Initial simulations produced no activity, and it was necessary to compensate for missing excitatory input from neurons external to the model. We estimated that the number of missing synapses for the full nbS1 and seven hexagon subvolume as approximately two and seven times the number of internal synapses, based on Oh et al., 2014. We model the effect of these missing synaptic inputs explicitly as time-varying and statistically independent somatic conductance injections, using Ornstein–Uhlenbeck (OU) processes that mimic aggregated random background synaptic inputs (Destexhe et al., 2001; Figure 4B1; see also ‘Discussion’). The mean (OUμ\begin{document}$OU_{\mu}$\end{document}) and standard deviation (OUσ\begin{document}$OU_{\sigma}$\end{document}) are defined as a percentage of an individual cell’s input conductance at its resting membrane potential. The choice of OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} for different populations and [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} (Figure 4B2) determines the model’s emergent dynamics and mean firing rates (Figure 4B3). Initial simulations showed that using the same value of OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} for all neurons makes some populations highly active whilst others are silent or produces network-wide bursts. Finding population-specific OU\begin{document}$OU$\end{document} parameters which produce stable in vivo-like activity is challenging, however, due to the non-linearity and computational cost of simulations.

We developed an algorithm that efficiently calibrates population-specific OU\begin{document}$OU$\end{document} parameters for different values of [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}, which affects the strength and reliability of synaptic transmission (see ‘Synaptic physiology’). Additionally, it fixes the ratio OUσ/OUμ\begin{document}$OU_{\sigma}/OU_{\mu}$\end{document}, denoted ROU\begin{document}$R_{OU}$\end{document}, across all neurons to specific values representing the amount of noise in the extrinsic inputs (Figure 4B2). As extracellularly derived firing rates are known to be severely overestimated to an unknown degree (Olshausen and Field, 2006; Wohrer et al., 2013; Buzsáki and Mizuseki, 2014), the algorithm finds parameters which produce realistic inter-population firing rate ratios at different global levels of activity (Figure 4B3). Specifically, to account for uncertainty in the firing rate bias during spontaneous activity from extracellular spike sorted recordings it targets mean spontaneous firing rates of neuron populations that are a constant fraction PFR\begin{document}$P_{FR}$\end{document} of in vivo reference values, for 10 PFR\begin{document}$P_{FR}$\end{document} values between 0.1 and 1. We refer to [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}, ROU\begin{document}$R_{OU}$\end{document} and PFR\begin{document}$P_{FR}$\end{document} as meta-parameters. The initial calibration was made for the seven hexagonal subvolume, and later generalized to the full nbS1 model.

The algorithm was first run for [Ca2+]o=1.1\begin{document}$[Ca^{2+}]_{o}=1.1$\end{document} mM, ROU=0.4\begin{document}$R_{OU}=0.4$\end{document}. Target firing rates for the 10 PFR\begin{document}$P_{FR}$\end{document} values were reached (Figure 4C) after five iterations of 10 simulations of 6.5 seconds (Figure 4D, left upper). Only three iterations were needed when calibration began using previously calibrated parameters for different ROU\begin{document}$R_{OU}$\end{document} and [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} (Figure 4D, right upper). This allowed us to parameterize extrinsic input for a range of combinations of the three meta-parameters (Figure 4D, lower and E, left) within biologically relevant ranges ([Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}: 1.05–1.1 mM; Jones and Keep, 1988; Massimini and Amzica, 2001; Amzica et al., 2002; Gonzalez et al., 2022; PFR\begin{document}$P_{FR}$\end{document}: 0.1–1.0; ROU\begin{document}$R_{OU}$\end{document}: 0.2–0.4; Destexhe et al., 2001). We found that the resulting mean conductance injections were highly population-specific (Figure 4E, center). The range of OUμ\begin{document}$OU_{\mu}$\end{document} values between populations was on average 5.2 times higher than the range of OUμ\begin{document}$OU_{\mu}$\end{document} values for a single population across meta-parameter combinations (Figure 4E, right). This was expected, as the missing mid-range innervation is known to have specific and heterogeneous laminar profiles (Felleman and Van Essen, 1991; Harris et al., 2019; Gao et al., 2022).

We estimated the number of missing synapses per neuron assuming a total density of E synapses of 1.1 synapses/µm, based on mean spine densities (Larkman, 1991; Datwani et al., 2002; Kawaguchi et al., 2006), and subtracting the number of synapses present in the model (Figure 4—figure supplement 2). We confirmed a strong correlation between this measure and required conductance injection (Figure 4F). Heterogeneity in synaptic density within and across neuron classes and sections makes estimating the number of missing synapses challenging (De Felipe and Fariñas, 1992). Changing the assumed synaptic density value of 1.1 synapses/µm would only change the slope of the relationship, however. Estimates of mean number of existing and missing synapses per population were within reasonable ranges; even the larger estimate for L5 E (due to higher dendritic length; Figure 4—figure supplement 2) was within biological estimates of 13,000±3500 total afferent synapses (De Felipe and Fariñas, 1992).

Rasters and histograms of spontaneous activity for two meta-parameter combinations are shown in Figure 4G1 (and for all combinations in Figure 4—video 1). The first simulation uses a higher ROU\begin{document}$R_{OU}$\end{document}, lower PFR\begin{document}$P_{FR}$\end{document}, and lower synaptic transmission reliability ([Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}). In the second simulation, we found larger fluctuations, correlated between E and I populations across layers. Overall, increasing [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} and PFR\begin{document}$P_{FR}$\end{document}, and decreasing ROU\begin{document}$R_{OU}$\end{document}, increases the amplitude of correlated fluctuations (Figure 4—video 1, Figure 4G2) and increases power at lower frequencies (Figure 4G3). This supports the notion that decreasing ROU\begin{document}$R_{OU}$\end{document} or increasing [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} shifts the model along a spectrum from externally (noise) driven to internally driven correlated activity. Note that the most correlated meta-parameter combination [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}: 1.1 mM, ROU\begin{document}$R_{OU}$\end{document}: 0.2, PFR\begin{document}$P_{FR}$\end{document}: 1.0 produced network-wide ‘bursting’ activity, which we define as highly synchronous all or nothing events (Figure 4—video 1). Such activity, which may be characteristic of epileptic activity, can be studied with the model but is not the focus of this study.

We reemphasize that the [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}, ROU\begin{document}$R_{OU}$\end{document}, and PFR\begin{document}$P_{FR}$\end{document} meta-parameters account for uncertainty of in vivo extracellular calcium concentration, the nature of inputs from other brain regions and the bias of extracellularly recorded firing rates. Whilst estimates for [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} are between 1.0 and 1.1 mM (Jones and Keep, 1988; Massimini and Amzica, 2001; Amzica et al., 2002; Gonzalez et al., 2022) and estimates for PFR\begin{document}$P_{FR}$\end{document} are in the range of 0.1–0.3 (Olshausen and Field, 2006), combinations of these parameters supporting in vivo-like stimulus-responses in later sections will offer a prediction for the true values of these parameters. Both these later results and our recent analysis of spike sorting bias using this model (Laquitaine et al., 2024) predict a spike sorting bias corresponding to PFR∼0.3\begin{document}$P_{FR}\sim 0.3$\end{document}, confirming the prediction of Olshausen and Field, 2006.

To study the firing rate distributions of different subpopulations and m-types, we ran 50-second simulations for the meta-parameter combinations: [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}: 1.05  mM, ROU\begin{document}$R_{OU}$\end{document}: 0.4, PFR\begin{document}$P_{FR}$\end{document}: 0.3, 0.7 (Figure 4—figure supplement 3). Different subpopulations showed different sparsity levels (proportion of neurons spiking at least once) ranging from 6.6 to 42.5%. Wohrer et al., 2013 considered in detail the biases and challenges in obtaining ground truth firing rate distributions in vivo, and discuss the wide heterogeneity of reports in different modalities using different recording techniques. They conclude that most evidence points towards long-tailed distributions with peaks just below 1Hz\begin{document}$1Hz$\end{document}. We confirmed that spontaneous firing rate distributions were long-tailed (approximately lognormally distributed) with means on the order of 1Hz\begin{document}$1\,Hz$\end{document} for most subpopulations. Importantly the layer-wise means were just below 1Hz\begin{document}$1\,Hz$\end{document} in all layers for the PFR=0.3\begin{document}$P_{FR}=0.3$\end{document} meta-parameter combination. Moreover, our recent work applying spike sorting to extracellular activity using this meta-parameter combination found spike sorted firing rate distributions to be lognormally distributed and very similar to in vivo distributions obtained using the same probe geometry and spike sorter (Laquitaine et al., 2024).

In the horizontal dimensions, under higher correlation regimes, fluctuations are spatially coordinated and global within the central hexagon of the simulated subvolume (Figure 4H, Figure 4—video 2). In depth, the size of fluctuations and level of correlated activity increases from supragranular to infragranular layers (Figure 4G1, I, left, Figure 4—video 1), suggesting that activity in deeper layers of the model is more internally driven. We characterized the effect of recurrent connectivity by measuring the layer-specific decrease in firing rates when neurons in the model are disconnected from each other. As expected, we found that the effect (quantified by the ratio between connected and disconnected firing rates: RC/U\begin{document}$R_{C/U}$\end{document}) increased from supra- to infragranular layers (Figure 4I, right).

By analyzing the underlying network structure, we observed a corresponding gradient in the topology of intra-layer synaptic connectivity from supra- to infragranular layers. We calculated the mean node participation of neuron populations in various dimensions (see ‘Methods’; Figure 4J, top). For dimension 1, this is simply the degree of a neuron; for dimensions above 1, this generalizes the notion to counting participation in dense, directed motifs of increasing size (directed simplices; Reimann et al., 2017). We found that correlations of this measure with the ratio of connected and disconnected firing rates increased with dimension (Figure 4J, bottom, 100% of data), indicating the importance of large directed simplices in shaping activity. Curiously, the correlations for higher dimensions were driven by a small number of neurons with very high node participation. This was indicated by a sharp drop in correlation when neurons above a given value were excluded (Figure 4J, bottom). Additionally, we studied the structural effect on the firing rate (here measured as the inverse of the inter-spike interval, ISI, which can be thought of as a proxy of non-zero firing rate). We found that for the connected circuit, the firing rate increases with simplex dimension; in contrast with the disconnected circuit, where this relationship remains flat (see Figure 4—figure supplement 4, red vs. blue curves and ‘Methods’).

