Mechanisms underlying the response of mouse cortical networks to optogenetic manipulation

Abstract

GABAergic interneurons can be subdivided into three subclasses: parvalbumin positive (PV), somatostatin positive (SOM) and serotonin positive neurons. With principal cells (PCs) they form complex networks. We examine PCs and PV responses in mouse anterior lateral motor cortex (ALM) and barrel cortex (S1) upon PV photostimulation in vivo . In layer 5, the PV response is paradoxical: photoexcitation reduces their activity. This is not the case in ALM layer 2/3. We combine analytical calculations and numerical simulations to investigate how these results constrain the architecture. Twopopulation models cannot account for the results. Networks with three inhibitory populations and V1like architecture account for the data in ALM layer 2/3. Our data in layer 5 can be accounted for if SOM neurons receive inputs only from PCs and PV neurons. In both fourpopulation models, the paradoxical effect implies not too strong recurrent excitation. It is not evidence for stabilization by inhibition.sufficiently strong, namely ifThe denominator in is the strength of the connection from the SOM population to J EE the VIP population. The numerator is the gain of the pathway which connects these two populations via the PCs. When the negative contribution of the disinhibitory J EE > J EE loop PCVIPSOMPC dominates in the expression of . It is the opposite when χ II . The stability of the balanced state provides other necessary conditions that J EE < J EE the interactions must satisfy (Materials and Methods). In particular, the determinant of the interaction matrix, , must be positive. J of the positive feedback loop, SOMXPCSOM, is sufficiently strong (Supplementary Materials, SMD). Obviously, this condition simplifies and reads J J J EX XS > J XX ES (4) Remarkably, this inequality does not depend on . This is in contrast to what J EE happens in Model 1 where the paradoxical effect occurs only if is small enough J EE (see Eq. (2)). https://docs.google.com/document/d/1UaHERm5J7ZX8fMIoyG42_mFfOzWPZq32QDjE_gxdSgk/edit?ts=5c9dfa46# 24/46 was already substantial for small light intensities, where the PCs were still significantly active. The twopopulation model cannot account for this feature. In Model 1, whether the network exhibits a paradoxical effect depends on the value of the ratio where . Here, , is theThe requirement that at baseline the network state is fully balanced and stable implies that J I0 Therefore, the PC population activity increases upon PC stimulation if J J J J IX XS > IS XX (SM61)

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

“…This is understandable given the newly realized complexity of the circuit; however, this is precisely the situation where a more formal modeling approach can be very fruitful. Toward this end, recent modelling efforts both at the large (Billeh et al, 2020) and smaller (del Molino et al, 2017;Kuchibhotla et al, 2017;Litwin-Kumar et al, 2016;Mahrach et al, 2020;Veit et al, 2017) scales have incorporated key aspects of interneuron diversity. These studies typically explore which aspects of cellular or circuit diversity are required to replicate a specific experimental finding.…”

“…1A; see Methods 1.1). The simplicity of the spiking dynamics makes our model amenable to a mean-field reduction which captures the bulk spiking activity of each subpopulation of neurons (where r E , r P , and r S denote the E, PV, and SOM populations respectively; see Methods 1.2), as has been done by similar studies of the E -PV -SOM cortical circuit (del Molino et al, 2017;Kuchibhotla et al, 2017;Litwin-Kumar et al, 2016;Mahrach et al, 2020). Figure 1: Tradeoff between two inhibitory motifs in the E -PV -SOM cortical circuit.…”

“…We present a circuit theory for previously developed multi-interneuron cortical circuit models (del Molino et al, 2017;Kuchibhotla et al, 2017;Litwin-Kumar et al, 2016;Mahrach et al, 2020;Veit et al, 2017) with the goal of giving a mechanistic understanding of how diverse inhibitory interneurons participate in the circuit level modulation of cortical responses. In particular, we consider modulatory inputs to SOM neurons which aim to shift the operative state of the full E -PV -SOM neuron circuit.…”

State-dependent regulation of cortical processing speed via gain modulation

“…Our theory may shed light on the effects of manipulation experiments. Optogenetic activation (inactivation) of specific E or I cells [83,84] has been modeled as an increase (decrease) of the afferent currents to those cells [56,85,86]. However, protein expression may not be complete across all cells of the targeted population, and even in the case of complete expression across the targeted population, different cells may be more or less sensitive to laser stimulation.…”

Equations governing dynamics of excitation and inhibition in the mouse corticothalamic network

“…The models suggest that following an I pulse to the cortex, both cortical E and I populations are suppressed because inhibition of E neurons removes drive from both neuronal classes. This is essentially the mechanism of an inhibitorystabilized network (Li et al, 2019;Mahrach et al, 2020;Tsodyks et al, 1997); indeed, our cortical models were of this type. Interestingly, the parameters of the corticothalamic model did not always show strong enough cortical excitation to alone qualify as ISN, yet when recurrent activity via thalamus was included, we again observed ISN-like behavior.…”