A biophysical account of multiplication by a single neuron

Nonlinear, multiplication-like operations carried out by individual nerve cells greatly enhance the computational power of a neural system^1-3, but our understanding of their biophysical implementation is scant. Here we pursue this problem in the Drosophila melanogaster ON motion vision circuit^4,5, in which we record the membrane potentials of direction-selective T4 neurons and of their columnar input elements^6,7 in response to visual and pharmacological stimuli in vivo. Our electrophysiological measurements and conductance-based simulations provide evidence for a passive supralinear interaction between two distinct types of synapse on T4 dendrites. We show that this multiplication-like nonlinearity arises from the coincidence of cholinergic excitation and release from glutamatergic inhibition. The latter depends on the expression of the glutamate-gated chloride channel GluClα^8,9 in T4 neurons, which sharpens the directional tuning of the cells and shapes the optomotor behaviour of the animals. Interacting pairs of shunting inhibitory and excitatory synapses have long been postulated as an analogue approximation of a multiplication, which is integral to theories of motion detection^10,11, sound localization¹² and sensorimotor control¹³.