This also demonstrates high variability between neurons, in line with biology, both structurally (Towlson et al., 2013; Nigam et al., 2016) and functionally (Wohrer et al., 2013; Buzsáki and Mizuseki, 2014). We next identified the cell types that are overexpressed in the group of neurons that have the 5% highest values of node participation across dimensions (Figure 4—figure supplement 5). This could inform theoretical point neuron models with cell-type specificity, for example. We found that while in dimension 1 (i.e., node degree) this consists mostly of inhibitory cells, in higher dimensions the cell types concentrate in layers 4–6, especially for TPC neurons. This is in line with our structural layer-wise findings in Figure 8B in Reimann et al., 2024.

We compared stimulus-responses with in vivo barrel cortex responses to both single whisker deflections and active whisker touches under anaesthetized (Reyes-Puerta et al., 2015b) and awake states (Yu et al., 2019), respectively. While the model is of non-barrel somatosensory regions, this nevertheless provides validations of overall excitability and the laminar structure of responses reflecting general trends of cortical processing. We activated a percentage (FP\begin{document}$F_{P}$\end{document}) of the VPM fibers projecting to the central column of the seven-column subvolume (Figure 5A1). For each selected thalamic fiber, spike times were drawn from VPM peristimulus time histogram (PSTH) recorded in vivo for the two stimulus types (Figure 5A2; ‘Methods’). For both stimulus types, a single thalamic stimulus was presented 10 times at 1-second intervals at three intensities (FP:5%,10%,15%\begin{document}$F_{P}:5\%,10\%,15\%$\end{document}).

For the parameter combination [Ca2+]o=1.05\begin{document}$[Ca^{2+}]_{o}=1.05$\end{document} mM, ROU=0.4\begin{document}$R_{OU}=0.4$\end{document}, PFR=0.3\begin{document}$P_{FR}=0.3$\end{document} and FP=10%\begin{document}$F_{P}=10\%$\end{document}, E and I populations in each layer show clear responses on each trial (Figure 5B; three trials shown), except for L1. Figure 5—videos 1 and 2 show all simulated combinations of the four meta-parameters. Out of 72 parameter combinations, 21 passed an initial assessment of in vivo similarity to the in vivo data based on latencies and decays (see ‘Methods’, Figure 5C, Figure 5—figure supplement 1). Responses remained localized to within 600 μm\begin{document}$\mu m$\end{document} of the stimulus location (Figure 5D, Figure 5—video 3). In vivo, layer-wise I populations precede the corresponding E populations and response latencies increase with distance from thalamus, except for the fast response of L4 I. The latencies and decays are matched by criteria passing simulations (Figure 5C, E, left), except for a longer L4 I latency, and shorter and longer sustained responses of L2/3 E and L4 E. PV+ and Sst+ subpopulations respond reliably in layers 2–6, but the 5HT3aR+ subpopulation responses are weaker and less reliable (Figure 5—figure supplement 1). Under the active whisker touch paradigm, PV+ latencies precede Sst+ latencies in vivo, and either precede or are simultaneous with Sst+ latencies in silico (Figure 5E, right).

The passing parameter combinations form a contiguous region in the parameter space (Figure 5F), characterized by combinations of low PFR\begin{document}$P_{FR}$\end{document}, [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} and FP\begin{document}$F_{P}$\end{document} with higher ROU\begin{document}$R_{OU}$\end{document}, which displayed weakly correlated spontaneous activity (compare Figure 5F with Figure 4G2). This offers a prediction that true in vivo firing rates are within the range of these lower FRs. Specifically, simulations with PFR\begin{document}$P_{FR}$\end{document} from 0.1 to 0.5 robustly support realistic stimulus-responses, with the middle of this range (0.3) corresponding with estimates of in vivo recording bias; both the previous estimates of Olshausen and Field, 2006 and from a spike sorting study using this model (Laquitaine et al., 2024). The remaining results apply to the criteria passing simulations. We characterized the magnitude of responses by RE\begin{document}$R_{E}$\end{document}, the ratio between the peak of the evoked response and the pre-stimulus baseline activity level. Assuming that extracellular sampling biases are similar during spontaneous and evoked activity, RE\begin{document}$R_{E}$\end{document} provides a bias-free metric for comparing response magnitude with in vivo. Decreasing ROU\begin{document}$R_{OU}$\end{document} and PFR\begin{document}$P_{FR}$\end{document}, and increasing [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} and FP\begin{document}$F_{P}$\end{document} led to a global increase of RE\begin{document}$R_{E}$\end{document}, and results matched in vivo closely for a large part of the parameter space (Figure 5F).

Interestingly, the parameter combination closest to in vivo was central in the parameter space of criteria passing simulations (Figure 5G, left). Values of RE\begin{document}$R_{E}$\end{document}, normalized by the mean RE\begin{document}$R_{E}$\end{document} across populations, were remarkably constant (Figure 5G, right), indicating that variation of the parameters provides a global scaling of response magnitude. Moreover, I populations matched the in vivo reference closely, while the responses of L2/3 E were slightly greater, and for L4 E and L5 E slightly weaker. The region of the parameter space where responses match in vivo for the active whisker touch stimulus was the same as for single whisker deflections (Figure 5—figure supplement 2). Latencies were also similar to in vivo, with the main discrepancy being slower responses in L4 (E and I). With respect to the meta-parameters, we found that the best match for the anesthetized state was characterized by lower firing rates (PFR\begin{document}$P_{FR}$\end{document}) and reduced external noise levels (lower ROU\begin{document}$R_{OU}$\end{document}) compared to the awake active whisker touch paradigm (white areas in Figure 5F, Figure 5—figure supplement 2B). These results fit expectation for anaesthetized and awake states respectively, and provide predictions of their spontaneous firing rates, noise levels and corresponding in silico regimes.

Response sparsity (i.e., the proportion of neurons spiking at least once following a stimulus) varied across populations and meta-parameter combinations, but was around the range of 10–20% reported in vivo in the barrel cortex (Barth and Poulet, 2012; Figure 5—figure supplement 1D). Interestingly, excitatory population responses were sparser than the corresponding inhibitory layer-wise populations across layers. The observed heterogeneous layer-wise population sparsities offer a prediction for in vivo. Moreover, the majority of responding cells spike only once to single whisker deflections (Figure 5—figure supplement 1E), as reported in vivo (Isbister et al., 2021).

In the canonical model of the cortex (reviewed, e.g., in Lübke and Feldmeyer, 2007; Feldmeyer, 2012) information from the thalamus arrives to L4, then propagates to L2/3, from there to L5 (which serves as the main cortico-cortical output layer) and lastly to L6 (which projects back to the thalamus). The coordinated action of all layers of S1 is required for high-level behavioral tasks (Park et al., 2020). As the canonical model is based on the highest layer-wise density of axons, it cannot describe all interactions in the cortex. For example, VPM does not only innervate L4, but also the border of L5 and L6, as well as the bottom of L2/3 (Meyer et al., 2010; Constantinople and Bruno, 2013; Sermet et al., 2019).

To study how L4 contributes to the stimulus preference of L2/3 PCs, Varani et al., 2022 used optogenetic inactivation of L4 PCs during whisker stimulation and quantified the changes in the subthreshold response of L2/3 PCs. They found that the early phase of the subthreshold response significantly differed from the control condition if the whisker was deflected in either the most or the least preferred direction (see the top and bottom rows of their Figure B,C). From this they concluded that both L4 and VPM contribute to the direction tuning of L2/3 PCs. After reproducing their experimental conditions in silico (Figure 6A, B, Figure 6—figure supplement 2; see ‘Methods’), we confirmed that we can reproduce their results, that is, subthreshold responses of L2/3 PCs decreased, when L4 PCs were inhibited (Figure 6C for preferred direction whisker stimulation; see ‘Methods’).

We then leveraged our in silico setup to study what Varani et al., 2022 could not because of methodological limitations. In our reading, the authors aimed to test how direct E connections from L4 PCs to L2/3 PCs influence the stimulus representation in L2/3. This connection cannot specifically be blocked in vivo, instead (95% of) the L4 PC population is inhibited (as well as some lower L3 PCs). In our setup, we could selectively block the connection and found almost the same result (compare Figure 6C and D, left). This extends the conclusion of Varani et al., 2022: L4 PCs contribute to the stimulus preference of L2/3 PCs via direct E connections, and not via disynaptic inhibition.

The authors also discussed studying L5 PCs’ contribution to L2/3 responses (as a large fraction of L5 PC axons terminate in L2/3), but this is infeasible with current mouse lines. Leveraging our model, we found that L5 contributes much less to subthreshold L2/3 traces than L4 (Figure 6D, right). Extending to other presynaptic layers, we found that the contribution of L2/3 is similar to that of L4, whereas inputs from L6 are negligible (Figure 6D, right). Whilst mouse lines targeting L5 PCs might arrive soon (which could validate our prediction), blocking L2/3 connections between L2/3 cells without hyperpolarizing the same L2/3 population seems only achievable in silico.

Shapiro et al., 2022 compared the modulatory effects of optogenetic activation of interneuron subtypes on contrast tuning of neurons in V1. Whilst visual regions differ from somatosensory regions, the study provided an opportunity to explore the generality of interactions between E and I subpopulations. We therefore created a version of the study in silico, presenting spatio-temporally modulated patterns with various contrast levels through the VPM inputs (Figure 6E, F; see ‘Methods).

Overall, we found within the single simulated column 228 PCs and 259 PV+ interneurons with robust contrast tuning of their responses (see ‘Methods’). Within spike detection range of a vertically penetrating extracellular electrode (50 µm; Henze et al., 2000; Buzsáki, 2004), we found 15 PCs and 13 PV+ interneurons with robust tuning, which is roughly comparable to the original study (average of 8.2 tuned PCs and 3.0 PV +neurons per mouse Shapiro et al., 2022). Unlike the original study we found no Sst+ neurons with robust tuning.

Additionally, we found the following results, all in line with Shapiro et al., 2022: The firing rates of both PCs and PV+ neurons were affected by optogenetic activation of the PV+ subpopulation (Figure 6G), resulting in changes to the contrast tuning curves of these populations (Figure 6H, Figure 6—figure supplement 4A). The main effect of the optogenetic manipulation was an increase in contrast tuning for PV+ and a decrease for PCs. However, at high contrasts, we observed a paradoxical effect of the optogenetic stimulation on L6 PV+ neurons, reducing their activity with increasing stimulation strength (Figure 6—figure supplement 4B; Mahrach et al., 2020). This effect did not occur under gray screen conditions (i.e., at contrast 0.0) with a constant background firing rate of 0.2 Hz or 5 Hz, respectively (not shown). The individual tuning curves could be accurately fit by sigmoidal functions (rPV+2=0.995±0.008\begin{document}$r_{PV+}^{2}=0.995\pm 0.008$\end{document}), and consequently the effect of optogenetic activation could be quantified in terms of changes to the fitted parameters (Figure 6H2 inset, Figure 6—figure supplement 5; ‘Methods’). We found great variability between neurons with increasing trends for parameter m\begin{document}$m$\end{document} in PV+ and c50\begin{document}$c_{50}$\end{document} in PCs, and decreasing trends for Rmax\begin{document}$R_{max}$\end{document} in PV+ and both m\begin{document}$m$\end{document} and Rmax\begin{document}$R_{max}$\end{document} in PCs. Unlike in Shapiro et al., 2022, we found in addition an increasing trend of c50\begin{document}$c_{50}$\end{document} also in PV+ interneurons (Figure 6—figure supplement 5).

