Introduction

Functional connectivity (FC) describes the relationship between functional activity in one brain region and that in another. In previous approaches, two spike trains were analyzed by a cross-correlation histogram [1, 2]; then, this method was applied to positron emission tomography and functional magnetic resonance imaging (fMRI) [3]. Subsequently, the time-series correlation between two regions has become widely used as a measure of undirected FC [4]. Underlying such functional connectivity, a structural connectivity (SC) substrate exists, and its relationship with FC has been investigated using various modalities [5, 6, 7, 8, 9, 10, 11]. In humans, FC-SC correlations between resting-state (rs-) fMRI and diffusion tensor imaging have been explored, and studies have shown high relationships of r=0.66 for 66 regions and r=0.54 for 998 regions [6, 7]. Other studies have examined the relationship between rs-fMRI and SC based on retrograde tracing from 145 injection sites in the left cortex of marmosets (r=0.379 for 9862 voxels, Ext.Data.Fig.2-1c) [10] and the relationship between calcium imaging and SC based on electron microscopy (EM) in the hemibrain of Drosophila melanogaster (D. melanogaster) [12] (r=0.74 for 37 regions) [9]. Because of the disparity in species, number of ROIs, and modalities, a direct comparison across them becomes difficult. Therefore, in this study, we used whole-brain [13] and hemibrain [12] EM connectome data, which are currently considered to be the most detailed, and whole-brain calcium imaging data [14] of D. melanogaster to comprehensively investigate the relationship between FC and SC across various ROI shapes and numbers. Our results of the FC-SC correlations in the fly hemibrain compared to the human cortex at various ROIs showed roughly 1.08–1.24 times higher FC-SC correlations in the fly (Fig. 2d), and no large divergence was observed between the two species.

Fig. 1

Fig. 2

Because of the strong relationship between FC and SC, they can be used to investigate inter-individual variability in D. melanogaster. In particular, the FlyWire whole-brain and FlyEM hemibrain connectome data have been compared [15, 16], and widely different results are observed with cell typing [16]. However, these studies have yet to clarify whether these differences in connectome between the two individuals are attributed to inter-individual variability or some other reasons. Therefore, we compared these two EM connectomes based on the averaged FC of eight flies. FlyEM was scanned at a resolution of 8×8×8 nm, and the connectome data has a “confidence” threshold that indicates the degree of synaptic detection. Conversely, FlyWire was scanned at a resolution of 4×4×40 nm, and it had a “CleftScore” [17] threshold that shows the degree of synaptic detection. In fact, the thresholds initially employed by FlyWire and FlyEM caused large differences in post-synapse numbers; as such, we adjusted for the thresholds and compared the EM connectome data in each fly. We found that FlyEM clearly had higher values (more accuracy) than FlyWire in its FC-SC correlation and detection. In our judgment, this difference was not caused by inter-individual variability; instead, it was attributed to differences in the accuracy of detection and annotation of dendrites, axons, and synapses because of the voxel anisotropy.

