A circuit mechanism for independent modulation of excitatory and inhibitory firing rates after sensory deprivation

Abstract

Diverse interneuron subtypes shape sensory processing in mature cortical circuits. During development, sensory deprivation evokes powerful synaptic plasticity that alters circuitry, but how different inhibitory subtypes modulate circuit dynamics in response to this plasticity remains unclear. We investigate how deprivation-induced synaptic changes affect excitatory and inhibitory firing rates in a microcircuit model of the sensory cortex with multiple interneuron subtypes. We find that with a single interneuron subtype (parvalbumin-expressing [PV]), excitatory and inhibitory firing rates can only be comodulated-increased or decreased together. To explain the experimentally observed independent modulation, whereby one firing rate increases and the other decreases, requires strong feedback from a second interneuron subtype (somatostatin-expressing [SST]). Our model applies to the visual and somatosensory cortex, suggesting a general mechanism across sensory cortices. Therefore, we provide a mechanistic explanation for the differential role of interneuron subtypes in regulating firing rates, contributing to the already diverse roles they serve in the cortex.

Keywords: cortical circuits; interneurons; network model; sensory deprivation; synaptic plasticity.

Fig. 1.

Spiking network response to synaptic changes induced by brief MD. (A) Network schematic of synaptic connections among neurons with J denoting the overall coupling scale, $g_{\text{rc}}$ as the dominance of recurrent inhibition, and $g_{\text{fw}}$ as the dominance of feedforward inhibition. The parameters to model MD-induced synaptic plasticity are: depression of feedforward drive to excitatory neurons (${\delta }_{\text{E}}<1$) and to PV interneurons (${\delta }_{\text{P}}<1$) and potentiation of recurrent excitation to PV interneurons (${\zeta }_{\text{PE}}>1$) and of recurrent inhibition from PV to excitatory neurons (${\zeta }_{\text{EP}}>1$) (see Materials and Methods). (B) Network firing rate in the (${\delta }_{\text{E}},\hspace{0.17em}{\delta }_{\text{P}}$) plane as fold change of baseline firing rate (top right corner, ${\delta }_{\text{E}}={\delta }_{\text{P}}=1$) for excitatory neurons (Upper) and PV interneurons (Lower). (C) Network firing rate in the (${\zeta }_{\text{EP}},\hspace{0.17em}{\zeta }_{\text{PE}}$) plane as fold change of baseline firing rate (bottom left corner, ${\zeta }_{\text{EP}}={\zeta }_{\text{PE}}=1$). (D) Combined feedforward (through the E/I ratio of feedforward synaptic changes, ${\rho }_{\text{EI}}={\delta }_{\text{E}}/{\delta }_{\text{P}}$) and recurrent plasticity (through the potentiation of recurrent excitation to PV interneurons, ${\zeta }_{\text{PE}}$). Network firing rate in the (${\zeta }_{\text{PE}},\hspace{0.17em}{\rho }_{\text{EI}}$) plane as fold change of baseline firing rate (bottom left corner, ${\zeta }_{\text{PE}}={\rho }_{\text{EI}}=1$).

Fig. 2.

Firing-rate changes in response to MD depend on the network coupling scale J. (A) Schematic to determine the overlap of facilitating and suppressive response areas of excitatory and PV neurons. The thresholded plane of responses (Fig. 1) for both neuron types is used to compute the total facilitating area and quantify how closely excitatory and PV firing rates follow each other through the overlap of facilitation and suppression. (B) Network with feedforward depression only (Fig. 1B). Fractional area of facilitation for excitatory neurons ($F_{\text{E}}$; gray), PV interneurons ($F_{\text{P}}$; blue), and the overlap between excitatory and PV response areas ($O_{\text{EP}}$; orange) as a function of the overall coupling scale J. The green diamond shows the value of J used in Fig. 1 (ISN), and the black triangle shows the value of J used in SI Appendix, Fig. S1 (non-ISN). (C) Same as B for recurrent potentiation only (Fig. 1C). (D) Same as B for combined feedforward and recurrent plasticity (Fig. 1D). (E) Normalized rate change of PV interneurons in response to additional input to them as a function of coupling scale J. Additional input is given as increase in ${\delta }_{\text{P}}$ (from 1 to 1.1). Norm., normalized.

