A diffusion model of the transient response of the cochlear inner hair cell synapse

Abstract

One class of models of hair cell synaptic function that has been investigated in recent years consists of one or more reservoirs of synaptic material connected to other reservoirs and/or the synaptic cleft by means of diffusion paths. One such general model is considered here, comprising two reservoirs and a global source of synaptic material connected in series and releasing material into the synaptic cleft by a diffusion path characterized by an intensity-dependent permeability. The explicit form of the solution of the model for a sudden onset of stimulation is derived: The solution comprises two exponentially decaying terms plus a constant. This solution is shown to have a unique inverse. This allows the determination of the parameters of the model directly from experimental data from auditory-nerve fibers in the Mongolian gerbil. The behavior of the derived model parameters with variation of stimulus intensity is demonstrated, and implications for synaptic function are discussed.

Tonotopic Distribution of Short-Term Adaptation Properties in the Cochlear Nerve of Normal and Acoustically Overexposed Chicks

“…This adaptation to a steady-state level occurs in stages, which in the literature are grouped into four classes based on the time constant (t): rapid (t õ 1-10 ms), short-term (t õ 10-100 ms), long-term (t õ 1-10 s), and very long-term (t õ 10-240 s) (Harris and Dallos 1979;Westerman and Smith 1984;Javel 1996). Adaptation models have invoked a series of depletable vesicle Breservoirs^in hair cells to account for the stages (Schwid and Geisler 1982;Smith and Brachman 1982;Geisler and Greenberg 1986;Westerman and Smith 1988). This depletion hypothesis is supported by work on goldfish saccular afferents where excitatory postsynaptic potentials (EPSPs) decrease in amplitude during a constant acoustic stimulus .…”

A phenomenological model of the synapse between the inner hair cell and auditory nerve: Long-term adaptation with power-law dynamics

“…The parameters were determined according to the derived equations ͑Appendix A of Westerman and Smith, 1988͒ based on the desired response characteristics for the onset and steady-state responses of the post-stimulus time histograms ͑PSTHs͒ to tones ͑Appendix in Zhang et al, 2001͒. The onset response of the model AN fiber is governed by exponential adaptation with two time constants ͑2 and 60 ms͒. The other parameters of the three-store diffusion model in the exponential adaptation stage were set to produce spontaneous activity and rate saturation at higher stimulus levels ͑Zhang et al, 2001͒.…”

“…Although the mechanism that gives rise to synaptic adaptation is not completely understood, it could be caused either by the depletion of neurotransmitter from a readily releasable presynaptic pool of neurotransmitter ͑Moser and Beutner, 2000; Schnee et al, 2005;Goutman and Glowatzki, 2007͒ or by the desensitization of post-synaptic receptors ͑Raman et al, 1994͒. Modeling the adaptation in the IHC-AN synapse has been a focus of extensive research over the last several decades. Early attempts employed a single-reservoir system with loss and replenishment of transmitter quanta ͑Schroeder and Hall, 1974;Sujaku, 1974, 1975͒, and later models added extra reservoirs ͑or sites͒ or more complex principles of transmitter flow control ͑Furukawa and Matsuura, 1978;Furukawa et al, 1982;Ross, 1982Ross, , 1996Schwid and Geisler, 1982;Smith and Brachman, 1982;Cooke, 1986;Meddis, 1986Meddis, , 1988Westerman and Smith, 1988͒. In general, the transmitter in these models lies in reservoirs or sites close to the presynaptic membrane and diffuses between reservoirs within the cell and out of the cell to the synaptic cleft.…”

“…The diversity and complexity of adaptation pose a great challenge for successful modeling of the dynamics of this synapse. Two models with different structures have been developed independently in a series of studies ͑Meddis, 1986͑Meddis, , 1988Westerman and Smith, 1988;Carney, 1993;Zhang et al, 2001;Sumner et al, 2002. However, the mathematical descriptions of these two models are essentially equivalent despite their structural differences ͑Zhang and Carney, 2005͒.…”

Understanding hearing impairment through model predictions of brainstem responses

“…Instantaneous discharge rates in the auditory nerve were simulated using a time-varying three-store diffusion model (Westerman and Smith (1988)) that has been used in several studies to simulate the IHC/AN synapse ; Zhang et al, (2001); Zilany et al, (2009)). The parameters were chosen to be identical to those in a past study that achieved realistic steady-state rate-level functions for pure-tone stimulation .…”