The mechanics of correlated variability in segregated cortical excitatory subnetworks

Abstract

Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Figure 1.. Mean field model of segregated E populations.

A: Illustration of experimentally observed connectivity motif; the red $\left(E_1\right)$ and orange $\left(E_2\right)$ populations connect with lower probability than average. B: Schematic of main experimental observations: $E_1-E_2$ correlations were higher than would be predicted from their low connectivity. C: Model schematic. Black traces and arrows denote noise sources. Red arrows indicate excitatory recurrent connections where the dashed line connotes weakened connection strength. Feedforward stimulus drive omitted for clarity. D: Example realization of network activity to a sustained, fixed stimulus. Colors as in (A). E: $E_1$ auto-correlation function and F: $E_1-E_2$ cross-correlation function for the illustrated rate traces. For panels D, E and F: $c=0.5$.

Figure 2.. Highly correlated regime in weakly coupled excitatory network relies on correlated feedforward inputs.

A: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ as a function of $W_{EE}$ and the magnitude of shared input noise $c$. Dashed pink line indicates $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)=0.6$, approximating the value reported in Kim et al. (2018b). B: Schematic of example synaptic paths through the network, along with their contribution to the cross-covariance, relating to the path expansion Eq. 4. The inherited row refers to correlated paths stemming from correlations in the feedforward input, while the recurrence row arises from the recurrent connections across the populations. C: Contributions of paths of given order to networks (left) and the total correlation (right) for the parameters $W_{EE}=0.25$ and $c=0.65$ (star from panel (A)). All panels: $\alpha =0.1$.

Figure 3.. Weakly coupled network.

A: Network model schematic as in Figure 1C. Blue lines indicate recurrent inhibitory connections. B: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ as a function of $\left|W_{EI}\right|$ and $W_{IE}$. C: Illustrations of first and second order paths. D, E: (Left) Contributions of $E$ (red outlined bars) and $I$ (blue outlined bars) to the net $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$. (Right) Schematic of dominant correlating pathway. Colored stars denote locations in B. Red star: $W_{EI}=-1,W_{IE}=0.07$; blue star: $W_{EI}=-0.05,W_{IE}=2$. For all panels $\alpha =0.15$.

Figure 4.. Global inhibition in ISN regime.

A: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ as a function of $W_{EI},W_{IE}$ with $c=0$. B: Top: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ along the yellow path in A. Gray region: unstable; green region: positive correlations; purple region: negative correlations. Bottom: eigenvalues of the circuit along the yellow path in A. C, D: Top: example rate traces (colors as in Fig. 3B). Bottom: auto- and cross-correlation functions computed numerically (black) and theoretically for the dominant timescale (blue dashed). Stars indicate parameter values shown in B. Here, $\alpha =0.2$.

Figure 5.. Segregated I subpopulations produce robust positive correlations.

A: Model schematic. Input structure is consistent with Fig. 3A but omitted for clarity. B: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ as a function of $W_{EI},W_{IE}$ with $c=0$. C: $\mathrm{C}\mathrm{o}\mathrm{r}\mathrm{r}\left(E_1,E_2\right)$ as a function of added connections between $I_1,I_2$ (left); $I_1\to E_2$ and $I_2\to E_1$ (middle); $E_1\to I_2$ and $E_2\to I_1$ (right). Added connections $W_{ij}$ are initialized to the same as elsewhere in the network, and scaled by: $\zeta ,I\leftrightarrow I;\beta ,I\to E;\gamma ,E\to I$. Dashed turquoise line denotes $\zeta ,\beta ,\gamma =0,W_{EI}=W_{IE}=1$.