We explored how functional activity contributed to the FC. In textbook terms, post-synapses on dendrites receive neurotransmitters and conduct an action potential along nerve fibers if they are excitatory; and pre-synapses on axons release neurotransmitters [18, 19]. In calcium imaging, the pre-synaptic activity in each region is detected as calcium signals, which represent functional activity. Then the FC is detected as the synchronization of functional activities. However, the synaptic arrangement on the neurons revealed in the EM connectome shows pre- and post-synapses that are highly intermingled in many neurons (i.e. input and output locations may be intermingled across axon and dendritic arbors); thus, signal transmission may be complex [19, 15, 13, 20]. Nerve cells include non-spiking neurons such as visual neurons, CT1 amacrine cells [21, 22, 23, 24, 25], interneurons in the antennal lobe [26], and APL cells in the mushroom body [27, 28, 29]. In D. melanogaster. these cells show localized functional activity taking place on a portion of the dendrite. In CT1 and APL cells, the pre- and post-synapses are highly intermingled (Fig.4a, Ext.Data.Fig.4-2). Therefore, we wanted to investigate the presence of these unsegregated synapse-type neurons in the brain. We defined the pre- and post-synapse segregation index (PPSSI) and found that only some cells have a clear synaptic segregation, and many neurons have unsegregated synapses. When we extracted synapses with a particularly low segregation (high intermingling) and compared them between SC and FC, we found a significantly higher FC-SC correlation. Conversely, neurons with a high segregation had significantly lower FC-SC correlations. Many Drosophila brain neurons are interconnected [30]. As such, we similarly investigated reciprocal synapses [31, 32, 33, 34, 35], whose function is clearer than that of other unsegregated synapse types. When we extracted such reciprocal synapses, the FC-SC correlation was significantly higher. Our results indicated that unsegregated synapses contributed more to the FC. In other words, local activity due to unsegregated synapses could be considered the more essential functional activity. Unsegregated synapses are found not only in flies but also in mammals [31, 32, 18, 36, 37, 38], including humans (Ext.Data.Fig.1-2 from [39]). Localized functional activity from pre-synaptic population dynamics can be observed by calcium imaging or detected through the neurovascular coupling with astrocytes [40] via fMRI. Although modalities vary, the FC-SC correlation between humans and flies does not considerably differ, as shown earlier. Since various fMRI pre-processing and analysis methods can be directly applied to pre-synaptic population dynamics in this study, functional activity is locally compartmentalized in the whole brain, which is common among various species.

Results

Investigation of the optimal nuisance factor removal method for calcium imaging

First, the optimal pre-processing of the calcium imaging data of D. melanogaster was investigated. The registration method used in fMRI was applied to the calcium image (Ext.Data.Fig.1-1) to register to the FDA template [14] (Fig. 1b). Then, various nuisance factor removal methods (details in Methods) were applied to the ROI time-series to generate the FC matrices of eight flies (Fig. 1a). Three types of ROIs were used in the analysis: ROIs based on the anatomical neuropil, commonly used in Drosophila (hemibrain ROI), ROIs based on k-means clustering of the SC matrix of 146,604 voxels in the hemibrain (SCKm), and ROIs based on distance-based clustering of voxels in the hemibrain (DistKm). SCKm can provide ROIs close to the shape of the anatomical neuropil across various ROI counts (Ext.Data.Fig.2-1a), while DistKm can provide ROIs that are completely unrelated to the anatomical neuropil. Next, a correlation analysis and ROC curve analysis were performed using the SC matrices based on FlyEM and the FC matrices with these ROI types (Fig. 1a). Fig. 1d-f shows the FC-SC correlation results, FC-SC detection results, and the normalized total score of FC-SC detection and correlation (details in Methods), respectively. After the comparison of the raw (leftmost) and removal methods for various ROI types, the combination of polynomial detrending [41] & tCompCor [42] was found to yield the optimal results. The optimal removal methods were found to differ between fMRI [10] and calcium imaging data, and these results are further described in the Discussion section.

Comparison of the FC-SC correlation between humans and flies

Spatial smoothing is useful for absorbing inter-individual variability and conducting second-level group analysis [10, 43]. Here, we explored the effect of spatial smoothing (of the calcium imaging data) on various ROI counts in DistKm (Fig. 2a) and SCKm (Ext.Data.Fig.2-1a) ROIs. In DistKm, smoothing was highly effective, and the optimal kernel radius of the Gaussian filter was around 23 voxels (52.44 μm) for various ROI counts (Fig. 2b). In SCKm, smoothing was ineffective for ROI count below 100, while the kernel radius above 16 voxels (36.48 μm) was effective for ROI count above 100 (Ext.Data.Fig.2-1b). SCKm has a larger variation in volume for each ROI count than DistKm (Fig. 1c, Fig. 2e); as such, the effect of spatial smoothing is likely unstable. Next, we investigated whether the combination of spatial smoothing and Poly-tCompCor was effective. We found that this combination was significantly more effective than smoothing alone for SCKm and DistKm (Fig. 2c, Mann–Whitney U test p<1.67e-4 Bonferroni corrected). Conversely, the combination of a high-pass filter and nuisance factor removal overlapped for the purpose of noise removal, and the effect was degraded (Ext.Data.Fig.2-1d), as found in fMRI [10].

