state of the animal. Information from the FB2B_a neurons is fed to other FB tangential neurons, FB interneuron types (including some hΔ and vΔ neurons), intermediate types (such as the FC neurons), and output neurons (such as the FR neurons, Figure 41B). The FB2B_a neurons also get input in the FB from the other layer 2 FB tangential neurons and from the columnar FC1 neurons (Figure 41C). Such a connectivity profile is typical of most FB tangential neuron classes, as shown in Figures 42—44.

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Figure 42

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Some FB tangential neuron types in FB layers 2 and 8 have been proposed to have a major role in visual learning (Liu et al., 2006). In such a situation, the tangential neurons could be ideally placed to provide information about positive or negative reinforcers, a function typically carried out in the fly brain by DANs. Indeed, several FB tangential neurons are known to be DANs (discussed further below), as indicated by the gray bars in the connectivity matrix in Figure 42. DANs are not the only neuromodulatory neurons amongst the FB tangential neurons. It is likely that several other FB tangential neurons may be modulatory and peptidergic, but we could only confirm one additional such neuron, the octopaminergic OA-VPM3 (Figure 42, first row in the connectivity matrix).

Overall, the FB tangential neurons primarily target the intra-FB network and rarely target the PFN neurons, the major source of columnar input to the FB (Figure 42). This intra-FB targeting by potential contextual and neuromodulatory signals further emphasizes the importance of the FB’s interneurons and recurrent network in shaping circuit dynamics in the structure.

As with the ring neurons of the EB, the FB’s tangential neurons synapse onto each other near their presynaptic specializations in the FB (Figure 43). However, in contrast to the ring neurons, there are far fewer neurons in each FB tangential type, and their subnetworks seem less tightly clustered, making it more difficult to detect hierarchies amongst the potential contextual inputs (squares marked in Figure 43). Like the ring neurons, all tangential neurons of the FB, including the DANs, also receive considerable intra-FB input near their presynaptic sites in the FB, (Figure 44A), much of it from their targets (Figure 44B).

We also examined the connectivity matrix within and across different FB tangential neuron types at the level of individual neurons (Figure 45A). Similar to the ring neurons, a subset of FB tangential types have reciprocal connections between the individual neurons within that type. For example, FB2I neurons interact strongly with each other, and these interactions are spread uniformly across columns within their layer of innervation (Figure 45B). If these interactions are inhibitory, as is the case with ring neurons, such connectivity may facilitate a competition between similar contextual inputs that are vying to influence navigational computations based on the columnar position of the bump. We revisit this possibility in ‘Discussion.’

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FB tangential neurons receive much of their input in central brain regions like the SMP/SIP/SLP (Figures 28 and 40F), which, in turn, receive inputs from many other parts of the brain, such as the MB, consistent with the idea that FB tangential neurons enable the modulation of CX-controlled behavior, perhaps according to context and internal state. Our knowledge of the precise nature of these signals has been limited by a lack of extensive characterization of inputs to these less structured brain regions. A notable exception is the set of inputs that arrive from the MB. The MB is thought to be a center for associative learning (Cognigni et al., 2018; Modi et al., 2020). It receives inputs from nearly all sensory modalities, is innervated by multiple types of DANs (Li et al., 2020), and provides an architecture to flexibly convert sensory information from thousands of Kenyon cells (KCs) into experience-dependent (and DAN-mediated) valence signals carried by the MB’s output neurons, the MBONs. MBONs broadcast these valence signals to other areas of the brain, but how these signals drive the fly’s behavioral responses is not fully understood. In this section, we analyze pathways connecting the MB and the CX. Communication between these structures may play an important role in sleep (Dubowy and Sehgal, 2017; Sitaraman et al., 2015), memory consolidation (Berry et al., 2015; Dag et al., 2019; Donlea, 2019), context-dependent feeding decisions (Sareen et al., 2020; Scaplen et al., 2021; Scaplen et al., 2020), and perhaps also the conversion of the MB’s valence signals into goal-directed actions during navigation (Collett and Collett, 2018; Sun et al., 2020).

As described in a companion paper on the MB (Li et al., 2020), about half of the MBONs directly synapse onto FB tangential neurons that target the middle layers (4–6) of the FB (Figure 46A). Some MBONs contact only a single type of FB tangential neuron. For example, MBON09 connects exclusively to FB4R (Figure 46Bi). Many other MBONs contact multiple downstream targets in the FB. MBON04, for example, targets FB tangential neurons in both layers 1 and 6 (Figure 46Bii).

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MBONs of different neurotransmitter types, both excitatory and inhibitory, often converge onto the same FB tangential neurons (lines of different colors in Figure 46A; see Li et al., 2020 for how neurotransmitters for each of the MBONs were identified). For example, the glutamatergic (and likely inhibitory) MBON04 and the cholinergic (excitatory) MBON12 both contact FB4A (Figure 46A and Biii), and two MBONs that express different (likely) inhibitory neurotransmitters, MBON05 (glutamate) and MBON09 (GABA), converge onto FB4R, along with a third excitatory (cholinergic) MBON21 (Figure 46A).

FB neurons are not the only CX neurons targeted by direct projections from the MB. The glutamatergic MBON30 neuron type targets the LCNOp neurons (Figure 46Biv) that themselves feed the PFNp columnar neurons. The strength of these direct connections varies widely. Some, such as connections from MBON09 and MBON21 to FB4R, represent a significant fraction of their downstream target’s input (longer bars in Figure 46—figure supplement 1B), while others are much weaker in the influence that they exert on even their most preferred downstream partners in the CX (short bars in Figure 46—figure supplement 1B). Note that, as explained in an early section of the article, our summary plots and connectivity matrices exclude connected pairs whose connection weights fall below our threshold (for significance criteria, see Materials and methods). Thus, Figure 46A, for example, shows slightly fewer connections than the equivalent figure in the companion paper on the MB connectome (Li et al., 2020). This dependence of connectivity on the threshold chosen is shown in Figure 46—figure supplement 1A and C.

In addition to these direct connections, MBONs also connect to both dorsal and ventral layers of the FB through intermediate neurons in regions like the SMP, SIP, and CRE (Figure 47). Several of these one-hop pathways feature a mix of convergence and divergence from different MBONs onto neurons in intermediate layers (complete set of paths in Figure 47—figure supplement 1). Note, once again, that not all MB-to-CX pathways involve FB tangential neurons. For example, MBONs 26 and 31 reach the CX, and even the FB, through the LAL and the LCNO and LNO neurons (Figure 47E).

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In some cases, we could use what is known about the KC inputs to different MBON types (see Figure 15 in Li et al., 2020) to determine the type of sensory information in specific downstream FB tangential neurons (Figure 47C and D). For example, several MBONs conveying valence signals associated with visual information send divergent streams of information to an intermediate layer of neurons in diverse brain regions. These intermediate neurons, in turn, feed FB tangential neurons of different classes that go to both ventral and dorsal layers of the FB (Figure 47C). MBONs that receive thermosensory and hygrosensory information project to a largely different set of intermediate neurons, which project to their own, largely distinct set of FB tangential neurons (and LNO neurons) (Figure 47D).

In ‘Discussion,’ we examine the potential role of the connectivity between the MB and FB in navigation, sleep, and memory consolidation.

Previous studies have established a functional role for several types of dFB tangential neurons in tracking sleep need and controlling sleep-wake states (reviewed in Artiushin and Sehgal, 2017; Donlea, 2017; Dubowy and Sehgal, 2017; Helfrich-Forster, 2018). Specifically, a heterogeneous population of tangential neurons targeted by the R23E10 GAL4 line (Figure 48A and B; Qian et al., 2017) encodes sleep need through changes in both intrinsic excitability and spontaneous firing rates, and induces sleep when activated (Donlea et al., 2014; Donlea et al., 2018; Donlea et al., 2011; Liu et al., 2016; Ni et al., 2019; Pimentel et al., 2016; Qian et al., 2017). Counteracting these sleep-promoting populations are wake-promoting DANs (Liu et al., 2012; Ueno et al., 2012) that are able to inhibit neurons contained in R23E10 (Pimentel et al., 2016).

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The specific neuron types composing these sleep- and wake-promoting populations remain mostly unknown. To address this, we matched individual neurons in R23E10 to their corresponding EM-defined neuron type by comparing their light- and EM-level morphologies (Figure 48—figure supplements 2–7, Videos 14–15, see Materials and methods). This analysis identified nine neuron types, each composed of 1–3 neurons per hemisphere, that are targeted by the R23E10 line (Figure 48C and D). These neurons occupy type-specific layers and sublayers of the FB, where most of their presynaptic specialization reside and innervate distinct regions of the SMP/SIP/SLP, where they form mixed arbors containing mainly postsynaptic specializations (Figure 48B and D). To identify the wake-promoting DANs of the dFB, we took a similar approach, which involved generating a split-GAL4 line, SS56699, that drives expression in three TH + neurons per hemisphere belonging to the PPL1 dopaminergic cluster and then matching these tangential neurons to their corresponding EM neuron types: FB5H, FB6H, and FB7B (Figure 49, Video 16).

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Figure 49

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How are the sleep-promoting neurons in R23E10 connected to the wake-promoting PPL1 DANs, and how does the network regulate sleep-wake states? To begin to address this question, we looked at the connectivity between these neuron types within the dFB, where their arbors overlap most strongly and where the majority of their presynaptic sites reside (Figure 50). Plotting neuron-to-neuron connectivity revealed a densely recurrent network, but with variable connection strengths, even across neurons of the same type (Figure 50A). Not surprisingly, given its more ventral arbors, the dopaminergic FB5H neuron type lacks direct connections with the types present in R23E10. Figure 50B shows a network graph of the connectivity between R23E10 neuron types and the two remaining DAN types. The network can be roughly divided into two clusters: one containing layer 6 neurons and the other layer 7 neurons. Each cluster contains both putative sleep-promoting R23E10 neuron types and a putative wake-promoting DAN type. Importantly, the two DAN types make reciprocal connections to nearly every 23E10 neuron in their layer. This simple motif resembles the classic ‘flip-flop’ circuit model of brain state regulation thought to underlie sleep-wake control in mammals (reviewed in Saper et al., 2010). In this model, wake-promoting and sleep-promoting neuron types have reciprocal inhibitory connections, ensuring that only one population is active at a time. While dopamine is known to inhibit R23E10 neurons (Ni et al., 2019; Pimentel et al., 2016), it is currently unknown whether R23E10 neurons inhibit DANs (Figures 51—53, Figure 53—figure supplement 1).

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The ability of R23E10 neurons and dFB DANs to regulate sleep-wake states likely depends on their upstream and downstream connections, which remain largely unknown. We found that the dFB sleep-wake neuron types have the potential to influence a large number of neuron types both inside and outside the FB (Figure 51). Sleep-wake types target both columnar and tangential neuron types within the FB, and also have downstream targets in the SMP/SIP/SLP, consistent with the presence of mixed arbors in these regions. Similarly, many upstream neuron types have the potential to influence the sleep-wake neurons (Figure 52), especially through inputs to their dendritic arbors in SMP/SIP/SLP (see early section on ‘Assessing the relative importance of different synaptic inputs’). Within the FB, many of the neurons upstream of sleep-wake neuron types are also downstream of sleep-wake types, forming recurrent loops. For example, FB6A and FB6C_b are reciprocally connected with OA-VPM3, a wake-promoting octopaminergic neuron type with processes spanning many brain regions (Ni et al., 2019; Seidner et al., 2015). The physiological relevance of these candidate upstream and downstream connections remains to be determined, providing many targets for future physiological investigation.

Previous studies have suggested that a recurrent loop links sleep-wake circuits in the dFB with those in the EB (Donlea et al., 2018; Liu et al., 2016), but identifying the neurons and pathways involved has proven challenging. To address this, we constructed a network graph that contains the dFB types identified above, a few of their main partners, as well as previously reported CX sleep-wake neuron types: ER5 (Liu et al., 2016), ExR1 (i.e., ‘helicon cells’; Donlea et al., 2018), and ExR3 (Liu et al., 2019). This analysis revealed that three neuron types – ExR1, ExR3, and hΔK – directly link sleep circuits in the EB with those in the dFB through distinct channels (Figure 53).

ExR1 and ExR3 form a subnetwork in the EB with extensive reciprocal connections involving ER5 and ER3d types. ER5 neurons are known to be involved in homeostatic sleep control (Liu et al., 2016; Raccuglia et al., 2019) and receive circadian input from the anterior-projecting DN1 pathway (Figure 6; Guo et al., 2018; Lamaze et al., 2018). ER5 neurons also synapse onto EL neurons, which target nearly all other ring neuron types in the EB (see Figure 10F for network graph). This may allow ER5 neurons to impact activity throughout the EB circuit. ER3d neurons innervate the inferior-posterior portion of the BU, a region known to contain glomeruli that lack ipsilateral or contralateral visual receptive fields (Omoto et al., 2017; Shiozaki and Kazama, 2017). In addition, ER3d neuron types are targeted by a driver line that labels neurons expressing the 5HT7 serotonin receptor and have been previously implicated in the serotonergic ExR3 sleep-wake circuit of the EB (Figure 53—figure supplement 1; Liu et al., 2019). Finally, hΔK neurons have purely dendritic inputs in the EB, where they receive input predominately from PEN_b neurons. This may be one pathway by which the head direction signal, whose amplitude correlates with the fly’s locomotor activity (Turner-Evans et al., 2017), can be passed directly to dFB circuits.

ExR1, ExR3, and hΔK neurons all send projections to the dFB, where they connect with distinct clusters (indicated as gray regions in Figure 53). The largest cluster consists of a recurrent FB network that includes PFGs, a putative neuromodulatory columnar type (as discussed in a later section), FB6A neurons, which are contained in 23E10, as well as ExR3 and hΔK neurons. While this cluster is anchored by FB6A, it seems likely that even sleep-wake neuron types that lack direct connections with ExR1 and hΔK may be able to influence their activity since sleep-wake neuron types are recurrently connected, as described above.