Comparing three abstract mathematical models (Shapiro et al., 2022; ‘Methods’), we found that the saturation additive model best captured the effect of the optogenetic manipulation for PV+ neurons (Figure 6—figure supplement 6A, B1), as in the reference study. The relative contributions of saturation and addition varied strongly between individual neurons (Figure 6—figure supplement 6C1). At low intensities of the optogenetic manipulation, this distribution matched qualitatively the results of Shapiro et al., 2022, but at higher intensities we observed a shift towards stronger saturation. Combining the saturation additive model with a simplified, population-level model of PC firing (Shapiro et al., 2022; ‘Methods’) provided a good description of the observations (Figure 6—figure supplement 6B2) with relative contributions of saturation and addition that qualitatively match the reference (Figure 6—figure supplement 6C2).

Prince et al., 2021 studied how different I subpopulations represent signals that are encoded as changes in the firing rate or synchronicity of PCs (Figure 6I). We repeated their study in silico (Figure 6J), but using in vivo-like conditions as the authors have suggested in their ‘Discussion’. The original study pointed out the importance of membrane properties and short-term dynamics of synaptic inputs onto the subpopulations in shaping the results. Note that the lower synaptic reliability in vivo weakens synaptic depression (Borst, 2010), and the ongoing background input leads to higher membrane conductance (Destexhe et al., 2001); therefore, our results are expected to differ substantially and provide an independent prediction for a different dynamic state. While in the original in vitro study stimulation of 10 PCs was sufficient to find a decodable signal, we expected a larger number to be required under our in vivo-like conditions due to the lower [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}, and the higher level of noise (see ‘Methods).

Indeed, we found little discernible mutual information in I spiking for the activation of 10 PCs, but that mutual information increased with the number of activated neurons (Figure 6K, right). For 1000 activated neurons each of the three I subpopulations in L2/3 showed clear but qualitatively unique modulation for both encoding schemes (Figure 6J). As in Prince et al., 2021, we found differences in the encoding capabilities of the I subpopulations (Figure 6K). We found strongest encoding in PV+ neurons for both schemes, and overall low encoding strength in Sst+ neurons. Further, we found overall low amounts of mutual information for the synchronous stimulus, which is in line with Prince et al., 2021, as they linked encoding of that stimulus to depressing synaptic dynamics, which would be weakened in vivo.

We next explored how certain trends in inhibitory targeting observed in a recent mouse electron microscopic connectome (Schneider-Mizell et al., 2025; Figure 7A) affect spontaneous and evoked activity. Consequently, an alternative connectome which quantitatively recreates these trends has been built (Reimann et al., 2024). We refer to this as the Schneider–Mizell compatible connectome (SM-connectome). It ensures that PV+ neurons target the perisomatic region, VIP+ neurons target other inhibitory neurons, and cells in L1 connect predominantly monosynaptically. Consequently, inhibition onto E neurons is sparser and closer to the soma (Figure 7A2). After validating the presence of these trends, we characterized how this affects the dynamics of the spontaneous and evoked states (Figure 7A3). Note that individual synapses were recalibrated to preserve the pathway specific reference PSP amplitudes. As expected, the largest change was for PV+ neurons where the average number of vesicles in the release-ready pool NRRP\begin{document}$N_{RRP}$\end{document} was increased by 2.4 times.

Inspite of this, the change in connectivity affected the activity sufficiently that recalibration of missing synaptic compensation was needed to attain the target firing rates for the original meta-parameter combinations (Figure 7—figure supplement 1). Mean conductances onto I neurons had to be increased, indicating the efficacy of the newly introduced I-I targeting by VIP+ neurons (Figure 7B1). On the other hand, conductances for E neurons remained roughly the same, except for L6. Curiously, we found that the firing rates of I populations were reduced when the internal connectivity was activated compared to when it was inactive, further highlighting the efficacy of the I-I targeting (Figure 7B2, Figure 7—figure supplement 1). For E neurons in L2-5, activating internal connectivity increased firing rates, but less than in the original connectome. As the number of inhibitory synapses innervating them decreased (Figure 7A2), this indicates that the placement of PV +synapses closer to the soma increased the efficacy of inhibitory as expected. Taken together, this indicates that in the SM-connectome, I populations are more externally driven and more internally inhibited (as a function of proximity to L4), and L6 E more internally driven during spontaneous activity. Over the different meta-parameter combinations, correlation in the network decreased relative to the original circuit with some exceptions (Figure 7B3, Figure 7—figure supplement 1). This indicates that activity in the SM-connectome is shifted slightly towards a more asynchronous state.

By correlating the structural and functional changes we concluded that the increased conductance injection into the I populations can be explained by the increased inhibitory synapse count (Figure 7C). Conversely, the mostly decreased synapse counts for E populations did not lead to a decrease of conductance injection, further indicating that the more perisomatic positioning of PV+ synapses compensates for the reduced synapse counts.

The lack of effect onto most of the E populations disappeared in the evoked state (Figure 7D). Overall, responses increase strongly in L23 and slightly decreased in L5 and L6 (Figure 7D1), while latencies of responses increased in every layer (Figure 7D2), suggesting different roles of the more specific inhibitory targeting in different layers.

Studying somatic membrane potentials for different subpopulations in response to whisker deflections shows that PV+, L23E, and L4E subpopulations are largely unaffected in the SM-connectome (Figure 7E). Interestingly, Sst+ and 5HT3aR+ subpopulations show a strong hyperpolarization in the late response that is not present in the original connectome. Interestingly, this corresponds with a stronger late response in L5/6 E populations, which could be caused by disinhibition due to the Sst+ and 5HT3aR+ hyperpolarization. This could be explored further in follow-up studies using our connectome manipulator tool (Pokorny et al., 2025).

After calibrating the model of extrinsic synaptic input for the seven-column subvolume, we tested to what degree the calibration generalizes to the entire nbS1. Notably, this included the addition of mid-range connectivity (Reimann et al., 2024). The total number of local and mid-range synapses in the model was 9138 billion and 4075 billion, that is, on average full model simulations increased the number of intrinsic synapses onto a neuron by 45%. Particularly, we ran simulations for PFR∈[0.1,0.15,...,0.3]\begin{document}$P_{FR}\in[0.1,0.15,...,0.3]$\end{document} using the OU parameters calibrated for the seven-column subvolume for [Ca2+]o=1.05\begin{document}$[Ca^{2+}]_{o}=1.05$\end{document} mM and ROU=0.4\begin{document}$R_{OU}=0.4$\end{document}. Each of these full nbS1 simulations produced stable non-bursting activity (Figure 8A), except for the simulation for PFR=0.3\begin{document}$P_{FR}=0.3$\end{document}, which produced network-wide bursting activity (Figure 8—videos 1 and 2). Activity levels in the simulations of spontaneous activity were heterogeneous (Figure 8B, Figure 8—video 3). In some areas, firing rates were equal to the target PFR\begin{document}$P_{FR}$\end{document}, whilst in others they increased above the target (Figure 8C). In the more active regions, mean firing rates (averaged over layers) were on the order of 30–35% of the in vivo references for the maximum non-bursting PFR\begin{document}$P_{FR}$\end{document} simulation (target PFR:0.25\begin{document}$P_{FR}:0.25$\end{document}). This range of firing rates again fits with the estimate of firing rate bias from our paper studying spike sorting bias (Laquitaine et al., 2024) and the meta-parameter range supporting realistic stimulus-responses in the seven-column subvolume. This also predicts that the nbS1 cannot sustain higher firing rates without entering a bursting regime.

The subregion with consistently higher firing rates was the upper-limb representation (S1ULp), separated from subregions of lower activity by the dysgranular zones (S1DZ, S1DZO). This demonstrates that the larger spatial scale of the model supports several independently acting functional units. Locations with higher firing rates were accompanied by higher spiking correlations of the local population (Figure 8B2, Figure 8—video 3), indicating activity that was more driven by intrinsic excitation. Unlike in the simulations of smaller volumes, the correlation emerged mostly from short, transient packets of activity in L6 (Figure 8A). Consequently, deviation from the target PFR\begin{document}$P_{FR}$\end{document} in those cases was largest in L6 (Figure 8C). Taken together, it appears as if the additional synapses from mid-range connectivity moved the model along the spectrum from extrinsically vs. intrinsically driven, but further for some regions than for others. We confirmed a divergence into two populations: one with correlation slightly increased from the simulations of smaller volumes, and one with almost maximal correlations (Figure 8D). This distinction was determined mostly in L6 with increases of correlations in other layers remaining small.

The distance dependence of correlations followed a similar profile to that observed in a dataset characterizing spontaneous activity in the somatosensory cortex (Reyes-Puerta et al., 2015a; compare red line in Figure 8I with Figure 8—figure supplement 1). In the in vivo dataset spiking correlation was also low but highest in lower layers, with short ‘up-states’ in spiking activity constrained to L5 and 6 (see Figure 1E and F in Reyes-Puerta et al., 2015a). In the model, they are constrained to L6.

We repeated the previous single whisker deflection evoked activity experiment in the full model, providing a synchronous thalamic input into the forelimb sub-region (S1FL; Figure 8E, Figure 8—videos 4–6). Responses in S1FL were remarkably similar to the ones in the seven-column subvolume, including the delays and decays of activity (Figure 8F). However, in addition to a localized primary response in S1FL within 350 μm\begin{document}$\mu m$\end{document} of the stimulus, we found several secondary responses at distal locations (Figure 8E, Figure 8—video 6), which was suggestive of selective propagation of the stimulus-evoked signal to downstream areas efferently connected by mid-range connectivity. The response of the main activated downstream area (visible in Figure 8E) was confined to L6 (Figure 8G). In a follow-up study using the model to explore the propagation of activity between cortical regions (Bolaños-Puchet and Reimann, 2024), it is described how the model contains both a feedforward projection pattern, which projects to principally to synapses in L1 and L23, and a feedback-type pattern, which principally projects to synapses in L1 and L6. On visualizing the innervation profile from the stimulated hexagon to the downstream hexagon, we can see that we have stimulated a feedback pathway (Figure 8—figure supplement 1).