The optimal FC-SC correlation for various ROI counts was determined. Results showed that the correlation decreased proportionally to the logarithm of the ROI count (Fig. 2d). This was also compared between flies and mammals. At approximately 50 ROIs, the difference was nearly 1.08-fold to 1.22-fold (r=0.66 for humans and r=0.71-0.81 for flies [SCKm, DistKm]); by contrast, at approximately 1,000 ROIs, the difference was roughly 1.12-fold to 1.24-fold (r=0.54 for humans and r=0.6-0.67 for flies), which was not a considerable difference. The difference was slightly larger (1.21 to 1.5-fold: r=0.378 for marmosets and r=0.46-0.57 for flies) than the marmoset results at around 10,000 ROIs (Ext.Data.Fig.2-1c). Although SCs for flies and humans were obtained from single individuals, the tracer data is a composite from 52 marmosets [44], which might contribute to the difference with the fly’s FC-SC correlation.

Comparison between FlyEM and FlyWire connectome data

We used the FlyEM’s SC to compare the averaged FC of eight flies. In this section, we also used the FlyWire connectome data [45] to compare the FC and each SC, and possibly reveal the inter-individual variability of the two EM connectome data. As mentioned earlier, FlyEM has a synaptic “confidence” threshold and contains 21.4 million post-synapses in the hemibrain region at its initial value of 0. Conversely, FlyWire has a ‘CleftScore’ [17] threshold and 18.8 million post-synapses at its initial value of 50. Since the number of post-synapses differs at each threshold, we set the confidence threshold of 0.8 as high as possible, thereby increasing the FC-SC correlation (Fig. 3d, ExtFig.3-1b). Then we adjusted the CleftScore to 140, which has a post-synapse number of approximately 11.4 million (Fig. 3a). These thresholds were used for all analyses in this study. When we displayed the maximum Z-projection of the synapse point cloud of post-synapse counts in each voxel, we found that the trends in synapse detection completely varied (Fig. 3b). In each region, FlyEM had more synapses in the mushroom bodies (aL, bL, etc.) and in the major neuropils of the central nervous system (CNS; EB, FB, NO, and PB). In comparison, FlyWire had more synapses in the visual system (LO and ME) and in the periesophageal neuropils (CAN and FLA; Fig. 3c). In the FC-SC correlation of each region, FlyEM had higher values in most regions at 58:5 (Fig. 3e, ExtFig.3-1a). As a result, FlyEM r=0.73 differed from FlyWire r=0.68 at the matrix level (Fig. 3d). Both datasets were from genotype Canton-S-G1×w1118 adult females; FlyEM was five-day-old [12], and FlyWire was seven-day-old [13]. Although brain development may differ depending on the rearing environment, the tendency to detect synapses substantially varied. We attribute this to differences in detection accuracy resulting from the resolution of EM scanning, but not to inter-individual variability. We next used the FlyWire connectome data to investigate the ratios of neurotransmitter input (ExtFig.3-2a) and output (Fig. 3f) in each region. The highest percentage was acetylcholine (62.8%±14.2%), followed by glutamine (15.5%±9.2%), then GABA (11.4%±8.2%) in neurotransmitter output. The analysis of the relationship between this ratio and FC-SC correlation in each neurotransmitter revealed significant correlations for acetylcholine (r=0.39, p=0.0013) and GABA (r=-0.25, p=0.046). That is, the higher the percentage of excitatory connections, the higher the FC-SC correlation; conversely, the higher the percentage of inhibitory connections, the lower the FC-SC correlation. In humans, FC-SC correlations are lower in the evolutionarily expanded Brodmann area 39,45 and the temporal lobe [8]; therefore, these areas may have more long range inhibitory connections [46, 47, 48].

