Multiplicative computation by a looming-sensitive neuron

We investigated an identified neuron whose output firing rate may be described by a multiplicative interaction between two distinct inputs, excitatory and inhibitory, converging onto its dendritic tree. An additional inhibitory component that could play a role in this computation has also been identified, presynaptic to the cell. Selective activation and inactivation of feed-forward and presynaptic inhibition suggest that feed-forward inhibition plays a predominant role and that the multiplicative computation is implemented within the neuron itself. The role played by axonal sodium conductances in this computation was investigated by pharmacological inactivation and by characterization of the relation between membrane voltage and firing rate. This revealed that sodium channels act both to temporally advance the response and as an expansive non-linearity, mapping membrane voltage to firing rate in a nearly exponential manner. These results are consistent with an implementation of multiplication based on addition in logarithmic coordinates followed by exponential transformation of two simultaneously active feed-forward inputs to this neuron.