These results identify a complex network that may allow for communication between sleep-wake circuits in the FB and those in the EB. However, the vast majority of the input and output to sleep-wake neuron types involve additional pathways, most of which have not been functionally characterized, as described above. For example, most of the output from dFB sleep-wake neuron types is onto other FB neurons, raising the possibility that inducing sleep may involve previously unrecognized neuron types and pathways (Dag et al., 2019; Tomita et al., 2020). For example, Lei, Keleman et al. (in preparation) have identified the neuron that corresponds to the sleep-promoting split-GAL4 line SS57264 described in Dag et al., 2019 as FB2B_a. This neuron is not connected to the R23E10 neurons by the columnar neurons in a single step, so these sleep-promoting mechanisms are not obviously coordinated.

Not all connections in CX accessory structures feed into feedforward output circuits. In fact, we found that output synapses in four structures –the GA, ROB, RUB, and BU – are mostly to other CX neurons, forming recurrent CX-to-CX pathways (Figure 56A). Recurrent pathways via the BU – an important input hub to the EB – are formed exclusively by ExR neurons (Figure 56B, see earlier section on the ExR neurons). These recurrent pathways likely serve to modulate inputs to the EB. In contrast, pathways through the GA, ROB, and RUB are composed of EB and FB columnar neurons (Figure 56B). We will focus on these three structures below.

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The GA, ROB, and RUB are paired across the midline and are selectively innervated by either the left or right PB-projecting population of columnar neurons (Figure 56C). The GA appears to primarily house recurrent connections between CX neurons, creating CX-to-CX recurrent loops that may allow EB columnar neurons to form connectivity patterns independent of their EB arborizations (Figure 56D). For example, all EPG and PEG neurons arborize in the GA. Depending on which EB wedge the neurons innervate, they target either the dorsal or ventral GA compartment (Figure 56E; this compartment specificity was previously described in Wolff et al., 2015). In their respective compartments, EPG neurons then synapse onto PEG neurons, resulting in a checkerboard-like connectivity pattern (Figure 56D). As a result, each set of columnar neurons innervating one GA subcompartment comprises four tiles separated by 90° increments. The functional significance of this motif is currently unknown. A few non-columnar types also participate in recurrent motifs between the GA and the EB. ER6, one of the few ring neuron types that does not connect to EPG neurons in the EB (Figure 11A, Figure 56Fii), is recurrently connected to both EPG and PEG neurons in the GA (Figure 56D), and to PEG neurons in the EB (Figure 56F). ExR6 also outputs to the EPG neurons in the GA (Figure 56—figure supplement 1A), and ExR6 and EPG neurons are recurrently connected in the EB (Figure 14—figure supplement 3). Finally, it is worth noting that EPG neurons also receive strong input from a LAL neuron of unknown function in the GA (Figure 56—figure supplement 1A). In summary, the GA mostly hosts recurrent connectivity motifs between EPG, PEG, and a defined subset of ER and ExR neurons.

Some columnar neuron types, such as the EL and PFGs neurons, do not target the GA proper. Instead, they target an undefined region surrounding the GA termed the GA surround (GAs). In the GAs, EL neurons appear to primarily form all-to-all connections to other EL neurons from the same hemisphere (Figure 56D and Fi). Curiously, neither the EL neurons nor the PFGs neurons make many synapses in the GAs. We therefore looked in the EM images for evidence of other signaling mechanisms. We found that the synapses formed by both PFGs and EL neurons are elongated-bar (E-bar rather than T-bar) synapses (Shaw and Meinertzhagen, 1986; Takemura et al., 2017a) and that they contain dense core vesicles (DCVs) (Figure 56—figure supplement 1B–D). DCVs have been associated with neuropeptide or neuromodulator release (Burgoyne and Morgan, 2003; Hammarlund et al., 2008; Nassel and Winther, 2010), suggesting that synaptic activity in the GA may be broadly regulated in ways that have not yet been explored.

The round body (ROB) and rubus (RUB) are innervated by the FB columnar PFR and FR neurons, respectively (Figure 56C). Both PFR types arborize in the ROB. There, PFR_a receives input only from PFR_b, while PFR_b neurons make all-to-all within-type connections as well as a number of output connections (Figure 56—figure supplement 2A and B). The most significant connection in the ROB appears to be from PFR_b to the only non-CX neuron targeting a large extent of the ROB, LAL002, which in turn connects to several other non-CX neurons in the LAL and CRE (Figure 56—figure supplement 2B and C). Similar to PFR neurons in the ROB, only one of the FR neurons, FR1, forms strong within-type all-to-all connections in the RUB (Figure 56—figure supplement 3A). However, unlike in the ROB, both FR1 and FR2 make connections to non-CX partners in the RUB (Figure 56—figure supplement 3B). Notably, the sets of downstream partners as well as the output pathway circuits of FR1 and FR2 are largely distinct (Figure 56—figure supplement 3B and C). Thus, while the ROB and RUB contain recurrent connections between CX columnar neurons like the GA does, they differ from the GA in that they can also be considered CX output structures. Some of their outputs will be described in later sections.

CX output neurons that project to other regions that are less tightly linked to the CX – like the LAL, CRE, or SMP – also participate in feedback pathways. Indeed, pathways that start with a CX output neuron and reach another CX neuron directly or indirectly outside of the CX account for a large fraction of the total output pathway weights of most CX output neurons (Figure 57A). For example, 75% of the outputs of the ExR7 neurons feed pathways that reenter the CX, mostly through ER neurons and FBt neurons. In a structure associated with motor control, such feedback could enable a broad class of neurons, including all the columnar neurons, to be notified of an upcoming CX-initiated action (see ‘Discussion’).

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Not all CX output neurons contribute equally to feedback pathways. Feedback constitutes only 25% of total pathway weights out of the PFL neurons, and the ExR8 neuron type contributes virtually nothing to pathways that feedback into the CX. This corresponds to differences between output neuropils. Most synapses made by CX output neurons in the LAL, WED, and PS are to ‘true’ outputs pathways that leave the CX, whereas the situation is more mixed in regions like the CRE and SMP (Figures 56A and 57A).

Unsurprisingly, the major input types of the CX – ER neurons and FBt neurons – are the main recipients of synapses from feedback pathways (Figure 57A, Figure 57—figure supplement 1). Some columnar types are also targeted by feedback pathways, and these pathways usually involve columnar-to-columnar recurrence, similar to the motifs we described in the GA, ROB, and RUB (Figure 57B, Figure 57—figure supplement 1B). Moreover, only weak feedback pathways connect EB and FB neurons. EB columnar neurons and ExR neurons mostly talk between themselves (Figure 56, see also Figure 15), whereas FB neurons mostly reach FB tangential neurons (Figures 56B and 57A). EB-FB and FB-EB pathways outside the CX are largely absent and weak when present because EB neurons and FB neurons innervate nonoverlapping areas outside of the CX (Figure 54B) and therefore form few direct connections between each other in these accessory regions. However, there are a few notable exceptions. For example, the PFL types participate in output pathways that feed back into the EB through ER and ExR neurons (Figure 57Ci and Cii). Additionally, PFL2 and PFL3 neurons reach several LAL-NO neuron types (Figure 57Ci and Ciii). Since the PFL2 and PFL3 neurons are hypothesized to carry motor commands (see ‘Discussion’), these pathways from the PFL neurons to the EB and NO could be used to bring self-motion information back into the CX in the form of efference copies.

Above we described how CX-neuron-to-CX-neuron connections outside of the CX are most commonly made between neurons originating in the same core CX structure (EB or FB). We next asked if these same neuron types also connect inside the CX, and if so, what types of motifs best captured their connectivity patterns inside and outside the CX (Figure 58). Following the same line of analysis that we used for analyzing ExR connectivity (Figure 15), we distinguished three possible motifs (Figure 58A): ‘canonical feedback,’ ‘parallel connections,’ and ‘linked targets.’ The ‘canonical feedback’ motif corresponds to cases in which CX output neurons make synapses outside of the CX onto other CX neurons, which, in turn, project back to a core CX structure in which they contact the original output neurons. For example, PFL1 neurons provide convergent input to FB2B_b neurons, which then feed back onto PFL1 neurons in the FB (Figure 58B). Similar feedback motifs have frequently been found to be involved in inhibitory gain control and gating (Womelsdorf et al., 2014). In our example, if FB2B_b were to be inhibitory, it would potentially allow PFL1 neurons to regulate the timing and magnitude of their output. The fact that many ER neurons are known to be inhibitory makes gain control through feedback loops a potential function of those motifs in the EB. The second motif involves ‘parallel connections’ from one type onto another in multiple structures. For example, neurons of the tangential type FB6T synapse onto neurons from the ipsilateral FB6E type in both the SMP/SIP and the FB (Figure 58C). The function of such a motif is not clear, but it is likely to depend on the extent to which electrical activity in these neurons is compartmentalized. The third and final motif involves neurons projecting to ‘linked targets.’ These recurrent subnetworks are composed of multiple neuron types that connect to each other in the CX while sharing a common input outside the CX. A prominent example of such a case is the FB8F_a neuron type that projects to a set of FB6 neurons interconnected in the FB (Figure 58D). This linked target motif could allow a CX output neuron to regulate the activity of a group of CX neurons as a whole.

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Neurons that participate in any one of three motifs are usually part of a larger network containing several motifs (Figure 58B–D, left panels). However, not all CX output neurons participate equally in all three motifs (Figure 58E), and this may reflect different functional roles. In the EB, EPG, PEG, and ExR2 and ExR3 neurons participate in all three motifs. This is likely a consequence of the high degree of recurren

ce between EB columnar, ring, and some ExR neurons. Such recurrence could help sustain ring attractor dynamics in the EB-PB network. In the FB, the columnar neurons making the strongest contributions to downstream networks outside the CX (PFL, FS, and PFR_b neurons) almost exclusively form canonical-feedback motifs. These neuron types constitute the main channels by which the CX communicates with the rest of the brain and likely modulates the fly’s actions; feedback inhibition – if indeed it is inhibition – could enable greater temporal precision and faster switching between different actions while also controlling the amplitude of these outputs. Finally, the linked-target motif is predominant in the dorsal layers of the FB. This motif may be involved in controlling dedicated modules associated with behavioral state and sleep (see ‘Discussion’).

Pathways that leave the CX and send information on to other brain regions are necessary for the CX to exert its influence on the fly’s behavior. For example, during sleep, the CX is thought to trigger the consolidation of courtship memories by driving DANs that project to the MB (Dag et al., 2019). The CX also influences the fly’s wakefulness and activity levels based on internal states, such as circadian rhythm (Liang et al., 2019) and the need for certain nutrients (Sareen et al., 2020). To this end, the CX is well known to play an important role in the initiation and direction of movement (Bender et al., 2010; Guo and Ritzmann, 2013; Harley and Ritzmann, 2010; Kathman et al., 2014; Krause et al., 2019; Martin et al., 2015; Poeck et al., 2008; Rayshubskiy et al., 2020; Strauss, 2002; Strauss and Heisenberg, 1993; Triphan et al., 2010; Triphan et al., 2012). Besides directly regulating motor pathways, the CX may also exert its influence by modulating the gain and tuning of early pathways.

Different CX neurons make vastly different contributions to downstream networks (Figure 59A), reflecting their unequal number of synapses (Figure 54C), number of downstream targets (Figure 55E), and contribution to CX-to-CX loops (Figure 57A, Figure 57—figure supplement 1A). The PFL, PFR_b, and FS4 neurons are the strongest contributors to pathways external to the CX, followed by ExR8, FR, and FS1-3 neurons. FC neurons, ExR7, ExR3, and a handful of FB tangential neurons make weak contributions. All other CX neurons innervating structures outside of the CX that we considered are purely involved in CX-to-CX loops. For the sections that follow, note that our efforts to characterize networks downstream of the CX were limited by our inability to identify neurons with projections outside the hemibrain volume, and also by the limited characterization of neurons in less structured brain regions like the CRE, WED, or SMP. Indeed, for all CX output types, most of the downstream targets were in such less studied neuropils, limiting our ability to extract functional insight (Figure 59A).

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The majority of neurons in networks downstream of the CX receive only a very small contribution from the CX (Figure 59B). We focused on analyzing the neuron types that receive more than 0.5% of their inputs from pathways originating in the CX. Plotting the weights of pathways from CX neurons onto strong downstream targets (see Materials and methods) and clustering them by their inputs revealed that these targets are largely segregated. The majority of external targets receive significant input from only one CX type (Figure 59C). This segregation of targets stems from the anatomical segregation of the CX neurons synapses (Figure 54B) and is maintained several synapses downstream (Figure 59—figure supplement 1). We found that this occurs because each CX output type targets a distinct ‘module,’ a set of neurons much more connected to each other than to neurons of other modules (Figure 59—figure supplement 2, Videos 17–22). It is therefore likely that CX output channels differ in the information that they carry, with each channel serving the distinct functional needs of its downstream circuits. This segregation raises the intriguing possibility that different output neuron types may control distinct sets of behaviors (see ‘Discussion’).

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When mapping the CX downstream networks at the scale of the brain region (Figure 59D), this segregation is less apparent. Even if each type targets a distinct set of regions, many CX output networks cover similar regions. The CRE, the LAL, the SMP, and SIP are reached by most FB output neurons, whereas both the PFL and ExR7/8 neurons target the ventral neuropils. When plotting the synapses of those downstream targets, the finer-scale segregation by downstream target type is partially visible as subclusters within brain regions (Figure 59E, Figure 59—figure supplements 3 and 4). The emerging picture is one where every CX output neuron type targets a relatively strongly interconnected subnetwork that is only weakly linked to the target subnetworks of other CX output neurons (Figure 59—figure supplement 2). Finally, columnar organization is lost at the output stage. All neurons of each columnar type converge onto the same neurons (Figure 59—figure supplement 5). This suggests that heading or head direction information may be lost in downstream partners and that the output modules could act as simple functional units (see ‘Discussion’).

