Untangling stability and gain modulation in cortical circuits with multiple interneuron classes

Abstract

Synaptic inhibition is the mechanistic backbone of a suite of cortical functions, not the least of which is maintaining overall network stability as well as modulating neuronal gain. Past cortical models have assumed simplified recurrent networks in which all inhibitory neurons are lumped into a single effective pool. In such models the mechanics of inhibitory stabilization and gain control are tightly linked in opposition to one another -meaning high gain coincides with low stability and vice versa. This tethering of stability and response gain restricts the possible operative regimes of the network. However, it is now well known that cortical inhibition is very diverse, with molecularly distinguished cell classes having distinct positions within the cortical circuit. In this study, we analyze populations of spiking neuron models and associated mean-field theories capturing circuits with pyramidal neurons as well as parvalbumin (PV) and somatostatin (SOM) expressing interneurons. Our study outlines arguments for a division of labor within the full cortical circuit where PV interneurons are ideally positioned to stabilize network activity, whereas SOM interneurons serve to modulate pyramidal cell gain. This segregation of inhibitory function supports stable cortical dynamics over a large range of modulation states. Our study offers a blueprint for how to relate the circuit structure of cortical networks with diverse cell types to the underlying population dynamics and stimulus response.

Common rules underlying optogenetic and behavioral modulation of responses in multi-cell-type V1 circuits

“…Furthermore, we establish a mathematical link between cell-type-specific response to perturbation and sub-circuit stability. By implementing those insights in these data-compatible models we provide new evidence, aligned with convergent experimental 15 and theoretical 33 arguments, that PV interneurons play a major role in circuit stabilization. Subsequently, we build upon the link between low-dimensional and high-dimensional models provided by mean-field theory 26,35 , and are able to construct a family of high-dimensional rate models that fit the experimentally observed distribution of activity of each cell-type and its dependence on contrast.…”

“…3 b,c ). We conclude that a first novel descriptor of the operating regime of circuits with multiple cell-types, is PV-stabilization, meaning that potential circuit instability is stabilized by PV cells and not by SOM cells (see also 33 ). This describes most of our models that are consistent with the data, but about 20% show paradoxical SOM response at higher contrasts (in addition to paradoxical PV response) and so are stabilized by the combination of PV and SOM and not by either alone.…”

“…As biological realism increases, making parameter-independent predictions or even locating the parameters that situate a biologically insightful model in the correct network state becomes exponentially difficult. Current approaches range from detailed heterogeneous network models 29,30 which lack mathematical tractability, to simpler and insightful homogeneous models whose parameters are either chosen according to currently available connectivity data [31][32][33][34] or to account for stimulus-evoked responses 17,20 , but that neglect within-cell-type diversity and are therefore limited in their predictive power.…”

“…First, there is little consensus on how to generalize the fundamental link between stabilization and response to perturbations to the case of multiple inhibitory types 8,9 . The inhibitory sub-circuit is composed of multiple elements with three types -parvalbumin-(PV), somatostatin-(SOM), and vasoactive-intestinal-peptide (VIP) expressing cells that constitute 80% of GABAergic interneurons in the mouse primary visual cortex (V1) 10 .…”

A solution to temporal credit assignment using cell-type-specific modulatory signals

“…To study the impact of our learning rule on network performance and dissect the effects of its different components, we train RSNNs using five different approaches for each task. These, illustrated in 3, are as follows: (i) BPTT, which updates weights using exact gradients shown in Figure 3ai; (ii) E-prop [23], the state-of-the-art method for biologically plausible training of RSNNs, shown Figure 3aii; (iii) TRTRL, the truncated RTRL given in (7) without the cell-type approximation, shown in Figure 3aiii; (iv) MDGL, which incorporates the cell type approximation given in (11) and (12) using only two cell types, shown in Figure 3aiv; (v) NL-MDGL, a nonlocal version of MDGL, where the gain is replaced by w αβ =< w jp > j∈α,p∈β even for w jp = 0 so that the modulatory signal diffuses to all cells in the network, shown in Figure 3av. We note that factor ∂E ∂zj,t , which depends on future errors as mentioned earlier, participates in the generation of all training results pertaining to MDGL in the main text ( Figures 4-7); in supplementary materials, we derive an online approximation to MDGL and demonstrate (via simulation) that it does not lead to significant performance degradation ( Figure S3, Section S3.2).…”