As the model is homogeneous across the different subregions in terms of neuronal morphologies and physiology, we expected the differences in spontaneous and evoked activity across the model to be explained by the topology of synaptic connectivity (Reimann et al., 2024). While the extrinsic input from the OU injections was uncorrelated by design, synaptic input from local connectivity would feature at least some degree of correlation. This led to asking, how correlated was the input from mid-range connections? We estimated for each pair of mid-range connections innervating a 460 μm\begin{document}$\mu m$\end{document} hexagonal subvolume its spiking correlation and compared the resulting distribution to the correlation within the subvolume itself (see ‘Methods’; Figure 8H, upper). We found low correlations for most pairs, but with a significant number of high-correlation outliers for subvolumes with high internal correlations. Moreover, when we considered the mean of the measure, we found that it explains most of the variability in internal correlations, for both spontaneous (Figure 8H, lower) and evoked states (Figure 8—figure supplement 1).

This led to the following tentative explanation: Local connectivity provides inputs from within 500 μm\begin{document}$\mu m$\end{document}, which is virtually guaranteed to be correlated to some degree (Figure 8I upper vs. lower, orange). This is a result of connections being locally dense, as they are concentrated within a small neighborhood (Figure 8 lower, green vs. orange). mid-range connectivity originates from further away, sampling from different functional units that may or may not be correlated, and being more diluted (Figure 8I lower, green vs. blue). Consequently, mid-range inputs are likely to act not much different from the uncorrelated OU process, unless this is overcome by a non-random topology of mid-range connectivity.

Specifically, we considered the mid-range connectivity at meso-scale in terms of the graph of synapse counts between 460 μm\begin{document}$\mu m$\end{document} subvolumes. When the graph was thresholded at 8 million synapses, most subvolumes lacked connections at that strength completely, but others formed a single connected component, indicating the formation of a rich club (Colizza et al., 2006; Figure 8—figure supplement 1J, upper, red and orange). We found that subvolumes with high internal correlation were part of the rich club, or directly adjacent to one of its members (Figure 8J). In the presence of strong thalamic inputs, this could be overcome, as the increased activity level spread along sufficiently strong mid-range connections (Figure 8K), albeit with substantial delays between 60 and 100 ms. This could induce high correlations in strongly connected parts of the model, outside the rich club as well (Figure 8—figure supplement 1), and shows that the model supports selective propagation of activity to areas efferently connected with mid-range connectivity.

No materials were used in this computational work.

Neuron models from Reva et al., 2023 were made as follows. Ion channel conductance densities were optimized for a pool of reconstructed neurons, for which in vitro recordings had previously been made. Ion channel densities were then generalized to other neuron models of the same e-type. Resulting neuron models were only used in the construction of the model if the value of the cost function was within 5 standard deviations of the experimental mean.

For some electrical models, further adjustments were made to AIS sections to handle the large input currents present under conditions of high network activity. In short, for certain pyramidal cell morphologies, the AIS was replaced by a cylinder with a length of 60 μm\begin{document}$\mu m$\end{document}. Its diameter was manually calibrated such that the ratio of the AIS input resistance over the input resistance of somato-dendritic compartments was equal to 2. Afterwards, it was confirmed that the cost function of their electrical models remained below the threshold.

The Tsodyks–Markram synaptic model (Tsodyks and Markram, 1997; Markram et al., 1998; Fuhrmann et al., 2002; Loebel et al., 2009), upgraded to feature multi-vesicular release (Barros-Zulaica et al., 2019; Ecker et al., 2020) comprises the following parameters: peak conductance g^\begin{document}$\hat{g}$\end{document}, depression and facilitation time constants D\begin{document}$D$\end{document}, F\begin{document}$F$\end{document}, the decay time constant of the PSC τdecay\begin{document}$\tau_{decay}$\end{document}, the release probability USE\begin{document}$U_{SE}$\end{document}, the average number of vesicles in the release-ready pool NRRP\begin{document}$N_{RRP}$\end{document}, the Hill coefficient of the nonlinear [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} dependent scaling of release probability UHill\begin{document}$U_{Hill}$\end{document}, and finally g^ratio\begin{document}$\hat{g}_{ratio}$\end{document}: the NMDA/AMPA ratio for excitatory synapses, and the GABAB/GABAA\begin{document}$GABA_{B}/GABA_{A}$\end{document} ratio for inhibitory synapses. Where possible, pathway and synapse-type specific parameter values were taken from the literature, and after eventual corrections (for differences in the temperature and solutions used in the experiments), were put directly into the model using the technique described for the use case of hippocampal CA1 in Ecker et al., 2020. For example, parameters USE\begin{document}$U_{SE}$\end{document}, D\begin{document}$D$\end{document}, F\begin{document}$F$\end{document}, and UHill\begin{document}$U_{Hill}$\end{document} have previously been fitted for a number of pathways using data acquired from paired-recording experiments. Furthermore, g^ratio\begin{document}$\hat{g}_{ratio}$\end{document} parameter has been previously determined from outside-out patch recording experiments.

The remaining parameters (g^\begin{document}$\hat{g}$\end{document} and NRRP\begin{document}$N_{RRP}$\end{document}) were iteratively calibrated using an in silico setup reproducing the paired-recordings experiments detailed below. For this parameterization, all paired-recording data sources from Markram et al., 2015 were re-used. To further constrain the variance of EPSP amplitudes in L5 TTPCs, fitted parameters from Barros-Zulaica et al., 2019 were used. The dataset was also enriched with recent recordings from L6 (Qi and Feldmeyer, 2016; Yang et al., 2020; Yang et al., 2022). Instead of generalizing L4 E peak synaptic conductances for all thalamic fibers (as in Markram et al., 2015), synaptic conductances were constrained using EPSP amplitude measurements from thalamocortical slices (Beierlein and Connors, 2002; Beierlein et al., 2003). Fibers originating from POm were not present in Markram et al., 2015. Due to the lack of in vitro measurements, physiological parameters from VPM synapses were generalized to describe POm synapses.

Not all synaptic peak conductances can be measured with paired recordings due to the space-clamp artifact (Markram et al., 2015; Ecker et al., 2020), and estimating the number of release-ready vesicles is also challenging experimentally (Loebel et al., 2009; Barros-Zulaica et al., 2019). Thus, for synaptic pathways for which there was in vitro reference data, these two parameters were determined in a simulation-driven iterative process. Firstly, 50 pairs of in silico neurons were randomly sampled. Second, the postsynaptic cell was current-clamped, and the PSP at the soma of the postsynaptic cell in response to a presynaptic action potential was measured. This was repeated 35 times for each pair as in Ecker et al., 2020. Thirdly, the mean and the CV of these amplitudes were extracted and compared with reference in vitro data. Finally, peak conductance (g^\begin{document}$\hat{g}$\end{document}), and the average number of vesicles in the release-ready pool (NRRP\begin{document}$N_{RRP}$\end{document}) were adjusted to match the amplitude and CV of the in vitro reference (Ecker et al., 2020). In some cases, this resulted in reaching the lower bound of univesicular release (Barros-Zulaica et al., 2019).

Where experimental data was not available, mean synaptic physiology parameters from similar pathways were used (Markram et al., 2015; Ecker et al., 2020). For the VPM to L5 E pathway, the maximum of VPM to L4 E and VPM to L6 E conductances (instead of the mean) were used, based on resulting evoked firing rates found in a later modeling step (Figure 5—figure supplement 1C). To calibrate the mPSC frequencies of different pathways, single-cell simulations with different values of the spontaneous release frequency for all synapses of a set of 1000 cells in a given pathway were run. In these simulations, in silico voltage-clamp recordings were performed to measure the resulting mPSC frequency at the soma. This data was then fitted with a logarithmic function and the value of the spontaneous release frequency matching the in vitro reference value for the mPSC frequency was interpolated. As in vitro paired recording data is sparse, all available sources to determine synaptic parameters were reused for validation.

Activity in the model is compared with spike-sorted extracellular recordings from the barrel cortex of anesthetized rats (Reyes-Puerta et al., 2015b). The dataset contains single unit spike times for both spontaneous activity and responses to single whisker deflections, across six layer-wise neuron populations (L2/3 E, L2/3 I, L4 E, L4 I, L5 E, and L5 I). We extend the dataset using the average of L2/3 I, L4 I, and L5 I as a reference for L1 I and L6 I, and an alternative reference for L6 E (De Kock et al., 2007). The spontaneous firing rates of the nine neuron populations are collected in the vector of reference firing rates, VFR\begin{document}$\boldsymbol{V_{FR}}$\end{document}.

As a secondary comparison, we use a dataset of in vivo juxtacellular and whole-cell recordings of barrel cortex responses in awake mice during an active whisker touch paradigm (Yu et al., 2019). While the animal model is different, using this data enables comparison to awake responses of layer-wise E populations and I subpopulations (VIP+ [vasoactive intestinal peptide, a part of our 5HT3aR+ subpopulation], Sst+, FS [fast spiking, corresponding to our PV+ subpopulation]). Moreover, this allows validating the model against properties of cortical responses across similar but different paradigms, reducing the risk of over fitting.

Random background synaptic inputs, representing uncorrelated inputs from other brain regions not present in the model, are modeled as a conductance-based somatic injection (Figure 4B1). Specifically, we inject conductance signals described by an OU process (similar to Destexhe et al., 2001), given by the following equation:(1)dg(t)dt=−1τ[g(t)−g0]+D\begin{document}$$\displaystyle \frac{dg(t)}{dt} = -\frac{1}{\tau} [g(t) - g_0] + \sqrt{D} \chi(t)$$\end{document}

where g(t)\begin{document}$g(t)$\end{document} is the conductance signal, g0\begin{document}$g_{0}$\end{document} its mean value, τ\begin{document}$\tau$\end{document} is the decay time constant, D\begin{document}$D$\end{document} is the diffusion coefficient, and χ(t)\begin{document}$\chi(t)$\end{document} is a Gaussian white noise process. The diffusion coefficient can also be expressed in terms of the standard deviation σ\begin{document}$\sigma$\end{document} of the signal: D=2σ2τ\begin{document}$D=\frac{2\sigma^{2}}{\tau}$\end{document}. Note that we only consider an excitatory conductance signal representing mid-range excitatory drive, whereas local inhibitory input is deemed sufficient within the circuit model. As we are modeling a nonspecific random background noise, we use a different, uncorrelated OU process for each cell.

