Neuronal gain control is important for processing information in the brain. Shunting inhibition is not thought to control gain since it shifts input-output relationships during tonic excitation rather than changing their slope. Here we show that tonic inhibition reduces the gain and shifts the offset of cerebellar granule cell input-output relationships during frequency-dependent excitation with synaptic conductance waveforms. Shunting inhibition scales subthreshold voltage, increasing the excitation frequency required to attain a particular firing rate. This reduces gain because frequency-dependent increases in input variability, which couple mean subthreshold voltage to firing rate, boost voltage fluctuations during inhibition. Moreover, synaptic time course and the number of inputs also influence gain changes by setting excitation variability. Our results suggest that shunting inhibition can multiplicatively scale rate-coded information in neurons with high-variability synaptic inputs.