Although the majority of pathways that exit the CX lead to poorly characterized neurons, we did find many well-identified targets (Figure 60A and B). These targets include neuromodulatory or peptidergic neurons, MBONs, vPNs, and DNs, among others. Of these, some of the most prominent are MBONs receiving input from FR, FS, PFR_b, and FB8F_a pathways, vPN neurons receiving input from ExR8 and PFL3 pathways, and the DNs targeted by PFL2 and PFL3 pathways (Figure 60C). We discuss these pathways in more detail below.

Figure 60

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As discussed in an earlier section, the MB is a highly conserved center for associative learning and memory. These functions are, in part, mediated by interactions between MBONs and DANs. In the previous section (Figures 46 and 47), we focused on direct and indirect inputs from MBONs to the CX. We now turn our attention to information flow in the reverse direction. Such interactions could enable the CX to trigger the consolidation of courtship memories by driving DANs that project to the MB (Dag et al., 2019). More generally, these connections could play a role in modulating the learned behaviors that the MBONs are thought to drive (Aso et al., 2014b).

The FR, FS1, FS2, and PFR_b neuron types, and one type of FB tangential neuron type (FB8F_a), all send outputs to a weakly connected subnetwork of PPL DAN and MBON neuron types. This network is mostly located in the CRE and SMP (Figure 61A–B, Video 20). In that network, two MBON types receive direct input from one CX neuron type each: MBON30, from FR1 neurons (Figure 61D, also discussed in Li et al., 2020), and MBON27, from FS1B neurons. MBON27 and MBON30 are both ‘atypical MBONs,’ which receive some of their synaptic inputs outside the MB. This is to be expected as no CX neurons project directly to the MB. Within this network, single PPL and MBON neurons form small local subcircuits, interconnected by uncharacterized CRE and SMP neurons (Figure 61B–E). Interestingly, most of the prominent dopaminergic targets of the CX are PPL neurons innervating the MB. Only one PPL neuron in that set does not innervate the MB (PPL107). Neurons from the PAM cluster receive much weaker contributions (Figure 61A). PPL neurons are thought to carry punishment signals in the MB (Aso and Rubin, 2016), in contrast with the reward-associated PAM cluster. It would therefore appear that the CX could modulate learning in the MB by preferentially targeting punishment signaling neurons. Since this modulation is coming from columnar neurons of the FB, it is possible that the CX modulates punishment signals in an orientation-dependent manner.

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Overall, it is unclear what distinguishes the MBON neurons targeted by the CX. The MBONs in this subnetwork are not among the strongest MBON inputs to the CX (Figures 46 and 47). There is therefore no strong recurrent loop between the CX and the MB. One interesting exception is MBON30, which is weakly connected to some LAL-NO neurons (Figures 46 and 47). MBON27, on the other hand, is known to receive inputs from visual KCs in the MB and projects to DNs in the LAL (Li et al., 2020). Finally, MBON20 neurons, which are reached by PFR_b through a somewhat separate network (Figure 61B), are themselves strongly linked to two DNs, DNp42 and DNb05 (Li et al., 2020). DNp42 is required for innate aversive olfactory behavior (Huoviala et al., 2020). Besides the preferential targeting of punishment associated DANs, this is another indication that the CX to MB link may modulate aversion.

Two other neurons are associated with this CX to MBON subnetwork: mALD1, a giant AL neuron of unknown function (Figure 62—figure supplement 1C) and the large inhibitory oviposition interneuron oviIN (Figure 61B, Figure 61—figure supplement 1; Wang et al., 2020). These large neurons lie at the intersection of MB and CX outputs, where they can be flexibly modulated by both; this may be ideal for their potential role in triggering or modulating entire behavioral programs like oviposition.

Few of the vPNs, outputs from the optic lobes to the central brain (Mu et al., 2012; Panser et al., 2016; Wu et al., 2016), reach the CX. Instead, many vPNs interact fairly directly with motor pathways (Namiki et al., 2018). Nevertheless, we found links between CX outputs and a few vPNs, suggesting that the CX may selectively modulate specific, direct visuomotor pathways.

Four types of CX output neurons (PFL1, PFL3, PFR_b, and ExR8 neurons) interact with visual pathways (Figure 62A, Figure 62—figure supplement 1, Videos 17–18). Pathways originating from the PFL1, PFL3, and PFR_b neurons all target the output areas of a subset of vPNs. The PFL3 and PFL1 neurons reach three lobula columnar (LC) neurons (Figure 62B–G), whereas PFR_b indirectly contacts a range of lobula and medulla neurons (Figure 62—figure supplement 1). In all these cases, connections are axo-axonal (Figure 62C, E and G), meaning that these CX pathways likely regulate the output of the vPNs. Moreover, these connections are often reciprocal, which indicates that the vPNs also regulate the CX output pathways that target them. Finally, we also found that despite being reciprocally connected the CX output pathways only share a small fraction of their outputs with the vPNs they target (Figure 62—figure supplement 2). In short, FB output pathways and a select set of direct visuomotor pathways have the potential to influence each other’s outputs. These reciprocal connections may allow the direct visuomotor pathways and indirect CX-mediated pathways to compete for control of the fly’s actions.

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Most of the vPNs targeted by PFL1, PFL3, and PFR_b neurons are columnar in the optic lobes and project to well-defined optic glomeruli. These kinds of neurons are generally thought to convey information about specific visual features (Wu et al., 2016), but the details of which neurons convey which features are still incomplete. Of the neurons found here, only one type, LC10, has been investigated for its function. LC10 neurons, which interact with PFL3 pathways in the AOTU (Figure 62D and E), have been shown to be essential to the small object tracking system used by males to follow females during courtship (Ribeiro et al., 2018). The interaction between PFL3 and LC10 pathways could therefore prioritize changes of direction driven by the small object tracking system versus those driven by the CX. The other LC type in contact with PFL3, LC33 (Figure 62B and C), was first described in the hemibrain dataset (Scheffer et al., 2020). Interestingly, in both cases, PFL3 pathways are only connected with a subset of the LC neurons of a given type, suggesting that the visuomotor pathways influenced by (and influencing) the CX output pathways have specificities beyond the feature specificity conferred by individual vPN types. The LC type in contact with PFL1 pathways, LC27 (Figure 62F and G), was also first described in the hemibrain dataset (Scheffer et al., 2020). Given the predominance of the PLP and PVLP in PFL1 outputs (Figure 59Di), and the fact that the optic glomeruli are positioned at the PVLP and PVLP/PLP boundary, it is possible that PFL1 output pathways interact with other LC neurons that are not presently identified or that are only partially traced in the volume.

In contrast with those axo-axonal connections made between FB output pathways and visual columnar neurons, the ExR8 output pathway contacts ‘centrifugal’ (CH) visual neurons, that project from the central brain to the optic lobes. Specifically, ExR8 reaches the dorsal centrifugal horizontal (DCH) and ventral centrifugal horizontal (VCH) neurons in the PS (Figure 62H1, Video 22). CH neurons, whose response properties have been characterized in the blowfly (Hausen, 1976), are part of the horizontal-motion-sensing network of the lobula, where they are both pre- and postsynaptic. However, these neurons receive the majority of their inputs in the central brain. In blowflies, the VCH and DCH neurons are both nonspiking and inhibitory, and they confer their motion sensitivity to at least one of their downstream targets, the small-object-motion-sensitive FD1 neuron (Egelhaaf et al., 1993). All these neurons respond to motion both in the ipsilateral (front-to-back) and contralateral (back-to-front) direction. The FD1 neuron, in particular, has been hypothesized to suppress motion responses during saccades (Hennig et al., 2011). The ExR8 to CH projection is therefore one place where the CX can directly influence sensory processing (in this case, visual motion processing). The ExR8 have not yet been functionally characterized, but are unusual for an ExR neuron type in that they seem like ‘true’ CX output neurons (Figure 57A). In addition to its EB inputs, the ExR8 neuron type receives input in the ipsilateral NO1 from PEN_b neurons (Figure 25B). ExR8 could therefore relay information about angular velocity from the fly’s movements to circuits that detect visual motion and potentially suppress the visual responses that are the consequences of the animal’s own movements.

As mentioned above, the CX is known to play a role in determining the fly’s movements. Movements are controlled through DNs, which carry motor commands from the central brain to the VNC (Hsu and Bhandawat, 2016; Namiki et al., 2018). Light microscopy has enabled the identification of a few LAL-projecting CX neuron types that may link the CX to DNs (Hanesch et al., 1989; Heinze and Homberg, 2009; Lin et al., 2013; Wolff et al., 2015). A complete connectome should, in principle, allow us to identify all CX to DN neural pathways. However, the limited volume of the hemibrain has permitted at most one-third of these neurons to be identified (Scheffer et al., 2020). We used the identified DNs to focus our analysis of CX output neurons, while noting that a larger number of CX output neurons that project to other brain areas and to as-yet-unassigned neural segments might well make contributions to DNs that were difficult to identify in the hemibrain volume.

The main source of CX input to DNs comes from PFL2 and PFL3 neurons, with additional smaller contributions from ExR7, ExR8, and FR2 neurons (Figure 63A). Multiple DN types receive strong PFL2/PFL3 inputs. Most prominent among these are DNa02, DNa03, DNa04, and DNb01 neuron types, as well as a putative DNg neuron (5813078378). DNa02 is known to be involved in turning in walking flies (Rayshubskiy et al., 2020). DNa02, DNa03, DNa04, and DNb01 share inputs to varying degrees, suggesting that they could be part of an interacting premotor network. Since head direction- and heading-related information present in the FB is lost at the first synaptic relay in the LAL (Figure 59—figure supplement 5), the only obvious simple way asymmetries can arise downstream of the PFL neurons are through uneven innervation on the right or left side of the brain. All PFL2 neurons project to identical neurons on both sides of the brain, whereas left PFL3 neurons only contacts neurons in the right LAL, and vice versa. Consequently, the DN network is influenced symmetrically by PFL2 neurons and asymmetrically by PFL3 neurons. This is consistent with the hypothesis that PFL2 neurons control forward walking and/or fixation in flight, and that PFL3 neurons control turning. In such a scheme, turns in walking flies would be controlled by asymmetric modifications of the fly’s gait (DeAngelis et al., 2019; Strauss and Heisenberg, 1990) and turns in flight by asymmetric changes in wing kinematics (Muijres et al., 2015), both modulated by PFL3 neurons. No other CX output neurons appear to be in a position to execute such a function (also see ‘Discussion’). It is interesting to note that the DN neurons in question innervate a variety of leg and wing neuropils in the VNC (Namiki et al., 2018), suggesting that control of different actuators is somewhat integrated or coordinated in the LAL. PFL2 and PFL3 neurons also reach the moonwalker neuron MDN (Bidaye et al., 2014; Feng et al., 2020), which has a bilateral innervation pattern and is known to drive backward walking. This connection is almost exclusively contralateral (Figure 63—figure supplement 1A and B), a suggestion that the MDN could also be involved in asymmetric behaviors.

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PFL2 and PFL3 connections to their downstream DN targets are both direct and indirect through a LAL interneuron network (Figure 63B–E, Video 18). The LAL targets of PFL2 neurons on a given side contribute mostly to ipsilateral networks, while PFL3 neurons tend to also reach contralateral DNs through strong connections to midline crossing LAL neurons. Such neurons have been shown to function in flip-flop circuits mediated by inhibition in the silkworm moth brain (Iwano et al., 2010) and could participate in modulating left-right asymmetries in the activity of the output network (see ‘Discussion’). More generally, the heavily recurrent LAL networks could participate in the integration and coordination of activity between the different DNs.

ExR7 also indirectly reach some DNs in this network (Figure 63B). Additionally, we observed that ExR8 neurons target, through PS neurons (Figure 63—figure supplement 1C–E), a different set of DNs thought to innervate neck and haltere neuropils (Namiki et al., 2018). This connection, taken together with the ExR8 connection to the CH neurons (Figure 62H and I), suggests that ExR8 could play a role in controlling head movements and their interplay with optic flow signals.

Finally, FR2 reaches DNp32 through a SMP interneuron (Figure 63—figure supplement 1F). It is likely that a lot of similar connections in the dorsoposterior part of the brain are missed because they lie outside the hemibrain volume.

As mentioned previously, the columnar identity of the PFL neurons is lost in their targets in the LAL (Figure 59—figure supplement 5). However, we did notice that PFL neurons that innervate certain PB glomeruli consistently provide stronger inputs to their downstream targets in the LAL than PFL neurons coming from other glomeruli. Figure 64 shows that the outputs of the left PFL3 neurons are strongest for the individual PFL neurons that innervate PB glomerulus L3. This observation can partly be explained by the difference in the number of neurons that innervate each glomerulus (Figure 24—figure supplement 1). By symmetry, R3 innervating PFL neurons would similarly be expected to contribute the strongest output on the right side.

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Assuming that PFL3 neurons drive turns, and that the turn amplitude depends on the differential activity between the targets of the PFL3 neurons in the left and right LAL, this asymmetry could have consequences on the behavior of the animal in the absence of any stimulus and FB influences (unlikely though this may be). L3 and R3 are ~180° apart; when the bump is in L3, it is also near R7 and vice versa. Therefore, if the EPG bump of activity was in L3 or R3 and passed to the PFL3 neurons, the asymmetries in PFL3 output would then generate a turn. Only when the PFL3 outputs are symmetric, in R5/L5, would no turn be generated (see ‘Discussion’). Input to the PFL3 neurons in the FB could confer flexibility on such a scheme (Rayshubskiy et al., 2020). Interestingly, the inhomogeneities we observed are strongest for the LAL interneurons targeted by the PFL3 neurons rather than their direct connections to the DNs (Figure 64A). This may mean that the LAL interneuron network plays a crucial role in shaping any rotational or translational signals generated by the CX.

