Gain control of firing rate by shunting inhibition: Roles of synaptic noise and dendritic saturation

Adjusting input-output gain is crucial for information processing by the brain. Gain control of subthreshold depolarization is commonly ascribed to increased membrane conductance caused by shunting inhibition. But contrary to its divisive effect on depolarization, shunting inhibition on its own fails to divisively modulate firing rate, apparently upsetting a critical tenet of neural models that use shunting inhibition to achieve gain control. Using a biophysically realistic neuron model, we show that divisive modulation of firing rate by shunting inhibition requires synaptic noise to smooth the relation between firing rate and somatic depolarization; although necessary, noise alone endows shunting inhibition with only a modest divisive effect on firing rate. In addition to introducing noise, synaptic input is associated with a nonlinear relation between somatic depolarization and excitation because of dendritic saturation; this nonlinearity dramatically enhances divisive modulation of firing rate by shunting inhibition under noisy conditions. Thus, shunting inhibition can act as a mechanism for firing rate gain control, but its modulatory effects (which include both divisive and subtractive components) are fully explained only when both synaptic noise and dendritic saturation are taken into account.