Multiplicative computation in a visual neuron sensitive to looming

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Abstract
Multiplicative operations are important in sensory processing1,2,3,4,5, but their biophysical implementation remains largely unknown5,6,7,8,9,10. We investigated an identified neuron (the lobula giant movement detector, LGMD, of locusts) whose output firing rate in response to looming visual stimuli has been described by two models, one of which involves a multiplication. In this model, the LGMD multiplies postsynaptically two inputs (one excitatory, one inhibitory) that converge onto its dendritic tree11,12; in the other model, inhibition is presynaptic to the LGMD13,14. By using selective activation and inactivation of pre- and postsynaptic inhibition, we show that postsynaptic inhibition has a predominant role, suggesting that multiplication is implemented within the neuron itself. Our pharmacological experiments and measurements of firing rate versus membrane potential also reveal that sodium channels act both to advance the response of the LGMD in time and to map membrane potential to firing rate in a nearly exponential manner. These results are consistent with an implementation of multiplication based on dendritic subtraction of two converging inputs encoded logarithmically, followed by exponentiation through active membrane conductances.