Fig. 3

Fig. 4

Unsegregated synapses contribute considerably to functional connectivity

We compared FC-SC in the macroscopic regions, and we also investigated the relationship between the synapses, the source of functional activity (pre-synaptic population dynamics), and FC. First, we examined the synaptic segregation in whole-brain neurons because many neurons showed pre- and post-synaptic intermingling. Then, we determined how unsegregated and segregated synapses affected the FC. To quantify synaptic segregation, we developed the PPSSI (Fig. 4d). Using DBSCAN [49] with a radius of 3 μm (details on Methods), we clustered synapses in each neuron and calculated the degree of segregation for each cluster (cPPSSI). We then multiplied the cPPSSI by the fraction of the synapse number and obtained the sum to determine the PPSSI of each neuron. Fig. 4b shows the result of applying PPSSI to 139,255 whole-brain neurons of FlyWire. The result showed a histogram resembling a normal distribution. When we created unsegregated ranking (details in Methods) by considering the number of synapses, APL and CT1 cells occupied the top 1–4 positions, indicating that we efficiently extracted unsegregated neurons (Fig. 4a, Ext.Data.Fig.4-3a). APL was also at the top for FlyEM (Ext.Data.Fig.4-1a). Similarly, we established segregated ranking and successfully extracted neurons with a high degree of segregation (Fig. 4c, Ext.Data.Fig.4-3; Ext.Data.Fig.4-1c and Ext.Data.Fig.4-4 for FlyEM).

Next, synapses with a cPPSSI between 0 and 0.1 were extracted, and the SC matrices (unsegregated synapses) of neurons and synapses were created. Synapses were then randomly sampled to generate 99 null SC matrices (random synapses), centered around the total number of connections (2,373,100) in the SC matrix (unsegregated synapses), forming a normal distribution (Fig. 4e, p=0.832, details in Methods). The FC-SC correlations of the SC matrices (unsegregated synapses) of neurons and synapses were significantly higher than those of the randomly extracted samples (Fig. 4e, p=0, 6.5e-43; Ext.Data.Fig.4-1d for FlyEM). Therefore, unsegregated synapses might strongly contribute to FC. A similar analysis was performed on synapses with a cPPSSI of 0.9–1, which surprisingly showed a significantly lower FC-SC correlation (Fig. 4f, p=9.2e-14, 0; Ext.Data.Fig.4-1e for FlyEM). Therefore, segregated synapses may not be able to contribute to strongly to the FC, and these findings are further explored in the Discussion section.

Among unsegregated synapses, reciprocal synapses have been well studied [31, 32, 33, 34, 35] and their function is considered to be clear (Fig. 4g, Ext.Data.Fig.4-1f). The shortest distance of such reciprocal synapses was extracted from whole-brain neurons, shown in Fig. 4h (Ext.Data.Fig.4-1g for FlyEM). They are particularly abundant within 2 μm (Ext.Data.Fig.4-2a,c for CT1 and APL cells), and acetylcholine and GABA constitute the majority (Fig. 4h). The comparison of the SC matrix based on reciprocal synapses (<2 μm) with the null SC matrices showed that the FC-SC correlation was significantly higher (Fig. 4I, p=0, 2.7e-32; Ext.Data.Fig.4-1h for FlyEM). Therefore, unsegregated synapses and reciprocal synapses (<2 μm) strongly contributed to FC. Furthermore, since the FC was the average of eight flies, such synapses are likely functionally common among individuals.

Region suppression analysis during fly walking

The whole-brain calcium imaging dataset from Brezovec et al. [14] provides fly walking data. Since fMRI pre-processing methods can be applied to calcium imaging data, we investigated whether voxel-level analysis using a general linear model (GLM) [50] could be applied to the fly walking task (Fig. 5a, details in Methods). Fig. 5b shows the GLM analysis result. Similar to the results of Brezovec et al., our findings revealed that LAL, FB, and IPS neuropils showed strong activity; the GNG neuropil, which is highly connected to leg neuropils in the ventral nerve code [51], also exhibited strong activity. Although Brezovec et al. detected voxels that are strongly correlated with velocity, the GLM extracted voxels associated with walking behavior. Conversely, we found inactivity or strong suppression in the Wedge and AVLP neuropils. We searched for a GABA neuron that would fit with this phenomenon and managed to find one that extended its dendrites widely from the Wedge to AVLP neuropils (Fig. 5e, h). The synapse point cloud could also fit in this region (Fig. 5c). We called this neuron the Wedge-AVLP GABA neuron (WAGN). The Wedge neuropil receives mechanosensory (wind, sound) input and connects to WPNb neurons (Ext.Data.Fig.5-1a,b), which then connect to ER1 ring neurons that act as the fly’s compass [52, 53]. Interestingly, the left WAGN was strongly interconnected with WPNb tier 2/3 [54] and received input from 22 ascending neurons (ANs; Fig. 5d). Therefore, it may be a pathway that provides walking behavior feedback to the compass; however, wind caused by walking was absent in the experimental setup (the fly was fixed and walked on a treadmill), and may relate to the strong regional suppression that was observed. As such, further experimentation is needed to pursue this topic.

