Introduction

Sensory processing in the cortex is adjusted both by adaptation to the external environment and changes in the internal physiology of the animal associated with behavioural states such as attention, arousal and satiety^1–5. The mechanisms by which external and internal variables interact within the cortical circuitry are not understood. Here we investigate this question by analyzing how the change in state associated with locomotor activity impacts adaptation in primary visual cortex (V1) of mice⁶.

The dynamics of neurons in V1 reflect adaptation on multiple time-scales. In pyramidal cells (PCs), the initial excitatory response to an increase in contrast is followed by a fast (subsecond) decrease in gain reflecting depression in feedforward inputs from the LGN^7,8. This is immediately followed by a slower phase of adaptation that varies dramatically across the PC population: while some PCs depress in response to a high-contrast stimulus others simultaneously sensitize⁹. PCs within layer 2/3 are not, therefore, a homogenous population: to understand gain control we must take into account variations in local inhibitory circuits in which they are embedded.

The onset of locomotion signals changes in internal state associated with attention or arousal, acting in less than a second to amplify visual responses in PCs^3,10–12. A major driver of this increase in gain are cholinergic fibers arriving from the basal forebrain^2,13–15. Some of these fibers make direct synaptic connections that excite interneurons expressing vasoactive intestinal peptide (VIP)¹⁶, leading to amplification of PC responses through a VIP->SST->PC disinhibitory pathway. The majority of the cholinergic input, however, innervates V1 diffusely to modulate circuit function through extra-synaptic (muscarinic) receptors^2,13,16. In vitro experiments have shown that M1 and M3 receptors on soma and dendrites of PCs can increase excitability while M2 receptors on axonal compartments reduce synaptic release probability^16–18. Accounting for state-dependent changes in cortical processing therefore requires an integrated understanding of changes in both electrical activity and the strength of synaptic connections¹². The difficulty is that modulations of synaptic strengths are very hard to quantify in awake and behaving animals: recording from connected neuron pairs remains technically challenging and is limited to anaesthetized animals in which inhibitory microcircuits are severely compromised^19–21. Current understanding of synaptic modulation in cortical circuits is derived from ex vivo studies or inferred from indirect in vivo observations and modelling^12,22,23.

To understand how locomotion and adaptation interact in V1 of mice we used calcium imaging to record visual responses in PCs and the three major classes of interneuron (VIP, SST and PV) together with optogenetics to identify key interactions and a data-driven circuit model to estimate changes in synaptic weights. The model demonstrates that long-range inputs to VIPs that increase visual gain in the locomoting state also govern the time-course of adaptation over the behavioural time-scales of seconds. These inputs do not act uniformly across the PC population but preferentially increase the gain of neurons that sensitize to a high-contrast stimulus. Contrary to the prevailing model of gain control through the VIP->SST->PC pathway we find that visual responses in SSTs are not inhibited by locomotion but instead weakly enhanced. The model reconciles these observations through a neuromodulatory decrease in synaptic outputs across PCs and interneurons. Locomotion preferentially increases the gain of PCs that undergo the sensitizing form of adaptation because these receive a stronger SST connection than depressor PCs rendering them more sensitive to the weakening of SST synapses. These results provide an integrated view of the circuit mechanisms that adjust visual processing in V1 when an animal switches between resting and active states.

Results

Differential effects of locomotion on the fast and slow phases of adaptation

To understand how changes in brain state interact with adaptation in V1 we used two-photon calcium imaging to measure the activity of excitatory and inhibitory neurons in layer 2/3 during periods of rest and locomotion (Fig 1A, see Methods). The GCaMP6f signal in PCs responding to a high contrast stimulus (20° drifting grating at 1 Hz, 10 s duration) are shown in Fig. 1B. Locomotion increased the response averaged across all PCs by a factor of 2.2 ± 0.9. The dynamics of these responses varied widely between individual neurons; while some PCs responded with high initial gain and then depressed, others responded with low initial gain and then sensitized. This heterogeneity is illustrated by the raster plot in Fig. 1B which shows 522 neurons ordered by the time of peak activity: depression (early peak) and sensitization (late peak) were similarly represented in the two behavioural states (Fig 1B, top).

Figure 1.

The increase in gain during locomotion was manifested in two ways; a 6-fold increase in the number of PCs generating a significant response (Supplementary Table 1) and an increase in the average amplitude of these responses measured as the integral during the 10 s stimulus (Fig. 1B). To investigate how these changes in gain affected PCs undergoing different forms of adaptation we split the population into three groups of equal size based on the distribution of a metric called the adaptive index (AI; Methods). These groups were sensitizing (AI less than zero), intermediate and depressing (AI more than zero; Fig. 1C). The AI, when computed separately for rest and locomotion and averaged across the whole PC population, was similar during locomotion (-0.006 ± 0.3; mean ± sem) and rest (0.001 ± 0.9; Fig. 1C) but the amplitude of the visual response increased by a factor of 4.5 ± 0.7 in sensitizing PCs, 2.5 ± 0.3 in intermediate group and 2.2 ± 0.2 in depressors. Locomotion therefore increased the gain of sensitizing PCs about twice as strongly as depressors (Fig. 1D-G).

Locomotion was associated with a second notable change in the dynamics of the PC population – a narrower distribution of adaptive effects (Fig. 1C). Cells that depressed at rest showed a shift towards sensitization, while cells that sensitized showed a shift towards depression (Supplementary Figure 1). Although this convergence may partly reflect differences in variability between states, the more uniform dynamics of adaptation parallels the increased temporal correlation observed across the PC population in behavioural states characterised by locomotion²⁴.

The immediate spiking response to a high-contrast stimulus is dominated by depressing adaptation^7,8 but the raw signal from calcium reporter proteins such as GCaMP does not easily distinguish this phase because of the gradual accumulation of calcium in the neuron. Several algorithms for estimating spike rates from calcium signals are now in use^25–27 and we applied MLspike because it is based on a biological model of GCaMP activation and calcium dynamics that has been shown to perform better than others²⁸ (Fig. 2-A-C). The first component of the spiking response was followed by fast depressing adaptation, as expected from electrophysiology^7,8,29 (red arrows In Fig. 2A-B). During locomotion, the initial peak amplitude was not significantly different in PCs that depressed (1.15 ± 0.08 Hz) or sensitized (1.11 ± 0.08 Hz), indicating similar strength of the feedforward input across the PC population (Fig. 2C).

