Multiplicative gain modulation arising from inhibitory synaptic plasticity in the cerebellar nuclei

Neurons use the rate of action potentials to encode sensory variables. This makes the output rate as a function of input, also known as input-output (I–O) relationship, a core computational function in neuronal processing. The introduction, or increase, of a modulatory input, can transform this function in multiple ways: additive transformations result in a shift, and multiplicative transformations in a change of slope of the I–O relationship. This slope change is known as gain modulation, and it can implement important forms of neural computation such as coordinate transformations. Gain modulation can be found in a wide range of brain systems, including the cerebellum, where it can be enabled by synaptic plasticity at both excitatory and inhibitory synapses.
We use a realistic, conductance based, multi-compartmental model of a cerebellar nucleus (CN) neuron, to investigate the determinants of gain modulation mediated by synaptic plasticity. In particular, we are interested in the effect of short term depression (STD) at the inhibitory synapse from Purkinje cells (PCs) to CN neurons. Considering the inhibitory PC input as the driving input, we compare the I–O relationship of the CN neuron in the presence and absence of STD for 20 Hz of excitatory synaptic input from mossy fibers (MFs), and find that STD introduces a gain change, changing the slope of the I–O function. We then proceed to compare the transformation performed by the increase of the modulatory input from 20 to 50 Hz, in the presence and absence of STD. We find that the presence of STD in the inhibitory synapse introduces a multiplicative component in the transformation performed by the excitatory input, an effect that persists for different levels of STD, and various combinations of regularity and synchronicity in the input.