Fig. 5

The left WAGN resembles a hub neuron; however, like CT1 and APL cells, it has highly unsegregated synapses (PPSSI=0.133). Synapses on the medial side were highly segregated, but the lateral side was well unsegregated (Fig. 5h). It received input from ANs (212 synapses) mainly on the ventral side, and outputs to WPNb (65 synapses), widely from the medial to the lateral side (Fig. 5e). A histogram of the shortest straight-line distances between pre-synapses to WPNb and post-synapses from ANs is shown in Fig. 5f, and the closest distance was 852.3 nm (Fig. 5g). Many acetylcholine inputs (disynaptic inhibition [25]) were closer than this value (Fig. 5i), and many GABA inputs from ANs (Fig. 5f) further suppress such disynaptic inhibition. AVLP ventral suppression (Fig. 5b white arrows) may be the suppression from these ANs. Thus, a highly delicate and localized control is possibly exercised from WAGN to WPNb tier 2/3.

Discussion

Although nuisance factor removal methods such as global mean (GM) and aCompCor [42] are optimal for fMRI [10], calcium imaging showed different results. GM is the average of all voxels, and the regression of this signal is useful in fMRI because noise from the equipment and coils affects the entire voxel image. Conversely, in two-photon microscopy, noise does not affect all voxels because of the excitation of specific molecules by laser absorption, and GM does not show a positive effect. aCompCor extracts the component time-series from the voxel time-series of white matter and cerebrospinal fluid (CSF) via PCA and then performs a regression. In flies, the CSF had no ROI mask, but fibers had ROIs; therefore, fibers were used instead of the white matter. However, many synapses may exist around these fibers, and aCompCor was not as effective as in humans. Conversely, polynomial detrending [41] was highly effective (Fig. 1d-f), likely because of linear thermal noise and other factors caused by the continuous excitation of molecules (for 30 min). tCompCor [42] is the component time-series extracted by PCA from voxels with the top 1000 standard deviations among all voxels. It potentially captures minute fluctuations caused by fly movements and effectively removes them.

The SC matrix from a cPPSSI of 0.9–1 synapses resulted in a significantly lower FC-SC correlation than the SC matrix from randomly selected synapses (Fig. 4f for FlyWire, Ext.Data.Fig.4-1e for FlyEM). This result was surprising, but we propose several possible reasons. Neurons with highly segregated synapses include ascending neurons (ANs) and descending neurons (DNs), (Ext.Data.Fig.4-3b). They also have a small number of unsegregated synapses (i.e. Sep rank9: PPSSI=0.959, Sep rank11: PPSSI=0.964). They are thought to be specialized for input or output in the CNS regions and may show large differences between SC and FC. Another reason is that these neurons may have widespread logical OR inputs and outputs. In Fig. 4c, an action potential at one point in the input synapse (blue) is likely transmitted to all red synapses. Such an OR circuit-like disproportionate input–output possibly causes a mismatch with the FC, because the functional activity in the output region originates from activity at a single location. These neurons are likely those whose FC are difficult to capture. Conversely, neurons with highly unsegregated synapses may capture the inputs of neighboring synapses, such as forming a logical AND circuit, correlating well with the output regions.

The FC-SC correlation was highly dependent on ROI count in both flies and humans (Fig. 2d). Through optimal nuisance factor removal and smoothing, we achieved r=0.87 at 20 ROIs. Furthermore, by applying Spearman correlation instead of Pearson, we obtained r=0.928. Thus, for a reasonably small ROI count the correlation was very high; however, for 10,000 ROIs, the correlation decreased to r=0.57. This phenomenon could be attributed to the presence of highly segregated synapses. Such neurons are widespread in the CNS (Fig. 4b, Ext.Data.Fig.4-2f) and are thought to provide logical OR circuits. When ROI volume was large (when the ROI count was small), a single ROI could cover the distributed input synapses. However, when a ROI was divided, input synapses were also divided across many ROIs, and the mismatch between SC and FC would increase. Other possibilities include the presence of gap junctions and FC due to neuropeptides [55], but they are outside of the scope of the present study and their relationship with ROI count is unclear.

