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.

The timing of action potentials is an important determinant of information coding in the brain. The shape of the EPSP has a key influence on the temporal precision of spike generation. Here we use dynamic clamp recording and passive neuronal models to study how developmental changes in synaptic conductance waveform and intrinsic membrane properties combine to affect the EPSP and action potential generation in cerebellar granule cells. We recorded EPSCs at newly formed and mature mossy fiber-granule cell synapses. Both quantal and evoked currents showed a marked speeding of the AMPA receptor-mediated component. We also found evidence for age- and activity-dependent changes in the involvement of NMDA receptors. Although AMPA and NMDA receptors contributed to quantal EPSCs at immature synapses, multiquantal release was required to activate NMDA receptors at mature synapses, suggesting a developmental redistribution of NMDA receptors. These changes in the synaptic conductance waveform result in a faster rising EPSP and reduced spike latency in mature granule cells. Mature granule cells also have a significantly decreased input resistance, contributing to a faster decaying EPSP and a reduced spike jitter. We suggest that these concurrent developmental changes, which increase the temporal precision of EPSP-spike coupling, will increase the fidelity with which sensory information is processed within the input layer of the cerebellar cortex.

Interneurons are critical for neuronal circuit function, but how their dendritic morphologies and membrane properties influence information flow within neuronal circuits is largely unknown. We studied the spatiotemporal profile of synaptic integration and short-term plasticity in dendrites of mature cerebellar stellate cells by combining two-photon guided electrical stimulation, glutamate uncaging, electron microscopy, and modeling. Synaptic activation within thin (0.4 μm) dendrites produced somatic responses that became smaller and slower with increasing distance from the soma, sublinear subthreshold input-output relationships, and a somatodendritic gradient of short-term plasticity. Unlike most studies showing that neurons employ active dendritic mechanisms, we found that passive cable properties of thin dendrites determine the sublinear integration and plasticity gradient, which both result from large dendritic depolarizations that reduce synaptic driving force. These integrative properties allow stellate cells to act as spatiotemporal filters of synaptic input patterns, thereby biasing their output in favor of sparse presynaptic activity.