A Cell-Level Mechanism of Contrast Gain Control

The gain of neurons’ responses in the auditory cortex is sensitive to contrast changes in the stimulus within a spectrotemporal range similar to their receptive fields (Rabinowitz et al., 2012), which can be interpreted to represent the tuning of the input to a neuron. This indicates a local mechanism of contrast gain control, which we explore with a minimal mechanistic model here. Gain control through noisy input has been observed in vitro (Chance et al., 2002) and in a range of computational models (Ayaz and Chance, 2009; Longtin et al., 2002). We investigate the behaviour of the simplest of such models to showcase gain control, a stochastic leaky integrate-and-fire (sLIF) neuron, which exhibits gain control through divisive normalisation of the input both with and without accompanying subtractive shift of the input-response curve, depending on whether input noise is proportional to or independent of its mean. To get a more direct understanding of how the input statistics change the response, we construct an analytic approximation to the firing rate of a sLIF neuron constituted of the expression for the deterministic case and a weighted average over the derived approximate steady-state distribution of conductance due to poissonian synaptic inputs. This analytic approximation qualitatively produces the same behaviour as simulations and could be extended by spectrotemporally tuned inputs to give a simple, physiological and local mechanism of contrast gain control in auditory sensing, building on recent experimental work that has hitherto only been described by phenomenological models (Rabinowitz et al., 2012). By comparing our weighted average firing rate curve with the commonly used sigmoidal input-response function, we demonstrate a nearly linear relationship between both the horizontal shift (or stimulus inflection point) and the inverse gain of the sigmoid and statistics derived from the sLIF model parameters, thus providing a structural constraint on the sigmoid parameter choice.