| Recent studies have shown that interaural-phase-difference-sensitive neurons in the inferior colliculus (IC), unlike neurons in the lower level structures, respond differently to auditory stimuli presented under static and dynamic conditions (e.g., [60]). In the present work we develop new mathematical models to explore the cellular mechanisms, underlying the dynamic sound processing. Our models are firing-rate-type, but also include firing rate adaptation and post-inhibitory rebound (PIR). One formulation is in terms of the short-time-averaged voltage (AV model), and, unlike conventional firing rate models, it has subthreshold dynamics (e.g., hyperpolarization).; We show with a combination of analytical and computational methods that most properties of responses to dynamic stimuli in IC can be explained by the convergence of the excitatory and inhibitory inputs, and presence of adaptation and PIR. In particular, adaptation creates phase advance of dynamic responses relative to static response; phase advance may be increased by PIR and masked in vivo by transmission delay; adaptation increases the amplitude of the dynamic response relative to the static case; PIR can create strong dynamic response in the silent portion of the static tuning curve; adaptation and PIR underlie hysteresis in responses to partial range sweeps; tuned inhibitory input creates asymmetry of the cell's tuning properties; dynamic effects are increased in presence of inhibition blocker.; We make predictions that (1) the phase advance should be observed in in vitro experiments, and may be modified by changing strength of adaptation and PIR; (2) tuning properties of inhibition may be tested with extracellular recordings in inhibition blockade or induction experiments in vivo; (3) presence of PIR may be manifested by multimodal shape of the hysteresis curve; (4) hysteresis is increased with width of the sweep and there is an optimal range of sweep rates.; We also confirm our results with a generic spiking model (integrate-and-fire). After that we derive a quasi-steady-state averaged model from integrate-and-fire model under assumptions of slowly varying input and slow adaptation dynamics, and compare its properties to the AV model. |
