  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, 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 and in a range of computational models.
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. 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.
