Abstract
The cortical microcircuit can dynamically adjust to dramatic changes in the strength, scale, and complexity of its input. In the primary visual cortex (V1), pyramidal cells (PCs) integrate widely across space when signals are weak, but integrate narrowly when signals are strong, a phenomenon known as contrast-dependent surround suppression. Theoretical work has proposed that local interneurons could mediate a shift from cooperation to competition of PCs across cortical space, underlying this computation. We combine calcium imaging and electrophysiology to constrain a stabilized superlinear network model that explains how the four principal cell types in layer 2/3 (L2/3) of mouse V1– somatostatin (SST), parvalbumin (PV), and vasoactive intestinal peptide (VIP) interneurons, and PCs transform inputs from layer 4 (L4) PCs to encode drifting gratings of varying size and contrast. Using bidirectional optogenetic perturbations, we confirm key predictions of the model. Our data and modeling show that network nonlinearities set up by recurrent amplification mediate a shift from a positive PC-VIP feedback loop at small size and low contrast to a negative PC-SST feedback loop at large size and high contrast to support this flexible computation. This may represent a widespread mechanism for gating competition across cortical space to optimally meet task demands.
Introduction
The brain must process sensory inputs across a wide range of sensory environments and perceptual goals. When sensory signals are weak, adding of activity in ensembles encoding congruent evidence across space (“corroboration”) could optimize detection; when signals are strong, subtraction of congruent signals (“explaining away”) could optimize discrimination or localization (Sceniak, et al. 1999, Hawken, et al. 2001, Nauhaus, et al. 2009). For a sensory code to capture this flexible functional interaction, neural ensembles encoding distinct elements of sensory evidence must be able to rapidly change the nature of their interaction, competing or cooperating depending on sensory inputs.
Causal and correlative evidence suggests that with increasing contrast, interactions across cortical space become less cooperative and more competitive (Nauhaus, et al. 2009, Sato, Häusser and Carandini 2014). However, the network mechanisms underlying this shift are incompletely understood. Theoretical work has proposed that local inhibition mediates the transition from cooperative to competitive spatial interactions (Angelucci et al., 2017; Schwabe et al., 2010); yet whether distinct interneuron subtypes play dissociable roles is unknown (Rubin et al., 2015). In this study, we determine how a cortical microcircuit of genetically defined interneuron subtypes underlies this shift from cooperation to competition across cortical space.
Three interneuron subtypes, parvalbumin-(PV), somatostatin-(SST) and vasoactive intestinal peptide-(VIP) expressing, comprise 80-85% of cortical interneurons. All three subtypes have been found to shape the sensory coding properties of pyramidal cells, the primary output neurons of cortex, in distinct ways to facilitate cortical encoding of sensory features (Adesnik et al., 2012; Ayzenshtat et al., 2016; Lee et al., 2012; Rudy et al., 2011; Wilson et al., 2012). VIP cells specialize in inhibition of other interneurons (Pi, et al. 2013, Lee, et al. 2013, Pfeffer, et al. 2013) and may thus play a crucial role in gating cortical competition. VIP cells receive feedback excitation from higher areas (Zhang, et al. 2014) and strong neuromodulatory input from the midbrain (Fu, et al. 2014) which positions them to mediate top-down control of flexible functional interactions in the cortex (Wang & Yang, 2018; Yang et al., 2016). Recent work has shown that VIP cells, like PCs and PV cells, are highly surround suppressed (Dipoppa et al., 2018), are sensitive to low contrasts (Millman et al., 2019), and prefer spatially heterogeneous as opposed to homogeneous textures (Keller, Roth, Caudill, et al., 2020). Because VIP cells preferentially innervate SST cells (Pfeffer et al., 2013), which are known to control spatial summation in the cortex (Adesnik, et al. 2012), we hypothesized a novel role for VIP cells, in contributing to the contrast dependence of cooperation and competition across cortical space.
Because cortical neurons’ firing rate depends superlinearly on their input current (Anderson, et al. 2000, Miller and Troyer 2002), effective monosynaptic connection strength depends on the activity level of the postsynaptic neuron. A relatively inactive neuron, whose average membrane potential is far from its spike threshold, is insensitive to changes in its input. On the other hand, a highly active neuron, depolarized close to action potential threshold, will sensitively transduce changes in its synaptic inputs to changes in its spike rate. Because postsynaptic neurons’ activity is tuned to stimulus features, effective monosynaptic connection strength can itself show stimulus tuning. Because polysynaptic effects depend on the activity of all intervening cell types, the stimulus tuning of total functional connectivity can be combinatorially complex. Tuned functional connectivity via polysynaptic effects in a superlinear network could represent a computationally powerful mechanism for shaping interactions between ensembles encoding distinct features of the sensory environment (Ahmadian et al., 2013; Del Molino et al., 2017; Rubin et al., 2015).
We hypothesized that cortical VIP-SST inhibitory microcircuitry in combination with cell-intrinsic firing rate nonlinearities underlies contrast dependent surround suppression. We combined experiment and theory to test whether firing rate nonlinearities dynamically set effective monosynaptic connection strengths, and via polysynaptic effects the total functional connectivity, between the four principal cortical subtypes to flexibly support cooperation or competition of PCs across space. To achieve this, we first recorded from the major cell types of the upper cortical layers in V1 with two photon imaging and electrophysiology while stimulating V1 with drifting gratings of varying size and contrast. We then used these comprehensive observational data to fit a circuit model that could explain contrast-dependent shifts from cooperation to competition across space in terms of shifting effective connection strength between genetically defined populations of neurons with superlinear responses to input current. Finally, we tested core predictions of this model with targeted optogenetic perturbations of VIP cells while measuring the impact on all other cell types. The insight that superlinearity per se could powerfully shape network responses was critical to interpreting optogenetic effects: at steep points in their superlinearities, neurons were more sensitive to perturbations. Residual effects, those not explained by activity level in the unperturbed condition, sensitively reflected the underlying functional connectivity of the network.
We find that VIP and SST activity outline contrasting regimes of sensory coding in PCs. In the VIP-dominated regime, when the network is weakly activated by stimuli of low contrast and small size, increasing PC activity drives VIP cells, which in turn disinhibit PCs, closing a positive PC-VIP feedback loop. PCs show surround facilitation and are highly sensitive to changes in contrast. Conversely, in the SST-dominated regime, when the network is strongly activated by stimuli of high contrast and large size, increasing PC activity instead drives SST cells, which in turn inhibit PCs, closing a negative feedback loop. PCs show surround suppression and are weakly sensitive to changes in contrast. Thus, the VIP-dominated regime optimizes the dynamic range of contrast encoding at the expense of the coding of space, while the SST-dominated regime optimizes dynamic range of size encoding at the expense of the coding of contrast. Our model explains that high spontaneous drive to VIP cells competes with spatially broad PCàSST drive to establish these disparate regimes of cortical operation. With increasing size and contrast, positive PC-VIP feedback, promoting cooperation of PCs across space, is gradually replaced by negative PC-SST feedback, promoting competition across space. We test key predictions of this model by showing that optogenetically enhancing the spontaneous drive to VIP cells powerfully drives activity in the positive feedback-dominated small and low contrast regime, and more weakly in the negative feedback-dominated large and high contrast regime. Finally, we show that contrast-dependent recurrent amplification within the PC-PV subnetwork enhances the difference between these two regimes of circuit operation. This work provides a detailed explanation for flexible cooperation and competition across cortical space by virtue of cortical microcircuitry and the intrinsic superlinearity of neurons. Furthermore, it establishes a generalizable approach for predicting and explaining how physiological or optogenetic perturbations propagate through a highly recurrent network.
Results
Cell-type specific encoding of size and contrast in the mouse primary visual cortex
To study a paradigmatic example of flexible cooperation and competition across cortical space, we first probed the logic of contrast-dependent surround suppression in layer 2/3 pyramidal cells (L2/3 PCs) of the primary visual cortex (V1). We recorded neural activity in awake, head-fixed mice (fig. 1a) using cell type-specific calcium imaging (fig. 1b). After mapping each neuron’s receptive field, we independently varied the size, contrast, and direction of drifting gratings while keeping their location constant. We measured responses using deconvolved event rate (fig. 1c, see Methods), and first restricted our analysis to neurons within 10 degrees of retinotopic space of the center of the stimulus representation, and trials on which the animal was not locomoting (see Methods). To specifically examine tuning for size and contrast, we averaged responses across the directions sampled. We first asked how size tuning varied as a function of contrast. Prior electrical recordings from unidentified cell types in monkeys (Cavanaugh et al., 2002; Kapadia et al., 1999; Levitt & Lund, 1997; Sceniak et al., 1999), cats (Polat et al., 1998; Sengpiel et al., 1997; Toth et al., 1996), and mice (Ayaz et al., 2013; Nienborg et al., 2013; Vaiceliunaite et al., 2013) have established that surround suppression in V1 increases with increasing contrast. Consistent with these findings, we found that at high contrast, L2/3 PC responses showed strong bandpass size tuning, peaking sharply at small sizes, while at low contrast, responses peaked more broadly, and at larger size (fig. 1d). Because stimuli of increasing size drive activity in distal (surrounding) regions of cortical space, this is consistent with a picture in which surround PCs cooperate with center PCs at low contrast (supporting broad size tuning) and compete with center PCs at high contrast (supporting sharp tuning for small sizes).
A) Mice were head-fixed and free to run on a circular treadmill, while passively viewing a monitor showing drifting gratings of varying size, contrast, and direction. B) Transgenic mouse lines were used to express gCaMP6s in defined subsets of neurons. C) Event rate deconvolved from gCaMP fluorescence was used to estimate neural activity. D) Averaged deconvolved event rates in L2/3 PCs are plotted against drifting grating patch size, with different contrasts plotted separately. Event rates are normalized to the mean across all stimuli and all neurons within each imaging session. In all size tuning plots, darker color corresponds to higher contrast. E) Surround modulation index (SMI) is defined as the response to 60° gratings divided by the response to the preferred size for each contrast. Each transparent line corresponds to an imaging session, and the solid line corresponds to the average across sessions. F) To quantify the contrast dependence of surround suppression, the SMI at the lowest contrast (6%) is subtracted from the SMI at the highest contrast (100%). This difference of SMI corresponds to the magnitude of contrast dependence of surround suppression. G) The same tuning curves as in D) are plotted, separated by size, with contrast varying along the x-axis. In all contrast tuning plots, darker color corresponds to larger size. H) Naka-Rushton functions were fit to contrast tuning curves for each L2/3 PC experiment. Plotted is C50, the contrast evoking a half-maximal response for the fit Naka-Rushton function, as a function of size, for each experiment (transparent lines) and averaged (bold lines). I) As a global metric of size-dependent contrast sensitivity, we compute the difference in C50 between the 5° and 36° size. J-Q) Same as D), G), for L4 PCs, L2/3 PV cells, L2/3 SST cells, and L2/3 VIP cells, respectively. ** significantly different from zero, p < 0.01, Wilcoxon signed rank test. Error bars represent bootstrap SEM equivalent.