Figure 2.

Comparing activity at rest and while running revealed a powerful effect on both first and second phases of the response but this varied across the PC population. In the sensitizing tertile the initial peak driven by feedforward input underwent a relative increase of 2.1 ± 0.7 and the response integrated over the whole stimulus period a relative increase of 4.7 ± 1 (Fig. 2D). But in the depressing tertile, locomotion did not significantly change the initial fast response while the integrated response only increased by a factor of 1.4 ± 0.3 (Fig. 2E). Changes in internal state associated with locomotion do not, therefore, act uniformly across the PC population but preferentially increase the gain of neurons that undergo the sensitizing form of adaptation (Fig. 2F).

A data-driven model of contrast adaptation and the effects of locomotion

To understand how an active behavioural state differentially alters gain across PCs we constructed a population model of signal flow based on neuronal input-output functions expressed as firing rates^30–32 (see Methods). The model took into account three aspects of circuits in layer 2/3: i) the measured response dynamics of PCs and the three major types of interneurons (Fig. 2G-L); ii) the dynamics of signals that arrive from other brain regions (Fig. 3A), and iii) the known connectivity patterns of neurons within this layer (Fig. 3B). Code and example data sets are available at https://github.com/lagnadoLab/CortexModel.

Figure 3.

i) The dynamics of neurons in layer 2/3

A key determinant of the magnitude and direction of slow adaptive changes in a PC is the local inhibitory microcircuit in which it is embedded: PCs in which direct SST inputs dominate over PV inputs tend to sensitize while those in which PV inputs dominate depress⁹. We therefore also experimentally measured the effects of locomotion on gain and adaptation in the three major interneuron types to use their response dynamics in the model (Fig. 2G-L). VIPs underwent the strongest modulation: the density of responsive neurons changed by a factor of 3 (Supplementary Table 1), and the integrated amplitude of these responses by a factor of 5.1 ± 1.0 (Fig. 2G). Simultaneously, locomotion caused the ratio of sensitizing (AI <0) to depressing (AI > 0) VIPs to increase from 1.3 at rest to 9 (Fig. 2J). PVs were more weakly modulated, with integrated responses changing by a factor of 1.7 ± 0.2 while the ratio of sensitizers to depressors also increased from 1.8 to 6.1 (Fig. 2H and K). In contrast, locomotion did not significantly alter the number of responsive SST neurons or the amplitude of their responses (gain factor of 1.2 ± 0.2; p = 0.28; Fig. 2I and L). This observation was surprising given that VIPs powerfully inhibit SSTs and locomotion activates a VIP->SST->PC disinhibitory pathway often highlighted as an important contributor to gain control^11,33,34. However, the influence of this pathway is known to vary, consistent with reports that SST response to locomotion depend strongly on the visual stimulus^3,12. A major aim of the model, therefore, was to take a more integrated view of gain control that considered multiple interacting pathways within layer 2/3.

The distribution of response dynamics in interneurons was more homogeneous than in PCs. The probabilities of a PC being sensitizing (AI <0, P_sens) or depressing (AI > 0, P_dep) were both ∼0.5 (Fig. 1C), but during locomotion sensitization dominated in VIPs and PVs (P_sens = 0.9) while depression dominated in SSTs (P_dep = 0.8; Fig. 2J-L). These more consistent, cell-type-specific dynamics allowed us to represent each interneuron class by its characteristic average response (Fig. 2G-I), which we used as empirical input to a population mean-field model. Mean-field models have been widely used to describe the average behaviour of large populations of interacting neurons without simulating each neuron individually^30,35,36. The network was represented by a system of four first order ordinary differential equations³⁰:

where 𝑖, 𝑗 are iterating through the four neuronal populations (PC, VIP, PV and SST), 𝑗 is a presynaptic population and 𝑖 postsynaptic, 𝑟 is a firing rate and τ_i is the time-constant for that population. 𝑓(𝑥) is a neuronal input-output function and here we used a rectified power law³². The terms 𝑤_𝑖𝑛 𝐼𝑛 express the connection weights and amplitude of external inputs, and 𝑏_𝑖 the baseline activity of postsynaptic cell i. The connection weight between populations j and i, 𝑤_j𝑖, is simply the product of the total number of synaptic connections, 𝐶_j𝑖, and the average strength of an individual synapse between neuron type j and i, 𝑠_j𝑖:

To compare the model to experiments, it was important to consider that not all presynaptic neurons are activated by the stimulus and, even if they are, they do not all activate the postsynaptic population because the connection probability (𝑝_j𝑖) is usually less than one. If, for instance, electrodes are placed on a PC and a nearby PV interneuron the probability of them being connected is only ∼0.37 at distances less than ∼150 μm while the average probability of an SST interneuron is even lower at ∼0.27^37–39. These factors can be taken into account by expanding relation 2 as

where 𝑁_j is the number of responsive presynaptic cells, defined as described in Methods. Below we infer changes in individual synaptic weights (𝑠_j𝑖) associated with a transition into the active state by comparing experimentally measured changes in 𝑁_j (Supplementary Table 1) to changes in connection weights (𝑤_j𝑖) estimated by fitting the model.

ii) The dynamics of signals entering layer 2/3

Excitatory signals entering layer 2/3 are of three main types^40,41: feedforward (FF) drive originating from the lateral geniculate nucleus (LGN) and transmitted via layer 4, feedback from higher order cortices (FB)^42,43 and modulated inputs (SS), such as those gated by cholinergic signals from the basal nuclei¹¹. Electrophysiology has shown that FF inputs to layer 2/3 are dominated by fast depressing adaptation occurring within a few hundred milliseconds and the fast phase of adaptation in PCs fell within this range^7,8 (Fig. 2A-B). Calcium imaging in vivo has shown that drifting gratings lasting seconds can also generate a slower sensitizing component in FF inputs that enter layer 2/3 from layer 4^22,44. The FF input was therefore modelled with both these components, as shown in Fig. 3A.

The second type of input to V1 is feedback from higher visual areas^45–47 and SST interneurons are one of their targets^46,48,49. We have limited understanding of the dynamics of the FB signal over the time-scale of our stimulus, so, for simplicity, it was modelled as a step beginning at a delay of 380 ms after stimulus onset (Fig. 3A).

