Multiplicative gain changes are induced by excitation or inhibition alone

We model the effects of excitation and inhibition on the gain of cortical neurons. Previous theoretical work has concluded that excitation or inhibition alone will not cause a multiplicative gain change in the curve of firing rate versus input current. However, such gain changes in vivo are measured in the curve of firing rate versus stimulus parameter. We find that when this curve is considered, and when the nonlinear relationships between stimulus parameter and input current and between input current and firing rate in vivo are taken into account, then simple excitation or inhibition alone can induce a multiplicative gain change. In particular, the power-law relationship between voltage and firing rate that is induced by neuronal noise is critical to this result. This suggests an unexpectedly simple mechanism that may underlie the gain modulations commonly observed in cortex. More generally, it suggests that a smaller input will multiplicatively modulate the gain of a larger one when both converge on a common cortical target.