The FS4A and B neuron types also show an interesting asymmetry (Figure 65A shows it for FS4A), where neurons innervating the leftmost part of the FB make the strongest contribution to their postsynaptic targets. This asymmetry is likely related to the fact that these neurons innervate the AB. The innervation pattern in the FB is denser on the side that does not go to the AB. FS4A prominently targets neurons projecting to the flange (FLA) (Figure 65B). The FLA, also known as the dorsal tritocerebrum, belongs to the SEZ and is thought to control food intake (Hartenstein et al., 2018; Rajashekhar and Singh, 1994), suggesting that FS4A neuron may be involved in directing feeding behaviors. What role this asymmetry could play in feeding behaviors is unclear. It is however reminiscent of the recent report that neurons linking the AB to the dorsal layers of the FB (likely vΔA_a) play a crucial role in coordinating feeding behaviors to fructose sensing (Musso et al., 2021).

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Many of the neurons and circuits that receive projections from CX output neurons have never been investigated experimentally. Beyond brain regions that are directly downstream of CX output neurons (e.g., the LAL for PFL neuron types, the CRE for FC, FR, and PFR neuron types, the SMP/SIP for the FS neuron types), a few other, more distant neuropils reappear regularly in these downstream circuits. The IB and ATL are targeted by prominent neurons in the PFL3, FS3, FC2C, and PFR_b downstream networks. The lateral part of the PLP is part of the PFL1, FC1E, and FR1 networks. As mentioned before, LC neuron output circuits likely also innervate some parts of the lateral PLP (Scheffer et al., 2020). The ExR8 and a FS1B networks reach ventral brain regions (SPS/IPS down to the GNG). Deciphering the organization and function of those areas will be necessary to obtain a complete picture of the many ways in which the CX likely shapes the fly’s behavior.

Our analysis of the ‘true’ outputs of the CX reveals that PFL2 and PFL3 neuron types connect to DNs, enabling flexible, context- and goal-dependent control of the fly’s orientation and locomotion. There are also indications of interactions between CX-related output circuits and more direct visual output pathways, suggesting that these different sensorimotor pathways may differentially modulate each other during specific behavioral contexts. The more dorsal output networks of the FB, which act through other columnar neurons (FC, FS, FR, and PFR_b), are likely involved in modulating and directing behaviors that depend on the animal being correctly oriented in its surroundings. Those behaviors could be innate, like oviposition or feeding, or learned and influenced through the CX to MBON network. A prominent feature of nearly every layer of these output circuits is strong feedback to the CX, indicating that information related to the fly’s intended actions is relayed back to the core CX structures. All these output circuits are also densely recurrent, a feature that should enable fine-tuning and coordination during action selection. Despite the incompleteness of our analyses, it is clear that information from the CX influences a wide variety of targets across the brain, from neurons that arborize in sensory systems to DANs and DNs.

Head direction representations enable an animal to flexibly rely on a variety of different cues, including self-motion, to orient. Work in Drosophila and other insect species has established that the CX builds a stable head direction representation using information from ring neurons, which convey directional sensory cues, such as polarized light, visual landmarks, and wind direction (Figure 66A and B, Table 5; Heinze and Homberg, 2007; Homberg et al., 2011; Okubo et al., 2020; Seelig and Jayaraman, 2015; Varga and Ritzmann, 2016). In Drosophila, visual head direction information reaches the CX via the anterior visual pathway, which appears to convey different visual information in separate, parallel ‘channels’ (Figures 66A, B, 6—8; Omoto et al., 2017; Seelig and Jayaraman, 2013; Shiozaki and Kazama, 2017; Sun et al., 2017; Timaeus et al., 2020). Some ‘channels’ of this pathway have been characterized functionally, while the function and sensory tuning of other groups of neurons remains elusive. For example, most of the ring neurons (and their inputs) in the superior BU are spatiotemporally tuned to visual features with some degree of orientation preference (Seelig and Jayaraman, 2013; Sun et al., 2017) and the pathway through the anterior BU appears to be dedicated to polarization signals (Hardcastle et al., 2020) (see below). In contrast, little is known about the role of ring neurons that get their inputs in the inferior BU in informing the head direction representation (Omoto et al., 2017; Shiozaki and Kazama, 2017). Wind stimuli reach the compass circuitry through a separate input pathway via the LAL (Okubo et al., 2020), and it is unknown whether other sensory modalities are conveyed through this route.

Figure 66

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Our connectivity-based analysis suggests that there are 22 ring neuron types, 18 of which receive inputs via the anterior visual pathway. In contrast, an anatomical and developmental characterization of ring neurons found only 11 distinct morphological types (Omoto et al., 2018). Notably, our connectome-based typing likely represents a subdivision of the previously suggested types rather than a drastic reorganization. Given that past neurophysiological studies have only tested tuning to a relatively small number of sensory stimuli, it remains to be seen how many functionally distinct input types exist.

The connectome reveals mechanisms by which sensory stimuli are integrated to inform the fly’s head direction estimate. Our findings suggest that different cues exert differing levels of influence on the EPG neurons that carry the head direction representation (Figure 66C). A prioritization of certain sensory cues is reflected in the relative locations of synaptic input from different sensory streams onto the EPG dendrites in the EB (Figure 12E), in the relative weight of those inputs (Figure 11A), in the feedback that some ring neuron pathways receive from the EPG neurons (Figure 13—figure supplement 1B), and in the relative weight of across-type inhibition from some ring neuron types onto others (Figure 13A and C). The implicit hierarchy of ring neuron inputs to the fly compass indicates that the EPG head direction representation preferentially tethers to environmental references that are likely to indicate a global direction. Bright visual landmarks, for example, may originate from celestial bodies such as the sun, but they could also be generated by local terrestrial objects (e.g., gaps in a forest canopy). By contrast, a polarization pattern in the sky, if available, represents a reliable global reference, which might explain the observed circuit motifs that suggest the preferential use of polarization cues to update the fly’s head direction representation (Figure 66C). However, the relatively high connection strength between ER4m and EPG neurons may also arise from this fly not being exposed to polarized light stimuli (see Materials and methods). Such deprivation could have prevented these connections from being subjected to the synaptic depression that other visual pathways may have experienced (Fisher et al., 2019; Kim et al., 2019) (but note that there is no evidence yet for long-term structural changes at any of these synapses).

Particularly when navigating over long distances, skylight cues allow the head direction representation to be tethered to global landmarks such as the sun and to the polarized light patterns of the sky (Heinze and Reppert, 2011). Indeed, polarized light e-vector information has long been thought to be important for the determination of sky compass-based head direction in many insects. A dorsal band of the insect eye called the dorsal rim area is structurally specialized for the detection of polarized light e-vectors in the sky (Labhart, 1999). Despite their comparatively small dorsal rim area (Fortini and Rubin, 1991; Wada, 1974; Wernet et al., 2003), flies can also use polarized light cues to determine their heading (Hardcastle et al., 2020; Mathejczyk and Wernet, 2019; Warren et al., 2018; Weir and Dickinson, 2012; Wernet et al., 2012). Sensory information about the celestial polarization pattern reaches the Drosophila CX via a dedicated pathway to the ER4m neurons (Hardcastle et al., 2020; Weir et al., 2016, Figures 6—8). Although only five ER4m neurons from each hemisphere show strong tuning to e-vector orientation, this tuning collectively covers a large part of the 180° range of possible e-vector orientations (Hardcastle et al., 2020; Weir et al., 2016). However, in contrast to the position of the sun, the 180° symmetric polarized light patterns do not immediately provide the ability to distinguish a specific direction from one directly opposite to it.

The CX connectome suggests that the fly’s compass may have evolved a solution to this problem. For the polarization-tuned ER4m neurons, we observed that synapse numbers to EPG neurons varied smoothly along the circumference of the EB, but with mirror-symmetric profiles for ER4m neurons from the left and right hemisphere, respectively. If synapse counts correlated with synaptic strength, this would result in stronger connections from ER4m neurons of the left hemisphere for EB wedges on the right half of the EB and stronger connections from the right hemisphere to the left half of the EB (Figures 11D and 67A). This structure was even more clearly revealed when we analyzed the pairwise correlation of EPG neurons according to their ER4m inputs (Figure 11—figure supplement 1, Figure 67B): all EPG neurons on the right side of the EB were positively correlated with each other, while being anticorrelated with those on the left side, and the inverse pattern was observed for the left EPG population. Given that polarized light has a 180° symmetry (Hardcastle et al., 2020; Weir et al., 2016), this connectivity pattern may allow the fly to generate a complete, 360° head direction representation from polarized light input (Figure 67B).

Figure 67

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One possible mechanism by which this could be achieved hinges on the geometry of the fly’s polarization sensors in the dorsal rim area and how it interacts with the natural polarization pattern of the sky. The receptive fields of the fly’s polarization sensors in the left and right eye face the contralateral celestial hemisphere and tile a small strip along the rostral-caudal axis of the fly (Figure 67C and D; Heinze, 2014). Along this strip tuning to e-vectors varies continuously and covers nearly the full 180° range of possible e-vector orientations. Given the naturalistic celestial polarization pattern schematized in Figure 67C, the geometry of the slightly curved receptive field ‘strip’ might act as a rough ‘matched filter’, such that neurons in the dorsal rim area on the side of the sun (facing the contralateral sky) are systematically more strongly activated than those on the side facing away from the sun (Figure 67D). The all-to-all inhibition between left and right ring neurons in the EB (Figure 13A) may then systematically select either the left or the right ring neurons to tether the head direction depending on which direction the fly is facing relative to the current position of the sun, thus disambiguating the 180° mirror symmetry in the polarization signal.

In locusts, TL-neurons, homologs of the fly’s ring neurons, and PB neurons have been shown to exhibit matched-filter-like tuning to the full-sky polarization patterns generated by the sun (Bech et al., 2014; Zittrell et al., 2020). A corollary of these studies is that individual TL neurons in the locust have receptive fields that span large parts of the sky. Indeed, the area of the sky that is sampled by photoreceptors in the dorsal rim area is significantly larger in locusts compared to flies (Heinze, 2014), and it is plausible that further sensory processing along the anterior visual pathway towards the CX differs between species as well, in which case different insects might employ different strategies for disambiguating polarized light stimuli.

The mechanism described above would not require that the sun be directly visible, but it might still be beneficial to have ring neurons that have multimodal tuning to both polarized light and sun-like stimuli. Such cells have been described in other insects (el Jundi et al., 2015; Heinze and Reppert, 2011; Pegel et al., 2018; Pfeiffer et al., 2005). While this has yet to be demonstrated experimentally, multimodal ring neurons tuned to both visual features and polarized light e-vector orientation may also exist in flies. Hardcastle and colleagues report polarization-tuned neurons in the superior bulb (Hardcastle et al., 2020), where tuning to bright features has also been observed (Omoto et al., 2017; Seelig and Jayaraman, 2013; Sun et al., 2017).

Besides visual cues, mechanosensory wind stimuli can drive the fly’s head direction system in the EB (Okubo et al., 2020; Figures 9 and 66B). Information about wind direction reaches the EB via ring neurons that arborize in the LAL. Wind tuning has been demonstrated in both ER3a and ER1 neurons, although only ER1 neurons were able to update the head direction estimate (Okubo et al., 2020). Analysis of the connectome suggests that both the ER1 and ER3a neuron populations consist of multiple types with distinct inputs. We found that only ER1_b and ER3a_b neurons got strong inputs from cells that we believe to be the wind-sensitive LAL138 (WL-L) and WPN neurons (Figure 9; Okubo et al., 2020; Suver et al., 2019). The connectivity of these two ring neuron types onto EPG neurons, with strong connections from ER1_b but no connections from ER3a_b neurons, is consistent with the observation that ER1 but not ER3a neurons can drive the head direction representation (Figure 11A). It is also noteworthy that in the EB, ER1_b neurons deviate from the within-type all-to-all inhibition motif that all other ring neurons show in the EB (Figures 13A and 66C). A possible reason is that an accurate mapping from ER1 neuron activity to a head direction representation requires pooling information from multiple ring neurons at once (Okubo et al., 2020). Our analysis also suggests that ER1_b input to the EPG neurons is suppressed by ER1_a neurons, but it is presently unknown whether ER1_a neurons also encode wind direction or whether these neurons are tuned to a different stimulus (Figure 66C). ER1_a and ER1_b inputs in the LAL are distinct and unfortunately little is known about the inputs ER1_a receives.

Whether over short or long distances, olfactory cues are strong indicators of good food sources. Flies are known to fly upwind when they encounter an appetitive odor (Budick and Dickinson, 2006), a strategy also employed by other insects navigating to an odor source (Carde and Willis, 2008). A robust navigational strategy would allow an insect to maintain the same heading using other cues even if the wind were to transiently die down. Based on the proximity of different ring neuron inputs to the putative spike initiation sites of EPG neurons, the head direction representation is likely to be strongly tethered to wind direction by input from ER1_b neurons (and perhaps also ER1_a neurons, although their function is currently unknown) (Okubo et al., 2020). If visual cues are flexibly mapped onto head direction representation using this wind direction input as a reference (Fisher et al., 2019; Kim et al., 2019), the EPG compass could allow the fly to preserve its heading using those cues even in the absence of wind.

The relative importance of synapse location in determining the cues to which the EPG compass tethers will only be clear with in-depth investigations of EPG neuron biophysics. More broadly, future studies of ring neuron and EPG interactions should provide an implementation-level understanding of a variety of computations related to dynamic multisensory integration (Pouget et al., 2002) and the resolution of conflicts between cues of different reliability (Deneve et al., 2001; Hoinville and Wehner, 2018; Wystrach et al., 2015).