The third type of inputs to layer 2/3 are visually-activated signals that are strongly sensitizing in the locomoting state and drive slow sensitization. The dynamics of this signal were inferred from the visual response of VIPs measured experimentally during locomotion (Fig. 2G). We used these measurements because optogenetic experiments confirmed that activity in VIPs drove adaptation in downstream SST neurons, to which they are known to connect strongly^11,33,34 (Fig. 3C-D). To carry out this test we had to express the inhibitory photoprotein ArchT in VIPs and GCaMP6f in SSTs. Expressing different proteins in two interneuron populations was achieved by crossing a recombinant mouse line expressing Cre (VIP-Cre) with a Flippase expressing line (SST-Flp), then injecting two viral vectors that were Cre and Flippase dependent respectively (see Methods). Suppressing activity in VIPs almost completely abolished the slow component of adaptation in SSTs (Fig. 3D). Visually-driven inputs to VIPs include local recurrent excitation³³ and inputs from higher visual areas⁵³, and the combined dynamics of the later were modelled on the VIP response (Fig. 3E). This slow sensitizing signal appears quite distinct from inputs from the basal forebrain which provide a binary locomotion state signal but have been found not to respond to visual stimuli⁵⁴. Notably, the dynamics of sensitization in VIPs were similar to sensitization in PCs suggesting that this input dominated slow adaptation throughout the network (Supplementary Figure 2).

iii) Connectivity within layer 2/3

Cortical connections have been probed using a number of approaches, including viral tracing⁵⁵, electrophysiology^33,37,39 and optogenetics³⁸, and we only considered connections that have been consistently observed in layer 2/3 and are strong enough to significantly influence the circuit (Fig. 3B). Not all neuron types connect; SST interneurons, for example, do not interact with each other while the very small number of connections from VIPs to PCs were neglected because these are not strong enough to significantly influence the circuit^33,38.

Using optogenetic manipulations to constrain model solutions and test its predictive ability

The model was fit to average populational responses of PCs and interneurons by adjusting the weights 𝑤_j𝑖of external and internal connections in layer 2/3 (see Methods). Given the large parameter space spanned by the model, many solutions were of similar quality. Rather than identifying a single optimal solution, our fitting procedure revealed a region of parameter space that yielded good fits.

First, we generated 100,000 sets of evenly distributed initial parameters using Sobol sampling^22,56,57. Of these, only 37 produced “good” solutions with chi-square < 10 in the locomotion condition, defining the approximate boundaries of the viable region. Next, this parameter subspace was explored further by local optimization using 20,000 Sobol initial conditions for each synaptic weight. This produced ∼9000 good solutions in the locomotion condition with similar average and standard deviation to the initial 37. We then applied a third stage involving a series of experiments in which interneuron activity was altered optogenetically, which constrained the number of good solutions (to ∼900) and the viable region of parameter space (Fig. 4). This third stage could not be usefully applied to data at rest because there were not enough recording episodes across all four optogenetic conditions and responses were smaller and more variable than during locomotion²⁴. We therefore limited the number of solutions by using a lower chi-square value of 3. The average parameter values after reducing the number of good solutions through all the steps are used to analyze the predictions of the model in Figs. 5 and 6.

Fig. 4.

Figure 5.

Figure 6.

The first optogenetic manipulation was to over-activate SSTs by expressing the excitatory photoprotein ChrimsonR using a Cre-dependent viral vector. Simultaneously, responses were recorded in PCs using GCaMP6f under the CaMKII promoter. The intensity of the photo-activating light was adjusted to increase the activity of SST interneurons by an average factor of ∼2 in locomoting animals, as estimated in a separate series of experiments⁹. Fig. 4A (top) shows how the average PC response in the locomotion state was reduced compared to interleaved control trials.

Scaling the average SST activity within the model by a factor of 1.7 while leaving all other parameters constant provided an accurate description of the change in average PC activity in only 74% of the original ∼9000 solutions (Fig. 4C). In other words, although a broad region of parameter space could reproduce the control data, introducing this optogenetic manipulation eliminated roughly one-quarter of the solutions, thereby narrowing the admissible parameter space.

After this first filtering step, we sequentially reduced the number of good solutions by constraining to results of SST silencing, PV activation and PV silencing, in this order. We found that while SST silencing and PV activation reduced the number of solutions to 25% and 11% of the original 9000, adding the last filter, PV silencing, had little further effect (Fig. 4C). Furthermore, connection weights remained identical when applying the first three optogenetic constraints compared to applying the fourth (Fig. 4D). PV silencing therefore served as a validation step: it confirmed the region of parameter space defined by the three previous filters instead of further refining it.

Locomotion increases PC gain but weakens their local synaptic output

Behavioural modulation of connection weights within layer 2/3 have been very hard to quantify experimentally, making it unclear how far changes in internal state adjust cortical processing through changes in neuronal activity as opposed to modulation of synaptic weights^14,16. We used the model constrained by the four optogenetic manipulations to infer changes in synaptic weights. First, we investigated the action of locomotion averaged across the whole PC population (Fig. 5) and then explored why the subset of PCs that sensitize is modulated more strongly than those that depress (Fig. 6).

All the model solutions that allowed a good fit to the average visual responses in the four cell types closely followed both the fast and slow phases of adaptation at rest and during locomotion, as exemplified by the average solution (Fig. 5A-D, Supplementary Figure 3). Unsupervised clustering analysis identified a single cluster of solutions for locomotion and another for rest, indicating that these parameter sets form a continuum rather than falling into distinct categories. Moreover, examination of the distribution of each parameter revealed that all were unimodal, with no evidence for multiple peaks or clusters (data not shown). This pattern is consistent with gradual transitions within a single family of network configurations and supports the use of the mean as a representative summary. The average connection weights (Equation 2, w_ij) at rest are shown in the heatmaps in Fig. 5E and the relative changes with locomotion are summarized in Fig. 5F, calculated as:

