Synaptic depression enables neuronal gain control

To act as computational devices, neurons must perform mathematical operations as they transform synaptic and modulatory input into output firing rate1. Experiments and theory suggest that neuronal firing typically represents the sum of synaptic inputs1-3, an additive operation, but multiplication of inputs is essential for many computations1. Multiplication by a constant produces a change in the slope, or gain, of the input-output relation, amplifying or scaling down the neuron's sensitivity to changes in its input. Such gain modulation occurs in vivo, during contrast invariance of orientation tuning4, attentional scaling5, translation-invariant object recognition6, auditory processing7 and coordinate transformations8,9. Moreover, theoretical studies highlight the necessity of gain modulation in several of these tasks9-11. While potential cellular mechanisms for gain modulation have been identified, they often rely on membrane noise and require restrictive conditions to work3,12-18. Because nonlinear components are used to scale signals in electronics, we examined whether synaptic nonlinearities are involved in neuronal gain modulation. We used synaptic stimulation and dynamic-clamp to investigate gain modulation in granule cells (GCs) in acute cerebellar slices. Here we show that when excitation is mediated by synapses with short-term depression (STD), neuronal gain is controlled by an inhibitory conductance in a noise-independent manner, allowing driving and modulatory inputs to be multiplied together. The nonlinearity introduced by STD transforms inhibition-mediated additive shifts in the input-output relation into multiplicative gain changes. When GCs were driven with bursts of high-frequency mossy fibre (MF) input, as observed in vivo19,20, larger inhibition-mediated gain changes were observed, as expected with greater STD. Simulations of synaptic integration in more complex neocortical neurons confirm that STD-based gain modulation can also operate in neurons with large dendritic trees. Our results establish that neurons receiving depressing excitatory inputs can act as powerful multiplicative devices even when integration of postsynaptic conductances is linear.