Recent studies have proposed an important role for fast-timescale, short-term plasticity of synaptic connections between ring and EPG neurons in enabling the EPG compass to quickly adapt to different sensory settings (Figure 66D; Fisher et al., 2019; Kim et al., 2019). The connectome suggests that the ring neuron network may also preselect more salient cues for the compass through all-to-all inhibitory connectivity within each type. The precise impact of all-to-all inhibition on the ring neuron network’s preprocessing of localizing cues that are used to generate the head direction representation will depend on the timescale of the inhibitory conductance (Ermentrout, 1992), which is as yet unknown. If the inhibitory conductance is fast, all-to-all inhibition would create winner-take-all dynamics in which a few ring neurons receiving the strongest inputs effectively shut down all other ring neurons. In sensory settings characterized by a single dominant sensory cue, such as the sun or polarized light e-vector orientation in a desert landscape during the day (Coyne et al., 1982; Weir and Dickinson, 2012), only a handful of ring neurons with appropriately tuned receptive fields (Fisher et al., 2019; Omoto et al., 2017; Seelig and Jayaraman, 2013; Shiozaki and Kazama, 2017; Sun et al., 2017) would be active within each type for any particular head direction. Fast all-to-all inhibition in this setting would enhance the activity of the most dominant ring neuron within each type and would minimize the impact of noise from the others, which might otherwise disrupt the stability of the EPG compass.

However, stable and unique heading representations are also generated within scenes with multiple strong cues, such as within a forest or when walking on the branches of a tree, as long as the two-dimensional arrangement of cues allows for a unique determination of heading (Kim et al., 2019). In the presence of multiple salient cues, we would expect multiple ring neurons to respond with comparable strength for any given heading of the fly and several to respond weakly to any additional visual cues (‘clutter’) in the scene. Although fast all-to-all inhibition in this scene would still filter out these weaker responses, it could allow multiple, strongly responsive ring neurons to remain active for each heading. A slower inhibitory conductance would, in this situation, induce oscillatory spiking dynamics between these multiple ‘winners’ (Ermentrout, 1992), a situation that has been referred to as ‘winnerless competition’ (Rabinovich et al., 2001), and that has been suggested to be useful for sequential memory (Seliger et al., 2003).

Ring neuron responses are not determined purely by sensory cues. These neurons appear to be modulated by state, maintain a baseline level of activity, and may be biophysically configured to support oscillatory population activity linked to sleep need (Raccuglia et al., 2019). The many additional inputs that many ring neuron types receive in the BU (Figure 8) provide clues as to how the activity of these neurons might be modulated by the fly’s behavior and its internal state. The visually tuned superior BU ring neurons primarily receive input from a large interhemispheric AOTU neuron (AOTU046), which may mediate dynamic stimulus selection through delayed contralateral inhibition (Sun et al., 2017). The same group of ring neurons also shows changes in activity with the fly’s behavioral state (flight versus walking) (Seelig and Jayaraman, 2013) and indeed many of these neurons receive input from the dopaminergic ExR2 neuron that has been linked to changes in the fly’s motor activity (Kong et al., 2010; Liang et al., 2019; Tao et al., 2020). A different set of ring neurons that receive their inputs in the inferior BU receives strong inputs from two ExR neurons – ExR1 and ExR3 – that have been linked to the control of sleep (Figures 8 and 15; Donlea et al., 2018; Liu et al., 2019), and may gate sensory stimuli according to the fly’s behavioral state (Donlea et al., 2018).

The fly’s head direction representation tethers to directional sensory cues conveyed by ring neurons, but is also updated by self-motion cues (Green et al., 2017; Green and Maimon, 2018; Hulse and Jayaraman, 2019; Seelig and Jayaraman, 2015; Turner-Evans et al., 2017; Turner-Evans et al., 2020) and is maintained across periods of immobility (Seelig and Jayaraman, 2015). Strong experimental and theoretical evidence suggests that the representation is maintained by a ring attractor network (Kim et al., 2017c), which includes at least some of the recurrently connected columnar neurons that link the EB and the PB: the EPG, PEN_a, PEN_b, and PEG neuron types (Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020). The patterns of connectivity between individual neurons of these types are consistent around the entire EB and across the length of the PB. Similarly, the broad connectivity patterns of individual neurons within these types to tangential neurons – Δ7 neurons in the PB and different types of ring neurons in the EB – are similar across these structures. Notably, however, two distinct classes of neurons (EPGt neurons and the P6-8P9 neurons, Figures 18 and 21, respectively) only innervate the edges of the network; both innervate the outer glomeruli of the PB, and the EPGt neurons also innervate the corresponding wedges in the EB. These types may help to stitch together what might otherwise be a discontinuity in the ring attractor network. Indeed, the EPGt neurons in the left and right PB arborize in wedges in the EB that lie directly in between the wedges occupied by the EPG neurons on either side of the potential discontinuity (in PB glomeruli 1 and 8). The EPGt neurons may therefore represent angular positions halfway between the edge angles, bridging the gap. We note, however, that the Δ7 neurons and the P6-8P9 neurons that output in these outer glomeruli each receive unique input from different sets of EPG neurons, making it hard to assign a clear corresponding EB angle to glomerulus 9 (Figure 68Ai).

Figure 68

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The hemibrain connectome further allowed us to identify several neuron types and connectivity motifs that are likely involved in the network’s function, but whose roles await experimental investigation. Many of these additional types are tangential neurons. Some of them appear to provide additional sources of inhibition, potentially regulating overall network activity (Franconville et al., 2018; Turner-Evans et al., 2020). The ER6 neurons, for example, receive input from the EPG and PEG neurons in the GA and send outputs to the PEG, EL, and PEN_b neurons in the EB (Figure 10, Figure 13—figure supplement 1, Figure 56), potentially modulating the EPG-to-PEG-to-PEN_b-to-EPG feedback loop. Furthermore, many of the ExR neurons make connections to and receive input from EB columnar neurons (Figure 14). The PB receives neuromodulatory input from the dopaminergic LPsP neurons and the octopaminergic P1-9 neurons (Figure 23). The LPsP neurons may enable changes in synaptic strength in the PB. Such plasticity in the PB has been suggested to allow flies to calibrate their directed movements to their body size (Krause et al., 2019). In sensory brain regions, octopaminergic neurons are known to modulate neuronal conductances based on the fly’s behavioral state (Strother et al., 2018; Suver et al., 2012), and it is an open question whether the P1-9 neurons play a similar role in the PB. Notably, the Δ7 neurons connect recurrently to each other in the PB, but the function of this recurrence is unknown. One possibility is that recurrent Δ7 connections may increase the stability or robustness of the ring attractor network (Pisokas et al., 2020).

Two additional classes of columnar neurons also contact the ring attractor network: EL and IbSpsP. The connectivity pattern of EL neurons in the EB is remarkably similar to that of the EPG neurons (Figure 11), but their function is unknown. In the PB, the IbSpsP neurons bring input into specific glomeruli from regions associated with premotor functions, potentially allowing them to exert an influence on the dynamics of the bump in the PB.

The ring attractor network described above generates a single activity bump in the EB that encodes the fly’s head direction (Green et al., 2017; Heinze, 2017; Seelig and Jayaraman, 2015; Turner-Evans et al., 2017). The connectome allowed us to follow this activity bump through the CX as it gets duplicated, reformatted, recombined, and, finally, read out. In the process, we discovered network motifs that seem ideally suited for performing vector computations. These motifs place constraints on the network’s computational capacity and inspire conceptual models for how the network might function. We begin by describing how the activity bump is forwarded from the EB to the PB, where it is duplicated and reformatted into a sinusoidal profile. In subsequent sections, we consider how the FB network may recombine these bumps to perform vector computations in support of goal-directed behavior.

The EPG population divides the EB into 16 ‘wedges,’ suggesting that the fly’s head direction system samples angular space at 22.5° intervals (Figure 68A; Hanesch et al., 1989; Lin et al., 2013; Seelig and Jayaraman, 2015; Wolff et al., 2015). Importantly, this does not mean that the system cannot resolve head directions at resolutions higher than 22.5° since the differential activation of columnar neurons with distinct directional tunings can effectively represent any arbitrary angle within the 360° around the fly. From the EB, EPG neurons convey the HD bump to both the left and right PB, generating two bumps that are sampled at approximately 45° intervals (Figure 68A). Due to the EPG projection pattern (Wolff et al., 2015), there is a 22.5° shift in the directional tuning between EPG neurons in left and right PB, as recently confirmed by physiological recordings (Lyu et al., 2020). Importantly, the bumps in the left and right PB still encode the same head direction, but do so using sets of neurons whose sampling of angular space is shifted by 22.5°.

Within the PB, FB columnar neurons inherit a head direction bump directly from EPG neurons and indirectly through Δ7 neurons (Figure 68Bi; Franconville et al., 2018; Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020). The Δ7 populations appear ideally suited to reformat the EB bump into a sinusoidal profile, regardless of its original shape (Figure 20). Individual Δ7 neurons provide output to 2–3 PB glomeruli spaced ~180° apart (i.e., separated by seven glomeruli). Between these axonal compartments are dendritic segments whose EPG input weight is well fit by a sinusoid, suggesting that individual Δ7 neurons should have a sinusoidal tuning curve. Assuming the Δ7 population uniformly samples angular space (e.g., with a 45° sampling interval), this would manifest as two sinusoidal bumps across the PB, one in the left PB and one in the right PB (Figure 68Bii). Furthermore, recurrent Δ7 connections may enforce a sinusoidal activity pattern on the Δ7 population itself, which could improve the ability of Δ7 neurons to reformat the activity bump into a sinusoidal profile before passing it on to PB-FB types. The Δ7 population provides input to ~10 types of PB-FB neurons, effectively duplicating the activity bump in the process. As discussed below (Figure 69), this duplication may allow the FB network to recombine bumps in a way that implements a compact vector calculator (Figure 68C).

Figure 69

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Why might the Δ7 population reformat the activity bump into a sinusoidal shape? Perhaps because sinusoids are a particularly suitable representation for vector-based computations (Touretzky et al., 1993), since the sum of any two sinusoids of equal frequency is also a sinusoid. One way of schematizing this process is to use phasor diagrams (Figure 68D). Viewed in this way, the sinusoidal activity bumps become vectors whose magnitude reflects bump amplitude and whose angular position indicates bump phase, with each phase mapping to an allocentric direction. Adding vectors is equivalent to adding sinusoidal activity profiles.

Path integration is a canonical vector-based navigation strategy used by a diverse array of both flying and walking animals (reviewed in Collett, 2019; Heinze et al., 2018; Wehner, 2020), potentially including Drosophila (Brockmann et al., 2018; Corfas et al., 2019; Dethier, 1957; Kim and Dickinson, 2017a; Murata et al., 2017). In its most basic form, 2D path integration requires that an animal keep track of its direction and distance relative to a stored goal location, such as a food source or nest, often without the use of external landmarks. The direction and distance to the goal location is thought to be computed through the integration of self-motion signals and stored as a ‘home vector.’ To return to the goal location, animals are thought to generate appropriate motor commands by comparing their current heading to the stored home vector. While many insects are thought to generate and use visual snapshots of their surroundings to guide return trips (Collett et al., 2013; Collett and Zeil, 2018; Freas et al., 2019), and while such visual homing may involve the MB (Buehlmann et al., 2020; Collett and Collett, 2018; Kamhi et al., 2020; Sun et al., 2020), we will focus here on how a home vector might be constructed and read out in the CX using only a stable head direction signal, a situation that can arise in featureless landscapes or in darkness. Although there is as yet no definitive evidence that the CX is used for path integration, in the next few subsections, we show how a network built from FB-inspired circuit motifs could compute a translational velocity (TV) vector in an allocentric reference frame whose integration would yield a home vector. We note that the framework for vector computations that we describe below is likely to be useful for a much broader array of behaviors involving oriented action selection.

PFN neurons serve as the major columnar input to the FB network. The ±45° phase shift that is characteristic of all PFN neuron types (Figures 30 and 34) implies that activity bumps from the left and right PB would end up ~90° apart in the FB (Figure 69A). The amplitude of these activity bumps is likely to be strongly influenced by the different inputs that PFN neurons receive through their lateralized projections in the NO (Figure 25), setting up the possibility of bump-based vector computations in the FB. The PEN_a neurons, which are conjunctively tuned to head direction and angular velocity, perform a similar computation in the EB by providing phase-shifted input to the EPG neurons, thereby updating the position of the EPG bump when the fly turns (Green et al., 2017; Turner-Evans et al., 2017; Turner-Evans et al., 2020). Inside the FB, vector computations fed by phase-shifted PFN bumps whose amplitudes are controlled by different conjunctive signals could ultimately drive PFL neuron types to generate appropriate motor commands (Figures 39 and 63), an algorithmic idea (Hartmann and Wehner, 1995; Wittmann and Schwegler, 1995) for which an FB implementation was first proposed in Stone et al., 2017.

Although the intra-FB columnar network is highly recurrent, much of it is built from a limited number of circuit motifs (Figure 37). These motifs serve as the backbone of a 2D grid in which activity bumps are constrained to either maintain their phase (i.e., maintain their column) while moving across layers, or shift phase by 180° (i.e., shift by half the width of the FB). While some pathways directly connect PFN neurons to output pathways, such as those involving PFL neurons, many more pathways run through this 2D grid (Figure 33). Thus, the network has depth, providing multiple layers with which to process activity bumps. In addition, a large number of tangential neuron types selectively innervate different layers of the FB, suggesting that the FB’s vector computations are influenced by context and internal state. In the sections that follow, we draw from published experimental and theoretical work to explore the navigational implications of PB-FB neuron phase shifts. Importantly, for the purposes of discussion, we assume that the magnitude of PFN phase shift is precisely 90°, a simplifying assumption about symmetry in the circuit that ignores the type-to-type variability in estimated phase shifts across PFN types (Figures 30 and 34), the functional significance of which remains unknown. Similarly, we assume all LNO types to be excitatory, but the proposed conceptual models could be built from inhibitory LNO types as well. Finally, while the columnar structure of the various vΔ and hΔ types shows considerable variability, we assume these neurons can either maintain the phase of an FB bump or shift it by 180°.