Where free parameters predicted by the model could be compared with published experiment, there were several points of agreement. For instance, the relative strength of direct local connections to PCs were quantitatively similar to those measured using electrophysiology^37,38. There were, however, differences with other attempts to infer connection weights. Using our nomenclature, a recent modelling study²³ inferred a weight order in V1 at rest of 𝑤_{𝑃𝐶_𝑃𝑉} < 𝑤_{𝑃𝐶_𝑃𝐶} < 𝑤_{𝑃𝑉_𝑃𝑉} < 𝑤_{𝑃𝑉_𝑃𝐶}, while our results infer 𝑤_{𝑃𝐶_𝑃𝐶} < 𝑤_{𝑃𝐶_𝑃𝑉} < 𝑤_{𝑃𝑉_𝑃𝑉} < 𝑤_{𝑃𝑉_𝑃𝐶} (Fig. 5E). This difference may reflect our models incorporation of long-range modulatory inputs, which also allowed it to predict other experimental observations, including a locomotion-dependent amplification of the slowly modulated input to VIPs¹¹ and PCs⁵² and enhancement of feedforward drive to PCs^58,59. The incorporation of long-range modulatory inputs into the model were essential to accurately estimating connection weights within layer 2/3 because removing these inputs did not yield any solutions following the same quality criteria (Supplementary Fig. 4, see Methods).

The model indicates that locomotion increases the gain of PCs through a broad combination of circuit effects but of particular importance is a 25-50% reduction in the strength of inhibitory synapses made by SSTs and PVs (Equation 3, s_ij; Fig. 5G). Strikingly, the model also predicts that the total weight of connections from PCs to all types of interneurons is decreased by one to three quarters following locomotion (Fig. 5F). The total synaptic input that neuron i receives from j, I_ji, is proportional to the activity of j and can be expressed as:

Taking into account the 5-fold increase in the number of responsive PCs during locomotion (Supplementary Table 1) this leads to an estimated 90% decrease in synaptic strength across all PC targets (Fig. 5G). The model indicates that the large increase in PC and PV activity in the locomoting state is associate with a wide-spread decrease in the strength of their local synapses. This mechanism would allow large changes in the gain of signals leaving V1 for higher visual areas but without overexcitation of PC targets within the local circuit. The possible cholinergic mechanisms underlying these changes are considered in the Discussion.

In contrast to the rest of the local network, the average SST->VIP connection weight increased, by a factor of ∼8 (Fig. 5F). The number of responsive SSTs neurons increased by only 22% (Supplementary Table 1) indicating that the major cause was a strengthening of SST synapses (Fig. 5G). This differential pattern on excitatory synapses of PCs (suppression) and SSTs contacting VIPs (enhancement) could be consistent with known variations in the distribution of different muscarinic acetylcholine receptors (see Discussion).

Switching to the active behavioural state also increased the strength of specific inputs to layer 2/3, most obviously the FF connections to PVs and the SS and FB connections to VIPs (Fig. 5F). VIPs were the most striking target, explaining their dramatic increase in gain (Fig. 2G).

Another way to summarize the effects of locomotion is to consider the change in the total synaptic input (both excitatory and inhibitory) as PCs respond to the visual stimulus (Supplementary Table 2; equation 5; Fig. 5H). The last column in Fig. 5H shows this change, taking into account the input received from all connected populations averaged over the stimulus presentation. The net excitatory input driving the visual response is more pronounced in PCs and VIPs compared to PV and SST interneurons, consistent with the locomotion-associated changes in gain shown in Fig. 2. Notably, the model predicted almost zero net change in total input to SSTs, consistent with the negligible change in SST activity observed experimentally (Fig. 2I) but inconsistent with the simple VIP->SST->PC disinhibitory model. The overarching picture is that locomotion adjusts the gain of visual responses by modulating both excitatory signals entering layer 2/3 and the strength of local synaptic connections, expanding what has been observed in a previous study¹².

Differential modulation of SST inputs onto sensitizing and depressing PCs

Why do some PCs sensitize while others depress? Optogenetic manipulations of interneurons indicate that the direction and amplitude of slow adaptation reflect the balance between PV and SST inputs⁹. PVs sensitize (Fig. 2H), so PCs in which these inputs dominate tend to depress, while SSTs depress (Fig. 2I), causing PCs in which these inputs dominate to sensitize. To make these ideas quantitative, we fit the model separately to the sensitizing, intermediate and depressing PC subpopulations (Fig. 6A-C). At rest, all the external connections to PCs had similar weights irrespective of adaptive properties; the stand-out differences were in the local inhibitory connections (Fig. 6D). In qualitative agreement with the “balance model”, the direction of adaptation of a PC was dependent on the ratio of the PV and SST inputs, which increased progressively between the sensitizing, intermediate and depressing populations in both rest (0.9, 1.8 and 2.7, respectively; Fig. 6D) and locomotion (1.3, 1.7 and 2.7, respectively, Fig. 6E). We tested this prediction of the model by comparing the effect of optogenetic manipulations of SST and PV interneurons in the locomotion condition, confirming that sensitizers are more influenced by SSTs while depressors are dominated by PVs (Fig. 6F). This balance also influences the release from inhibition that different PCs undergo during locomotion, with sensitizers receiving less inhibition than depressors from SST interneurons, while the inverse pattern is observed for PV connections (Fig. 6G).

In principle, the differences in connectivity between sensitizing and depressing PCs could reflect synaptic strength. We found, however, only slight differences in the synaptic weight of all cell types connecting to PCs (Fig. 6H) and similar net total input between depressors and sensitizers (Fig. 6I). Again, the key difference was the SST:PV input ratio: sensitizers experienced a pronounced decrease in total SST inputs and increase in PV input (Fig. 6I). Notably, the increase in PC gain associated with locomotion did not correlate with changes in total inhibitory input (Fig. 6I), consistent with evidence that inhibition acts divisively rather than subtractively^60,61,62 (see Discussion). Overall, these results support the view that the enhanced gain observed in sensitizers is the result of their heightened exposure to a reduction in SST inhibition during locomotion.

