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A widely accepted view of computations in the brain relies on populationcoding, where the neural ensemble firing rate is modulated in a stable mannerto transmit information and perform various cognitive tasks. At the same time,oscillatory neural activity is specifically modulated in frequency, coherenceand power during cognitive performance. How the firing rate and oscillationsinteract remains a salient question. In this paper, we develop a theory for theinteractions between oscillatory signals and the firing rate of neuralpopulations based on activity of non-linear voltage-dependent NMDA synapses.Notably, we show under which conditions oscillatory inputs can control the meanfiring rate without loss of stability. Using mathematical analysis andsimulations of mean-field models, we demonstrate that presence of NMDA synapseson both the excitatory and the inhibitory neurons is critical for sinusoidaloscillations to significantly and stably increase the firing rate. Wecharacterize the oscillation-induced mean firing rate shift as a function ofthe fast and slow synaptic weights and demonstrate the parameter region, inwhich the effect under investigation is mostly pronounced. Results of our workmay help identify the properties of neural circuits that allow for constructivecontrol of the firing rate codes by large-scale neural oscillations.

Role of NMDA conductance in average firing rate shifts caused by external periodic forcing