In order to quantify the degree of surround suppression as a function of contrast, we computed a surround modulation index (SMI) defined as the response to 60° gratings (the largest shown) at a given contrast, divided by the response to the preferred size at the same contrast. We computed these metrics on the population-averaged tuning curves for each imaging session. SMI decreased monotonically, corresponding to strengthening surround suppression, with increasing contrast (fig. 1e). As a global metric for the contrast dependence of surround suppression, we computed the difference of SMI at 6% contrast and 100% contrast. We found that this difference was significantly positive (fig. 1f—Wilcoxon signed rank test, p<0.05), indicating that surround suppression increased in strength with increasing contrast.
Enhanced surround facilitation at low contrast has been theorized to enhance detectability of large textures. If this were the case, we would expect to see sensitivity to low contrast stimuli increase with size. We measured this change in sensitivity directly by taking a complementary view of the same data, examining contrast tuning at each size (fig. 1g). The C50, or contrast evoking half-maximal response, increased monotonically with size up to 36 ° (fig. 1h). As a global metric for the size dependence of contrast sensitivity, we computed the difference in C50 between 5° and 60° size; this difference was significantly positive (fig. 1i— Wilcoxon signed rank test, p<0.05). Thus, contrast sensitivity was enhanced at large sizes, consistent with spatial integration enhancing stimulus detectability.
We next asked whether these properties were robust across behavioral states and recording modalities. We found qualitatively similar results between the locomoting and non-locomoting conditions (fig. S1). To validate these measurements with electrical recordings, we performed analogous experiments in which we sampled V1 activity using multi-electrode arrays rather than calcium imaging. Regular spiking (RS) units could be compared with PCs in our calcium imaging data. Importantly, tuning measured with electrophysiology and calcium imaging closely agreed (fig. S2; non-locomoting, RS units, R=0.82, p=2×10-8, Wald test).
To address the network mechanisms that might contribute to PC size and contrast tuning, we next probed the tuning of other cell types in the circuit. First, we asked whether similar tuning properties were present in the primary input layer of cortex, layer 4 (L4). Indeed, L4 PCs on average showed similar tuning (fig. 1j,k), suggesting tuning of feedforward inputs contributes to contrast-dependent surround suppression. We then examined the principal inhibitory inputs to L2/3 PCs, local interneurons. Prior theoretical studies have proposed that local interneurons could support a contrast-adaptive code in PCs; one specific model predicts the existence of an inhibitory cell type that is selectively driven at high contrasts, driving surround suppression only under these conditions (Angelucci, et al. 2017). We first asked whether L2/3 PV cells, which share inputs with and strongly inhibit L2/3 PCs, might show enhanced selectivity for high contrast relative to L2/3 PCs. However, we found that in keeping with their high degree of shared inputs, tuning of PV cells closely matched that of PCs (fig. 1l,m). Fast spiking (FS) units measured using extracellular electrophysiology closely agreed with PV cell measurements (fig. S2; non-locomoting, FS units, R=0.84, p=7×10-9, Wald test). Therefore, we next examined a sec nd major L2/3 interneuron subtype, SST cells.
Previous work has implicated SST cells in contributing to surround suppression of PCs at high contrast (Adesnik, et al. 2012, Nienborg, et al. 2013). Although SST cells are known to prefer larger sizes than the other cortical cell types, how this depends on stimulus contrast is not known. In fact, SST tuning diverged sharply from that of PCs and PV cells. SST cells responded best at large size and high contrast, and weakly or not at all at small size and low contrast (fig. 1n). Examining SST contrast tuning at varying size showed that at small size, they were insensitive to all but the highest contrast; stimuli that drove nearly maximal activity in PCs and PV cells only weakly drove SST cells (fig. 1o). Since SST cells receive strong excitation from L2/3 PCs (Adesnik, et al. 2012, Hakim, Shamardani and Adesnik 2018, Kapfer, et al. 2007, Karnani, et al. 2016), this difference in tuning was surprising.
This raised the possibility that strong inhibition from L2/3 VIP cells to SST cells counteracts PCàSST excitation to explain SST cells’ remarkable insensitivity to contrast. If this were true, VIP cells might show size and contrast tuning opposite to that of SST cells. VIP cells, which powerfully and preferentially inhibit SST cells (Pfeffer et al., 2013), exhibit the strongest surround suppression of all cell types at high contrast (Dipoppa, et al. 2018), and are highly sensitive to contrast at large size (Millman et al., 2019). Whether and how VIP contrast responses vary as a function of stimulus size, however, is not known. In line with our prediction, as a population VIP cells were selectively responsive at small size and low contrast, and strongly suppressed at large size and high contrast (fig. 1p; at a single neuron level, this population average reflected a mixture of behaviors, from strict contrast suppression, to bandpass size and contrast tuning (fig. S3)). Examining the same data as contrast tuning at varying size showed further stark differences between SST and VIP cells. Unlike SST cells’ monotonic contrast tuning, VIP cells on average showed bandpass contrast tuning, with the preferred contrast decreasing with increasing size (fig. 1q). These data demonstrated that SST and VIP cells differentially encode stimulus size and contrast, and demarcate disparate regimes of visually-evoked inhibitory circuit activity – one in which VIP is active but SST is largely silent, and one in which SST is active and VIP activity is strongly suppressed. Thus, average VIP and SST responses were strongly anti-correlated across sizes and contrasts (fig. S4a, p=5×10-5, Wald test).
Next, we asked how SST and VIP activity might relate to functional interactions of PCs across space. To address this, we first computed a local metric for PC spatial integration at each size and contrast: the slope of PC size tuning curves (fig. S4b). This metric was positive where PC responses were increasing with increasing size (surround facilitating), and negative where PC responses were decreasing with increasing size (surround suppressing). We then plotted this metric against the difference between SST and VIP activity (which we termed the SST – VIP axis) for each stimulus condition. Indeed, we found that surround facilitation was strongly anti-correlated with movement along the SST – VIP axis (fig. S4c, R=-0.36, p=0.03, Wald test). We next asked whether the slope of PC contrast responses could likewise be explained by the differential activity of VIP and SST cells; as a metric for contrast sensitivity, we measured the local slope of PC contrast responses in a similar way (fig. S4d). Indeed, movement along the SST – VIP axis was strongly anti-correlated with PC contrast tuning slope (fig. S4e, R=0.44, p=7×10-3). Thus, in the VIP-dominated regime, PCs sensitively encoded contrast, and in the SST-dominated regime, PCs sensitively encoded spatial features.
A recurrent network model explains size and contrast tuning of the four cell-type circuit
The data presented above show that VIP and SST activity demarcate disparate regimes of inhibitory circuit operation in V1 L2/3. To understand mechanistically how these regimes might arise, and how they could give rise to contrast-dependent cooperation and competition of PCs across space, we developed a data-driven recurrent network model. The goal of this model was to explain how feedforward drive from L4, recurrent connectivity, and cell-intrinsic superlinearities interact to dynamically shift PC functional connectivity across space from cooperative to competitive with increasing stimulus size and contrast.
Using the comprehensive physiological data presented above, along with the responses of neurons of each cell type located in the surround of the stimulus representation (fig. S5), we fit a superlinear stabilized network model (see Methods). This model simulated two spatial domains (center and surround) each containing five cell types (fig. 2a): L4 PCs, which serve as feedforward inputs, and the four L2/3 cell types. In the model, each L2/3 cell type received a linear combination of inputs from each other population, transformed through a static nonlinearity to determine its firing rate (Miller and Troyer 2002) whose dynamics were described by:
A) The rate-based network model consisted of five cell types, spread across two spatial domains. Using gradient descent on a loss function defined based on the calcium imaging data, we optimized a set of weights describing connection strengths among these cell types. Connections between two cell types across spatial domains were attenuated by a cross-space weight that was allowed to vary based on the postsynaptic cell type. B) Synaptic weight matrix between cell types averaged across model fits, and size tuning of all five modeled cell types, by contrast. C) Violin plots of bias currents to each cell type. D) Schematic depicting stimulus-dependent effective connections between PCs, and SST and VIP cells. Effective connection strengths are given by the product of synaptic weight and firing rate nonlinearity slope. For small and low contrast stimuli, VIP cells sit at a steep point in their firing rate nonlinearity, and SST cells at a shallow point.
Here, r is a vector representing the firing rate of each cell type, W is the matrix of synaptic connection strengths, h is a vector of external inputs and bias currents, and f represents the static nonlinearity. Importantly, the network was constrained to be in an inhibitory stabilized regime across all stimulus conditions (Sanzeni et al., 2020). Importantly, many model fits were able to recapitulate key tuning features for each cell type (fig. 2b), including the contrast dependence of surround suppression of PCs and PV cells, the low contrast sensitivity and high size sensitivity of SST cells, and bandpass contrast tuning of VIP cells. We next analyzed the behavior of the best fitting models, starting from randomly initialized model parameters (see Methods) to identify robust features of network parameters explaining the calcium imaging data. The synaptic weight matrix averaged across successful model fits is presented in fig. 2b. Notably, many of the connection weights in these fits correspond well to known connections from prior studies, including the strong connections among PCs and PV cells, and the strong reciprocal inhibition between SST cells and VIP cells (Pfeffer et al., 2013). Distributions of model parameters across successful model fits are shown in fig. S6.