Discussion

Adaptation is a fundamental aspect of sensory processing across cortical areas but it has not been clear how it is adjusted by changes in behavioural state that modulate these circuits. Here we have demonstrated that an active state acts on V1 to preferentially amplify responses in PCs that exhibit sensitizing adaptation over behavioural time-scales, with minimal effects on depressing PCs (Figs. 1 and 2). A data-driven network model indicates that locomotion modulates both the external inputs arriving to V1 and local synaptic connections. The differential modulation of the PC population reflects variations in their local inhibitory circuits: sensitizing PCs receive proportionally stronger SST input relative to PV input making them more susceptible to the locomotion-driven decrease in SST inhibitory strength (Fig. 6). More generally, these results build from the simple model of gain control through the VIP→SST→PC disinhibition pathway ^11,63 by also considering the broader neuromodulatory actions of the cholinergic input to V1. The results, summarized in Fig. 7, indicate that locomotion increases the gain of PCs through a combination of circuit effects, including an increase in external inputs and a decrease in local inhibition (Figs. 5 and 6). We have not so far been able to identify other functions that correspond with sensitizing and depressing PCs: the initial gain of the visual response (Fig. 2C), receptive field location⁹ and orientation tuning⁹ are not significantly different between these groups.

Figure 7.

Gating of the feedforward signal

The increase in gain during locomotion was profound: the number of PCs responding to the stimulus increased by a factor of six (Supplementary Table 1) and the average amplitude of those responses by a factor of 2-3 (Figs. 1 and 2). About 70–80% of PCs in layer 2/3 send axon collaterals to higher visual areas^64,65 so these combined effects will strongly amplify the feedforward visual signal, at least to the drifting grating stimulus used here. The local recurrent signals are, however, strongly damped by a wide-spread decrease in the strength of recurrent PC synapses subject to local modulation (Fig. 5). This decoupling of spiking activity and synaptic efficacy suggests a mechanism by which V1 can amplify its output to downstream targets, such as higher visual areas, without generating excessive excitation in the local recurrent network. Such a mechanism could be important for maintaining the stability of computations that rely on balanced excitation and inhibition within V1. We suggest that the suppression of PC output reflects a gating mechanism that allows feedforward communication to be selectively boosted while shielding local circuits from saturation. This prediction could be tested by performing paired electrophysiological recordings of PC→PC connections during state transitions, but direct measurements of changes in synaptic strength in the cortex of behaving mice are currently extremely challenging - most of the available evidence is inferred from circuit-level activity patterns and in vitro studies.

Acetylcholine release triggered by activity in the basal forebrain and prefrontal cortex acts across large areas through volume transmission^15,66 but different muscarinic receptor types are expressed at specific locations, very often presynaptically, which provides spatiotemporally specific modulation⁶⁷. The reduction in strength of local PC synapses during locomotion inferred from the model is in line with the known actions of acetylcholine on presynaptic M2 receptors, which reduce glutamate release at PC terminals^16–18. Many cortical areas are subject to modulation through the cholinergic input that they receive ^15,66, raising the possibility that signals from the basal forebrain also contribute to the increase in external input predicted by the model (Figure 5F).

Locomotion shapes cortical dynamics through multiple pathways

The first effect of locomotion was to enhance a slow sensitizing signal activated by the visual stimulus, the major target of which was VIP interneurons (Fig. 3). The source of this signal is likely the higher visual areas⁴³ gated by acetylcholine, and optogenetic experiments demonstrate that it determined the dynamics of adaption in SSTs (Fig. 3 and Supplementary Figure 2). The second major effect predicted by the model was an over 90% reduction in the strength of PC synapses across all targets (Fig. 5G), consistent with a range of evidence obtained in vitro demonstrating that M2 muscarinic receptors cause presynaptic inhibition^16,17,68. A similar mechanism likely operates at PV, where release probability is reduced by M2 and M4 receptors^69–71. However, the situation is different for SST interneurons. Our modelling shows that VIPs receive weak SST inputs at rest and that these synapses are potentiated during locomotion (Fig. 5E-G). This is likely to reflect a post-synaptic action of M1 receptors which have been shown to enhance postsynaptic GABA_A currents in visual and somatosensory cortices^71,72. In contrast, SST inputs to PCs and PVs appeared weaker during locomotion.

SSTs are a heterogenous class of inhibitory cells that target other cortical neurons in two distinct ways. The most numerous subtype, Martinotti cells, synapse on distal apical dendrites of PCs in layer 1 and show strong depressing adaptation, while Non-Martinotti cells generate more variable responses^48,73,74. We suggest that SSTs contacting VIP interneurons are predominantly Non-Martinotti cells because they are the only subtype known to be enhanced by acetylcholine through M1 and M3 receptors in vitro⁷⁵. It may also be that other neuromodulatory systems contribute to these mixed effects, including noradrenaline, serotonin and dopamine^2,11. The models might be refined by splitting SSTs into two populations once their responses are measured separately⁷⁶, but a more critical next step is to test the predicted changes in synaptic strength. As for PC→PC connections, the best way to test this would be to make paired electrophysiological recordings of identified SST→PC and SST→VIP connections during state transitions.

A key insight from our modelling is that the relative strength of PV and SST inputs predicts both the direction of PC adaptation and the degree of locomotion-induced gain modulation (Fig. 6). Depressing PCs receive stronger PV input, consistent with their rapid and temporally precise inhibition⁷⁷. In contrast, sensitizing PCs receive relatively stronger SST input which slowly depress to drive sensitization⁹. These differences in PV:SST ratio may also contribute to the changes in gain associated with locomotion: because SST→PC inputs decrease substantially during locomotion (Fig. 5), PCs already dominated by SST input exhibit the largest gain enhancement. It is well established that there are substantial variations in the inhibitory input patterns to PCs but it is unclear how far these reflect the development of specific wiring patterns as opposed to the variability that will arise from random connections^37,78,79. PV and SST interneurons are much sparser than PCs⁸⁰ and connect to them with low probabilities^37,39, such that simple random connectivity can give rise to PCs receiving different proportions of PV and SST inhibition – a pattern that at least partially occurs in V1⁸¹.

Modulation of SST→PC inputs during changes in brain state

An intriguing prediction of our model is that the number of SST→PC synapses onto sensitizing PCs weaken whereas their PV→PC inputs increase selectively during locomotion (Fig. 6I). As a result of these opposing effects of inhibition, the total net input does not differ substantially from that of depressor PCs. There has been controversy regarding the computational form of SST and PV inhibition onto PCs: under certain experimental conditions SST inhibition has been described as subtractive and PV divisive⁶⁰, while different manipulations show the opposite^61,62. Although in our model we initially considered both types of inhibition subtractive, one possibility is that SST interneurons induce divisive inhibition during rest, such that their effect strengthens disproportionately with increasing inhibition. This may therefore account for the marked gain increase we observed in sensitizer PCs, which receive stronger SST inhibition. In principle, this prediction could also be tested by targeted recordings of identified SST→PC connections during state transitions.