Fig. 3.

Network structure and spiking activity in the model with two subtypes of interneurons. (A) Schematic connectivity in the network with two subtypes of interneurons. (B) Spike raster of activity in the network with K = 1.6 nS. (C) Firing rates as a function of K. The green diamond shows the value of K used in B.

Fig. 4.

SST feedback selectively inverts PV responses. (A) Network firing rate in the (${\delta }_{\text{E}},\hspace{0.17em}{\delta }_{\text{P}}$) plane as fold change of baseline firing rate (baseline in top right corner) for excitatory (Top), PV (Middle), and SST (Bottom) neurons in the network with strong SST feedback (K = 1.6 nS). (B) Network firing rate in the (${\zeta }_{\text{EP}},{\zeta }_{\text{PE}}$) plane as fold change of baseline firing rate (baseline in bottom left corner). (C) Network firing rate in the (${\zeta }_{\text{PE}},\hspace{0.17em}{\rho }_{\text{EI}}$) plane as fold change of baseline firing rate (baseline in bottom left corner). (D) Network with feedforward depression only. Fractional area of facilitation for excitatory neurons ($F_{\text{E}}$; gray), PV interneurons ($F_{\text{P}}$; blue), and the overlap between excitatory and PV response areas ($O_{\text{EP}}$; orange). (E) Same as D for recurrent potentiation only. (F) Same as D for combined feedforward and recurrent plasticity. The green diamond in D–F shows the value of K used in A–C. Norm., normalized.

Fig. 5.

The inversion of responses of PV interneurons emerges as a function of the SST feedback. (A) Relative change of steady-state rate induced by current injection to PV interneurons as a function of SST feedback κ. The rate of each population is normalized to its baseline firing rate (BL) before additional current injection. (B) Dynamics of the linear population rate model following onset of step current to PV interneurons for $\kappa =0.5$ (Left), $\kappa =0.8$ (Center), and $\kappa =1.2$ (Right). Colors are the same as in A. a.u., arbitrary units.

Fig. 6.

Combining feedforward and recurrent plasticity in S1. (A) Schematic for combined recurrent and feedforward plasticity in S1: shift in recurrent E/I ratio through ${\zeta }_{\text{EP}}$, shift in feedforward E/I ratio through increasing firing threshold of PV interneurons (${\xi }_{\theta }$). (A, Inset) The f–I curve of a single LIF neuron for baseline firing threshold (dark blue) and with increased firing threshold (light blue). The excitability of PV interneurons is decreased via the parameter ${\xi }_{\theta }$. (B) Network firing rate as fold change of baseline firing rate (baseline in bottom left corner) in the (${\zeta }_{\text{EP}},\hspace{0.17em}{\xi }_{\theta }$) plane in the network with only one type of interneurons (PV). (C) Network firing rate as fold change of baseline firing rate in (${\zeta }_{\text{EP}},\hspace{0.17em}{\xi }_{\theta }$) plane in the network with two subtypes of interneurons (PV and SST), with strong SST feedback K = 1.6 nS.

Fig. 7.

An ISN with strong SST feedback can capture the independent modulation of excitatory and inhibitory firing rates observed during brief MD. Firing rates of excitatory (black) and PV (red) neurons at MD1 (Left) and at MD2 (Right), normalized by the firing rates before MD induction, are shown. Data are extracted from ref. and reproduced in the spiking network in the ISN regime that includes strong feedback from SST and in an ISN without SST feedback (Materials and Methods). Experimental data are mean ± SEM; simulation data are mean ± SD.