Thus, effective PCàVIP connection strength is stronger than PCàSST. At large size and high contrast, the opposite is true. E) Effective connection strength between PC and SSTs (orange) or VIP (magenta) is plotted as a function of contrast, at 22° size, F) Modeled responses of SST or VIP to weak activation of PCs in both layers and spatial pixels are plotted as a function of contrast, at 22° size. G) Violin plots of cross-space weights for each cell type. H) Schematic depicting stimulus-dependent cooperation and competition between PCs across space. At small size and low contrast, surround PCs more effectively drive VIP cells, disinhibiting center PCs by inhibiting SST cells. At large size and high contrast, surround PCs more effectively drive SST cells, inhibiting center PCs. I) Top: schematic of the modeled perturbations, eliminating either PCàSST or PCàVIP connections. Bottom: Modeled responses of center PCs to weak activation of surround PCs are plotted as a function of contrast, at 22° size. Orange: same but deleting the PCàSST connection. Magenta: deleting the PCàVIP connection. J) The difference between center PC responses to surround PC activation at 100% contrast, and 0% contrast, at 22° size, for the intact network, and after deleting the PCàSST and PCàVIP connections. In the intact network, the difference is significantly larger across successful model fits (p < 10-3, p < 10-6, Wilcoxon signed-rank test). Error bars represent 16th to 84th percentile of model fits.
Our first goal was to understand the opposing contrast sensitivity of VIP and SST cells. Starting from spontaneous (0° size, or 0% contrast) activity, increasing PC activity seemed to first drive VIP activity and not SST activity, at small size and low contrast, and subsequently to suppress VIP activity while driving SST activity, at large size and high contrast. We first asked how a single set of synaptic weights could support these seemingly opposite effects depending on stimulus. We reasoned that a key ingredient might be the superlinear increase of firing rate with increasing input current. With this superlinearity, active neural populations would be sensitive to subsequent changes in their input, while inactive populations would be insensitive. Thus, the importance of a given connection in shaping network activity would increase with the activity level of the postsynaptic cell type.
First, we asked why at small size and low contrast, increasing PC activity drove VIP cells but not SST cells. We reasoned that high spontaneous drive to VIP cells could play a role. If spontaneous drive to VIP (“bias current” in the model) outweighed spontaneous drive to SST, then the slope of the VIP firing rate nonlinearity should be steep for low levels of sensory activity, while the slope of the SST firing rate nonlinearity should be shallow. Thus initially, starting from spontaneous activity, increasing PC activity could robustly drive VIP cells, but not SST cells. Consistent with this notion, in our physiological data VIP cells exhibited nearly half maximal activity during spontaneous activity, while SST cells exhibited only 10% of their maximal activity (fig. S4f). In keeping with this empirical result, across successful model fits, the bias current to VIP cells was more positive than the bias current to SST cells (fig. 2c, fig. S7a). In the model, this differential bias current supported the VIP-dominated regime at small size and low contrast.
Next, we aimed to understand what shifts the network to an SST-dominated regime in response to large and high contrast gratings. With increasing size and contrast, we hypothesized that growing levels of PC activity could allow SST cells to overcome VIP cells’ initial advantage in spontaneous input current and ultimately outcompete them (fig. 2d). This would be possible if SST cells could more effectively convert increases in PC activity to inhibitory SSTàVIP current, than VIP could convert PC activity to inhibitory VIPàSST current. One possible mechanism would be if SSTàVIP weights were larger than VIPàSST weights. Indeed, across successful model fits, SSTàVIP weights were on average 110% stronger than VIPàSST weights (fig. S7b). Thus, in the model, powerful SSTàVIP inhibition supported the SST-dominated regime at large size and high contrast.
We next asked how the network transitioned from the VIP-dominated to the SST-dominated regime. First, we expected that with increasing contrast, monosynaptic excitation from PCs should more strongly drive SST cells, and more weakly drive VIP cells. To test this hypothesis in the model, we computed “effective monosynaptic connection strengths” for each pair of cell types and for each stimulus condition. We defined effective monosynaptic connection strengths from the presynaptic population I to the postsynaptic population j as the synaptic weight matrix elements wiàj multiplied by the slope of the postsynaptic firing rate nonlinearity φj. We examined effective connection strength at 22°, a size at which we observed surround suppression at the highest contrast and nearly flat size tuning at low contrast.
Consistent with the conceptual explanations presented above, we found that during spontaneous activity, PCàVIP effective connection strength outweighed that of PCàSST (fig. 2e). PCàVIP effective connection strength then gradually decreased with increasing contrast, while PCàSST effective connection strength gradually increased (fig. 2e), ultimately overtaking it at 50-100% contrast. This suggested that as contrast increases, PCs more effectively recruit SST cells compared with VIP cells, helping to explain the contrast-dependent shift from a VIP- to an SST-dominated regime.
Having characterized the effective monosynaptic connection strength from PCs to SST cells and VIP cells, we then asked how the full polysynaptic effect of PCs on these cell types, or functional connectivity, changed with increasing contrast to shape their tuning. We simulated the impact of small excitatory current injections to L2/3 PCs, propagating through the full recurrently connected network, on VIP and SST firing rates (fig. 2f—see Methods). Indeed, as contrast increased, driving PC activity increasingly drove SST cells, but increasingly suppressed VIP cells. In fact, by simulating current injections of increasing, finite magnitude to PCs starting from spontaneous activity, we were able to reconstitute opposing tuning of SST and VIP cells, with SST cells showing superlinear responses to increasing PC activity, and VIP cells showing bandpass responses, peaking at intermediate levels of PC activity (fig. S7c). Deleting either the VIP bias current (fig. S7d) or the SSTàVIP weight from the model (fig. S7e) abolished this behavior, tipping the competition in favor of SST and VIP cells, respectively, across contrasts. This supported the idea that a large stimulus-independent current to VIP cells competes with strong stimulus-dependent SSTàVIP inhibition to support opposing regimes of VIP and SST activity depending on stimulus size and contrast.
To understand the significance of these opposing regimes of VIP and SST activity, we then examined the monosynaptic connectivity of the VIP-SST subnetwork across cortical space. Above, we proposed that SST activity should support surround suppression by participating in disynaptic inhibition across space. If this were true, we would expect that SST cells should strongly integrate inputs across the two modeled spatial domains. Indeed, across successful model fits, SST cells had substantially higher cross-space weight than the other three L2/3 cell types (fig. 2g). Next, we expected that PC-SST feedback could be important for promoting competition between PCs across space. In turn, we reasoned that PC-VIP feedback might suppress competition by controlling tuning of SST cells (fig. 2h).
To measure cooperation and competition between PCs across cortical space in the model, we simulated the effect of excitatory current injections to L2/3 PCs in the surround, on L2/3 PCs in the center. The model predicted surround PCs should increasingly suppress center PCs with increasing contrast (fig. 2i). To test the importance of PC-SST feedback for this contrast-dependent competition, we deleted PCàSST connections, allowed the rest of the network to settle to a new steady state, and then repeated the activation of surround L2/3 PCs as before. Eliminating this connection promoted cooperation at all contrasts, and weakened the contrast dependence of this competition overall (fig. 2i,j), demonstrating that in the model, PC-SST negative feedback is critical for contrast-dependent competition across space. Deleting PCàVIP connections in a similar way promoted competition across all contrasts, and weakened the contrast dependence of this competition overall (fig. 2i,j). This demonstrated that in the model, a balance of negative PC-SST feedback and positive PC-VIP feedback is necessary for the contrast dependence of cooperation and competition between PCs across space.
Optogenetic dissection of the VIP-SST subnetwork’s role in contrast dependent surround suppression
The computational model explained that PC-SST feedback supports competition between PCs across space, while PC-VIP feedback supports cooperation. This implies that VIP cells might directly shape the tuning of SST cells. Indeed, the model predicted that suppressing VIP cells would significantly alter the response properties of SST cells (fig. 3a). To empirically test this, we examined the impact of optogenetically silencing VIP cells on SST responses using simultaneous one photon optogenetics and two photon calcium imaging. We simultaneously measured neural activity in VIP cells, SST cells, and PCs (see Methods and fig. S8) while silencing VIP cells using Cre-dependent eNpHR3.0. We first confirmed the efficacy of optogenetic silencing of VIP cells (fig. S9b). Red illumination through the microscope objective robustly suppressed activity in eNpHR3.0-expressing VIP cells approximately linearly across stimuli by about 67% (fig. S9c-h, R=0.91, p=1×10-9).
A) Model: predictions for the impact of inhibitory current injection to VIP on the responses of SST cells to gratings of various contrasts and sizes. Shown is a scatter plot of SST event rate with light off, vs. difference between light on and light off, for stimuli of varying size (dot size) and contrast (dot color—increasing from cold to warm colors). B) Same as A), but for experimental VIP silencing. C) SST event rate as a function of size, at 6% contrast, in the light off (black) and light on (yellow) condition. D) Same as C), for 100% contrast. E) SST event rate as a function of contrast, at 5° size. F) Same as E), for 60° size. G) C50 as a function of size. C50 is significantly reduced by VIP silencing at the 11° size, and across sizes. Error bars represent bootstrap SEM equivalent.
Consistent with model predictions, silencing VIP cells potently facilitated SST cells across all sizes and contrasts (fig. 3b). This demonstrated that VIP cells crucially regulate visually driven SST-activity. More importantly, we next asked whether the remarkable insensitivity of SST cells to low contrast stimuli could be explained by inhibition from VIP cells. If VIP activity is necessary for tuning the contrast sensitivity of SST cells, silencing VIP cells should preferentially facilitate SST responses to low contrast. Indeed, we found that silencing VIP cells preferentially potentiated SST cells’ responses to low contrast (fig. 3c), and only more weakly facilitated SST responses to high contrast (fig. 3d). This was true across sizes (fig. 3e,f). As a result, the sensitivity of SST cells to contrast increased significantly, measured as a decrease in the C50 of their contrast tuning across sizes (fig. 3g, p < 0.05, Wilcoxon signed-rank test). This demonstrates that VIP cells shape the contrast sensitivity of SST cells by strongly suppressing their responses to low contrast.
Having established that VIP activity was necessary for suppressing SST responses to low contrast, we next asked how this effect would propagate through the network polysynaptically to PCs, which only receive weak or sparse monosynaptic inhibition from VIP cells (Pfeffer et al., 2013). Because intrinsic firing rate nonlinearities in L2/3 PCs have been found to give rise to non-intuitive asymmetries in optogenetic perturbations (Phillips & Hasenstaub 2016), we measured the impact on PCs of both activation and silencing of VIP cells. A previous model of this microcircuit predicted that disconnecting VIP cells from the network (equivalent to completely silencing them) would suppress PC responses selectively to low contrast, while leaving responses to high contrast unaffected (Millman et al., 2019). However, because superlinearity was a key driver of tuning properties in our network model, one might predict the opposite: that silencing of VIP cells could more strongly suppress PCs at high contrast, when PCs are at a more sensitive point in their firing rate nonlinearity (see schematic, fig. 4a). We conceived a purely phenomenological simple superlinear model, in which the effect of bidirectional (silencing or activating) optogenetic perturbations on response to a given stimulus linearly increases with increasing network activity in the control (light off) condition (fig. 4b). By contrast, in a simple linear model, the effect of optogenetic perturbations would be constant with respect to control activity level. This phenomenological model allowed us to partition optogenetic effects into two components: a component that could be explained purely by the activity level in control conditions for a specific visual stimulus (fig. 4c), and a residual component that could not (fig. 4d). We reasoned that this residual component, not explained simply by network superlinearity, might be informative of recurrent network mechanisms. Using our network model, we could then separately probe the roles of modeled synaptic connections in generating each component.