Despite the PFN phase shifts, the two 90°-separated activity bumps arising from a single PFN type cannot propagate independently through the FB network because nearly all single neurons and neuron types that are postsynaptic to PFN neurons sample from left and right populations equally (Figure 35). Instead, each postsynaptic FB type likely sums the bumps from the left and right PFN populations, indicating that each postsynaptic type represents a single, summed bump that will propagate through the FB network.

Much like the PEN neurons, the PFN neurons innervating the left PB project to the right NO and neurons innervating the right PB project to the left NO, where they receive input from various LNO types (Figure 25; Lin et al., 2013; Wolff et al., 2015). One potential function that this differential NO input to the left and right PFN populations could serve is to produce a new, transformed directional representation that could take on angles ±45° around the fly’s instantaneous head direction. For example, as shown in Figure 69B, a strong excitatory input to the right nodulus would increase the bump amplitude of the left PFN population relative to the right PFN population. In turn, the summation of these two bumps by a postsynaptic neuron type in the FB would result in a new bump that lies closer to that of the left PFN population.

Figure 69C shows phasor diagrams of this process. Critically, because these vectors can only take on positive values (firing rates above 0), such differential input could only shift the resulting vector’s phase by ±45° around the fly’s instantaneous head direction. What might this transformed directional representation encode? The answer likely depends on the nature of the input that PFN neurons receive from LNO types (Figure 25; Wolff and Rubin, 2018). Recent work in Drosophila has shown that some PFN neurons show differential activity in the NO that reflects the fly’s turning behavior during flight (Shiozaki et al., 2020), but the nature of the rotational velocity signal remains to be determined. We briefly outline two hypothetical scenarios that differ in the specific information carried by PFN neurons.

Directly wiring sensors to actuators in different ways can, in principle, allow a simple agent to display a variety of behaviors (Braitenberg, 1984). But flies, like most animals, have to deal with an additional complication. Some of their sense organs are on body parts that are different from those that enable them to move. PFN phase shifts could enable coordinate transformations, such as converting the allocentric head direction representation into an allocentric body direction representation (Figure 69D; Andersen and Cui, 2009; Andersen et al., 1993; Batista, 2002; Bicanski and Burgess, 2020). Flies make head movements that change their head-body angles by as much as 30° during both flight (Duistermars et al., 2012) and walking (Fujiwara et al., 2017; Geurten et al., 2014). In this scenario, LNO neurons that provide input to PFN neurons arborizing in the left and right NO would encode how much the head is rotated to one or the other azimuthal direction of the body’s axis, perhaps derived from proprioceptive information (Paulk and Gilbert, 2006; Preuss and Hengstenberg, 1992). When properly calibrated, such differential input could allow the PFN phase shift (which, at 45°, is sufficient to encode the entire range of head-body angles) to rotate the head direction vector by an angle equal to the head-body angle. This would effectively transform the fly’s head direction vector into an allocentric body direction vector. To do so, the network could use gain fields (Andersen et al., 1993; Pouget and Sejnowski, 1997; Pouget and Snyder, 2000; Salinas and Abbott, 2001; Zipser and Andersen, 1988), with an intermediate layer composed of PFN neurons whose head direction tuning curves are gain-modulated by shared input related to the head-body angle. The neuron types downstream of PFN neurons would complete the coordinate transformation through their structured sampling of PFN neurons with distinct directional tunings. Coordinate transformations such as these may be useful when combining allocentric directional representations with body-centered velocity estimates to estimate direction and distance. We return to this idea in more detail in subsequent sections on vector computations related to path integration.

A second scenario is shown in Figure 69E. if we assume that an LNO type carries a motor efference copy of the fly’s rotational velocity, as has been shown to exist in the fly visual system (Fujiwara et al., 2017; Kim et al., 2017b; Kim et al., 2015), then bump shifts driven by differential input to the left and right PFN populations could function as a forward model (Webb, 2004) that encodes a prediction of the fly’s future head direction or body direction. Why might a forward model of head or body direction be useful? Intracellular recordings from neurons in the ring attractor network have revealed that PEN activity is tuned to the fly’s rotational velocity, but that this activity lags behavior by ~100 ms (Turner-Evans et al., 2017). Similar lags may result from propagation delays in neural processing, either along sensory pathways into the EB or in passing the bump from EB to FB. In situations where flies might rely on the CX to direct their movements, especially in time-critical scenarios, such delays in updating the compass could be costly. One way to overcome this is for the PFN network to compute the fly’s approximate future head or body direction so that navigational decisions can effectively be made in real time, a strategy that dragonflies have been shown to use during rapid prey capture maneuvers (Mischiati et al., 2015). A forward model could also allow the fly to distinguish changes in its head or body direction associated with voluntary movements from those induced by external disturbances, such as changes in wind direction (Currier et al., 2020). More generally, matching the predicted head and body direction with the actual direction could enable the fly to fine-tune its movements to produce intended motor outputs (Krause et al., 2019). As described below, PFL neuron types have anatomical phase shifts that appear well-suited to perform such comparisons (Figure 73).

The PFN neuron types that the computations hypothesized above might involve are as yet unclear. However, our analysis of PFN inputs from LNO types does allow us to draw some inferences about the sort of self-motion information that different PFN neuron types might carry. For example, considering that PFL2 neurons provide selective feedback to the LNO3 neuron type and considering that the PFL3 neurons feed the LCNOp neurons (Figure 57C), we would hypothesize that the former may provide its downstream PFN neurons – the PFNv neurons (Figure 27) – with efference information related to translational (and potentially forward) movement and that the latter my provide its PFN targets – several PFNp subclasses (Figure 27) – with efference information related to rotational movements. In addition, many LNO types are downstream of pathways from vPNs (Figure 5), consistent with the use of optic flow-based self-motion signals (Stone et al., 2017). Furthermore, given that LNO types are the target of multiple input pathways, these neurons could carry combinations of sensory and motor signals to encode self-motion. Physiological recordings in behaving flies would be needed to test such hypotheses.

Phase shifts of a single PFN neuron type could enable the generation of vectors that are within ±45° of the fly’s instantaneous head direction. Intriguingly, the FB network appears to be wired to expand this range to allow for computations with vectors of arbitrary angles.

As shown in Figure 70, the vΔ and hΔ neuron types could, in principle, allow for vector computations across arbitrary azimuthal angles. In this example, we consider two hypothetical PFN populations (PFN1 and PFN2), both with 45° contralateral phase shifts, as shown in the phasor diagrams in Figure 70B. On their own, these PFN populations are limited to directional representations spanning 45° around the head direction signal that they inherit. However, an excitatory hΔ (or an inhibitory vΔ) would invert the PFN2 vectors, shifting them by 180°. Thus, if a postsynaptic neuron type were to sum the input from the noninverted PFN1 neuron population and an inverted PFN2 neuron population, it could form a representation of any arbitrary vector over the full 360° range, even though the PFN1 and PFN2 populations are individually range-limited (Figure 70B and C). A similar inversion could happen at the level of the PB if one PFN population were to receive excitatory Δ7 input while the other received inhibitory Δ7 input, which is likely how the 180° separation of PEN_a and PEN_b population bumps is generated and maintained in the PB (Green et al., 2017; Turner-Evans et al., 2017). Together, the noninverted PFN1 and inverted PFN2 neuron populations form a basis set of four basis vectors, all separated by 90° (Figure 70C). As mentioned previously, the requirement for PFN neurons to have a positive firing rate prevents any single PFN population from forming a basis set on its own; instead, forming a basis set requires four independent bumps located at 90° intervals. When this situation is achieved, independent NO input could alter the relative amplitudes of bumps carried by each of the four PFN populations (inverted and noninverted PFN1 and PFN2 populations), enabling their sum to encode a vector with any angle (Figures 70C and 25) and could thus represent such independent vectors. Importantly, during navigation, the orientation of this set of four vectors would be dynamically updated with the head direction representation, such that any computations derived from these vectors would be independent of the fly’s current head direction (Figure 70—figure supplement 1).

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Could the intra-FB network support the construction of arbitrary vectors, which requires two layers beyond PFN input? The type-to-type network graph in Figure 33A suggests that there are many pathways within the FB’s 2D grid that could potentially implement a four-vector basis set. We chose two arbitrary PFN types, PFNd, and PFNp_c, and used their connectivity with two downstream vΔ and hΔ neuron types – vΔK and hΔA – to illustrate how this might work (Figure 70—figure supplement 2). We also show how a downstream neuron type – PFL3 in this case – could sum the input from the vΔ and hΔ to represent arbitrary vectors determined by independent NO inputs to the left and right PFNd and PFNp_c populations (Figure 70—figure supplement 2C). Physiological investigations will be required to establish which of the FB’s many pathways implement such computations, and whether or not the large number of these pathways is an indication of vector computations in different behavioral contexts.

Having established that the FB network of Drosophila could, in principle, compute arbitrary vectors, we now explore the potential utility of PB-FB phase shifts and intra-FB connectivity motifs for path integration. A variety of models have been proposed for path integration (Benhamou, 1997; Benhamou et al., 1990; Benhamou and Séguinot, 1995; Bernardet et al., 2008; Cheung, 2014; Gallistel, 1990; Goldschmidt et al., 2017; Haferlach et al., 2007; Hartmann and Wehner, 1995; Issa and Zhang, 2012; Jander, 1957; Kim and Hallam, 2000; Kim and Lee, 2011; Maurer, 1998; Merkle et al., 2006; Mittelstaedt, 1983; Mittelstaedt and Mittelstaedt, 1973; Müller and Wehner, 1988; Stone et al., 2017; Vickerstaff and Di Paolo, 2005; Wittmann and Schwegler, 1995). These models have several differences, including whether the home vector is stored in an allocentric reference frame or an egocentric reference frame, and whether it is stored using a ‘static vectorial basis’ or a ‘dynamic vectorial basis’ (for details, see Heinze et al., 2018; Vickerstaff and Cheung, 2010). Here we focus on models that store the home vector in an allocentric reference frame using a static vectorial basis (Hartmann and Wehner, 1995; Stone et al., 2017), which has been shown to have several theoretical advantages (Cheung and Vickerstaff, 2010; Vickerstaff and Cheung, 2010) and whose implementation is directly suggested by the FB’s network architecture. Path integration models can be further divided into two groups according to whether the home vector is stored and read out as independent components or as a single vector.

An example of the first type of path integration model, which stores the home vector as two independent components, was recently put forward by Stone et al., 2017. This work combined anatomical and functional data from bees, including physiological recordings of optic flow-sensitive LNO neurons and EM data, to build an anatomically inspired model of path integration based on the projection and innervation patterns of CX neurons, but without access to their synaptic connectivity. The model utilized PB-FB phase shifts to read out a home vector and, importantly, could also account for holonomic motion, which occurs when animals move in directions that are not aligned with their head/body axis, an issue we return to below. At its core, this model and those derived from it (Le Moel et al., 2019) function by modulating the amplitude of left and right PFN bumps according to the insect’s motion in the leftward or rightward direction, respectively. Integration of the left and right PFN activities can then store a home vector as two independent components. During readout, a population of PFL neurons is assumed to compare the insect’s current head direction to that of directions 45° to the left and to the right to decide which direction is closer to the implicitly stored home vector. This 45° ‘functional offset’ (phase-shift) was derived from physiological recordings, demonstrating that some LNO neurons function as optic flow sensors whose optimal expansion points are 45° to the left and right of the bee (Stone et al., 2017), a feature we return to below. While conceptually elegant, one major feature of this model is inconsistent with the anatomy and connectivity of the homologous neurons in the Drosophila connectome. In particular, the model requires that the left and right PFN bumps independently propagate to right and left PFL populations, respectively. This operation is unlikely to be supported by the FB columnar network since every neuron and neuron type postsynaptic to PFN neurons receives input from both the left and right populations (Figure 35).

In the next two sections, we use the additional anatomical and connectivity information provided by the CX connectome to propose two conceptual models for computing an allocentric TV vector whose integration could be stored as a single home vector. The first model builds on the work of Stone et al., 2017 and uses PFN offsets to simplify home vector computation. The second model is more relevant to walking insects and incorporates a head-to-body coordinate transformation to compute the fly’s TV vector. In both cases, the key computation performed by the FB network is a coordinate transformation that ensures that egocentric velocity signals and allocentric directional representations are directionally aligned.

Flying insects are thought to perform visual odometry by relying on optic flow sensors to estimate their velocity relative to the ground (Leitch et al., 2020; Srinivasan, 2014; Srinivasan, 2015), consistent with leg-based cues being of little use and motor signals being unreliable in the face of external perturbations, like gusts of wind. In addition, during flight many insects make banked turns involving body rolls that are accompanied by gaze-stabilizing head rotations that keep the head near the horizontal plane (Kim et al., 2017b; Muijres et al., 2015). Importantly, flight trajectories often contain a significant sideslip component as well, during which the insect’s TV is in a direction that is different from that of its head-body axis (Braun et al., 2012).