Given the diversity of morphologies and electrical behaviors of cells in our circuit, we scale the mean and standard deviation of the injected signal based on individual cell properties. Specifically, we compute the input resistance Rin\begin{document}$R_{in}$\end{document} of each cell at its resting potential, then take its reciprocal value Gin=1/Rin\begin{document}$G_{in}=1/R_{in}$\end{document} (units of conductance). The mean g0\begin{document}$g_{0}$\end{document} and standard deviation σ\begin{document}$\sigma$\end{document} of the injected conductance signal are then expressed as percentages OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} of this input conductance Gin\begin{document}$G_{in}$\end{document}:(2)g0=OUμ100∗Gin\begin{document}$$\displaystyle g_0 = \frac{OU_{\mu}}{100} * G_{in}$$\end{document}(3)σ=OUσ100∗Gin\begin{document}$$\displaystyle \sigma = \frac{OU_{\sigma}}{100} * G_{in}$$\end{document}

The OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} percentage values are used in the calibration technique described in the following sections. To reiterate, OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} scale the mean of the injected conductance and the size its fluctuations respectively.

OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} are parameterized separately for each of nine populations (layer-wise E and I combinations; Figure 4B2), leading to 18 parameters, grouped into two 9-dimensional vectors OUμ\begin{document}$\boldsymbol{OU_{\mu}}$\end{document} and OUσ\begin{document}$\boldsymbol{OU_{\sigma}}$\end{document}. Spontaneous firing rates across populations, denoted by the vector CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document}, are then determined by the vectors OUμ\begin{document}$\boldsymbol{OU_{\mu}}$\end{document} and OUσ\begin{document}$\boldsymbol{OU_{\sigma}}$\end{document}, and [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}. The objective of the calibration procedure is to determine a mapping that outputs the OUμ\begin{document}$\boldsymbol{OU_{\mu}}$\end{document} and OUσ\begin{document}$\boldsymbol{OU_{\sigma}}$\end{document} required to achieve a particular set of firing rates CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document}, for a given [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}.

This requires two simplifications: First, we reduce the space of possible OUμ\begin{document}$\boldsymbol{OU_{\mu}}$\end{document} and OUσ\begin{document}$\boldsymbol{OU_{\sigma}}$\end{document} values by fixing OUσ=OUμ∗ROU\begin{document}$\boldsymbol{OU_{\sigma}}=\boldsymbol{OU_{\mu}}*R_{OU}$\end{document}, where ROU\begin{document}$R_{OU}$\end{document} is a prespecified constant that controls the level of noise assumed to be present in the external synaptic input. Second, we learn the mapping only for dynamical states where the firing rates of the nine populations are a proportion of reference in vivo firing rates, that is, CFR=PFR∗VFR\begin{document}$\boldsymbol{C_{FR}}=P_{FR}*\boldsymbol{V_{FR}}$\end{document}, with PFR∈[0,1]\begin{document}$P_{FR}\in[0,1]$\end{document} (Figure 4B2). This is based on the assumption that extracellular spike detection sampling biases (Olshausen and Field, 2006; Wohrer et al., 2013) affect all populations equally.

The mapping can be written as ΨCa2+,ROU:CFR↦OUμ\begin{document}$\Psi_{Ca^{2+},R_{OU}}:\boldsymbol{C_{FR}}\mapsto\boldsymbol{OU_{\mu}}$\end{document} and is simplified into two separate mappings which are determined separately and then combined (Figure 4—figure supplement 1). The first mapping finds values of the 9 output parameters OUμ\begin{document}$\boldsymbol{OU_{\mu}}$\end{document}, for a given ROU\begin{document}$R_{OU}$\end{document}, which produce particular unconnected firing rates UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} (i.e., where the neurons in the network are not connected to each other). The second then maps between UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} and CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document}.

The first mapping χ:(ROU,UFR)↦OUμ\begin{document}$\chi:\left(R_{OU},\boldsymbol{U_{FR}}\right)\mapsto\boldsymbol{OU_{\mu}}$\end{document}, is attained by running 1-second simulations over various combinations of OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} (Figure 4—figure supplement 1). ROU\begin{document}$R_{OU}$\end{document} constrains OUμ\begin{document}$OU_{\mu}$\end{document} and OUσ\begin{document}$OU_{\sigma}$\end{document} to a line of possible combinations in the 2D space. We generate an approximation of χ\begin{document}$\chi$\end{document} based on linear interpolation between the results of simulations along the line. Note, in particular, that χ\begin{document}$\chi$\end{document} is independent of [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}.

Given the mapping χ\begin{document}$\chi$\end{document}, the remaining problem is to determine the values of UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} that achieve certain target firing rates given by PFR∗VFR\begin{document}$P_{FR}*\boldsymbol{V_{FR}}$\end{document}, for PFR∈[0,Pmax]\begin{document}$P_{FR}\in[0,P_{max}]$\end{document} and each combination of [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} and ROU\begin{document}$R_{OU}$\end{document}, that is, to determine the mapping ϕCa2+,ROU:UFR↦CFR\begin{document}$\phi_{Ca^{2+},R_{OU}}:\boldsymbol{U_{FR}}\mapsto\boldsymbol{C_{FR}}$\end{document}. This is done by measuring values of CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document} produced for given values of UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} in a number of simulations. However, instead of exploring the whole parameter space of possible UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} values, we only explore a small number of values of UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} which we expect to produce the target CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document} values. This is done by iteratively learning the mapping ϕCa2+,ROU:UFR↦CFR\begin{document}$\phi_{Ca^{2+},R_{OU}}:\boldsymbol{U_{FR}}\mapsto\boldsymbol{C_{FR}}$\end{document} and in each iteration using ϕ\begin{document}$\phi$\end{document} to predict UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document} values that bring the dynamics closer to the target firing rate, that is, by sampling values given by UFR=ϕ−1(CFR)=ϕ−1(PFR∗VFR)\begin{document}$\boldsymbol{U_{FR}}=\phi^{-1}(C_{FR})=\phi^{-1}(P_{FR}*\boldsymbol{V_{FR}})$\end{document} for 10 equidistant values of PFR∈[0,Pmax]\begin{document}$P_{FR}\in[0,P_{max}]$\end{document}. The initial guess of ϕ\begin{document}$\phi$\end{document} is simply the identity, that is, assuming no effect of connecting the network, with Pmax=0.5\begin{document}$P_{max}=0.5$\end{document}. All other iterations use Pmax=1.0\begin{document}$P_{max}=1.0$\end{document}.

We update ϕ\begin{document}$\phi$\end{document} by fitting an exponential: CFR=α∗eβUFR+κ\begin{document}$\boldsymbol{C_{FR}}=\alpha*e^{\beta\boldsymbol{U_{FR}}}+\kappa$\end{document} to the values of UFR\begin{document}$\boldsymbol{U_{FR}}$\end{document}, CFR\begin{document}$\boldsymbol{C_{FR}}$\end{document} measured on the latest iteration (Figure 4—figure supplement 1). In a recurrently connected network such as our model, the connected firing rate of a population depends on the firing rates of all other populations in complex and nonlinear ways. This is addressed by our simplification to restrict the compatible dynamic states, where by definition the target firing rate of one population determines the target firing rates of all others.

The firing rates of the L2/3 I and L4 I and L6 I populations could not be sufficiently lowered for PFR<0.2\begin{document}$P_{FR} \lt 0.2$\end{document} and PFR<0.1\begin{document}$P_{FR} \lt 0.1$\end{document}, respectively, as they spontaneously fired even at their resting potentials (Figure 4—figure supplement 1D).

We first approximated ϕ\begin{document}$\phi$\end{document} for [Ca2+]o=1.1\begin{document}$[Ca^{2+}]_{o}=1.1$\end{document} mM and ROU=0.4\begin{document}$R_{OU}=0.4$\end{document}. To reduce the number of iterations steps needed for other combinations of [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document} and ROU\begin{document}$R_{OU}$\end{document}, we initialized the optimization process with the mapping ϕ\begin{document}$\phi$\end{document} obtained for this parameter pair instead of basing it on the identity (Figure 4—figure supplement 1D, lower; Figure 4—figure supplement 1). Only for PFR\begin{document}$P_{FR}$\end{document} above 0.8 and [Ca2+]o=1.1\begin{document}$[Ca^{2+}]_{o}=1.1$\end{document} mM did we have to slightly relax our acceptance criteria (Figure 7D, lower). Additionally, [Ca2+]o=1.1\begin{document}$[Ca^{2+}]_{o}=1.1$\end{document} mM, PFR=1.0\begin{document}$P_{FR}=1.0$\end{document}, and ROU=0.2\begin{document}$R_{OU}=0.2$\end{document} led to bursting activity uncharacteristic of in vivo activity and was excluded from further study.

The spike times of single whisker deflection stimuli were drawn from a PSTH of VPM neurons in response to 3 ms mechanical single whisker deflections made at 1  Hz in urethane anesthetized rats (Diamond et al., 1992; Figure 5A2). Since the in vivo data for cortical responses to single whisker deflections was from responses to 2 ms mechanical whisker deflections, we compressed the tail of the VPM PSTH to allow a direct comparison with in silico responses (Figure 5A2). A VPM PSTH for the active whisker touch stimulus was used from the same dataset as the corresponding cortical responses (Yu et al., 2019).

Firstly, in silico responses were compared to data from the C2 barrel of the anaesthetized rat in response to single whisker deflections made at <1 Hz. For the active whisker touch stimulus, in vivo activity was used from aggregated over principal barrels corresponding to the untrimmed whisker.

As an initial test of similarity with the corresponding in vivo dataset, trial-averaged PSTHs were first calculated for each parameter combination, both for all neurons, and for each of the layer-wise E and I populations. We then tested whether the latencies, 50% and 25%-decay points of the trial-averaged PSTHs were respectively no more than 10 ms, 10 ms, and 40 ms later than those of the corresponding in vivo populations, and that there was no secondary rise in the PSTHs after the initial decay (by testing that none of the PSTHs for individual populations were more than 35% above baseline after 75 ms). L1 I was excluded from these tests, as it showed little or no response to the stimulus and we had no in vivo reference. These tests allowed us to split the 4D parameter space into two regions, one where in silico responses are consistent with in vivo responses, and another where they are not (see ‘Results’).