A) Schematic model for predicting the effects of VIP perturbations. PC activity is intrinsically superlinear, with both network suppression and network facilitation increasing in strength with increasing network activity. B) If the effect of optogenetic perturbation is entirely described by a superlinear curve, as in A), the light on – light off activity (Δ activity) given light off (control) activity will fall along a monotonically increasing (decreasing) curve for facilitating (suppressing) perturbations. If the curve in A) is an exponential, the curve describing changes in activity is a straight line. C) Schematic scatter plot of Δ activity, vs. control activity, with best fit line in yellow. “Residual” effects are defined as the difference between the actual change in activity, and best fit line. D) Schematic plot of residual effects vs. contrast. E) Scatter plot of PC Δ firing rate vs. control firing rate for simulated inhibitory current injection to VIP, with L4 activity held constant. In yellow is the least squares linear fit, with shading indicating bootstrap 68% confidence intervals. Dot size and color are as in fig. 3A. F) Same as A), for simulated excitatory current injection to VIP. In red is the least squares linear fit, with shading indicating bootstrapped 68% confidence intervals. G) Experimentally measured Δ PC event rate in response to VIP silencing, vs. control event rate. Linear fit is plotted as in C). H) Same as G), but for VIP activation.. I) Residual effect of simulated VIP inhibitory current injection in E) not captured by the best fit line. J) Same as I), but for simulated VIP excitatory current injection in F. K,L) Same as I), J), but for experimental VIP silencing and activation, respectively, in G),H). M-P) Residual effect at 100% − 0% contrast, for 5° and 60° size, for data in I-L), respectively. Error bars indicate bootstrap SEM equivalent. Shading on fit lines indicates 68 percent confidence interval of linear fits.
First, we sought to distinguish whether our network model was operating in the regime exemplified in (Millman et al., 2019), or in a regime where superlinearity dominated responses to optogenetic perturbations. If the latter were true, the simple superlinear model should capture much of the optogenetic effects. Because our network model took L4 PC activity as feedforward input, it was first necessary to measure the direct effects of bidirectional VIP manipulations on L4 PCs (see fig. S10a,b and Methods). We then simulated bidirectional current injections to VIP cells, combined with the empirically measured bidirectional effects on L4 PCs. Across a range of simulated current injection magnitudes, the full recurrent network model predictions were broadly in line with the simple superlinear model, with higher control firing rates predicting stronger suppressive effects of VIP silencing (fig. 4e, R=-0.72, p=0.0, Wald test) and stronger facilitating effects of VIP activation (fig. 4f, R=0.16, p=2×10-13, Wald test). This agreed with the simple superlinear model prediction, and contrasted with the prediction of (Millman et al., 2019). This was true also when excluding the effect of VIP manipulations on L4 PCs in the model (fig. S11). Our network model predicted that despite VIP cells’ low activity level at high contrast, perturbations to VIP cells would be differentially amplified by the network depending on the strength of PC activity in control conditions, thus increasing with contrast overall.
To test this model prediction experimentally, we virally expressed Cre-dependent eNphR3.0-mRuby3 or ChrimsonR-tdTomato in VIP cells in separate mice, and gCaMP6s in all L2/3 neurons using the hSynapsin promoter (see Methods). As with VIP silencing, we confirmed the efficacy of optogenetic activation of VIP cells. Red illumination through the microscope objective drove robust activity in ChrimsonR-expressing VIP cells across stimulus conditions (fig. S12a,b), although optogenetic facilitation was somewhat stronger for small and low contrast stimuli (fig. S12c-h). Importantly, in control mice expressing no opsin, the optogenetic stimulation light alone produced no systematic facilitation or suppression of visual responses (fig. S13). This confirmed that the observed effects were due to the optogenetic perturbation per se. Next, we analyzed the impact of perturbing VIP cells on the activity of all gCaMP6s-expressing neurons not labeled with a red fluorophore (primarily PCs). In both VIP silencing and VIP activation experiments, PC responses with the optogenetic light off agreed well with responses we measured previously using calcium imaging in transgenic gCaMP-expressing mice (fig. S14; VIP silencing, R=0.95, p=3×10-12, Wald test; VIP activation, R=0.84, p=3×10-7, Wald test). As predicted by the full recurrent network model, across stimulus conditions, high PC activity in control conditions predicted stronger suppressing effects of VIP silencing (fig. 4g, R=-0.64, p=2×10-12, Wald test), and stronger facilitating effects of VIP activation (fig. 4h, R=0.45, p=2×10-8, Wald test).
Importantly, the simple superlinear model, in which control activity levels completely determined the effect of optogenetic perturbations, could explain much but not all of the effect of bidirectional VIP manipulations on PC activity. We next examined the residual effects of optogenetic perturbations that were not captured by the simple superlinear model: specifically, the difference between the actual change in activity and the best fit line prediction of change in activity from control activity. We reasoned that these residuals might shed light on the recurrent network mechanisms that mediate the contrast dependent shift from cooperation to competition via the VIP-SST network. If competition between PCs across space increased with increasing contrast, as predicted by the recurrent network model, we might expect this to support a strong negative feedback loop at high contrast, limiting the network’s response to VIP activation at high contrast but permitting it at low contrast. We optimized the magnitude of excitatory and inhibitory current injected to VIP cells for each model fit, to maximize dynamic range of PC competition across space (see Methods and fig. S17). Although modeled residual effects of VIP silencing were small (fig. 4i), modeled residual effects of VIP activation were in keeping with this prediction (fig. 4j). PC facilitation in response to VIP activation was stronger than expected by the simple superlinear model at low contrast, and weaker than expected at large size and high contrast. Experimental results of VIP silencing (fig. 4k) and activation (fig. 4l) showed a similar asymmetry. Across all conditions, VIP activation at 60° size showed the strongest contrast dependence of residuals, defined as the residual effect at 100% contrast – 0% contrast (fig. 4m-p).
We then asked how this asymmetric contrast-dependent residual effect of bidirectional VIP manipulation affected contrast-dependent surround suppression in the experimental data. Although VIP silencing significantly suppressed visual responses across most stimuli (Fig. 5a,b), it did not significantly affect the surround modulation index (SMI) at any contrast (fig. 5c), and thus there was no significant change in ΔSMI between 6% and 100% contrast (fig. 5d). Similarly, there was no significant change in contrast sensitivity at any size (fig. 5e-h). We corroborated these calcium imaging results by recording neural activity using extracellular electrophysiology in a separate cohort of mice. In these electrophysiological experiments, we also compared the optogenetic effects between the non-locomoting an the locomoting condition (fig. S15), and as above, saw no brain-state dependent difference. We also found similar effects in RS and FS units (fig. S15). These measurements confirmed that VIP silencing did not substantially alter the contrast dependence of surround suppression.
A) Size is plotted on the x-axis, and PC event rate on the y-axis, for 6% contrast, the lowest tested, in the light off condition (black) and light on condition (yellow). B) Same as A) for 100% contrast. C) Surround modulation index is plotted as a function of contrast, in the light on and light off conditions. D) Change in SMI between the light off and light on condition, with each line an experiment. E) Same as A), B), but responses to increasing contrast are plotted for fixed 5° size, in the light off and light on condition. F) Same as E), but for 60° size. G) C50 is plotted as a function of size, for the light off and light on conditions. H) Bar plot of change in C50 between 5° and 60° size, for the light off and light on conditions, with lines indicating individual imaging sessions. I-P) Same as A-H), but for optogenetic activation of VIP cells. * significant difference, p < 0.05 (Wilcoxon signed-rank test). Error bars indicate bootstrap SEM equivalent.
On the other hand, VIP activation enhanced visual responses across all conditions. For the same control activity level, activating VIP cells disproportionally facilitated PCs in response to large, low contrast stimuli (fig. 5i), but less so for large, high contrast stimuli (fig. 5j). As a consequence, VIP activation enhanced the contrast dependence of surround suppression overall, evident as an increase in SMI specifically at low contrast (fig. 5k,l) and an increase in ΔSMI between 6% and 100% contrast. This change in contrast-dependent surround suppression could not be explained by the simple superlinear model alone (fig. S16), and therefore was a result of the asymmetric contrast-dependent residual effects of VIP activation. Similarly, VIP activation increased size dependence of contrast sensitivity (fig. 5m-p).
We next returned to our recurrent network model to ask whether this asymmetric contrast-dependent residual effect of VIP activation was tied directly to contrast dependent spatial competition between PCs. If this were the case, we would expect manipulations that suppressed the contrast dependence of PC spatial competition to suppress the contrast dependence of residual effects of VIP activation. Previously, we found that the contrast dependence of PC spatial competition in the model depended on an interplay between two feedback loops: a PC-VIP feedback loop, primarily active at low contrast, and promoting cooperation, and a PC-SST feedback loop, primarily active at high contrast, and promoting competition. Having established that these feedback loops supported the contrast dependence of PC spatial competition, we next asked whether they also supported the contrast-dependent residual effect of VIP activation on PC responses that was evident in our previous simulations. While deleting PCàVIP weights or PCàSST weights only weakly affected simulated responses to VIP silencing (fig. 6a,b respectively), the same manipulation dramatically reduced simulated responses to VIP activation (fig. 6c,d respectively). Similarly, these manipulations significantly and asymmetrically reduced residual effects of VIP activation, and not silencing (fig. 6d-g), as well as the contrast dependence of these residuals (fig. 6h-k). This suggested that the asymmetric contrast-dependent residual effect of VIP activation, which was necessary for enhancement of contrast-dependent surround suppression, was a result of contrast-dependent spatial cooperation and competition between PCs. The model predicted that this asymmetric residual effect at low contrast was a generic result of facilitating feedforward drive to the L2/3 network, not only via manipulation of VIP activity (fig. S10c,d). Further, the asymmetry could be explained by enhanced contrast dependence of positive PC-VIP feedback specific to moderate increases in PC and VIP activity, with decreases in activity, and large increases in activity, causing a much weaker reduction in this contrast dependence (fig. S17). Thus, modeling results supported the idea that residual effects of VIP activation we observed were signatures of contrast-dependent competition between PCs across space, mediated by the VIP-SST subnetwork.