The FB’s recurrent circuitry described above could use self-motion information to compute a flying insect’s allocentric TV vector. One potential model is shown in Figure 71. This model is composed of two PFN neuron types that receive independent input from two hypothetical LNO neuron types, LN1 and LN2 (Figure 71B), for which there are multiple candidates (Figure 25). It exploits the FB network’s ability to form a set of four basis vectors to compute a single TV vector. To do so, it employs the optic flow sensors described by Stone et al., 2017 – with their preferred expansion points spaced at 45° intervals around the fly’s head – to modulate the amplitudes of the four basis vectors such that their sum encodes an instantaneous allocentric TV vector (Figure 71C–E). Importantly, this model relies on the fact that the basis vectors and optic flow sensors are directionally aligned (Figure 71C and D). That is, at every moment in time, each bump in the basis set has its amplitude modulated by a velocity input that senses movement in the same direction as encoded by the bump. Much like the model of Stone et al., 2017, this model can account for holonomic motion (i.e., an animal’s movements in directions not limited to its heading and head direction). Another feature of this model is that it should be insensitive to head movements in the yaw plane since the optic flow sensors and FB basis vectors are both in head-centered coordinates. A recent study found that, similar to the optic flow sensors described above, some PFN neuron types and their LNO inputs are preferentially tuned to air flow oriented ~45° to left or right of the fly’s head (Currier et al., 2020), providing for a second potential velocity estimate whose tuning is aligned to PFN basis vector. The next conceptual model explores how this might work in walking insects, when the velocity sensors may be in a body-centered reference frame while the directional representation is in a head-centered allocentric reference frame.

Figure 71

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Could the FB network compute an instantaneous TV vector in cases where its velocity and directional estimates are in different reference frames? The model shown in Figure 72 explores such a scenario using a hypothetical example of a walking fly whose velocity estimates are computed using cues that operate in an egocentric, body-centered reference frame. These velocity estimates could be derived from motor efference copies or proprioceptive cues, and we assume the existence of estimates for both forward (parallel to the body axis) and sideslip (perpendicular to the body axis) velocity. Computing a TV vector in this scenario is more complicated than in the previous model because the direction of the head and that of the body are not necessarily aligned, which requires a head-to-body coordinate transformation. As shown in Figure 72B–D, this model uses the head-body angle to compute the total TV vector as the sum of two components, which represent the distance traveled parallel and perpendicular to the fly’s body axis. To compute the parallel and perpendicular components of the TV vector, the model uses two basis sets that receive NO input related to the head-body angle as well as either a forward or sideslip velocity signal.

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A circuit for computing the component of the TV vector parallel to the fly’s body axis is shown in Figure 72B, which involves two calculations that occur in parallel. The circuit recruits two independent PFN populations, one to encode movement in the forward direction, and the other for movement in the backward direction. A velocity signal increases the amplitude of the two PFN vectors that point in the direction the fly is moving (for the example situation in Figure 72B, in the forward direction), resulting in a vector whose amplitude encodes velocity and whose direction is either the fly’s head direction (Figure 72B), or its reverse head direction, which would be captured by the PFN2 population in Figure 72B. At the same time, an input related to the head-body angle transforms the head-centered vector into a body-centered vector, as described above (Figure 69). The result is a single vector encoding the component of the fly’s movement parallel to the body’s axis in either the forward or backward direction. As mentioned above, this sort of computation could employ gain fields (Andersen et al., 1993; Pouget and Sejnowski, 1997; Salinas and Abbott, 2001), but with the transformed representation (i.e., body direction) being scaled by the fly’s velocity in the process.

The component of the TV vector that is perpendicular to the fly’s body axis could be computed using the same circuitry as above, but with right/left sideslip velocity signals (Figure 72C) instead of forward/reverse velocity signals. As shown in Figure 72—figure supplement 1, such a circuit would work regardless of whether the fly is sideslipping right or left or whether its head is to the right or left of the body axis. The output of these two circuits could then be summed to compute a single vector that encodes the fly’s instantaneous TV in an allocentric reference frame (Figure 72D).

The conceptual models described above – one for flight and the other for walking – could, in principle, compute an allocentric TV vector whose integration would yield an exact home vector. To accomplish this, the models use coordinate transformations to ensure that allocentric vectors are directionally aligned with the egocentric velocity estimates that control their amplitudes. While these particular models highlight the general utility of such transformations, the FB circuitry could, in principle, accommodate many similar models. In addition, it is possible that animals structure their movements during outbound paths to simplify the computation of the TV vector. For example, if an animal were to only move forward during outbound paths, then circuit components dedicated to encoding backward motions would not be needed by the path integration circuit, a feature explicitly used by the model of Stone et al., 2017. Similarly, it is possible that an exact solution is not always required to perform path integration. For example, if a model generates errors that tend to cancel out during the integration process, the home vector can still effectively guide behavior. The local search behavior of foraging Drosophila, for example, involves relatively short loops that may not require a precise accounting of the goal location (Brockmann et al., 2018; Haberkern et al., 2019; Kim and Dickinson, 2017a). In most situations, the fly should also be able to use local sensory cues in addition to path integration during such search behaviors. Finally, it is possible that egocentric velocity signals could come prealigned to FB bumps, assuming that the LAL could implement the trigonometric functions needed to scale velocity signals according to, for example, head-body angle. Taken together, these models highlight the connectome’s ability to inspire novel, implementation-level hypotheses about network computation. They also provide a framework for generating many similar models, with specific implementations that likely depend on cell type, species, and behavioral need. Ultimately, evaluating models like these necessarily requires physiological recordings from animals in specific behavioral contexts. Indeed, two contemporaneous studies have discovered direct physiological evidence that FB circuits compute the fly’s TV and have independently proposed theoretical models that are conceptually similar to those described above (Lu et al., 2020b; Lyu et al., 2020). Yet, it is currently unclear if the output of this computation encodes the fly’s TV vector or just the phase of this vector. Similarly, how the type-to-type variability in PFN phase shift magnitude (Figure 34) affects these computations requires future study. Finally, it is also possible that tangential neurons carrying feedback or self-motion signals (Weir and Dickinson, 2015; Weir et al., 2014) could scale the magnitude of these vectors within the FB network itself.

Theoretical work has suggested several potential ways to integrate TV vectors. First, TV could be integrated and stored using two separate circuits: a ring attractor that encodes the angle of the home vector and a line attractor that encodes the length of the home vector (Hartmann and Wehner, 1995). Rather than keeping track of the distance traveled in each allocentric direction, this network would shift the columnar location of an activity bump to encode the phase of the home vector. Solutions like these seem unlikely to be implemented by the FB since they require FB-centered attractors with circuit motifs for shifting the bump, similar to those found in the EB-PB attractor, which we see no evidence for in the FB network. Second, the model of Stone et al., 2017 employed 18 neurons per FB column and used structured recurrent connections between them to integrate and store a two-component home vector (Stone et al., 2017). The hemibrain connectome provides little evidence for such structured recurrent PFN connections, especially in the NO, where some PFN types show all-to-all connectivity. Finally, the conceptual models described above allow for the computation of a single TV vector (Figures 71 and 72), suggesting that the FB network could simply integrate the corresponding activity bump and store the resulting home vector directly. In doing so, this integration processes would function by keeping track of the distance traveled in each allocentric direction. How might the network integrate the TV vector and store the resulting home vector?

Integration and storage could occur through several complementary mechanisms operating at different scales, from changes in synaptic strength or the excitability of individual neurons to persistent activity (Major and Tank, 2004) at the single neuron (Yoshida and Hasselmo, 2009) or network level (Aksay et al., 2007). In addition, integration and storage mechanisms may vary across species and environmental context depending on the animal’s needs. For example, desert ants can maintain multi-day memories of multiple goal vectors to food sites and remember home vectors over 1–2 days (Wehner et al., 2004). This sort of long-term maintenance would favor stable storage mechanisms, such as changes in synaptic strength. In contrast, Drosophila performing relatively brief local searches close to a food source may rely on short-term mechanisms that could involve persistent neural activity. The connectome alone does little to constrain the space of possible storage mechanisms, but it can provide information regarding the likely site of storage and inspire a few conceptual models for how the vector could be stored.

Several considerations narrow the potential site of home vector storage in Drosophila. In the framework of the above conceptual models, the home vector would be stored downstream of the four-vector basis sets used to compute the TV vector. The PFL2 and PFL3 neuron types are well positioned to read out the home vector by comparing it to the fly’s instantaneous head direction (see section below), suggesting that the home vector is perhaps stored by neuron types that provide inputs to the PFL neurons. The PFL neuron types could also store the home vector themselves. Some insects are likely to maintain more than one goal vector (Dacke and Srinivasan, 2008; Mangan and Webb, 2012), but the PFL neurons could store these different goal vectors through input-synapse-specific presynaptic (Goldschmidt et al., 2017) or postsynaptic plasticity. In addition to direct PFN input, PFL2/3 neurons receive shared input from a handful of hΔ types, several FC2 types, one or two vΔ types, and many FB tangential neuron types, each of which could also potentially store a home vector.

Several potential storage mechanisms seem plausible. Many hΔ neuron types have within-type recurrent connections, forming small loops that connect pairs of hΔ neurons that encode directions 180° apart. If the biophysical properties of these neurons allowed for graded, persistent activity, and hΔ neurons have inhibitory connections, each column-pair could encode the direction traveled along one dimension. Alternatively, while the FC neurons providing input to PFL2/3 neurons largely lack within-type recurrent connections, they could maintain a vector in working memory through graded changes in their excitability or activity. Finally, the FB’s tangential neurons could potentially store home vectors through column-specific plasticity, as is known to occur between ring neurons and EPG neurons. In general, some recurrent architectures may allow for the storage of home vectors (Wittmann and Schwegler, 1995), but an FB ring attractor, if it were to exist, would likely not allow for home vector storage since these networks have the undesirable property of forming a single activity peak at the expense of the activity in distance columns that would be needed to fully encode the home vector.

Overall, although the connectome can do no more than rule out some circuit implementations of how the home vector might be stored, it should prove useful in prioritizing a search for the likely neural targets for such a function. It is important to note that the entire circuitry described above must function in different modes depending on the animal’s behavioral needs – integrating direction and distance traveled to update the home vector when the fly is searching, but switching to reading out the home vector when the fly is attempting to return to a previously visited spot. The likeliest candidates for such behavioral mode switching are the FB’s tangential neurons.

Once formed, how might an insect ‘read out’ the home vector to return to its goal location? In our formulation, the home vector points from the nest to the insect’s current location. Returning home, then, requires that an insect move in a direction opposite to the home vector. To accommodate the other behaviors and computations that these circuits are likely to be involved in, we refer to the home vector as the ‘stored vector,’ which is read out to orient the insect along a ‘goal vector’ (Figure 73, bottom panel). However, unlike an ant or bee, the fly is not a central place forager. Thus, ‘goal’ in this context refers only to a spot that the fly is likely to return to during a local search, such as a food source (Brockmann et al., 2018; Kim and Dickinson, 2017a). PFL neurons are generally regarded as the major columnar output of the FB network (el Jundi et al., 2015; Hanesch et al., 1989; Heinze et al., 2013; Heinze and Homberg, 2008; Homberg, 1985; Lin et al., 2013; Skutt-Kakaria et al., 2019; Wolff et al., 2015). Their PB-FB offsets strongly implicate them in reading out stored vectors in ways first proposed by theoretical work (Hartmann and Wehner, 1995; Wittmann and Schwegler, 1995) and then, at the implementation level, by Stone et al., 2017. In particular, PFL neurons may use their PB-FB phase shifts to compare the fly’s instantaneous head direction, which they receive in the PB, to that of the stored vector, which they may receive in the FB, to generate appropriate motor commands to guide the fly to its goal. In doing so, they effectively generate egocentric motor commands based on allocentric directional variables. Interestingly, each of the three PFL types have characteristic phase shifts that strongly predict their involvement in generating distinct motor commands (Figure 73).

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PFL2 neurons may use their 180° phase shift and bilateral LAL projections to increase the fly’s forward velocity when its heading is directly away from the stored vector, which in our formulation is towards the goal location (Figure 73A, bottom panel). Unlike the other PFL types, PFL2 neurons receive only a single bump as input in the PB (Figure 39). This suggests that the population cannot make left versus right activity comparisons. In agreement with this, individual PFL2 neurons make bilateral projections to the left and right LAL. Because of their 180° phase shifts, the PFL2 population activity will be largest when the fly is heading directly towards its goal location. The above characteristic suggests that PFL2 neurons are ideally suited to generate a motor command related to forward velocity.

PFL3 neurons may use their 90° phase shifts and lateralized LAL projections to orient the fly towards the goal. As shown in Figure 73B, their 90° offset predicts that the left and right PFL3 populations will have their maximum activity when the fly is 90° to the right or left of the goal direction, respectively. If the left PFL3 population generates left turns and the right PFL3 populations generated right turns, then the orienting behavior of the fly will have two equilibrium points: a stable equilibrium that occurs when the fly is oriented towards the goal direction and an unstable equilibrium when the fly is oriented in the opposite direction. This sort of read out would ensure that flies orient directly towards the goal location. It is additionally possible that across-column inhomogeneities in the EPG-> PFL synaptic profile (Figure 73—figure supplement 1) and in the PFL-> LAL network (Figure 64) may provide the fly with a ‘default goal’ in the absence of any FB input, similar to a hypothesis recently advanced in an independent study (Rayshubskiy et al., 2020). The 45° offset of PFL1 neurons may serve a related function, although they target distinct downstream neurons compared to PFL2/3 (Figure 57C). One possibility is that the PFL2/3 neurons affect body orientation while the PFL1 population controls a separate variable, such as sideslip or head-body angle. Ultimately, it is also important to remember that brain regions like the LAL and CRE house complex recurrent networks with inter-hemispheric pathways that are likely to be inhibitory (see Output sections) (Iwano et al., 2010). These networks are likely to play a major role in the transformation of PFL population activity into motor commands for the fly, something that our hypotheses do not incorporate.

