A model for signal transmission in an ear having hair cells with free-standing stereocilia. IV. Mechanoelectric transduction stage.

A model is described for mechanoelectric transduction in hair cells with free-standing stereocilia in the alligator lizard cochlea. The model relates the angular displacement of the stereocilia to the receptor potential in the absence of the hair cell's membrane capacitance whose effect is considered elsewhere (Leong and Weiss, 1985, in preparation). The model consists of two parts: a population of membrane ionic channels and an electric network that relates the channel conductance to the equivalent resistance of the hair cell. The membrane ionic channels tend to open when the stereociliary tuft is displaced toward the kinocilium (or basal body) and tend to close when the tuft is oppositely displaced. The fraction of channels that is open for a given tuft displacement is governed by Boltzmann statistics and the energies of open and closed configurations of the channels are separated by a single energy barrier whose height depends on the angular displacement of the stereociliary tuft. The resulting channel conductance is a hyperbolic-tangent type function of the angular displacement of the stereociliary tuft. The channel conductance is coupled to the rest of the hair cell by an equivalent electric network containing constant resistance and a capacitance. The Thévenin equivalent resistance change across the basolateral membrane of the hair cell, called the transducer function, is also a hyperbolic-tangent type function of angular displacement. The parameters of the channel conductance and the values of resistances in the hair-cell electric model determine the scale factors and the location of the operating point of this hyperbolic-tangent type function. The hyperbolic-tangent type function is a specific example of a class of monotonically decreasing and saturating, or sigmoidal, transducer functions. The spectral properties of sigmoidal transducer functions are examined for sinusoidal angular displacements of amplitude theta. General results are obtained for arbitrary sigmoidal transducer functions; particular results are obtained for the hyperbolic-tangent type function. General conclusions concerning spectral components of the resistance change include: all spectral components are independent of the frequency of the angular displacement; the constant or DC component can be positive or negative; the fundamental component is 180 degrees out of phase with the angular displacement, i.e. the resistance decreases when the stereocilia are displaced towards the kinocilium; for small values of theta, the magnitude of the nth harmonic tends to grow as theta n for n greater than 0; the zeroth harmonic or DC component grows as theta 2.(ABSTRACT TRUNCATED AT 400 WORDS)