A) Scatter plot of modeled change in firing rate, vs. control firing rate, both normalized to mean across stimuli, in response to inhibitory current injection to VIP cells, after deleting PCàVIP connections. Transparent dots and lines in all panels correspond to the baseline condition, without deleting any connections. Dot size and color are as in fig. 3A. B) Same as A), after deleting PCàSST connections, respectively. C,D) Same as A), B), but for modeled excitatory current injection to VIP cells. E-H) Residual effect of VIP silencing and activation in A-D), respectively, defined as effect minus expectation based on linear fit to control (light off) firing rate. I-L) Residual effect at 100% −0% contrast, for 5° and 60° size, for data in E-H), respectively. Error bars indicate bootstrap SEM equivalent. Shading on fit lines indicates 68 percent confidence interval of linear fits.
Recurrent amplification drives the network superlinearity that enforces contrast dependent surround suppression
Our modeling and optogenetic results suggested that network superlinearity critically shapes cooperative and competitive interactions across space, and thus the sensory code. To address the origin of this superlinearity, we considered two possibilities: it could be generated purely by the cell-intrinsic firing rate nonlinearity, or also steepened by PC-PC recurrent excitation. To distinguish between these two possibilities, we simulated the effect of direct current injection to PCs in several conditions. First, to isolate the cell-intrinsic response, we deleted all synaptic connections in the network and compared this to the intact condition. Deleting all connections made network nonlinearity much more shallow (fig. 7a, black solid black versus dashed black line). This suggested that recurrent circuits contributed substantially to network superlinearity. Next, we selectively deleted PC-PC weights while leaving all other connections intact. This yielded a substantially shallower response to current injection than the full network response, and shallower even than the cell-intrinsic firing rate nonlinearity alone (Fig. 7a, gray solid line). This suggested that PC-PC recurrent excitation is critical to this superlinearity, and in its absence, powerful feedback inhibition from PV cells may suppress network superlinearity even below the cell-intrinsic nonlinearity. To test this, we deleted all recurrent connections among the PC-PV subnetwork (PC-PC, PC-PV, and PV-PV), while leaving all other connections intact. In this scenario, current injections to PCs yielded a superlinear response similar to the cell-intrinsic firing rate nonlinearity alone (Fig. 7a, blue line). Notably, deleting PC-PV connections alone drove the network to instability (data not shown). Thus, within the network model, recurrent amplification by the PC-PV subnetwork generated a second and more powerful network nonlinearity, building on the cell-intrinsic firing rate nonlinearity.
A) Schematic of modeled perturbations. We measure the response of simulated neurons for (1) no network connections (cell-intrinsic response), (2) the baseline condition (all connections intact), (3) PC-PC connections selectively deleted, and (4) PC-PC, PC-PV, and PV-PV connections deleted. Plotted at right is the simulated L2/3 PC firing rate in response to direct current injections to L2/3 PCs, vs. the current injected, for the four conditions considered, at the 0% contrast condition. Shading indicates 16th to 84th percentile. B) Simulated response of L2/3 center PCs to excitatory current injection to L2/3 surround PCs, for 22° size, at increasing contrast. Also plotted are the same responses for PC-PC connections deleted, or all recurrent connections among PCs and PV cells deleted. C) The difference between center PC responses to surround PC activation at 100% contrast, and 0% contrast, at 22° size, for the baseline case, and after deleting PC-PV connections, or all connections among PCs and PV cells. At baseline, the difference is significantly larger across successful model fits (p < 10-7, p < 10-7, Wilcoxon signed-rank test). D) Scatter plot of simulated change in L2/3 PC activity vs. baseline activity in response to inhibitory current injection to VIP cells, plus empirically measured suppression of L4 PCs, after deleting all recurrent connections among PCs and PV cells. Transparent dots and lines in all panels correspond to the baseline condition, without deleting any connections. Dot size and color are as in fig. 3A. E) Same as D), but for simulated excitatory current injection to VIP cells, plus empirically measured facilitation of L4 PCs (same as 4F), after deleting all recurrent connections among PCs and PV cells. F,G) Residual effect of VIP perturbation in D), E), respectively, defined as effect minus expectation based on linear fit to baseline firing rate. H, I) Residual effect at 100% − 0% contrast, for 5° and 60° size, for data in F), G), respectively. J) Schematic summarizing primary findings. At low contrast and small size, VIP cells are highly active, enhancing the effective weight of the PC-VIP connection. This results in a disinhibitory positive feedback loop, facilitating PC responses and promoting cooperation among PCs. At high contrast and large size, SST cells are highly active, enhancing the effective weight of the PC-SST connection. This results in a negative feedback loop, suppressing PC responses and promoting competition among PCs. Recurrent amplification within the PC-PV subnetwork strengthens both the positive PC-VIP and negative PC-SST feedback loops. Error bars in B), C) indicate 16th to 84th percentile of model fits. Error bars in D-G) indicate bootstrap SEM equivalent. Shading on fit lines indicates 68 percent confidence interval of linear fits.
We next asked what role intrinsic connections within the PC-PV subnetwork played in shaping contrast-dependent cooperation and competition of PCs across space. Consistent with recurrent PC-PV connections amplifying the effect of contrast-dependent PC-VIP and PC-SST feedback loops, we found that in the absence of connections among PCs, or among PCs and PV cells, PC competition across space depended much more shallowly on contrast (fig. 7b,c).
Because superlinearity could explain the control activity dependence of VIP optogenetic effects, we reasoned that the PC-PV network could powerfully shape this dependence, via the steepness of the network nonlinearity. We next asked how the network nonlinearity generated by recurrent PC-PV connections shaped the impacts of VIP perturbations on PCs. To this end, we simulated optogenetic VIP activation as before with the full network intact, or when deleting recurrent weights among PCs and PV cells. Based on the enhancement of network superlinearity by recurrent weights among PCs and PV cells, we first expected that the activity dependence of PC responses to VIP perturbations (as captured by the simple superlinear model above) would be strongly affected. Indeed, while effects of simulated VIP silencing were only modestly affected by deleting weights in the PC-PV subnetwork (fig. 7d), across stimuli, the same manipulation substantially reduced the effects of simulated VIP activation (fig. 7e).
Previously, we found that this contrast-dependent spatial competition had signatures in the residual effects of bidirectional VIP perturbations, compared to the predictions of a purely superlinear prediction. In principle, we reasoned that positive feedback loops within this subnetwork could shape the residual effects we observed above, by amplifying the strength of the PC-VIP and PC-SST feedback loops shaping PC competition across cortical space. Based on our simulations of deleting PC-VIP and PC-SST connections, we predicted that the reduced contrast dependence of spatial competition we observed after deleting connections in the PC-PV subnetwork would result in a dramatic reduction in residual effects of VIP activation on PC responses at low contrast. As shown above, for the intact network, VIP silencing generated small residual effects on PCs; deleting recurrent PC-PV weights dampened even these small residual effects. For the intact network, VIP activation generated a large contrast-dependent residual effect on PCs (fig. 7i) and deleting recurrent PC-PV weights severely dampened these residual effects (fig. 7j). This suggested that, within our simulations, the small and low contrast-selective effect of VIP activation, depends critically on positive feedback loops within the PC-PV subnetwork. Thus, the model explains that PC-PV recurrent amplification sets up a steep network superlinearity that synergizes with a PC-VIP positive feedback loop at small size and low contrast to favor cooperation across space, and with a PC-SST negative feedback loop at large size and high contrast to favor competition (fig. 7k).
Discussion
We combined experiments and computational modeling to address the circuit mechanisms that gate cooperation and competition across cortical space. We studied contrast-dependent surround suppression in the primary visual cortex as a paradigmatic example of such flexible cooperation and competition. Although discovered more than two decades ago, a circuit mechanism for how the same cortical circuit dynamically shifts between a cooperative and competitive operating regime based on the size and contrast of the visual stimulus has been lacking. As the same cell types and circuits exist throughout cortical areas, the findings of this study may generalize beyond the visual cortex to more broadly explain how cortical circuits adjust functional interactions across cortical space to meet task demands.
Through a combination of calcium imaging, electrophysiology, optogenetic perturbations, and network modeling, we show that a transition from positive PC-VIP feedback at low contrast, to negative PC-SST feedback at high contrast, explains the contrast dependence of surround suppression. Because SST cells strongly integrate PC inputs across space, these positive and negative feedback loops couple PCs across space. The PC-PV subnetwork amplifies the strength of both feedback loops. We tested core predictions of this model experimentally by optogenetically perturbing VIP cells. First, as predicted by the superlinearity of the network, both VIP silencing and activation have the strongest effects when PC activity is highest, namely at small size and high contrast. On top of this activity-dependent effect, VIP activation had a large, asymmetric residual effect that was unexplained by PC activity level, positive at low contrast and negative at high contrast. Our network model explains that this residual effect is a consequence of contrast-dependent PC competition across space. Further, due to network superlinearity, building on the cell-intrinsic superlinearity, the contrast dependent enhancement of PC-VIP positive feedback by VIP activation is stronger than the contrast-dependent suppression of PC-VIP positive feedback by VIP silencing, contributing to the asymmetry. We found the partitioning of optogenetic effects into an activity-dependent component and a residual component to be important to our interpretation of the optogenetic results. The asymmetric effects of VIP activation and inactivation on pyramidal cell tuning are reminiscent of a recent study examining activation and inactivation of PV and SST cells in A1 (Phillips & Hasenstaub, 2016). Bidirectional perturbations, generally, are likely to provide rigorous tests of a predictive understanding of network dynamics.
The data and modeling presented above highlight that understanding strongly recurrently connected networks (within and beyond the cortex), requires a combination of causal perturbations and computational modeling. Without causal perturbations, computational models may be underconstrained. In contrast to the theoretical predictions of a recent study (Millman et al., 2019), we found that the effect of removing VIP activity from the network was not selective for low contrast stimuli, despite the fact that VIP activity was highest for those stimuli in control conditions. On the other hand, inferring recurrent network mechanisms from causal perturbations is likely to be difficult when unsupported by a computational model. The contrast dependence of PC coupling to the VIP and SST subnetworks, which our perturbations revealed, challenges the simplest linear intuitions of how the network might operate. Iteratively developing new intuitions instructed by recurrent network models, such as feedback loops and stabilization, may be crucial for developing a predictive understanding of neural function. Because one study cannot explore all possible causal perturbations, constraining models based on the results of multiple studies will likely become increasingly important. Incorporating the constraint that our modeled network occupy an inhibitory stabilized regime, established by causal perturbations in previous studies, was crucial to our understanding of the mechanism of network superlinearity.