Simulation of a morphologically detailed model first requires specifying the conditions (parameters and inputs) under which to perform the simulation. Given the correspondence between variables in the model and properties of biological systems, we are able to mimic to a certain extent the conditions and protocols of experimental studies. These are combinations of existing techniques or even techniques that cannot or have not yet been performed experimentally. On top of the compensation for missing external input and different [Ca2+]o\begin{document}$[Ca^{2+}]_{o}$\end{document}, we implemented further mechanisms to simulate specific experimental conditions. On a technical level, these comprise somatic current or conductance injections, adjustment of synaptic connectivity parameters, and selective activation of thalamic fibers. These are static conditions, however, in that their time course must be determined before the simulation is run. Somatic injections and connectivity adjustments can be targeted with single neuron or single pair resolution, respectively. To each thalamic fiber or neuron in the model, we can assign an arbitrary spike train, triggering synaptic release from all of its synapses with anatomically determined delays (from axonal conduction speed and path length). These mechanisms can target specific groups of neurons, for example, based on neuron properties, such as location, layer, m-type or e-type, or inhibitory subpopulation (determined based on me-type as in Markram et al., 2015; Figure 2B). We combined mechanisms to simulate various in vitro or in vivo experimental paradigms. Pathway lesions, for example, are simulated by selecting sets of pre- and postsynaptic neurons and removing all synaptic connections between them (Figure 6—figure supplement 1A). Simulated optogenetic stimulation, in addition to being targeted at specific groups of neurons, took into account the attenuation of light with depth for the wavelength being used. Neurons were then inhibited or excited according to the intensity of light reaching them (Figure 6—figure supplement 1B). Finally, sensory stimuli were simulated by generating instances of stimulus-specific stochastic spike trains activating the thalamic input fibers (Figure 6—figure supplement 1C).

We model optogenetic inhibition or activation of a neuron population through a current injection at the soma of each cell in the population, with an intensity proportional to the cell’s threshold current (see Reva et al., 2023; but with the technical caveat that we did not apply a hyperpolarizing holding current at the same time). To mimic the conditions of surface illumination, we considered the dependence of effective depolarization strength on cortical depth using a modified Beer–Lambert law approximation for the exponential attenuation of light intensity through scattering tissue (Al-Juboori et al., 2013; Azimipour et al., 2014, Figure 6—figure supplement 1B):(4)I(d)=I0exp⁡(−μeffd)\begin{document}$$\displaystyle I(d) = I_0 \exp(-\mu_{eff}\,d)$$\end{document}

where I(d)\begin{document}$I(d)$\end{document} describes the light intensity at depth d\begin{document}$d$\end{document} (in mm), with a maximum light intensity I0\begin{document}$I_{0}$\end{document} (on the surface of the cortex) and an effective attenuation coefficient given by(5)μeff=3μa(μa+μs′)\begin{document}$$\displaystyle \mu_{eff} = \sqrt{3 \mu_a (\mu_a + \mu_s')}$$\end{document}

Values for the absorption coefficient μa\begin{document}$\mu_{a}$\end{document} and the reduced scattering coefficient μs′\begin{document}$\mu_{s}^{\prime}$\end{document} were interpolated for the chosen wavelength from Mesradi et al., 2013. For implementation reasons, the targeted cells were grouped into depth bins and for each group the intensity at the center of the bin was used. Bins were equally distributed in terms of the injected current, and not in terms of depth. The value of I0\begin{document}$I_{0}$\end{document} was calibrated independently for each experimental paradigm.

Sensory inputs were simulated using a three-step procedure (Figure 6—figure supplement 1C2): First, a time series representing sensory stimulation is assigned to each selected thalamic fiber; second, the time series is optionally transformed with a fiber-dependent transfer function; third, a spike train is generated from the time series through a stochastic spiking process. Thalamic input fibers were associated with roughly columnar, overlapping volumes of the model that they formed synaptic connections in Reimann et al., 2024. Their centers were projected into the plane using a flat map of the model (Bolaños-Puchet et al., 2024), yielding [xζ,yζ]\begin{document}$[x_{\zeta},y_{\zeta}]$\end{document}, the flat locations of each fiber ζ\begin{document}$\zeta$\end{document}. A sensory stimulus was defined based on fiber location as ρζ(t)=ρ(xζ,yζ,t)\begin{document}$\rho_{\zeta}(t)=\rho(x_{\zeta},y_{\zeta},t)$\end{document}. The stimulus function could be partially stochastic and its value was evaluated for each time bin of the simulation (Figure 6—figure supplement 1C1). Next, a fiber could be associated with a transfer function υζ\begin{document}$\upsilon_{\zeta}$\end{document} that transforms the results of ρ\begin{document}$\rho$\end{document}. If none is mentioned, identity was used as transfer function. Finally, a spiking process ψ\begin{document}$\psi$\end{document} was used to instantiate a spike train for each fiber, based on its transformed time series. That is, the spike train associated with ζ\begin{document}$\zeta$\end{document} was Γζ=ψ(υζ(ρζ))\begin{document}$\Gamma_{\zeta}=\psi(\upsilon_{\zeta}(\rho_{\zeta}))$\end{document}. The processes used were stochastic, leading to different spike trains for fibers associated with the same time series. Different, specific ρ\begin{document}$\rho$\end{document}, υ\begin{document}$\upsilon$\end{document} and ψ\begin{document}$\psi$\end{document} were used for different experimental paradigms that will be further described below.

To study how input from L4 contributes to L2/3 subthreshold responses Varani et al., 2022 used a 500-ms-long whisker hold paradigm, while patch-clamping PCs in L2/3 in anesthetized and awake mice. We encoded the whisker hold stimulus as a step function (ρζ(t)=1\begin{document}$\rho_{\zeta}(t)=1$\end{document}, if 2000 ms ≤ t <2500 ms, 0 otherwise) in 10% of the VPM fibers within the seven-column subvolume. One of four transfer functions were assigned to each fiber, based on the types of kinetic response properties of thalamic neurons identified in Petersen et al., 2008. The types were selective for whisker position (υpos\begin{document}$\upsilon_{pos}$\end{document}), velocity (υvel\begin{document}$\upsilon_{vel}$\end{document}), acceleration (υacc\begin{document}$\upsilon_{acc}$\end{document}), or direction (υdir\begin{document}$\upsilon_{dir}$\end{document}), and were implemented asυpos(t)=rmax⋅ρ(t)\begin{document}$$\displaystyle \upsilon_{pos}(t) &= r_{max} \cdot \rho(t)$$\end{document}υvel(t)=rmax⋅(ρ(t+1)−ρ(t))\begin{document}$$\displaystyle \upsilon_{vel}(t) &= r_{max} \cdot (\rho(t + 1) - \rho(t))$$\end{document}υacc(t)=rmax⋅(ρ(t+1)−2ρ(t)+ρ(t−1))\begin{document}$$\displaystyle \upsilon_{acc}(t) &= r_{max} \cdot (\rho(t + 1) - 2\rho(t) + \rho(t-1))$$\end{document}υdir(t)=rmax⋅|ρ(t+1)−ρ(t)|+\begin{document}$$\displaystyle \upsilon_{dir}(t) &= r_{max} \cdot \vert\rho(t + 1) - \rho(t)\vert_+$$\end{document}

where rmax=150\begin{document}$r_{max}=150$\end{document} Hz denotes the firing rate of a thalamic fiber when its associated feature property is at the fiber’s preferred value. Transfer functions were randomly assigned to fibers with the fractions identified in Petersen et al., 2008 (Figure 6A, 11% coding for position and acceleration, 58% for velocity, and 20% for direction). The spiking process ψ\begin{document}$\psi$\end{document} was an adapting Markov process (Muller et al., 2007) with an adaptation time constant of 100 ms. As the whisker movements were short lasting, rates were evaluated at submillisecond (0.1) resolution.

Similarly to before, only the seven-column subvolume (210k neurons) was used for the simulations, and the in vivo-like state was realized as Ca2+=1.05\begin{document}$Ca^{2+}=1.05$\end{document} mM, ROU=0.4\begin{document}$R_{OU}=0.4$\end{document}, and PFR=0.3\begin{document}$P_{FR}=0.3$\end{document}.

The optogenetic inhibition in this experiment targeted 95% (in line with Varani et al., 2022) of excitatory cells in layer 4. The authors found a few cells which also tested positive for Halo at the bottom of L3 as well, but as they did not quantify it, we decided not to target any lower L3 PCs in the in silico version of the experiment. Based on the 595 nm wavelength (yellow light), parameters were set to μa≈0.49\begin{document}$\mu_{a}\approx 0.49$\end{document}mm−1\begin{document}$mm^{-1}$\end{document} and μs′≈4.12\begin{document}$\mu_{s}^{\prime}\approx 4.12$\end{document}mm−1\begin{document}$mm^{-1}$\end{document}. For the depth-based spatial binning of cells, five bins were used in L4. After scanning several values, I0\begin{document}$I_{0}$\end{document} was set to –200% as that reproduced the ≈ 10 mV hyperpolarization of L4 PCs observed in vivo. In line with the in vivo experiment, the optogenetic stimulus ended in a (100 ms long) ramp to avoid rebound spikes (Figure 6B).

When going beyond reproducing the same experimental conditions and instead leveraging the in silico nature of our setup, synaptic pathways were lesioned by selecting the excitatory population in a given layer as the presynaptic population and the excitatory population in L2/3 as the postsynaptic population and not instantiating the connecting synapses during the simulation.

L2/3 PCs had to meet three criteria to be included in the subsequent analysis. Firstly, their activity was required to remain subthreshold during the 500-ms-long whisker hold stimulus and in 200-ms-long time windows before and after the stimulus, both in control and in silico optogenetic runs. Second, they had to be innervated by at least one (active) VPM fiber. Third, the derivative of their voltage trace had to cross the 1  mV/ms threshold in a 20 ms time window after stimulus onset in the control simulation. The last two were motivated by comparing subthreshold voltages to voltage traces from Varani et al., 2022 that showed large, stimulus evoked EPSPs. Around 8% of L2/3 PCs in the central column met all the above criteria and their voltages were averaged to arrive to the traces shown in Figure 6C and D. Thus, unlike in the original analysis, cells rather than trials were averaged. The motivation for this approach is that while in vivo it is easier to repeat the same paradigm after establishing stable recording conditions in a given cell, in silico it is quicker to record from all cells in a single simulation, instead of repeating the stimulus several times.

Since our model comprises the nbS1 and not the V1 brain area, we modeled visual drifting gratings in a more abstract way, without taking specifics of the visual system into account. In particular, we defined ρ(xζ,yζ,t)\begin{document}$\rho(x_{\zeta},y_{\zeta},t)$\end{document} as a spatio-temporal rate pattern corresponding to linear sinusoidal drifting gratings for a fraction FP\begin{document}$F_{P}$\end{document} of 937 VPM fibers projecting to a single simulated column (30k neurons, 520 μm\begin{document}$\mu m$\end{document} diameter). For all other VPM fibers, ρ\begin{document}$\rho$\end{document} was zero. The gratings had a temporal frequency of ftemp=2\begin{document}$f_{temp}=2$\end{document} Hz and a spatial frequency of 0.03 cycles/degree, which we translated to fspat=0.001\begin{document}$f_{spat}=0.001$\end{document} cycles/μm\begin{document}$\mu m$\end{document} by assuming a cortical magnification factor in rat of 30 μm\begin{document}$\mu m$\end{document}/degree (Gias et al., 2005). In Figure 6E, the spatial grating patterns are illustrated at different points in time.