In this study, we applied fMRI techniques directly to calcium imaging in flies and found many similarities between humans and flies (Fig. 2d). The calcium signal represents pre-synaptic population dynamics and likely includes the localized functional activity of unsegregated synapses [25, 31, 32, 33, 34], such as non-spiking [21, 22, 23, 24, 25, 26] and sub-threshold neuronal activity [18]. For fMRI, the signal captures localized functional activity as blood-oxygenation-level-dependent signal via neuro vascular coupling [40]. These two signals can be pre-processed (Fig. 1, Fig. 2) and analyzed (Fig. 5a) in surprisingly similar ways. This is unlikely a coincidence, and it suggests that similar design concepts underlie neural circuits in flies and mammals. Using D. melanogaster as a model animal, we were able to elucidate detailed local functional activities around unsegregated synapses and compare these results to the brain activities of mammals, including humans.

Materials and methods

Preprocessing of D. melanogaster calcium imaging data

Whole-brain calcium imaging data of D. melanogaster were acquired by Brezovec et al. [14] and downloaded from DANDI (https://dandiarchive.org/dandiset/000727/0.240106.0043). 4D NIfTI image data (256×128×49 voxels, 3384 frames) were extracted from a NWB file by an in-house MATLAB script. The FDA template, made from in-vivo calcium imaging, was resized (256×128×49 voxels, 2.45×2.28×3.72μm for a voxel) and used as a template because the original thresholded FDA template [56] was extremely large (1652×768×479 voxels), and the calcium imaging file was large (more than 40 GB); therefore, a smaller template with the imaging data was preferably used. Preprocessing and image registration were performed using Statistical Parametric Mapping (SPM12) [57] and ANTs [58] (Ext.Data.Fig.1-1a). Motion and slice timing correction were performed using SPM12, and the averaged NIfTI image was registered by ANTs to the resized FDA template. Lastly, 4D NIfTI images were transformed using the transform information. The data contained n=9 flies, but 8 flies were used for the ROI-based analysis because of missing time-series in some ROIs in one fly. Nine flies were used in the GLM analysis.

Combinations of the following nuisance factor removal methods were investigated: global mean (average signal across all voxels), global signal (average signal across all brain voxels), mean white matter (average signal across fiber voxels), 6HMP (head motion parameters), 24HMP, aCompCor, tCompCor [42], and polynomial detrending (Poly) [41]. These methods were implemented by an in-house MATLAB script [59]. A full width at half maximum (FWHM) from 1 voxel (2.28 μm) to 30 voxels (68.4 μm), at a 1 voxel step, was investigated to determine the optimal spatial smoothing size for calcium imaging data. Temporal high-pass filters were also examined from 0.1 Hz to 0.001 Hz.

Transformation of EM connectome data into the resized FDA template

In the FlyWire case, connectome data, such as neurons and synapses, were downloaded from FlyWire Codex (https://codex.flywire.ai/) and Zenodo (https://zenodo.org/records/10676866) [13, 60, 45]. Detailed synapse data were saved in an Apache feather format, which was then converted to a CSV file. Synapse points were transformed from the FlyWire space to a JRC2018 female template [61] by the Python navis-flybrains package [61]. Since FlyWire coordinates are left and right reversed [13], they were flipped on the JRC2018 female template, and these points were transformed to the resized FDA template by ANTs. The use of these two templates facilitated precise data alignment across different modalities.

In the FlyEM case, the latest connectome data were downloaded from Janelia’s DVID website (https://dvid.io/blog/release-v1.2/). Like those in the FlyWire case, synapse points were transformed from the FlyEM space to a JRC2018 female template by the Python navis-flybrains package. These points were transformed to a resized FDA template by ANTs.

