The Cellular Basis for Hearing

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Hair cells constitute the cellular basis for hearing. Their primary role is to convert mechanical signal into electrical signal through the ion channels, called ``mechano-electrical transducer (MET) channels'', in the hair bundles of hair cells. Another important function of hair cells is to reciprocally amplify the mechanical input signal by working against damping due to viscous fluids in the organ. This thesis consists of theoretical investigations on hair cell function as the mechano-electrical transducer and as the cochlear amplifier.

First, we examine gating of two MET channels that are coupled to each other. While gating of MET channels has been successfully described by assuming that in a hair bundle, one MET channel is associated with one tip link, recent reports indicate that a single tip link is associated with more than one channel cite{Beurg2006,Beurg2009}. To address the discrepancy between the earlier models with the recent experimental observations, we describe gating of MET channels by assuming that each tip link is associated with two identical MET channels, which are connected either in series or in parallel. We found that series connection model predicts double minima of the hair bundle stiffness with respect to the hair bundle displacement if the minimum is below a certain positive value. In contrast, the parallel connection model makes predictions similar to the previous model that assumes a single channel for each tip link, within the physiological range of parameters. This explains how the earlier models assuming a single channel for each tip link has been successful in describing gating of MET channels. The parallel connection model of MET channels is, therefore, a reasonable assumption to explain most experimental observations. However, we show that turtle hair cell data may be compatible with the series connection model.

Second, we examine roles of hair cells as an amplifier in the cochlea. Hair cells are responsible for high sensitivity and frequency selectivity of hearing. This is attributed to motile mechanisms in hair cells, electromotility'' which indicates length change of outer hair cell driven by AC electrical potential across the membrane, and hair bundle motility'' which is an active movement of the hair bundle of hair cells. We first investigated the amplifying role of hair cells in the mammalian ear, including studies of both electromotility and hair bundle motility.

Electromotility is driven by the receptor potential, which is an AC electrical potential generated by gating of MET channels. Thus, the frequency characteristics of electromotility are determined by a low-pass filter, represented by the product of membrane resistance R and capacitance C with frequency roll off at about 0.1 of the highest audible frequency. This filter significantly decreases the efficiency of electromotility as an amplifier. In the thesis, we examine a proposal that the cochlear microphonic, the voltage drop across the extracellular medium by the receptor current, contributes to overcome this problem. We found that this effect can improve the frequency response. However, this effect alone is too small to enhance the effectiveness of electromotility beyond 10 kHz in the mammalian ear.

It has been experimentally found that the hair bundle motility in the mammalian ear is based on a ``release mechanism'', which is the fast component in the hair bundle's response to mechanical stimulation. In the release mechanism, the hair bundle responds in a way to reduce applied tension, similar to common mechanical relaxation with a damping. This observation is puzzling because hair bundle motility based on the release mechanism is expected to have an amplifying role. In the thesis we show that a release mechanism can indeed have a role in amplification if it takes place in a range where effective hair bundle stiffness has a negative value.

Finally we expand scope of investigation to avian hair cells, which must rely on hair bundle motility for amplification due to lack of electromotility. Specifically we evaluate the effectiveness of hair bundle motility in mammalian and avian ears. If hair bundle motility works for amplification, energy generated by the hair bundle must be, at least, greater than energy lost due to damping in the viscous fluid of cochlea. We compare work done by the hair bundle motility with the energy loss due to shear in the sub-tectorial gap during one cycle of small sinusoidal hair bundle displacement. This condition gives a frequency limit where the hair bundle motility can work as an amplifier in the cochlea. We obtain frequency limits for two mechanisms for hair bundle motility; one is based on the interaction between calcium and the MET channel and the other is based on the interplay between gating of the channel and the myosin motor. We show that the frequency limit obtained for each of these models is an increasing function of a factor that is determined by the morphology of hair bundles and the cochlea. Primarily due to the higher density of hair cells in the avian inner ear, this factor is about 10-fold greater for the avian ear than the mammalian ear, which has much higher auditory frequency limit. This result is consistent with a much greater importance of hair bundle motility in the avian ear than that in the mammalian ear.