As in Shapiro et al., 2022, we used five contrast levels C∈[0.06,0.12,0.24,0.5,1.0]\begin{document}$C\in[0.06,0.12,0.24,0.5,1.0]$\end{document}, which were defined as the Michelson contrast given the minimum and maximum luminance values Lmin\begin{document}$L_{min}$\end{document} and Lmax\begin{document}$L_{max}$\end{document}:(6)C(Lmin,Lmax)=Lmin−LmaxLmin+Lmax\begin{document}$$\displaystyle C(L_{min}, L_{max}) = \frac{L_{min} - L_{max}}{L_{min} + L_{max}}$$\end{document}

Since the physical quantity of luminance does not have a clear correspondence in our model, we used normalized luminance values Lmin\begin{document}$L_{min}$\end{document} and Lmax\begin{document}$L_{max}$\end{document} between 0.0 and 1.0 by computing the inverse Michelson contrast centered around a mean normalized luminance of 0.5. The resulting values of Lmin\begin{document}$L_{min}$\end{document} and Lmax\begin{document}$L_{max}$\end{document} where then scaled and shifted to the minimum and maximum rates of the sinusoidal modulation Rmin\begin{document}$R_{min}$\end{document} and Rmax\begin{document}$R_{max}$\end{document}, respectively, such that the peak firing rate at contrast 1.0 was given by Rpeak\begin{document}$R_{peak}$\end{document} and the mean of the modulation corresponding to the background firing rate at contrast 0.0 was given by Rbk\begin{document}$R_{bk}$\end{document}. The resulting sinusoidal input rate signal can be written as(7)ρζ(t)=R(t,lζ)=Rmin+0.5(Rmax−Rmin)[1+sin⁡(2πftempt−2πfspatlζ)]|+\begin{document}$$\displaystyle \rho_\zeta(t) = R(t, l_\zeta) = R_{min} + 0.5 (R_{max} - R_{min}) \Bigl[1 + \sin(2 \pi\,f_{temp}\,t - 2 \pi\,f_{spat}\,l_\zeta)\Bigr]\bigg\vert_+$$\end{document}

where t\begin{document}$t$\end{document} is the time in seconds, lζ\begin{document}$l_{\zeta}$\end{document} the linear position of ζ\begin{document}$\zeta$\end{document} within the grating, and |+\begin{document}$|_{+}$\end{document} denotes that firing rates are truncated to positive values only. Figure 6F illustrates a random series of rate signals corresponding to different contrasts. No transfer function was used, and spiking process ψ\begin{document}$\psi$\end{document} was an adapting Markov process (Muller et al., 2007) with an adaptation time constant of 100 ms. Values for FP\begin{document}$F_{P}$\end{document}, Rpeak\begin{document}$R_{peak}$\end{document}, and Rbk\begin{document}$R_{bk}$\end{document} were determined beforehand by a parameter optimization so that the resulting grating responses were qualitatively comparable with the ones reported by Shapiro et al., 2022; see the next subsection for details.

We ran a parameter scan to determine optimal values for FP\begin{document}$F_{P}$\end{document} (fraction of 937 VPM fibers projecting to the central column of our model to apply grating stimulus to), Rpeak\begin{document}$R_{peak}$\end{document} (peak firing rate at contrast 1.0), and Rbk\begin{document}$R_{bk}$\end{document} (background firing rate at contrast 0.0). This calibration was done by running 45 simulations using all combinations of parameter values in the ranges FP∈[0.5,0.75,1.0]\begin{document}$F_{P}\in[0.5,0.75,1.0]$\end{document}, Rpeak∈[5.0,10.0,15.0,20.0,25.0]\begin{document}$R_{peak}\in[5.0,10.0,15.0,20.0,25.0]$\end{document} Hz, and Rbk∈[0.05,0.1,0.2]\begin{document}$R_{bk}\in[0.05,0.1,0.2]$\end{document} Hz, and selecting the optimal combination amongst them. Each simulation lasted 40 seconds during which 20 contrast stimuli were presented for 1 second, followed by a 1 second (blank) inter-stimulus interval. Four contrast levels C∈[0.06,0.12,0.5,1.0]\begin{document}$C\in[0.06,0.12,0.5,1.0]$\end{document} were presented five times each in random order, which was sufficient to fit sigmoidal tuning functions with four parameters (see Equation 9).

We observed that especially under strong stimulus conditions the response rates of PCs to the first and second cycles of the sinusoidal grating pattern (1-second stimulus at ftemp=2\begin{document}$f_{temp}=2$\end{document} Hz) were quite different, with the second response largely attenuated due to synaptic depletion. Therefore, we extracted first and second peak firing rates r1\begin{document}$r_{1}$\end{document} and r2\begin{document}$r_{2}$\end{document}, respectively, from the PSTHs computed with 1 ms resolution and 20 ms Gaussian smoothing (Figure 6—figure supplement 3). We defined a measure of the normalized peak difference as the Michelson contrast of the peak rates r1\begin{document}$r_{1}$\end{document} and r2\begin{document}$r_{2}$\end{document}, given by(8)r^diff=r1−r2r1+r2\begin{document}$$\displaystyle \hat{r}_{diff} = \frac{r_1 - r_2}{r_1 + r_2}$$\end{document}

Additionally, we extracted average firing rates for each contrast level of the whole population of PCs within the full (1  second) as well as the first and second halves (0.5 second each) of the stimulation intervals. We then fitted sigmoidal tuning functions with parameters c50\begin{document}$c_{50}$\end{document}, m\begin{document}$m$\end{document}, n\begin{document}$n$\end{document}, and Rmax\begin{document}$R_{max}$\end{document} (see Equation 9) to these average tuning responses (Figure 6—figure supplement 5). Finally, as summarized in Figure 6—figure supplements 3 and 5, we selected the best combination of parameters based on the following selection criteria:

In order to combine these criteria independent of the actual scales of r^diff\begin{document}$\hat{r}_{diff}$\end{document}, c50\begin{document}$c_{50}$\end{document} and n\begin{document}$n$\end{document}, we computed their individual rank scores in decreasing (r^diff\begin{document}$\hat{r}_{diff}$\end{document}, c50\begin{document}$c_{50}$\end{document}: lower is better) or increasing (n\begin{document}$n$\end{document}: higher is better) order. We then selected the parameter combination with the highest product of rank scores, excluding the ones with peak firing rates r1\begin{document}$r_{1}$\end{document} and r2\begin{document}$r_{2}$\end{document} below rth\begin{document}$r_{th}$\end{document} and the ones with c50\begin{document}$c_{50}$\end{document} values close to 1.0 (border cases). We found an optimal parameter combination of FP=1.0\begin{document}$F_{P}=1.0$\end{document}, Rpeak=10.0\begin{document}$R_{peak}=10.0$\end{document} Hz, and Rbk=0.20\begin{document}$R_{bk}=0.20$\end{document} Hz which we used throughout this in-silico experiment.

Optogenetic stimulation was targeted at either 1654 PV+ or 822 Sst+ interneurons in a single column. We used parameters μa≈0.46\begin{document}$\mu_{a}\approx 0.46$\end{document} mm^-1 and μs′≈5.38\begin{document}$\mu_{s}^{\prime}\approx 5.38$\end{document} mm^-1, based on the wavelength of 470 nm (blue light; see Figure 6—figure supplement 1). I0\begin{document}$I_{0}$\end{document} was increased from 0% to 300% in steps of 50%.

We quantified contrast tuning responses in the same way as described by Shapiro et al., 2022 by least-squares fitting sigmoidal functions to the normalized tuning curves. Normalized tuning curves were obtained by computing the time-averaged firing rates of all 1-second stimulus intervals and dividing them by the mean baseline firing rate (i.e., w/o optogenetic stimulation) at the highest contrast level. The sigmoidal function was given by(9)R(c)=Rmaxcncn+c50n+m\begin{document}$$\displaystyle R(c) = \frac{R_{max}\,c^n}{c^n + c_{50}^n} + m$$\end{document}

where R(c)\begin{document}$R(c)$\end{document} describes the response amplitude at contrast c\begin{document}$c$\end{document}, m\begin{document}$m$\end{document} is the baseline response at minimum contrast, Rmax\begin{document}$R_{max}$\end{document} is the maximum increase above baseline, n\begin{document}$n$\end{document} defines the steepness of the curve, and c50\begin{document}$c_{50}$\end{document} is the contrast at half Rmax\begin{document}$R_{max}$\end{document}. We used the coefficient of determination (r2\begin{document}$r^{2}$\end{document} score) as a measure of the goodness of fit.

We identified PV+, Sst+, and pyramidal neurons with robust contrast tuning behavior under all conditions. In the experimental study of Shapiro et al., 2022, tetrode recordings were used together with spike sorting. Correspondingly, we only considered neurons firing at rates above 0.5 Hz under all stimulus conditions, meaning they could potentially be detected by spike sorting (Pedreira et al., 2012). In addition, we considered neurons as being robustly tuned if they had strictly monotonically increasing tuning curves.

Direct photostimulation effects on interneurons were modeled by a divisive scaling model Rdiv(c)\begin{document}$R_{div}(c)$\end{document}, a subtractive shifting model Rsub(c)\begin{document}$R_{sub}(c)$\end{document}, or a saturation additive model Rsat(c)\begin{document}$R_{sat}(c)$\end{document} (Shapiro et al., 2022). For fitting these models, the parameters c50\begin{document}$c_{50}$\end{document}, m\begin{document}$m$\end{document}, n\begin{document}$n$\end{document}, and Rmax\begin{document}$R_{max}$\end{document} of the underlying contrast tuning function R(c)\begin{document}$R(c)$\end{document} were kept constant at values obtained from baseline fits (i.e., w/o optogenetic stimulation). The divisive scaling model was defined as(10)Rdiv(c)=R(c)/g\begin{document}$$\displaystyle R_{div}(c) = R(c) / g$$\end{document}

with a scaling term g\begin{document}$g$\end{document}. The subtractive shifting model was given by(11)Rsub(c)=R(c)−h|+\begin{document}$$\displaystyle R_{sub}(c) = R(c) - h\,\Big\vert_+$$\end{document}

with a shifting term h\begin{document}$h$\end{document} and rectification to rates equal or above zero. The saturation additive model was defined as(12)Rsat(c)=R(c)+Sc−nc−n+c50−n+A\begin{document}$$\displaystyle R_{sat}(c) = R(c) + \frac{S\,c^{-n}}{c^{-n} + c_{50}^{-n}} + A$$\end{document}

with a saturation term S\begin{document}$S$\end{document} and an additive term A\begin{document}$A$\end{document}. We used the r2\begin{document}$r^{2}$\end{document} score to measure the goodness of model fits.

