Weakly nonlinear responses at low intrinsic noise levels in two types of electrosensory primary afferents

Abstract

Neuronal processing is inherently nonlinear — spiking thresholds or rectification in synapses are central to neuronal computations. Nevertheless, linear response theory has been instrumental in understanding, for example, the impact of noise or synchronous spikes on signal transmission, or the emergence of oscillatory activity. At higher signal-to-noise ratios, however, the third term in the Volterra series becomes relevant. This second-order susceptibility captures nonlinear interactions between pairs of stimulus frequencies. Theoretical results for leaky integrate-and-fire neurons suggest strong responses at the sum of two input frequencies only when these frequencies or their sum match the neuron’s baseline firing rate. We here analyze second-order susceptibilities in two types of primary electroreceptor afferents, P-units of the active and ampullary cells of the passive electrosensory system of the wave-type electric fishApteronotus leptorhynchus. In our combined experimental and modeling approach we find the predicted weakly nonlinear responses in some P-units with very low baseline interspike-interval variability and much stronger in all ampullary cells, which are less noisy than P-units. Such nonlinear responses boost responses to weak sinusoidal stimuli and are therefore of immediate relevance for wave-type electric fish that are exposed to superpositions of many frequencies in social contexts.