Spike generation in electroreceptor afferents introduces additional spectral response components by weakly nonlinear interactions

Abstract

Spiking thresholds in neurons or rectification at synapses are essential for neuronal computations rendering neuronal processing inherently nonlinear. Nevertheless, linear response theory has been instrumental for understanding, for example, the impact of noise or neuronal synchrony on signal transmission, or the emergence of oscillatory activity, but is valid only at low stimulus amplitudes or large levels of intrinsic noise. At higher signal-to-noise ratios, however, nonlinear response components become relevant. Theoretical results for leaky integrate-and-fire neurons in the weakly nonlinear regime suggest strong responses at the sum of two input frequencies if one of these frequencies or their sum match the neuron’s baseline firing rate. We here analyze nonlinear responses in two types of primary electroreceptor afferents, the P-units of the active and the ampullary cells of the passive electrosensory system of the wave-type electric fish Apteronotus leptorhynchus of either sex. In our combined experimental and modeling approach we identify these predicted nonlinear responses in those 31 out of 172 P-units that are characterized by low intrinsic noise. In contrast, the majority (22 out of 30) ampullary cells show nonlinear responses. Our results provide experimental evidence for nonlinear responses of spike generators in the weakly nonlinear regime. We conclude that such nonlinear responses occur in any sensory neuron that operates in similar regimes particularly at near-threshold stimulus conditions.

Significance statement The generation of action potentials involves a strong threshold nonlinearity. Nevertheless, the encoding of stimuli with small amplitudes by neurons with sufficient intrinsic noise can be well described as a linear system. As the stimulus amplitude is increased, new spectral components start to appear in the so called weakly nonlinear regime. Theory predicts nonlinear interactions whenever one or the sum of two stimulus frequencies matches the neuron’s baseline firing rate. Indeed, we find these interactions in a large set of electrophysiological recordings from primary electroreceptive afferents of a weakly electric fish. The nonlinear response components could boost sensory responses to weak signals emitted, for example, by distant conspecifics.