What are the consequences of the enhanced gain of sensitizing PCs during locomotion? One possibility is that these changes maintain responsiveness to low contrast and transient stimuli in a visual environment that has become more dynamic with a strong component of visual flow. By selectively enhancing PCs that resist rapid depression, the circuit may preserve sensitivity to behaviourally relevant stimuli^58,82. From a computational perspective, the ability to differentially modulate adaptive subpopulations allows the cortex to tune its operating regime to changes in behaviour. Locomotion not only modulates the synaptic and gain mechanisms we focus on here but can also enhance neural representations of visual stimuli in V1⁵⁸. Our findings might, therefore, also be interpreted in terms of broader theories of predictive coding and attention⁸³: locomotion likely reflects an internal state of heightened predictive engagement with the environment and selective amplification of sensitizing PCs could in principle support enhanced cortical representations of expected sensory features.

Methods

Key resources table

Animal preparation

All experimental procedures in mice were conducted according to the UK Animals Scientific Procedures Act (1986). These were performed at University of Sussex under personal and project licenses granted by the Home Office following review by the Animal Welfare and Ethics Review Board.

The animals were housed in polypropylene cages (21 cm × 35 cm) that contained nesting material, a shelter, a treadmill, a tunnel and wooden sticks. Mice were housed in groups of 2 - 3, except in some instances when reintegration into a group was unsuccessful after surgery. All animals were kept on an inverted 12-hour light-dark cycle. Results are reported from four VIP-Cre mice (VIP tm1(cre)Zjh/J Jackson #010908), fourteen SST-Cre (SST tm2.1(cre)Zjh/J, Jackson #013044), four SST-Flp (Sst tm3.1(flpo)Zjh; Jackson #028579) x VIP-Cre and ten PV-Cre (Pvalb tm1(cre)Arbr/J, Jackson #008069), all of them adult mice aged from P90 to P260 from either sex. Mice were prepared for head-fixed multiphoton imaging through a surgical procedure in a stereotaxic frame under isoflurane anaesthesia. A titanium head plate was attached to the skull and a 3 mm craniotomy was drilled to expose the brain as described in detailed previously⁹. We then expressed AAV1.CaMKII.GCaMP6f.WPRE.SV40 to image calcium activity in pyramidal cells, AAV9.CAG.Flex.GCaMP6f.WPRE.SV40 to image interneurons in Cre lines and AAV1.EF1a-FLEX(frt)-GCaMP6f-WPRE to image SSTs in Flp lines. To excite interneurons optogenetically we used rAAV9/Syn.Flex.ChrimsonR.tdTomato and to inhibit them we used AAV5.CBA.Flex.ArchT.tdTomato.WPRE.SV40.

Multiphoton imaging in vivo

During imaging sessions mice were free to run on a cylindrical treadmill placed under a two-photon microscope, with stimuli being presented on two monitors covering most of the visual field. Visual stimuli were sinusoidal gratings drifting upwards (100% contrast, 1 Hz, 10 s duration) generated using the Python library PsychoPy⁸⁴. The standard experimental protocol consisted of ten presentations of the stimulus with a 20 s interstimulus interval. When testing optogenetic manipulations these 10 trials were interleaved with 10 additional trials paired with illumination from an amber LED. The intensity of this LED was adjusted to activity of PCs to similar levels in different experiments. Running speed was measured with a rotary encoder and recorded through the imaging software (Scanimage5; Vidrio Technologies). The two-photon microscope (Scientifica SP1) employed a 16x water immersion objective (0.8 NA; Nikon) and imaging was carried out at a depth of 150-300 μm below the surface of the brain.

Raw movies were registered and segmented into regions of interest (ROIs) using the Suite2P package running in MATLAB 2021a⁸⁵ and further analysed using custom-written code in Igor Pro 8 (Wavemetrics). Here we only analyse results from the first imaging session in which the animal was exposed to the stimulus to avoid the effects of habituation observed over multiple sessions. Stimulus trials were only included for analysis if the mouse was running faster than 3 cm/s for more than 80% of the time. To calculate the response dynamics of PC, PV, SST and VIP populations we only included cells that were positively correlated with the stimulus. For each cell, the Pearson’s correlation coefficients was computed between its activity trace (ΔF/F) and a stimulus trace binarized as either stimulus off (0) or stimulus on (1) using the StatsLinearCorrelationTest Function in IgorPro (Wavemetrics). The threshold for significant positive or negative correlation was set at p < 0.05. Measurements of adaptive properties were confined to cells which were significantly positively correlated with the stimulus. The adaptive index (AI) was calculated from the GCaMP6f signal as AI = (R1 − R2)/(R1 + R2) where R1 is the average response over the period 0.5 - 2.5 s after stimulus onset and R2 is the average at 8-10 s.

Estimation of firing rates

To estimate firing rates from the recorded ΔF/F data we used the MLspike algorithm using initial parameters expected for GCaMP6f²⁵. Briefly, this finds the optimal spike train to fit the calcium fluorescence trace (ΔF/F) taking into account estimates of baseline fluorescence level and neuronal parameters including the amplitude of the unitary Ca²⁺ transient generated by a spike (A) and the decay time-constant of that transient (τ). These model parameters were obtained by maximum-likelihood autocalibration of ΔF/F traces, allowing conversion of relative fluorescence changes into inferred spike counts and corresponding firing rates.

In general, we followed recommendations and demos in the article and on the MLspike GitHub page. We set the range for A to be between 1 and 50% and τ was set at values from 0.05 to 3 seconds. The parameter A_max, which corresponds to the maximum amplitude of detected events, was 9, and the saturation parameter was set to 0.002. Finally, the Hill coefficient for Ca²⁺ binding to GCaMP6f was varied in the range from 1 to 3.75 with step sizes of 0.25.