In this study we considered PCs, PV cells, SST cells, and VIP cells as homogenous populations, and restricted most of our analysis to population averages. However, it is already well appreciated that each of the cell types breaks down into distinct sub-classes with unique physiological properties, anatomy, and circuit connectivity. Future work may uncover subpopulations of the interneurons we studied playing dissociable roles. For example, VIP cells are transcriptionally diverse, and molecular markers such as cholecystokinin and calretinin (He, et al. 2016), could define functional subclasses of VIP cells. Tuning diversity of VIP cells, like transcriptional diversity, has also been found to correlate with cortical depth (Dipoppa, et al. 2018). Diversity in tuning properties may align with diversity of functional roles in the cortical microcircuit. A recent study in the somatosensory barrel cortex found that a subpopulation of VIP cells co-expressing ChAT exert an inhibitory influence on PCs specifically in response to weak stimuli (Dudai, et al. 2020). A combination of intersectional genetic techniques and optogenetics, or two photon optogenetics, could yield further insight in the functional roles of distinct VIP populations in sensory coding. Furthermore, other 5-HT3aR+ interneurons not expressing VIP, particularly in layer 1, have been shown to have similar tuning for sensory signals as VIP cells (Abs et al., 2018; Mesik et al., 2015). Future work could clarify the extent to which these cell types act in concert with VIP cells or play disparate roles to control sensory coding. In addition to discrete variability between sub-classes of each cell type, continuous variability could be important, both in synaptic connections and in tuning properties. Future work could seek to model this variability, which might generate further hypotheses to be tested with more sophisticated optogenetic perturbations.
Translaminar inhibitory as well as excitatory connections are also likely to be important, particularly as VIP manipulations affect L4 as well as L2/3 activity. Future work expanding the scope of these experiments could clarify the extent to which translaminar feedforward and feedback connections shape the response properties of these cell types. Further, these cell types might differentially integrate feedback signals from higher areas (Keller, Roth, & Scanziani, 2020; Zhang et al., 2014), which could be important for their encoding of homogeneous textures as well as richer stimuli.
Furthermore, although we argue that the influence of VIP cells is likely to be important for network regimes optimizing detection, this study has examined only passively viewing mice, not animals motivated to detect weak signals. Behavioral context and salience of sensory inputs has been found to powerfully shape the tuning properties of these interneuron types, possibly to enhance coding properties of pyramidal cells. Future work combining two photon imaging of these cell types with behavior and network modeling could suggest possible dynamical mechanisms for this enhancement.
Despite these limitations, there is growing evidence that the circuit motifs examined in this study may generalize to other areas of the brain. In particular, in auditory cortex, a series of recent studies have uncovered analogous tuning properties and functional roles of the same interneuron types. VIP cells show bandpass tuning for sound amplitude (analogous to contrast) (Mesik, et al. 2015), while SST cells are insensitive to all but high amplitude tones (Li, Xiong, et al. 2015). Whereas PCs commonly prefer narrow spectral bandwidth (analogous to size) (Li et al. 2019), SST cells prefer broader spectral bandwidth (Lakunina et al., 2020). Silencing SST cells results in a reduction of lateral inhibition (Kato, Asinof and Isaacson 2017) and a facilitation of PC responses to broad spectral bandwidth sounds (Lakunina et al., 2020). Future work could examine the extent to which the L2/3 microcircuit in V1 and A1 occupies a similar dynamical regimes, and examine tuning properties of interneurons in S1 for space and intensity. How these insights extend to non-sensory cortices is an exciting area for future study.
Supplementary Figures
A) Size tuning curves of L2/3 PCs in the locomoting condition, averaged across experiments. B) Surround modulation index (SMI; response to 60° size / response to preferred size) of L2/3 PCs as a function of contrast in the locomoting condition. C) Change in SMI between 6% and 100% contrast for all three cell types. **, significantly greater than 0, p < 0.01. D-G) Same as A), but for L4 PCs, L2/3 PV cells, L2/3 SST cells, and L2/3 VIP cells, respectively. Error bars indicate bootstrap SEM equivalent.
A) Scatter plot of firing rate of regular spiking (RS) units recorded using extracellular electrophysiology, vs. PC event rate/mean across stimuli measured using calcium imaging for the equivalent stimuli, in the non-locomoting condition. Dot size and color are as in fig. 3A. B) Same as A), but for fast spiking (FS) units recorded using extracellular electrophysiology, vs. PV event rate/mean measured using calcium imaging. C) Size tuning curves, separated by contrast, for RS units plotted in A). D) Same as C) for FS units plotted in B). E) Surround modulation index (SMI), defined as the response to 60° gratings divided by response to the preferred size gratings, as a function of contrast, for L2/3 RS units. Each line is a single recording session, and the bold line corresponds to average across recording sessions. F) same as E) for L2/3 FS units. G) Difference of SMI between 6% and 100% contrast. Each dot corresponds to one recording session. H-N) Same as A-G), for the locomoting condition. ** significantly positive, p < 0.01; ***, p < 0.001. Error bars indicate bootstrap SEM equivalent.
A) Receptive field of an example SST cell (see Methods). Mapped using 10° drifting gratings of time-varying direction, shown for 1.5 seconds each. B) ΔF/F time course of size-contrast responses for the neuron shown in A; each curve represents the response to gratings of a given contrast, averaged across sizes and orientations. C) Size tuning of the same cell, split up by contrast. D-F) Same as A-C), for an example contrast-suppressed VIP cell. G-I) Same as A-C), for an example contrast-facilitated VIP cell. Error bars indicate bootstrap SEM equivalent.
A) Average event rate of SST cells, normalized to the mean across stimuli, is plotted on the x axis, with VIP responses plotted on the y-axis, likewise normalized to the mean across stimuli. Dot size and color are as in fig. 3A. On the basis of their negative correlation, we define an axis based on the difference between SST and VIP activity. B) On the x axis is plotted size, and on the y axis is plotted the local slope of PC size tuning curves. Where the slope is positive, cells undergo surround facilitation on average, and where the slope is negative, cells experience surround suppression. C) PC size tuning slope is plotted against the difference of SST and VIP event rate. D) Same as B), but for the local slope of PC contrast tuning curves. E) Same as C), but with PC contrast tuning slope rather than size tuning slope. F) Spontaneous activity of SST and VIP cells, as a fraction of maximal sensory-evoked activity. ** significantly different, p < 0.01, Wilcoxon signed rank test. Error bars indicate bootstrap SEM equivalent.
A) Size tuning of L4 PCs, including only those located within 10 visual degrees of retinotopic space of the center of the stimulus representation (left). Beyond 10 visual degrees (right). B-E) Same as A), for L2/3 PCs, PV cells, SST cells, and VIP cells, respectively. Error bars indicate bootstrap SEM equivalent.
A) Violin plots showing variability in synaptic input weights among model fits for each of the four L2/3 cell types modeled. B) Variance of intrinsic input noise for each cell type.
(A) VIP bias current is plotted against SST bias current, for all successful model fits. VIP bias currents are significantly larger than SST bias currents, p=8×10-16, Wilcoxon signed-rank test. B) VIPàSST weight is plotted against SSTàVIP weight, across successful model fits. SSTàVIP weights are significantly stronger (more negative) than VIPàSST weights, p=4×10-15, Wilcoxon signed-rank test. C) Starting from the network steady state for 0% contrast (dashed line), positive or negative current injections to PCs are modeled, and the resulting steady state firing rates of SST and VIP cells are plotted as a function of injected current to PCs. D) Same as C), but after deleting (setting to 0) VIP bias current. E) Same as C), but after deleting SSTàVIP weight. Shading indicates 16th to 84th percentile of model fits.
A) Outlines of putative VIP (membrane-bound mRuby3 expressing) cells, with red channel images. B) Analogous for putative SST (cytosolic tdTomato expressing) cells. C) Average red channel images for putative PCs (left), VIP cells (middle), and SST cells (right), aligned to the center of each cell. D) Red intensity (a.u.) as a function of radial distance from the center of the ROI. Each transparent line is one cell, and the bold line is the average. On the left, in magenta, are putative VIP cells, and on the right, in orange, are putative SST cells. E) Same plots as D), but normalized to the maximum value.
A) eNpHR3.0-mRuby3-labeled VIP cell from a VIP silencing experiment. B) ΔF/F averaged across all VIP cells, for gray screen trials following gray screen trials with no optogenetic stimulation. In yellow is the average trace for trials where the optogenetic stimulation light was on, and in black is the average trace for trials where the optogenetic stimulation light was off. C) Response of a VIP cell to gratings of varying size, at 6% contrast. In black is the light off response, and in yellow is the light on response. D) Same as B), for 100% contrast. E,F) Same as C), D), but for varying contrast, at 5° and 60° size, respectively. G) Scatter plot of light on vs. light off event rate for putative VIP cells at varying size and contrast. In yellow is the best fit line, with the intercept constrained to be 0. Dot size and color are as in fig. 3A. H) Residual effect of optogenetic manipulation not captured by the best fit line in G), for varying contrast, and at varying sizes. Shading and error bars represent bootstrap SEM equivalent.
A) Effect of VIP silencing on L4 regular spiking units measured using extracellular electrophysiology. Change in measured firing rate, normalized to mean light off firing rate, is plotted against light off firing rate, normalized to its mean, averaged across mice. Dot size and color are as in fig. 3A. B) Effect of VIP activation on L4 PCs measured using calcium imaging. Change in measured event rate, normalized to mean light off firing rate, is plotted against light off firing rate, normalized to its mean, averaged across mice. C) Response of L2/3 PCs to a modeled DC decrease in L4 PC firing rate across stimulus conditions. Change in firing rate, normalized to mean, is plotted against baseline firing rate. D) Same as C), but for a DC increase in L4 PC firing rate, across stimulus conditions. Error bars represent bootstrap SEM equivalent.
(A) Scatter plot of modeled change in firing rate, vs. baseline firing rate, both normalized to mean across stimuli, in response to inhibitory current injection to VIP cells, without perturbing L4 PC activity. Dot size and color are as in fig. 3A. B) Same as A), but for excitatory current injection to VIP cells. Error bars represent bootstrap SEM equivalent.
