NONLINEAR AND KINETIC ASPECTS OF CHANNELS GATING AND THEIR ROLE IN AUDITION

R. Patuzzi, Physiology, School of Biomedical and Chemical Sciences, The University of Western Australia.

The stochastic switching of membrane protein channels under thermal agitation between a finite number of discrete conformations leads to a nonlinear relationship between the (electrostatic) energy bias applied to the proteins and the probability of occupation of their discrete states. For small and simple perturbations the changes in state occupancy (and therefore channel conductance) are described by simple changes in channel properties that are exponential in time. When the perturbations are large and complex, however, as often occurs with transduction proteins in cell membranes, the responses of the membrane channels can be very complex, exhibiting an unexpected time course or a complex interaction between the components of a complex stimulus. A good example of these complex responses can be seen in the response of the stretch-sensitive mechano-electrical tranduction (MET) channels of the hair cells of hearing. When a large amplitude sinusoidal stimulus is applied to the hair bundle of hair cells, the probability of channel opening and therefore the membrane conductance and cell receptor current are highly non-sinusoidal, producing harmonic distortion in the receptor current, and ultimately in our perception of sound. This distortion accounts for our ability to hear sound over a million to one sound pressure range without damage to the ear. Moreover, when two sinusoidal stimuli are applied simultaneously (while listening to two musical notes in a chord, for example), the stimuli interact nonlinearly to produce the two-tone phenomena known as low-frequency biasing, two-tone interference and distortion tone generation. These interactions are not side-issues in hearing: they explain the masking of one sound by another, and even the fundamental origin of harmony in music. What is less appreciated is that the nonlinear mathematics of channel gating can produce other complex phenomena in the gating time-course, including non-monotonic changes in membrane conductance with a stepwise change in the stimulus (exponential turn-on and inactivation of membrane conductance). In the case of cyclic stimuli, such considerations predict an altered time-course of protein folding when two stimuli are presented simultaneously. In particular, the presentation of a sinusoidal stimulus during recovery from a previous stimulus can change the time-course dramatically (under some circumstances accelerating it), and the simultaneous presentation of two sinusoidal stimuli can produce less of a change in channel occupancy than each sinusoid alone, and with quite a different recovery time course. Aspects of these nonlinear interactions will be described, and their relevance to normal cochlear transduction and the response of the ear to overstimulation will be discussed.