Role of synaptic nonlinearity in persistent firing rate shifts caused by external periodic forcing

Information storage and processing in the brain largely relies on the neural population coding principle. In this framework, information is reflected in the population firing rate that reflects asynchronous irregular spiking of its constituent neurons. Periodic modulations of neural activity can lead to neural activity oscillations. Data indicate that such oscillations are ubiquitous in brain activity and are modulated, in frequency and amplitude, in a functionally meaningful manner. The relationship between oscillations and the population rate code remains an open issue. While ample works show how changes in the mean firing rate may alter neural oscillations, the reverse connection is unclear. One notable possibility is that oscillatory activity impinging on a neural population modulates its mean firing rate, thereby impacting information processing. We suggest that such modulation requires nonlinearities and propose nonlinear excitatory coupling via slow N-methyl-D-aspartate (NMDA) receptors as the prevalent mechanism. The aim of our paper is to theoretically explore to what extent the NMDA-related mechanism could account for oscillation-induced mean firing rate changes. We consider a mean-field model of a neural circuit containing an excitatory and an inhibitory population with linear transfer functions. Along with NMDA excitation, the model included fast recurrent excitatory and inhibitory connectivity. To explicitly study the effects of impinging oscillation on the rate dynamics, we subjected the circuit to a sinusoidal input signal imitating an input from distant brain regions or from a larger network into which the circuit is embedded. Using time-scale separation and time-averaging techniques, we developed a geometric method to determine the oscillation-induced mean firing rate shifts and validated it by numeric simulations of the model. Our results indicate that a large-amplitude stable firing rate shift requires nonlinear NMDA synapses on both the excitatory and the inhibitory populations. Our results delineate specific neural synaptic properties that enable neural oscillations to act as flexible modulators of the population rate code.