A) ChrimsonR-tdTomato-labeled VIP cell from a VIP activation experiment. B) ΔF/F averaged across all VIP cells, for gray screen trials following gray screen trials with no optogenetic stimulation. In red is the average trace for trials where the optogenetic stimulation light was on, and in black is the average trace for trials where the optogenetic stimulation light was off. C) Response of VIP cells to gratings of varying size, at 6% contrast. In black is the light off response, and in red is the light on response. D) Same as B, for 100% contrast. E,F) Same as C), D), but for varying contrast, at 5° and 60° size, respectively. G) Scatter plot of light on vs. light off event rate for putative VIP cells at varying size and contrast. In red is the best fit line, with the intercept constrained to be 0. Dot size and color are as in fig. 3A. H) Residual effect of optogenetic manipulation not captured by the best fit line in G), for varying contrast, and at varying sizes. Shading and error bars represent bootstrap SEM equivalent.
A) Scatter plot of size-contrast tuning responses for an example neuron from a VIP-eNpHR3.0 expressing mouse. On the x-axis are plotted light-off responses, and on the y-axis, light-on responses. In yellow is the best-fit slope transforming light-off to light-on responses, and in black is the unity line (slope = 1). Dot size and color are as in fig. 3A. B) Histogram of best-fit slopes for optogenetic experiments (yellow) and control experiments (black) in which identical illumination parameters were used. Each line corresponds to one imaging session. C,D) Analogous to A), B) for VIP-ChrimsonR experiments, with optogenetic experiments represented in red, and control experiments in black.
A) Scatter plot of event rate, normalized to mean, for synapsin-GCaMP6s responses in VIP silencing experiments, with the optogenetic stimulation light off, vs. transgenic GCaMP6s responses of pyramidal cells in non-optogenetic experiments, for the analogous stimuli. Dot size and color are as in fig. 3A. B) Same as A), but for responses in VIP activation, rather than silencing, experiments. Error bars represent bootstrap SEM equivalent.
A) Response of regular spiking (RS) units recorded using electrophysiology to drifting gratings of varying size, at 5% contrast, in the non-locomoting condition. B) Same as A, but at 80% contrast. C) Surround modulation index is plotted as a function of contrast, in the light on and light off case. D) Change in SMI between 6% and 100% contrast is plotted, for the light on and light off cases. Each line represents the average of units recorded over one experiment. E-H) Same as A-D), but for fast-spiking (FS) units. I-P) Same as A-H), but for the locomoting condition. The light on and light off conditions are not significantly different in D), H), L), or P), p > 0.05. Error bars represent bootstrap SEM equivalent.
A,B) Fig. 5C,K are reproduced here for clarity. C) As in A), surround modulation index is plotted as a function of contrast, for the VIP silencing data. In black is the light off condition. In red is plotted, rather than the true light on condition, the prediction of a linear fit to the light on condition, based on the light off condition. D) Same as C), for the VIP silencing case. Error bars represent bootstrap SEM equivalent.
A) Simulated response of VIP cells to small excitatory perturbations to PCs, as a function of contrast, at 22° size. Black curve corresponds to non-optogenetic condition. Yellow curve corresponds to simulated finite inhibitory current injection to VIP cells, along with empirically measured VIP silencing-dependent perturbation to L4 PCs. Red curve corresponds to simulated finite excitatory current injection to VIP cells, along with empirically measured VIP activation-dependent perturbation to L4 PCs. Current injection magnitudes are chosen to maximize average magnitude of residual effects of current injection. B) Same as A), but for PC responses to small excitatory perturbations to VIP cells. C) Slope and average magnitude of residual of best fit line between baseline activity level and effect of optogenetic perturbation on PCs, for simulated finite inhibitory current injections to VIP cells of varying magnitude, along with (fixed) empirically measured VIP silencing-dependent perturbations to L4 PCs. D) Same as C), but for simulated finite excitatory current injections, along with (fixed) empirically measured VIP activation-dependent perturbations to L4 PCs. E,F) Same as C), D), but after deleting modeled PCàVIP weights. G,H) Same as C), D), but after deleting modeled PCàSST weights. I,J) Same as A), B), but with current injection magnitudes corresponding to the maximal injection magnitude plotted in C), D). Error bars represent 16th to 84th percentile of model fits.
A) An example imaging plane of a Camk2a-tTA; tetO-GCaMP6s animal, used for recording L2/3 PCs. Computed by averaging motion corrected frames across an experiment. B-D) Same as A), for PV-Cre; TITL2-GCaMP6s, SST-Cre; TITL2-GCaMP6s, and VIP-Cre; TITL2-GCaMP6s, respectively. E) Example fluorescence (ΔF/F) trace with deconvolved event rate, from a L2/3 PC. Reproduced from fig. 1C. F) In a subset of control experiments, a longer inter-stimulus interval was used, so that evoked calcium transients did not overlap between successive trials. Orientation tuning in nine neurons with reliably estimated ΔF/F tuning curves (Pearson’s r > 0.5 between halves of the data, see Methods) is plotted, as measured using ΔF/F and deconvolved event rate. Values are normalized for each to lie between 0 and 1. Error bars represent bootstrap SEM equivalents. G) Cumulative distribution of Pearson’s r between ΔF/F and deconvolved tuning curves for two experiments (analyzing only neurons with reliably estimated ΔF/F tuning curves, n = 488/1131, 466/1060, respectively).
Methods
Experimental model details
All experiments were performed on mice between 1.5 to 14 months of age. CaMKII-tTA mice (RRID:IMSR_JAX:003010) crossed to tetO-GCaMP6s mice (RRID:IMSR_JAX:024742) were used when imaging L2/3 pyramidal cells. Both lines had been outcrossed to the ICR line (Charles River) for several generations. These mice were on a mixed background between outcrossed tetO-GCaMP and camk2-tTA on the C57/B6 background. For L4 PC experiments (resp. L2/3 SST, L2/3 VIP, and L2/3 PV experiments), Scnn1a-Tg3-Cre (resp. Sst-IRES-Cre, Vip-IRES-Cre, and Pv-IRES-Cre) mice were crossed to Ai162(TIT2L-GC6s-ICL-tTA2)-D mice (RRID:IMSR_JAX:031562).
For VIP optogenetic and calcium imaging experiments, Vip-IRES-Cre or Vip-IRES-Cre crossed to Sst-IRES-Flp were used. For optogenetic and electrophysiology experiments, Vip-IRES-Cre or Sst-IRES-Cre animals were used. Both female and male animals were used, and maintained on a 12:12 reversed light:dark cycle. All procedures were approved by the Animal Care and Use Committee of UC Berkeley.
Preparation for in vivo two photon imaging
Headplate attachment, habituation to running on a circular treadmill, and cranial window installation were performed as described previously (Lyall et al. 2020). Briefly, anesthesia was induced with 5% isoflurane and maintained at 1-3% during surgery. Respiratory rate and response to toe/tail pinching was monitored throughout surgery to ensure adequate anesthetic depth. 0.05 mg/kg of buprenorphine was administered subcutaneously for post-operative analgesia, and 2 mg/kg of dexamethasone as an anti-inflammatory. The scalp was disinfected with 70% alcohol and 5% iodine. The skin and fascia above the sensory cortices were removed and Vetbond (3M) was applied to the skull surface and wound margins. A custom titanium headplate was fixed to the skull with dental cement (Metabond). A cranial window was installed to provide for optical access to the cortex. A biopsy punch was used to create a 3.5mm diameter craniotomy over the left primary visual cortex. A window plug consisting of two 3 mm diameter coverslips glued to the bottom of a single 5 mm diameter coverslip using Norland Optical Adhesive #71 was placed over the craniotomy and sealed permanently using dental cement (Orthojet or Metabond). The dental cement was coated in a layer of black oxide to mitigate light leakage during subsequent experiments. Mice were provided at least two days to recover.
For VIP silencing experiments, neonatal Vip-IRES-Cre; Sst-IRES-Flp (P4–6) were briefly cryo-anesthetized and placed in a head mold. Transcranial injection of ∼45nl of undiluted AAV9-CAG-DIO-eNpHR3.0-mRuby3 (UPenn Vector Core) was performed using a Drummond Nanoject injector at three locations in left V1 using a glass pipette beveled to fine tip (∼30–60μm). With respect to the lambda suture coordinates for V1 were 0.0 mm AP, 2.2 mm L and injection was as superficial as possible under the skull.
For VIP activation experiments, Vip-IRES-Cre mice were injected with AAV9-syn-GCaMP6s (UPenn Vector Core) and rAAV9-syn-DIO-ChrimsonR-tdT (UNC Vector Core) virus in left V1. For VIP silencing experiments, Vip-IRES-Cre; Sst-IRES-Flp mice were injected with AAV9-syn-GCaMP6s (UPenn Vector Core) virus in left V1. Briefly, they were anesthetized and administered buprenorphine as described above. A dental drill (Foredom) was used to create a small burr hole 2.75 mm lateral to bregma. Then a WPI UltraMicroPump3 injector was used to inject 300-400 nL of the virus at a rate of 50 nL/min. Post-injection, the needle was left in the brain for 5 minutes to allow the viral solution to absorb into the tissue. Injected mice were provided 2-3 weeks with intermittent head-fixation over the circular treadmill to allow the infected neurons to ramp up expression of GCaMP6s.
Visual stimulus presentation, in vivo imaging, and pupil tracking
For visual stimulus presentation, the monitor was placed 13-15 cm from the eye. Animals were habituated to visual stimulation on the setup for at least two sessions prior to imaging. Before and/or after each experiment, receptive fields were mapped using 10° drifting grating patches. These patches had spatial frequency of 0.08 cycles per degree, and a temporal frequency of 1 Hz, with direction cycling through 0-360° over the course of 1.5 seconds. They appeared at randomly interleaved locations tiling a 40 x 40 visual degree grid, sampled at 5° intervals, with 1.5 second inter-stimulus intervals. In subsequent size-contrast experiments, the visual stimulus consisted of square wave drifting gratings, with directions tiling 0-360 degrees at 45° intervals, with a spatial frequency of 0.08 cycles per degree, and a temporal frequency of 1 Hz (calcium imaging experiments without optogenetics) or 2 Hz (calcium imaging and optogenetic experiments). Visual stimulus presentation lasted one second, followed by a one second inter-stimulus interval. Patch configurations, orientations, and sizes were pseudorandomly interleaved, and stimuli were generated and presented using the Psychophysics Toolbox (Brainard, 1997). Each distinct visual stimulus was displayed for 5-10 repetitions.
