Effectiveness, Active Energy Produced by Molecular Motors, and Nonlinear Capacitance of the Cochlear Outer Hair Cell

[+] Author and Article Information
Alexander A. Spector

Department of Biomedical Engineering,  Johns Hopkins University, 720 Rutland avenue, Traylor 411, Baltimore, Maryland 21205 e-mail: aspector@bme.jhu.edu

J Biomech Eng 127(3), 391-399 (Jan 05, 2005) (9 pages) doi:10.1115/1.1894233 History: Received August 31, 2004; Revised January 05, 2005

Cochlear outer hair cells are crucial for active hearing. These cells have a unique form of motility, named electromotility, whose main features are the cell’s length changes, active force production, and nonlinear capacitance. The molecular motor, prestin, that drives outer hair cell electromotility has recently been identified. We reveal relationships between the active energy produced by the outer hair cell molecular motors, motor effectiveness, and the capacitive properties of the cell membrane. We quantitatively characterize these relationships by introducing three characteristics: effective capacitance, zero-strain capacitance, and zero-resultant capacitance. We show that zero-strain capacitance is smaller than zero-resultant capacitance, and that the effective capacitance is between the two. It was also found that the differences between the introduced capacitive characteristics can be expressed in terms of the active energy produced by the cell’s molecular motors. The effectiveness of the cell and its molecular motors is introduced as the ratio of the motors’ active energy to the energy of the externally applied electric field. It is shown that the effectiveness is proportional to the difference between zero-strain and zero-resultant capacitance. We analyze the cell and motor’s effectiveness within a broad range of cellular parameters and estimate it to be within a range of 12%–30%.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Schematic sketches of outer hair cells electrically stimulated under conditions of three types: (a) standard voltage clamp condition; (b) condition simulating zero strain in the cell wall; and (c) condition simulating zero resultant in the cell wall. In case (b), the cell is prevented from electromotile length changes by a holding pipette and a rigid rod. In case (c), the cell is partially included in the microchamber, there is an exchange of the fluid between two, excluded and included, parts of the cell, and the additional pressure that causes the resultant in the cell wall is minimal.

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Figure 2

The differences between the capacitive characteristics of the cell determining the active properties of the molecular motors as functions of transmembrane potential Ψ0. Solid lines represent the difference between zero-resultant and zero-strain capacitances, cN−cε. Dashed-dotted lines represent the difference between zero-resultant and effective capacitances, cN−ceff. Dashed lines represent the difference between the effective and zero-strain capacitances ceff−cε. Four presented cases correspond to the following combinations of the parameters: (a) (γa=0.6×10−2N∕m and α=1V−1); (b) (γa=0.6×10−2N∕m and α=1.4V−1); (c) (γa=1.2×10−2N∕m and α=1V−1); and (d) (γa=1.2×10−2N∕m and α=1.4V−1).

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Figure 3

Active energies ΔEa(Ψ0) (solid lines) and ΔLa(Ψ0) (dotted lines) produced by the molecular motors as quadratic functions of the increment in the transmembrane potential ΔΨ for three values of the reference potential Ψ0 (27mV, −13mV, and −53mV). The former energy is the product of the resultant and active strain, and the latter energy is the product of the active force and active strain. Two presented cases correspond to different combinations of the parameters: (a) γa=0.6×10−2N∕m; α=1V−1 and (b) γa=0.6×10−2N∕m; α=1.4V−1.

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Figure 4

Effectiveness of the molecular motors of the outer hair cell as a function of the transmembrane potential Ψ0 for different combinations of the parameters. The solid, dashed-dotted, dashed, and dotted lines correspond, respectively, to the following combination of the parameters: (γa=1.2×10−2N∕m and α=1.4V−1); (γa=0.6×10−2N∕m and α=1.4V−1); (γa=1.2×10−2N∕m and α=1V−1); and (γa=0.6×10−2N∕m and α=1V−1)



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