Indirect effects on PCs receiving inhibitory input from optogenetically activated interneurons were modeled by a conductance-based model Rcond(c)\begin{document}$R_{cond}(c)$\end{document}, assuming a saturating additive model description of interneurons (Shapiro et al., 2022). Response rates under this conductance-based model were given by(13)Rcond(c)=[ΔV(c)−Vth]3|+\begin{document}$$\displaystyle R_{cond}(c) = \Bigl[\Delta V(c) - V_{th} \Bigr]^3\bigg\vert_+$$\end{document}

with a spike threshold Vth=3.4\begin{document}$V_{th}=3.4$\end{document} mV and rectification to rates equal or above zero. The membrane potential ΔV(c)\begin{document}$\Delta V(c)$\end{document} as a function of contrast was given by(14)ΔV(c)=gLRL+gE(c)RE+gI(c)RIgL+gE(c)+gI(c)−Vr\begin{document}$$\displaystyle \Delta V(c) = \frac{g_L\,R_L + g_E(c)\,R_E + g_I(c)\,R_I}{g_L + g_E(c) + g_I(c)} - V_r$$\end{document}

with values for leak conductance gL=6\begin{document}$g_{L}=6$\end{document} nS, leak reversal potential RL=−50\begin{document}$R_{L}=-50$\end{document} mV, excitatory reversal potential RE=0\begin{document}$R_{E}=0$\end{document} mV, inhibitory reversal potential RI=−65\begin{document}$R_{I}=-65$\end{document} mV, and resting potential Vr=−50\begin{document}$V_{r}=-50$\end{document} mV as reported by Shapiro et al., 2022. The excitatory synaptic conductance was given by(15)gE(c)=gE_maxcncn+c50n+gE_min\begin{document}$$\displaystyle g_E(c) = \frac{g_{E\_max}\,c^n}{c^n + c_{50}^n} + g_{E\_min}$$\end{document}

with the excitatory conductances at low/high contrast given by gE_min\begin{document}$g_{E\_min}$\end{document} and gE_max\begin{document}$g_{E\_max}$\end{document}, respectively. The inhibitory synaptic conductance was given by(16)gI(c)=gE(c)+Sc−nc−n+c50−n+ΔgIE_min+A\begin{document}$$\displaystyle g_I(c) = g_E(c) + \frac{S\,c^{-n}}{c^{-n} + c_{50}^{-n}} + \Delta g_{IE\_min} + A$$\end{document}

with an inhibitory conductance offset ΔgIE_min=2\begin{document}$\Delta g_{IE\_min}=2$\end{document} nS at low contrast relative to gE_min\begin{document}$g_{E\_min}$\end{document}.

In a first step, parameters S\begin{document}$S$\end{document} and A\begin{document}$A$\end{document} were set to zero and the model parameters c50\begin{document}$c50$\end{document}, gE_min\begin{document}$g_{E\_min}$\end{document}, gE_max\begin{document}$g_{E\_max}$\end{document}, and n\begin{document}$n$\end{document} were fit to baseline responses of PCs. In a second step, those parameter values were kept constant and the model parameters S\begin{document}$S$\end{document} and A\begin{document}$A$\end{document} were fit to PC responses under photostimulation conditions. Again, we used the r2\begin{document}$r^{2}$\end{document} score to measure the goodness of model fits.

We also compared the in vivo state of our model with the results of a recent in vitro study (Prince et al., 2021), which explored how neurons with different biophysical properties encode different types of signals. The in vitro study optically activated groups of 10 PCs in slices of L2/3 barrel cortex from mouse lines labeling fast-spiking (FS) and regular-spiking (RS) interneurons. Each PC was targeted individually and a binary signal was encoded either through changes in the rate of optical pulses applied to the 10 stimulus neurons, or through changes in the synchronicity of the pulses. The mutual information shared between the binary signal (when encoded either as changes in firing rate or synchronicity) and the firing rate of different inhibitory sub-types (recorded using whole-cell patch clamping in vitro) was analyzed.

While the in vitro stimuli used optical pulses targeted at single neurons with timings drawn from Poisson processes, it was not necessary to explicitly model such an optical stimulus in silico, as we can instead elicit spikes directly in the model. In the original study, the 10 stimulus neurons were uniformly separated in a grid-like pattern at horizontal and vertical distances of ~50 μm\begin{document}$\mu m$\end{document}. The binary signal alternated between two states at random intervals of 2–7 seconds. For the rate coding paradigm, the timings of the optical pulses for the 10 stimulus neurons were drawn from 10 independent inhomogeneous Poisson processes, with the rates of optical activation varying between 5 Hz and 0.5 Hz for the up and down states, respectively (average firing rate: 2.7  Hz). For the synchronous case, the timings of the optical pulses for the 10 stimulus neurons were drawn from a single inhomogeneous Poisson process during the up state, or 10 independent inhomogeneous Poisson processes during the down state. For the synchronous case, the firing rates of the up and down state were both 2.7 Hz. We therefore tested stimulus encoding using a range of stimulus neuron counts: from 10 to 1000.

In our interpretation of the study, mutual information was measured between the binary signal and neural activity during a 0–5 ms and 5–50 ms window following a change in the signal. These represented ‘early’ and ‘late’ stimulus encoding windows following the change in the signal, respectively. As the synchronous up state activated synchronous patterns at a rate of 2.7 Hz, we calculated that a synchronous pattern would only be activated during the early and late windows with probability 0.0135 (=2.7∗5/1000\begin{document}$=2.7*5/1000$\end{document}) and 0.1125 (=2.7∗45/1000\begin{document}$=2.7*45/1000$\end{document}), respectively. We therefore chose to use higher FR of 20 Hz for the synchronous up and down states, and to analyze mutual information between the binary signal and all 50 ms bins. To afford comparison with the rate code experiment type, we used 30 Hz and 10 Hz as the FRs of the up and down states respectively. We also compare stimulus coding during the first 50 ms following the stimulus change for both the synchronous and rate stimulus types.

Neurons were split into hexagonal subvolumes of a specified diameter d\begin{document}$d$\end{document} considering their locations in a flattened view (Bolaños-Puchet et al., 2024). Then, the number of mid-range connections within and between the hexagonal subvolumes were counted, yielding in S\begin{document}$S$\end{document}, the adjacency matrix of the resulting directed graph. Distances between hexagonal subvolumes were calculated by considering the centers of the hexagons in the flattened view. Furthermore, correlations of spiking activity of pairs of hexagonal subvolumes were also calculated. To that end, all spikes within a hexagonal subvolume were pooled and their number in 5 ms time bins; and lastly the Pearson correlations of the resulting time series were calculated. The correlation within a hexagonal subvolume was calculated similarly, but using the separate time series of the E and I populations. Together, this yielded F\begin{document}$F$\end{document}, the matrix of correlations of subvolumes. Based on S\begin{document}$S$\end{document} and F\begin{document}$F$\end{document}, the expected correlations of mid-range inputs was calculated as follows: Let i\begin{document}$i$\end{document} be a hexagonal subvolume and Si\begin{document}$S_{i}$\end{document} the column of S\begin{document}$S$\end{document} associated with input counts into i\begin{document}$i$\end{document}. Then P=Si⋅Si⊤\begin{document}$P=S_{i}\cdot S_{i}^{\top}$\end{document} is in the matrix of counts of pairs of inputs for all pairs of hexagonal subvolumes. Combining P\begin{document}$P$\end{document} and F\begin{document}$F$\end{document} allows one to estimate the distribution of correlations of mid-range inputs into i\begin{document}$i$\end{document}, albeit at the population rather than single-cell level. For the correlation in Figure 8A2, H, J1, a hexagon size of 400μm\begin{document}$400\mu m$\end{document} was used, while in Figure 8I2 a smaller size of only 50μm\begin{document}$50\mu m$\end{document} was used.

Given a connectivity graph G\begin{document}$G$\end{document}, a directed n\begin{document}$n$\end{document}-simplex in G\begin{document}$G$\end{document} is a set of n+1\begin{document}$n+1$\end{document} nodes which are all all-to-all connected in G\begin{document}$G$\end{document} in a feed-forward fashion, that is, such that any subset of these has a unique source and a unique sink (see Reimann et al., 2017 for more details). The n-node participation of a node v\begin{document}$v$\end{document} in G\begin{document}$G$\end{document} is the number of directed n\begin{document}$n$\end{document}-simplices this node is part of. In particular, for n=1\begin{document}$n=1$\end{document}, this is the total degree of the node in G\begin{document}$G$\end{document}. Thus, this can be thought of a generalization of the notion of degree that takes into account higher order interactions and has been shown to strongly correlate with other node centrality metrics Sizemore et al., 2018.

For any numeric property of neurons, for example, firing rate, we evaluate the effect of dimension on it by taking weighted averages across dimensions. That is for each dimension k\begin{document}$k$\end{document}, we take the weighted average of the property across neurons where the weights are given by node participation on dimension k\begin{document}$k$\end{document}. More precisely, let N\begin{document}$N$\end{document} be the number of neurons and V→∈RN\begin{document}$\overrightarrow{V}\in\mathrm{R}^{N}$\end{document}, be a vector of a property on all the neurons, for example, the vector of firing rates. Then in each dimension k\begin{document}$k$\end{document} we computemeank=1N∗∑(Park→)V→⋅Park→,\begin{document}$$\displaystyle \mathbf{mean}_{k}=\frac{1}{N*\sum(\overrightarrow{Par_{k}})}\overrightarrow{V}\cdot\overrightarrow{Par_{k}},$$\end{document}

where Park→\begin{document}$\overrightarrow{Par_{k}}$\end{document} is the vector of node participation on dimension k\begin{document}$k$\end{document} for all neurons and · is the dot product.

To measure the over and underexpression of the different m-types among those with the highest 5% of values of node participation, we used the hypergeometric distribution to determine the expected distribution of m-types in a random sample of the same size. More precisely, for each dimension k\begin{document}$k$\end{document} and m-type m\begin{document}$m$\end{document}, let Ntotal\begin{document}$N_{total}$\end{document} be the total number of neurons in the circuit, Nm\begin{document}$N_{m}$\end{document} be the number of neurons of m-type m\begin{document}$m$\end{document} in the circuit, Ctop\begin{document}$C_{top}$\end{document} be the number of neurons with the highest 5% values of node participation in dimension k\begin{document}$k$\end{document}, Cm\begin{document}$C_{m}$\end{document} the number of neurons of mtype m\begin{document}$m$\end{document} among these, and let P=hypergeom(Ntotal,Nm,Ctop)\begin{document}$P=hypergeom(N_{total},N_{m},C_{top})$\end{document} be the hypergeometric distribution.