Generation of regions of interest for the hemibrain

The hemibrain neuropil atlas (114 ROIs, including primary and sub-regions, aligned with the FlyEM space) was downloaded from Virtual Fly Brain (https://www.virtualflybrain.org/). ROI files were transformed from the FlyEM space to a JRC2018 female template by Java template-building scripts (https://github.com/saalfeldlab/template-building) [61]. They were transformed to a resized FDA template by ANTs. In Fig. 3, 63 primary ROIs mentioned above were used. The 52 ROIs in Fig. 1 were selected from the primary ROIs, and approximately 50 ROIs (those used by Turner et al. [9]) were selected. ROIs were segmented by SCKm (Fig. 1 and Fig. 2) via the k-means clustering of the SC matrix of 146,604 voxels in the hemibrain. They were also segmented by DistKm (Fig. 1 and Fig. 2) via the k-means clustering of the distance of 146,604 voxels in the hemibrain.

The SC matrix was calculated according to synapse locations and ROIs. Since synapse data formats differ between FlyEM and FlyWire, they were standardized by using post-synapses within ROIs. The input and output neurons at each ROI were extracted from the paired pre- and post-synapse data. Then the input and output neurons and their synapses that were common between ROI pairs were counted to create SC matrices for neurons and synapses. The FC matrix was calculated using the pre-processed voxel time-series and ROIs. The intensity of the voxels in the ROI was averaged to obtain the average intensity time-series of the ROI. Then, Pearson correlation was calculated between ROI pairs to generate the FC matrix. The correlation coefficients were z-transformed, calculated for eight flies, and then averaged to obtain the final FC matrix.

FC-SC detection and correlation

FC-SC correlation was calculated by taking the Pearson correlation between the logarithm of the SC matrix and the FC matrix, as done in other studies [6, 7, 10]. In the SC matrix, elements with zero connections become -Inf when logarithmically converted, so we substituted zero for them. Also, the diagonal elements of the FC matrix become Inf when z-transformed, so we replaced them with the maximum value of the matrix. For one FC matrix, we calculated its correlation with both the neuron SC matrix and the synapse SC matrix. FC-SC detection was calculated by ROC (Receiver Operating Characteristic) curve analysis. This gives the detection accuracy of the FC matrix when the SC matrix is used as ground truth. Thresholds were taken from 0% to 99% by 1% steps of all elements of the SC matrix, and 100 AUCs (Area Under the Curve) were calculated. The average of these AUCs is called the FC-SC detection. FC-SC correlation indicates the similarity of the two matrices, while FC-SC detection indicates the detection accuracy. Although the digit number of connections differs between neurons and synapses, FC-SC detection can absorb such differences. The FC-SC detection & correlation score was calculated as follows:

The FC-SC detection & correlation score is in the range of [0 2], where the larger the score, the higher the similarity and detection accuracy.

PPSSI

The PPSSI (Fig. 4d) was used in DBSCAN [49] with a radius of 3 μm to generate pre- and post-synaptic clusters. The radius was empirically defined by several criteria. Firstly, CT1 and APL cells have the shortest distance of reciprocal synapses, within 2 μm (Ext.Data.Fig.4-2a,c). In zebrafish, reciprocal synapses were defined within 2.5 μm [35]. Schneider-Mizell et al. [19] defined a twig as a branch within 3 μm from the backbone of the cytoskeleton, and 80% of synaptic inputs in motor neurons are in the twig. In addition, 97% of pre-synaptic sites are located at less than 3 μm from the mitochondria. Therefore, 3 μm was deemed appropriate for the synapse cluster radius. Once the synapse clusters were determined by DBSCAN, the degree of synaptic segregation for each cluster was calculated using the following formula:

where pre_i and post_i are the pre- and post-synapse counts in cluster i, respectively. The cPPSSI of each cluster (each synapse) is in the range of [0 1]. The PPSSI of each neuron was calculated as follows:

where N is the cluster number, and W is the total synapse count for a neuron.

