Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.Author Summary: Many neural computations, including sensory and motor processing, require neurons to control their sensitivity (often termed ‘gain’) to stimuli. One common form of gain manipulation is divisive gain control, where the neural response to a specific stimulus is simply scaled by a constant. Most previous theoretical and experimental work on divisive gain control have assumed input statistics to be constant in time. However, realistic inputs can be highly time-varying, often with time-varying statistics, and divisive gain control remains to be extended to these cases. A widespread mechanism for divisive gain control for static inputs is through an increase in stimulus independent membrane fluctuations. We address the question of whether this divisive gain control scheme is indeed operative for time-varying inputs. Using simplified spiking neuron models, we employ accurate theoretical methods to estimate the dynamic neural response. We find that gain control via membrane fluctuations does indeed extend to the time-varying regime, and moreover, the degree of divisive scaling does not depend on the timescales of the driving input. This significantly increases the relevance of this form of divisive gain control for neural computations where input statistics change in time, as expected during normal sensory and motor behavior.