A mathematical model was developed for exploring the sensitivity of low-frequency inferior colliculus (IC) neurons to interaural phase disparity (IPD). The formulation involves a firing-rate-type model that does not include spikes per se. The model IC neuron receives IPD-tuned excitatory and inhibitory inputs (viewed as the output of a collection of cells in the medial superior olive). The model cell possesses cellular properties of firing rate adaptation and postinhibitory rebound (PIR). The descriptions of these mechanisms are biophysically reasonable, but only semi-quantitative. We seek to explain within a minimal model the experimentally observed mismatch between responses to IPD stimuli delivered dynamically and those delivered statically (McAlpine et al. 2000; Spitzer and Semple 1993). The model reproduces many features of the responses to static IPD presentations, binaural beat, and partial range sweep stimuli. These features include differences in responses to a stimulus presented in static or dynamic context: sharper tuning and phase shifts in response to binaural beats, and hysteresis and "rise-from-nowhere" in response to partial range sweeps. Our results suggest that dynamic response features are due to the structure of inputs and the presence of firing rate adaptation and PIR mechanism in IC cells, but do not depend on a specific biophysical mechanism. We demonstrate how the model's various components contribute to shaping the observed phenomena. For example, adaptation, PIR, and transmission delay shape phase advances and delays in responses to binaural beats, adaptation and PIR shape hysteresis in different ranges of IPD, and tuned inhibition underlies asymmetry in dynamic tuning properties. We also suggest experiments to test our modeling predictions: in vitro simulation of the binaural beat (phase advance at low beat frequencies, its dependence on firing rate), in vivo partial range sweep experiments (dependence of the hysteresis curve on parameters), and inhibition blocking experiments (to study inhibitory tuning properties by observation of phase shifts).
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