Mice were head-fixed on a freely spinning running wheel under a Nixon 16x-magnification water immersion objective and imaged with a two-photon resonant scanning microscope (Neurolabware) within a light tight box. The imaging FOV was 430 by 670 um, with four planes spaced 37.5 µm apart imaged sequentially using an electrotunable lens (Optotune), sampling each plane at an effective frame rate of 7.72 Hz. For L2/3 imaging, imaging depth was 100 – 300 µm, and for L4 imaging, depth was 350 – 500 µm deep. Electrical tape was applied between the objective and the mouse’s headplate to block monitor light from entering the microscope.
Locomotion was monitored using a rotary encoder, with trials where mean absolute run velocity > 1 cm/sec classified as “locomoting” and < 1 cm/sec classified as “non-locomoting”. Eye movements were imaged using a Basler Ace aCA1300-200um camera, with a hot mirror (Edmund Optics) placed between the eye and the monitor reflecting infrared light for eye imaging while transmitting visible light for visual stimulation. Infrared illumination was provided by the two photon imaging laser, transmitted through the pupils, as well as a panel of 850nm LEDs (CMVision). Pupil location and diameter were tracked using custom MATLAB code.
Imaging and optogenetic stimulation
Optogenetic stimulation through the objective was performed with a 617 nm LED (Thorlabs), filtered through a 632/22 nm single-band bandpass filter (Semrock), at an amplitude through the objective of either 6 mW (VIP silencing experiments) or 1.5 mW (VIP activation experiments). Electrical tape between the mouse’s head and the objective served to mitigate direct visual stimulation by the optogenetic light. The PMT was not gated, but protected by a strict shortpass filter. Optogenetic illumination began 0.25 seconds prior to visual stimulus delivery, and ended 0.25 seconds after. Small square wave optogenetic artifacts visible on the PMT were subtracted in post-processing.
Calcium imaging analysis
Motion correction and ROI segmentation was performed using Suite2p (Pachitariu et al. 2017). Neuropil subtraction was applied as described in (Lyall et al., 2020). ΔF/F traces were calculated as
with baseline F0 computed over a sliding 20th percentile filter of width 3000 frames. Because the inter-stimulus interval was reduced in V1 recordings to permit more stimuli to be displayed, calcium transients overlapped between successive trials. Therefore, we deconvolved calcium traces for this data using OASIS with L1 sparsity penalty (Friedrich et. al., 2017), using ΔF/F traces as input.
To confirm that the deconvolution procedure did not distort tuning curve measurements, we performed two experiments with longer inter-stimulus intervals (3 seconds rather than 1 second), varying only stimulus direction, at fixed 15° size and 100% contrast, for 20-30 trials per condition. Because evoked calcium transients did not overlap between successive trials in this condition, tuning curves computed using ΔF/F and deconvolved event rate should agree quantitatively (Fig. S18f). To restrict our analysis to neurons for which our estimate of the tuning curve with ΔF/F was robust (e.g. neurons that were visually responsive and orientation-tuned) we randomly split trials into two halves, computed tuning curves for each half, and computed Pearson’s correlation coefficients between the two independent tuning curve estimates. We determined that a neuron’s tuning curve measurement was robust if the two estimates were correlated with r > 0.5 (n = 488/1131, 466/1060 for the two experiments). For these neurons, we then computed tuning curves based on all trials, using ΔF/F and deconvolved event rates. Indeed, we found that for both mice, ΔF/F and deconvolved estimates of tuning curves were correlated with r > 0.9 in ∼80% of neurons.
Retinotopic map estimation
Responses to receptive field mapping stimuli were fit using 2D gaussians. The underlying retinotopic map was estimated using linear regression of cell centers (in microns of cortical space) vs. receptive field centers (in degrees of visual space). For subsequent analyses, neurons were separated based on either their receptive field center relative to the center of the size-contrast stimulus, or based on their location on the estimated retinotopic map, relative to the center of the stimulus representation, as indicated in the text. For each FOV, the retinotopic map orientation relative to the rostral-caudal and medial-lateral axes, and cortical magnification, was confirmed to be consistent with V1.
Simultaneous imaging of VIP and SST activity using Cre-Flp
We used VIP-Cre SST-Flp mice, injected with GCaMP6s expressed in all neurons. SST cells expressed cytosolic tdTomato in a Flp-dependent manner, while VIP cells expressed Cre-dependent mRuby3 fused to eNpHR3.0. Using calcium imaging, we identified SST cells using their bright, cytosolic red signal, compared with the dimmer, membrane bound mRuby3 in VIP cells; they could be distinguished both by membrane localization and brightness of the red fluorophore (fig. S8).
Recurrent network model
For a detailed expanation, see Supplementary Note. Briefly, we modeled cortical space using two spatial domains. The first represented neurons within ten visual degrees of retinotopic space of the stimulus representation’s center; the second, neurons beyond 10 degrees. Activity in layer 4 pyramidal cells (L4 PCs) in each spatial domain was treated as input to the four recurrently connected layer 2/3 (L2/3) populations in each pixel. The full weight matrix describing synaptic connections between the four L2/3 cell types in each of the two spatial domains was modeled as the product of a cell type-dependent term, describing the connection strength of cell type I onto cell type j, multiplied by a term describing the integration across space, and a term describing integration across orientations, of the postsynaptic population j. Thus, the full 8×8 matrix of recurrent synaptic connections was described by a 4×4 matrix, plus a 4-dimensional vector. A similar procedure was used to generate the full 2×8 matrix of feedforward synaptic connections from L4 PCs. A four-dimensional vector gave the bias current for each L2/3 population. The linear combination representing synaptic input currents was then passed through a distinct static nonlinearity for each cell type. The shape of this nonlinearity was determined by the intrinsic variability in a given cell type’s input current, which was fit for each cell type.
Because r appears on both the left and right sides of equation (1), we say that solutions for r must in general be “self-consistent.” For each cell population and each stimulus condition, a stimulus-dependent residual current parameter was introduced, added to the synaptic input and bias currents, so that perfect self-consistency was not required at each step of the optimization. However, squared error penalties on these residual currents ensured that the final network parameters achieved nearly perfect self-consistency. The model fits were randomly initialized, and optimized using L-BFGS. The cost function incorporated both the calcium imaging data for all cell types, and the optogenetic silencing data (combining both calcium imaging and electrophysiology results). The optogenetic data were fit by linearizing the model around the firing rates in the unperturbed condition. Several synaptic weights (L4 PCàSST, SSTàSST, and VIPàPC) were constrained to be 0, and the PCàPC weight was constrained to be large, in the sense that the product wPC->PC φPC > 1, in units where the synaptic leak current is 1, for every stimulus condition (with φPC as defined below).
For steady state solutions to equation (1), the change in firing rate r expected from a small change in input current I can be computed as the product
where 𝜑 is the slope of the firing rate nonlinearity around the steady state solution r. Because I is itself a function of r, we were able to simulate the response of a cell population j to small current injections to population j by computing a “response matrix” R as in (Del Molino et al., 2017):
This amounts to linearizing r about a steady state solution to equation (1). Here, Δh is a vector of optogenetically induced currents, and 𝛷 is a diagonal matrix whose entries are the values of 𝜑 for each cell type. The matrix R yields the theoretical prediction for the effect of small current injections to a given cell population j, on any cell population i. This matrix changes as a function of stimulus via changes in r, and thus 𝜑 for each cell type.
We leveraged these recurrent network model fits to predict the effects of manipulations on network activity, some experimentally realizable with current technology, and some not. First, we simulated the deletion of certain synaptic connections. For these simulations, we allowed the network to evolve to a new steady state according to equation (1), after setting certain elements of the 4×4 L2/3 synaptic weight matrix to 0, with all other parameters held constant. Second, we simulated the injection of inhibitory (negative) or excitatory (positive) current to specific cell types, modeled as a stimulus-dependent DC offset to the synaptic input current for that cell type. Again, we allowed the network to evolve to a new steady state according to equation (1). In both of these cases, we computed both the perturbed steady state firing rates r, as well as the perturbed response matrix R, resulting from the perturbed values for 𝛷 and W.
For simulations of optogenetic silencing and activation of VIP cells, we tuned the magnitude of current injection for each model fit based on the computed response matrix. In particular, for both silencing and activation simulations, we chose current magnitude to maximize the dynamic range of the term corresponding to PC cooperation or competition across space (Rnear PC, far PC), defined as the absolute difference between the maximum and minimum values of Rnear PC, far PC across stimuli.
Quantification and statistical analysis
Statistically significant differences between conditions were determined using standard nonparametric tests in the SciPy library, including the Wilcoxon signed-rank test and Mann-Whitney U test. Analyses were performed on each ROI’s deconvolved event rate for each trial. A single trial’s response was calculated as the average deconvolved event rate during the entire 1 second of stimulation. 95% confidence intervals and SEM equivalents (68% confidence intervals) were generated via bootstrap. For validation of the deconvolution procedure, trials were split randomly into two halves, and tuning curves were computed on each half of trials. Neurons whose tuning curves computed on both halves of the data using ΔF/F agreed with Pearson’s r>0.5 were retained. For these neurons, tuning curves were computed across all trials using both ΔF/F and deconvolved event rate (fig. S18f,g).
Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Contributions
D.P.M., J.V., A.P., K.D.M., and H.A. conceived the study. D.P.M. performed the calcium imaging experiments. J.V. performed the extracellular electrophysiology experiments. D.P.M. designed and built the recurrent network model, and designed and carried out in silico experiments. D.P.M. and H.A. wrote the paper, with input from all other authors.
Acknowledgements
The authors acknowledge the GENIE Project, Janelia Farm Research Campus, and the Howard Hughes Medical Institute for the GCaMP6 viruses. Thanks to the members of the Adesnik Lab, particularly Hayley Bounds, Mora Ogando, and Hyeyoung Shin for helpful comments. Thanks also to Charles G. Frye, Sang Min Han, and Benjamin E. Smith. D.P.M. was supported by an NSF Graduate Research Fellowship. A.P. would like to acknowledge the support of the Swartz Foundation Fellowship for Theory in Neuroscience 2019-4 and 2020-6. H.A. is a New York Stem Cell Foundation-Robertson Investigator. This work was supported by The New York Stem Cell Foundation. This work was supported by NEI grant R01EY023756-01 and U19NS97613.
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