The discussion above supports the notion that the FB network has the computational capacity to compute, store, and read out vectors in support of goal-directed navigational behaviors. While we have focused on path integration as a canonical vector-based computation, Drosophila are known to perform several other behaviors that may rely on the formation of goal vectors, including: local search, a path-integration-based foraging strategy (Corrales-Carvajal et al., 2016; Dethier, 1957; Kim and Dickinson, 2017a); menotaxis, where a constant heading is maintained relative to an arbitrary goal direction to generate straight trajectories that support long-distance dispersal (Giraldo et al., 2018; Green et al., 2019; Haberkern et al., 2019; Leitch et al., 2020); place learning, which requires associating visual cues with the presence of a cool spot in an otherwise hot 2D environment (Melnattur et al., 2020; Ofstad et al., 2011); and the detour paradigm, where flies orient towards directions associated with attractive landmarks even after they have disappeared (Neuser et al., 2008). In addition, ethologically based studies in behaving insects have established a range of vector-based behaviors, from long-distance migrations that require a time-compensated sun compass (Heinze and Reppert, 2011; Perez et al., 1997) to the waggle dance that bees use to communicate the distance and direction of a food source (Frisch, 1967). The ability of some insects to store multiple goal vectors and the fact that different insect species may use vector computations to support distinct behaviors has important implications for FB circuits. The FB may have evolved as a general vector calculator that can be co-opted, whether by evolution or in support of distinct behaviors, to support vector-based navigation strategies generally. In support of this idea, FB circuits, neuron types, and motifs are highly conserved across insects (Strausfeld, 2012), including PB-FB phase shifts (Sayre et al., 2021). Additionally, the ability of some insects to store multiple goal vectors requires mechanisms for switching between them, a function perhaps mediated by the large class of FB tangential neurons that could convey context and state information to the columnar networks involved in vector operations.

Consistent with the CX’s involvement in navigation, several studies have implicated FB tangential neurons in sensorimotor processing. For example, ExFl1 neurons (Homberg, 1994; Liu et al., 2006; Weir et al., 2014; Young and Armstrong, 2010b), which are likely FB2B_a and/or FB2B_b neurons (Figure 41A), are strongly modulated by whether or not the fly is flying and are tuned to progressive optic flow (Weir et al., 2014), providing a potential indication of the fly’s current sensory and motor state. Similar activity patterns may be expressed by several other FB types as well (Weir and Dickinson, 2015). In addition, a recent study focused on the LH identified an FB tangential neuron type called PV5k1 (FB2H_a, FB2H_b, and/or FB2I_b) whose activation during closed-loop visual conditions leads to a reduction in the fly’s wingbeat frequency (Dolan et al., 2019). Sensorimotor signals like these are well positioned to influence CX-driven motor commands based on the fly’s immediate sensory environment and ongoing motor state.

Flexible behavior also requires animals to respond to their immediate sensory surroundings by evaluating past associations regarding the valence and novelty of available sensory cues. To investigate this, we focused on tracing pathways between the MB – the fly’s main learning and memory center – and the CX (Figures 46 and 47). In agreement with results from a companion manuscript focusing on the MB (Li et al., 2020) and trans-Tango-based circuit mapping (Scaplen et al., 2021), we found extensive pathways leading from MBONs to FB tangential neurons. In the context of navigation, the MB is considered a potential source of visual snapshot memory, which may allow insects to base their navigation decisions on remembered panoramic views (Collett and Collett, 2018; Sun et al., 2020). Consistent with this general notion, some FB tangential neuron types in FB layers 2 and 8 have been proposed to play a major role in visual learning (Liu et al., 2006). In addition, recent studies have implicated MB-to-CX pathways in behaviors other than navigation. For example, MB-to-CX circuits may be important for experience-dependent alcohol preference (Ojelade et al., 2019; Scaplen et al., 2021; Scaplen et al., 2020). In addition, MB-to-CX circuits are involved in consolidating courtship experience into long-term memory (Dag et al., 2019). The sheer number of connections between MBONs and FB tangential neurons suggests that this prominent pathway is involved in many behaviors that make use of valence and novelty signals extracted from past associations that the fly has made with its current sensory surroundings.

Animals also select their actions based on latent environmental variables, such as the time of day, which are predictive of environmental conditions like temperature and humidity. Flies are most active around dawn and dusk, and show consolidated periods of inactivity throughout the night and during a daytime siesta (Dubowy and Sehgal, 2017). This daily rhythm is imposed by outputs from the circadian network and functions to restrict behavior to appropriate times of day. Previous studies have identified a population of anterior-projection DN1 clock neurons that convey circadian information through TuBu neurons to EB ring neurons (Figures 6C and 7D; Guo et al., 2018; Lamaze et al., 2018). Thus, CX circuits are likely to receive circadian information that could be used to select behaviors according to time of day (Liang et al., 2019). Whether circadian pathways target other regions of the CX requires further investigation. In addition to receiving circadian inputs that could affect rest-activity rhythms, considerable evidence suggests that CX circuits are involved in tracking internal states, such as sleep need and nutritive state, which we turn to next.

While its functions remain largely unknown, sleep is associated with a variety of processes in Drosophila, including synaptic homeostasis (Bushey et al., 2011), memory formation and consolidation (Berry et al., 2015; Dag et al., 2019; Donlea et al., 2011), changes in gene expression (Cirelli et al., 2005; Zimmerman et al., 2006), and several metabolic processes (Kempf et al., 2019; Vaccaro et al., 2020). Sleep in flies is behaviorally defined as a reversible state of immobility that is homeostatically regulated and associated with an increased arousal threshold (Hendricks et al., 2000; Shaw et al., 2000). It is marked by drastic changes in brain-wide activity patterns (Nitz et al., 2002; Tainton-Heap et al., 2020; Yap et al., 2017). The neural circuits involved in tracking sleep need and inducing sleep are thought to partially reside in the CX. In particular, a heterogeneous population of FB tangential neurons labeled by the R23E10 GAL4 line induces sleep when activated and tracks sleep need through changes in baseline firing rate and intrinsic excitability (Donlea et al., 2011; Pimentel et al., 2016) (but see also Tainton-Heap et al., 2020). Similarly, ER5 ring neurons track sleep need, and reciprocal connections between the EB and dFB are hypothesized to form a core circuit for homeostatic control of sleep (Donlea et al., 2018; Liu et al., 2016). Counteracting these sleep-promoting neurons are wake-promoting DANs in the dorsal FB that are thought to promote wakefulness by inhibiting R23E10 neurons (Ni et al., 2019; Pimentel et al., 2016). Our connectomic analysis revealed extensive reciprocal connections between putative sleep- and wake-promoting populations within the dFB, which could function as a ‘flip-flop’ switch to ensure that only one population is active at a time (Saper et al., 2010). In addition, we identified a large number of previously undescribed pathways leading to and from sleep-wake neuron types whose potential involvement in sleep-wake control requires future investigation (Figures 51—55), including reciprocal pathways connecting neurons in the EB with those in the dorsal FB (Figure 53; Donlea et al., 2018; Liu et al., 2019).

Several limitations of the hemibrain dataset are notable in the context of sleep. Neurons that show structural changes as a function of the fly’s sleep-wake history (Bushey et al., 2011), such as ER5 (Liu et al., 2016), could have sleep state-dependent connections different from those described here; similarly, at present, the hemibrain connectome does not include reconstructed glia, which are also known to be involved in sleep-wake control (Blum et al., 2021; Sengupta et al., 2019); lastly, the hemibrain dataset cannot resolve the presence of gap junctions, which may also be important for sleep-wake control (Troup et al., 2018).

Recent studies have suggested that the CX is involved in internal state-based action selection beyond sleep-wake control. Within the EB, a population of ring neurons allows flies to assess the nutritive value of sugars, independent of their taste (Dus et al., 2013; Park et al., 2016). Similarly, tangential neuron types in the dorsal FB have been implicated in feeding decisions based on the nutritive value of foods, and they may incorporate past experience into these computations (Sareen et al., 2020). And vΔA_a columnar neurons, which innervate the AB and dFB, show oscillatory dynamics that depend on hemolymph glucose levels, and altering vΔA_a activity levels affects fructose preference (Musso et al., 2021). Together, these studies implicate CX circuits in nutrient homeostasis, a process important for successful foraging based on the fly’s metabolic needs (Corrales-Carvajal et al., 2016).

The need for high-level behavior selection may explain the potential interactions of circuits related to navigation, feeding, circadian rhythms, and sleep. Hungry flies, for example, are known to forgo sleep in favor of foraging (Keene et al., 2010). Similarly, both sleep and feeding are known to be under circadian control (Dubowy and Sehgal, 2017; Murphy et al., 2016; Xu et al., 2008), biasing their occurrence to appropriate times of day. Based on these considerations and the experimental evidence summarized above, it seems likely that the CX operates as a multifunctional network that can be dynamically reconfigured (Marder, 2012) to support a variety of goal-directed behaviors based on immediate sensorimotor variables, learned associations, time of day, sleep need, nutritive state, and other as-yet-unknown inputs. Such a view of the CX is consistent with the variety of neuromodulator and peptides released by FB neurons (Kahsai et al., 2012; Kahsai et al., 2010; Kahsai and Winther, 2011).

Our connectomic analysis identified circuit elements and motifs that may support appropriate action selection. Most notably, many tangential neuron types, including EB ring neurons, form dense recurrent connections, both within neurons of a type and across distinct neuron types. For example, the FB’s tangential neurons in layer 6 that have been implicated in sleep-wake control are highly recurrently connected. It is possible that some of these neurons or other neurons in their layer are involved in decision-making related to feeding (Musso et al., 2021; Sareen et al., 2020). If so, inhibitory interactions between these different tangential neurons may – akin to the interactions of ring neurons for sensory control of the fly’s compass – enable the fly to select appropriate actions based on internal need. Related to this, recent studies have reported oscillatory activity in ER5 ring neurons related to sleep-wake control (Raccuglia et al., 2019; Yap et al., 2017), but how the highly recurrent networks in the EB and FB might support such oscillations remains to be determined. One possibility is that all-to-all inhibition between ring neurons in the EB could, with the appropriate inhibitory conductances, induce such patterns of activity. A different issue raised by the highly recurrent architecture of sleep-wake networks concerns how activity may propagate in these networks. Artificial stimulation of neurons within such potentially self-regulating networks may trigger downstream activity that is never seen in more naturalistic situations, confounding the interpretation of experimental results. Testing such ideas will require a finer-resolution analysis of the role that these neurons play in the action selection process.

How might the CX’s columnar architecture support these distinct behaviors? Links between the CX’s role in sleep and navigation have begun to be explored both experimentally (Donlea et al., 2018; Liang et al., 2019) and computationally (Valle et al., 2020), but the CX connectome suggests that the number of pathways and neuron types that connect circuit elements known to be involved in these functions may have been underestimated. For example, the dFB tangential neurons involved in sleep-wake control contact many columnar neuron types (Figure 51). Although we believe this columnar structure – and the FB’s 2D grid more generally – to be convenient for vector computations, why this columnar structure may be needed for sleep-wake control or for feeding- and satiety-related computations remains mysterious. One possibility is that head direction or traveling direction signals may be used as proxies for tracking the quality or quantity of the fly’s waking experience, perhaps to estimate sleep and/or nutritional need. Alternatively, the FB’s navigational signals may be inherently activity-promoting since they likely drive premotor neurons in the FB. If so, these navigational signals may require suppression to establish a sleep state or to enable a hungry fly to stop on a patch of nutritive food. Another possibility, suggested previously (Donlea et al., 2018), is that tangential neurons may gate incoming sensory information, which could promote sleep or perhaps encourage a hungry fly to continue a feeding bout by ignoring distractors. Ultimately, if the columnar neurons are the main output of the CX, as seems likely, the FB’s tangential neurons must impact behavior through them.

Considering that the highest layers of the FB are associated with modulating the fly’s activity depending on sleep state and satiety levels, the connectivity pattern within the FB suggests that information about the fly’s current navigational state may enter the FB ventrally, that additional processing may happen in the middle layers, which receive considerable input from the MB, and that this processing may then determine the fly’s next actions (or inaction) in the dorsal layers. An additional possibility suggested by the flow of bump information from ventral to dorsal layers of the FB, and by the diffusion of columns in the dorsal layers, is that the specificity of actions is organized along the vertical axis of the FB, with oriented actions modulated and signaled by output neurons originating in the middle layers (see next section) and the fly’s overall state of activity modulated in directionally nonspecific ways by the highest layers.

Compared to the vector computation models suggested by the CX’s columnar structure, deriving connectome-inspired insights into the function of the CX’s action selection networks proved more challenging. One reason for this is that most FB tangential neurons receive input from CX-associated regions whose function remains poorly understood, like the SMP/SIP/SLP, making it hard to assign specific circuit functions to these neurons based on their inputs alone. In contrast, the vector computation models relied on a considerable amount of prior experimental data that, when mapped to the connectome, provided physiological hooks for generating novel hypotheses regarding circuit function. In addition, FB tangential types often have extensive reciprocal connections to other tangential types, which, given the absence of functional data, is hard to interpret. Once some of these functions are better understood, it may be possible to derive internal state hierarchies, like those we identified for directional sensory cues carried by EB ring neurons, which could suggest how the CX prioritizes different internal states. However, many of these internal states involve variables that evolve over time, such as nutritive state or sleep need, suggesting the underlying CX networks may undergo considerable plasticity that may not be apparent in connectome-level connectivity. The dynamic interaction of different internal state variables is likely also governed by neuropeptidergic signals that bathe the CX (Kahsai et al., 2012; Kahsai and Winther, 2011), but that our analysis did not capture. Finally, given our limited understanding of the variety of behavior the CX may support, understanding how internal state cues may factor into these behaviors is hard to predict at present. To better understand which behaviors the CX may be involved in, we used the connectome to identify output pathways, a topic we turn to next.