Model of the circuit in layer 2/3 of V1

We built a rate-based data-driven population model of the network circuit in the mouse visual cortex layer 2/3 (code and example data sets at https://github.com/lagnadoLab/CortexModel). The purpose of the model was to understand adaptive gain control during rest and locomoting states of four main neuron populations (PC, PV, SST, and VIP). Model parameters, both fixed and fitted, are listed in Supplementary Table 3.

The network was represented by the system of four mean-field first order ordinary differential equations (equation 1)³⁰. The neuronal input-output function, 𝑓(𝑥), was a rectified power law³²

where 𝑘 is a scaling coefficient which was set to 1. This is a rectified linear function with a lower threshold, , of zero to prevent negative values of firing rate and upper threshold of 25 to prevent run-away behaviour of the algorithm solving the network equations system. The exponent was set to n =2 but a linear activation function produced similar results during the fitting process, as observed by others⁸⁶.

Connectivity between and within populations is represented by total connection weight 𝑤_j𝑖which is dependent on both the number of responsive cells in the presynaptic population and the strength of individual synapses. The number of presynaptic neurons responding to the stimulus varied between rest and locomotion so to assess changes in synaptic strength caused by neuromodulators the total connection weight was divided by the number of responsive presynaptic cells (Supplementary Table 1 and equations 2 and 3 in Results). The aim of fitting the model to the average activity traces of each neuronal population was to obtain connection weights, 𝑤_j𝑖. Weights were set to zero where published work indicated that connections are very weak or non-existent, as between SST interneurons^33,38. The final connection weights matrix for connections within layer 2/3 was represented as:

based on the reasonable assumption that connection probabilities are constant on the time-scale of minutes.

External inputs driving activity

Three types of external input drove activity in the circuit which we termed feedforward (FF), slow sensitization (SS) and feedback input (FB): the forms and origins of these are discussed in Results. These were represented in Equation 1 by the variable 𝐼𝑛 that was specific for each input. The FF input was defined by the following system of equations:

The initial short fast-depressing component had an amplitude 𝐴_𝑓 and decayed exponentially with a decay rate 𝜆_𝑓. The variables 𝑠_{𝑠𝑡𝑎𝑟𝑡}, 𝑠_𝑑𝑒𝑙, 𝑠_𝑑𝑢𝑟, 𝑠_𝑘 represent stimulus start, delay in the initiation of the response in a cell, the stimulus duration and an offset after the initial peak, respectively. This offset defined the initiation of a second slow increase in feedforward input that has been observed in response to drifting gratings lasting seconds^22,44. At the end of the stimulus presentation, experimental traces decayed relatively slowly compared with the time-constant of the model neurons and this was accounted for by including an exponentially decaying component to the input with the argument 𝑑𝑒𝑐𝑎𝑦_𝑓.

The temporal form of the feedforward input measured experimentally reflects the application of a spatio-temporal Gabor filter to a sinusoidal wave of drifting gratings⁸⁷. This oscillation was clear in the activity of individual PCs but less evident in population averages because neurons responded with different phases, depending on the location of their receptive fields relative to the stimulus. This 1 Hz oscillation was most clearly observed in the average response of the SST population (Fig. 5C, bottom) which have larger receptive fields and therefore display less phase shifting⁴⁸. We did not, therefore, attempt to model the oscillatory component of individual neuronal responses and concentrated on capturing the average activity across populations. The feedforward input (FF) was defined as a step of duration 𝑠_𝑑𝑢𝑟 with initial amplitude (𝐼₅ + A_f) which then decayed to a steady state of 𝐼₅ with time-constant 210 ms, defined by fitting the initial peak of the average PC response. The steady state was half the initial maximum with A_f = 𝐼₅. The linear increase is a simplified representation of the sensitizing behaviour observed experimentally in layer 4 activity^22,44.

The slow sensitizing input was represented by the following system of equations:

where 𝑠_{𝑠𝑡𝑎𝑟𝑡}, 𝑠_𝑑𝑢𝑟 represent the time of the stimulus start and the stimulus duration, respectively. The slow sensitizing (SS) component is represented by a sigmoid function with an amplitude 𝐴_𝑠, growth rate 𝜆_𝑠, and centre of sigmoid shifted to a 𝑑𝑒𝑙 value from the stimulus starting time. Similarly to FF, the decay phase after the stimulus end was accounted for by the argument 𝑑𝑒𝑐𝑎𝑦_𝑠.

Finally, feedback input (FB) was represented by a step function:

where 𝑠_{𝑠𝑡𝑎𝑟𝑡}, 𝑠_{𝑓𝑏_𝑑𝑒𝑙𝑎𝑦}, 𝑠_𝑑𝑢𝑟 represent time of the stimulus start, delay in the initiation of the response in a cell and the stimulus duration, respectively. The amplitude of the stimulus is defined by 𝐴_𝑓𝑏. Similarly to FF and SS, the decay phase after stimulus end was accounted for by the argument 𝑑𝑒𝑐𝑎𝑦_𝑓𝑏. The amplitudes of A_fb, A_s and I_o were fixed around 1 Hz based on the average response of PCs during locomoting state (Fig. 2).

Fitting the model

To obtain values of connection weights we fit the model simultaneously to the average activity traces of the four neuronal populations using the LMFIT library in Python⁸⁸ by minimization of reduced chi-square parameter 𝜒²:

Where (𝑑𝑎𝑡𝑎_𝑖 − 𝑚𝑜𝑑𝑒𝑙_𝑖) represent an array of residuals between model and data points to be fitted, 𝑁 – is the number of datapoints, and 𝑒𝑝𝑠_𝑖 is the uncertainty of the data points. We weighted the data with uncertainty. We used standard errors from the locomotion and rest data.

Where 𝑁 is the number of data points and 𝑁_𝑣 is the number of variable parameters. We set the threshold chi-square value to be 10 for locomotion and 3 for rest, given their different variabilities. An ideal “good fit” would have a value of reduced chi-square around 1, as far as uncertainty is provided⁸⁸. We used standard errors of the mean (S.E.M) to weight the uncertainty of locomotion and rest data (eps). Additionally, to have a measure of fit quality independent of the data uncertainty and number of varied parameters we calculated root mean square error (RMSE) for each fit:

Parameter Search Strategy

Due to the high dimensionality of the parameter space, multiple parameter sets often produced similar values, indicating that networks with different connectivity profiles could generate similar activity patterns, which in turn made the results sensitive to the initial guess of parameters. While global optimization algorithms such as genetic algorithm and dual annealing were tested, they did not yield satisfactory performance for this model.