The unsegregated ranking was calculated based on the PPSSI and total synapse count of neuron k:

where PPSSI_k is the PPSSI of neuron k and W_k is the total synapse count of neuron k. This allows us to extract neurons with many inputs and outputs and highly unsegregated synapses. The segregated ranking was also calculated in the same way, using the following score:

A similar index to our PPSSI, namely, the segregation index, has been defined in the literature [19], but its use poses several problems. For neurons such as ANs and DNs, that have only input or output synapses, the segregation index results in calculations of 0 × ∞ or division by 0; consequently, calculation becomes impossible. Despite the [0 1] range of indices, the histogram is heavily biased toward 0 because of the use of the logarithm, and the mean is much closer to 0 than 0.5 (Ext.Data.Fig.4-1i, j). Therefore, in the present study, we developed the more robust PPSSI because it is less biased and its mean is close to 0.5 (Fig. 4b, Ext.Data.Fig.4-1b).

GLM Analysis for the fly walking task

GLM analysis (Fig. 5a) was performed to investigate the whole-brain functional activity during the fly walking task. Movement velocity data were extracted from an NWB file by an in-house MATLAB script. Walking was defined as 1σ (34%) or more of the movement velocity and divided into walking and other. Less than 10% of movement velocity was zero cut. The canonical calcium response function (CRF) was created by the gamma probability density function (a=1.7, b=0.25) in MATLAB based on the GCaMP6f response [62]. The walking-task time-series was transformed into a calcium response time-series by convolution with the CRF. GLM design matrices were created using the calcium response time-series and nuisance factors (polynomial detrending and tCompCor). In whole-brain voxels, smoothing was applied with a kernel radius of 8 voxels (18.24 μm). Then, a Tukey taper (taper size = 8) was used for GLM pre-whitening [63]. A mixed-effects model [43] was used for group analysis, and the t-value of each voxel was calculated via the second-level analysis of OLS regression with a Tukey taper. These analyses were implemented using in-house MATLAB scripts [64].

Statistical Analysis

A Mann–Whitney U test was used to examine whether the combination of spatial smoothing and nuisance factor removal was effective. Statistical significance was set at p<0.05, and Bonferroni correction was applied to correct the familywise error (FWE) rate. A permutation test was performed to analyze whether specific synapses (segregated, unsegregated, or reciprocal synapses) affect SC-FC correlation. The SC matrix (specific synapses) in the 63 ROIs in the hemibrain was generated, and its SC-FC correlation was calculated. Then, 99 null SC matrices (random synapses) were generated so that they would be normally distributed around the total number of connections in the SC matrix (specific synapses). Since the SC-FC correlations of the null SC matrices (random synapses) also roughly followed a normal distribution, the T-value of the SC-FC correlation of the SC matrix (specific synapses) was calculated using the cumulative distribution function of the normal distribution. For GLM analysis, a mixed-effects model was used for group analysis.

Data availability

Whole-brain calcium imaging data and walking behavior data in Drosophila Melanogaster can be downloaded from DANDI web site (https://dandiarchive.org/dandiset/000727/0.240106.0043). FlyWire connectome data can be downloaded from flywire codex (https://codex.flywire.ai/) and Zenodo web site (https://zenodo.org/records/10676866). FlyEM connectome data can be downloaded from Janeria’s DVID web site (https://dvid.io/blog/release-v1.2/).

Extended data figures

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Acknowledgements

The authors wish to thank Dr. Clandinin for providing valuable calcium imaging data and answering our question.

This research was supported by the program for Brain Mapping by Integrated Neurotechnologies for Disease Studies (Brain/MINDS 2.0) from the Japan Agency for Medical Research and Development, AMED. Grant number: JP24wm0625408.

Additional information

Code Availability

Software and code used in the current study is open source and publicly available from https://github.com/takuto-okuno-riken/flywalk

Authors’ Contributions

T.O. conceived of the presented idea. T.O. developed the theory, performed the computations. T.O. downloaded and processed fly data. T.O., A.W., H.O. and J.H. discussed the results and contributed to the final manuscript.

Ethics declarations

All experimental procedures were approved by the Experimental Animal Committee of RIKEN or by the Experimental Animal Committee of the National Center of Neurology and Psychiatry. The marmosets were handled by the “Guiding Principles of the Care and Use of Animals in the Field of Physiological Science” formulated by the Japanese Physiological Society.