Montgomery K A, Silber M, Solla S A
Mathematics Department, University of Utah, Salt Lake City, UT 84112, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 1):051924. doi: 10.1103/PhysRevE.75.051924. Epub 2007 May 30.
A mathematical model describing the coupling between two independent amplification mechanisms in auditory hair cells is proposed and analyzed. Hair cells are cells in the inner ear responsible for translating sound-induced mechanical stimuli into an electrical signal that can then be recorded by the auditory nerve. In nonmammals, two separate mechanisms have been postulated to contribute to the amplification and tuning properties of the hair cells. Models of each of these mechanisms have been shown to be poised near a Hopf bifurcation. Through a weakly nonlinear analysis that assumes weak periodic forcing, weak damping, and weak coupling, the physiologically based models of the two mechanisms are reduced to a system of two coupled amplitude equations describing the resonant response. The predictions that follow from an analysis of the reduced equations, as well as performance benefits due to the coupling of the two mechanisms, are discussed and compared with published experimental auditory nerve data.
提出并分析了一个描述听觉毛细胞中两种独立放大机制之间耦合的数学模型。毛细胞是内耳中的细胞，负责将声音引起的机械刺激转化为电信号，然后由听觉神经记录下来。在非哺乳动物中，已假定有两种独立的机制对毛细胞的放大和调谐特性起作用。已证明这些机制中的每一种模型都处于霍普夫分岔附近。通过假设弱周期强迫、弱阻尼和弱耦合的弱非线性分析，将这两种机制的基于生理学的模型简化为描述共振响应的两个耦合振幅方程系统。讨论了简化方程分析得出的预测结果，以及由于两种机制耦合带来的性能优势，并与已发表的实验性听觉神经数据进行了比较。