Instead, having access to the Artemis high performance computing cluster at Sussex University, we combined Sobol sampling⁸⁹ with local optimization methods. Sobol sampling provides uniform coverage of high-dimensional parameter space. We generated 100,000 sets of evenly distributed initial parameters and each Sobol-sampled parameter set was subsequently refined using local optimization. We tested Levenberg-Marquardt, Nelder-Mead, Powell and L-BFGS-B methods and noticed that Nelder-Mead and Powell performed across a broad parameter range, whereas Levenberg-Marquardt and L-BFGS-B methods were more effective for final fine-tuning. This two-stage procedure (global Sobol sampling of the initial parameters followed by local optimization) allowed us to systematically explore parameter space and quantify the variability of estimated connection weights. For the locomotion condition, we only obtained 37 solutions which were considered good fits for having chi-square lower than 10. In order to obtain more solutions for further filtering, we repeated the two-stage procedure limiting 20,000 Sobol initial conditions to a subspace to average ± 2SD for each synaptic weight, rendering 9,341 good solutions without changing the average and SD compared to the initial 37 solutions.

An important additional constraint was provided by requiring the model to fit the results of optogenetic manipulations of the PV and SST populations (Fig. 4), leading to a reduced number of sets of possible synaptic weights. In these experiments, the intensity of the LED was set to increase or decrease PV or SST activity by a known factor between 1.6 and 2.5, as measured empirically in other parallel experiments measuring GCaMP6f responses in these interneurons⁹. The average PV or SST activity trace was then scaled by the same factor for comparing the model to observed PC activity, and RMSE value calculated for each comparison in optogenetic tests. We had a total of 4 conditions: SST activation, SST inhibition, PV activation and PV inhibition which we used for sequentially filtering the original group of solutions in 4 filtering steps. The threshold for a good opto fitting in each step was chi-square value smaller than 0.16 and 1.2 < OptoParam < 4. This approach allowed us to reduce the set of synaptic configurations, yielding parameter sets that captured both the average circuit dynamics during locomotion and the network’s response to optogenetic perturbations.

For the resting state fits, we repeated the Sobol sampling and local fitting procedure using the same initial steps excluding optogenetic filtering, which allowed us to estimate mean parameter values and their variability (Supplementary Fig. 3). Optogenetic filtering was not feasible due to the noisier nature of these traces. Alternative versions of the model were tested by setting the connection weights of the tested connections to zero, this was performed with the SS and FB inputs. Notably, all the resulting solutions had chi-squared values above threshold indicating that slow sensitizing and feedback inputs are essential to explain circuit dynamics on these time-scales (Supplementary Figure 4).

To assess whether model parameters segregated into distinct groups, we applied unsupervised clustering using both K-means and DBSCAN algorithms. For K-means, we used the Elbow method and Silhouette analysis to estimate the optimal number of clusters. We further applied DBSCAN, estimating the neighborhood parameter (eps) from the 5th nearest neighbor distance using the KneeLocator method.

Fitting the model to subpopulations of pyramidal cells

The whole PC population was split into tertiles (sensitizers, intermediate cells and depressors) based on the distribution of adaptive index (Fig. 1). The average response of each subpopulation was then fit separately in for each of the good solutions from the locomoting and resting states using the two-stage fitting procedure explained above to assess changes in connectivity that describe the adaptive properties of each (Fig. 6). Three simplifying assumptions were made. First, that each subpopulation of PC receives the same shape of inputs as the average PC across the population. Second, only the synaptic weight of those connections directly targeting PCs were left free to vary while the other connections within the circuit were fixed. This was done because there is no change in activities of interneurons when separating a PC population into three subgroups and excitatory input from PCs to interneurons was taken as an average response of the whole PC population, similarly as during fitting of the whole network. Third, we used the initial conditions of the average models scaled to match amplitudes of subpopulations to average response. From Equations 1 and 6 the scaling factor is:

where 𝑤_𝑖 is a weight and 𝐴_𝑖 is an average amplitude of response during stimulus. Corresponding scaling multiplication factors for locomotion are: sensitizers = 1.1, intermediate = 1.2, depressors = 0.8, and for resting state are: sensitizers = 0.9, intermediate = 1.1, depressors = 0.9.

Statistical analysis

For the statistical tests not directly related with the model fitting we used the analytical software Igor Pro 8 and/or SPSS (’Statistical Package for the Social Sciences’, IBM). To determine if the mean of one group was significantly different from another group we used a t-test (two-sided) if the distribution was normally distributed or a non-parametric Mann–Whitney U test (MWU) if it was not. We used linear mixed modelling (LMM) to test for significant interaction between locomotion state and AI tertile (Fig. 1), because cells were not paired between locomotion and resting states. Locomotion state and AI tertile were defined as fixed variables and the animal ID was defined as the random variable. All values are given as as mean ± standard error of the mean (SEM) or mean ± standard deviation (SD) as indicated in each figure legend.

Supplementary Information

Locomotion-dependent changes in adaptive properties of PCs

Supplementary Figure 1.

Similar time-scales of sensitizing and depressing adaptation

Supplementary Figure 2.

Parameter subspace of valid solutions

Supplementary Figure 3.

Removing external inputs impairs model performance

Supplementary Figure 4.

Supplementary Table 1.

Supplementary Table 2.

Supplementary Table 3.

Data availability

All code and data reported in this paper will be shared by the lead contact upon request. Code and example data sets are available at https://github.com/lagnadoLab/CortexModel. Any additional information required to reanalyze the data reported in this manuscript is available from the lead contact upon request.

Acknowledgements

This work was supported by BBSRC grant BB/X009386/1, a PhD scholarship to SD from the Leverhulme Trust (DS-2017-011) and a Researchers at Risk Fellowship to YK from the British Academy and Council for At-Risk Academics (RaR/100503).

Additional information

Funding

UKRI | Biotechnology and Biological Sciences Research Council (AFRC) (BB/X009386/1)

• Leon Lagnado

Leverhulme Trust (The Leverhulme Trust) (DS-2017-011)

• Sina E Dominiak