Choe Y, Magnasco M O, Hudspeth A J
Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, NY 10021-6399, USA.
Proc Natl Acad Sci U S A. 1998 Dec 22;95(26):15321-6. doi: 10.1073/pnas.95.26.15321.
Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system's behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken's cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.
毛细胞对听觉刺激的放大增强了脊椎动物内耳的敏感性。外毛细胞的胞体收缩被认为介导了哺乳动物耳蜗的放大作用。在缺乏这些细胞的脊椎动物中，或许在哺乳动物中也是如此，毛束的主动运动可能是放大作用的基础。我们评估了一个数学模型，其中放大作用源于机械电转导通道的活动。假定Ca2+与通道的细胞内结合会促进通道关闭，这会增加门控弹簧的张力，并对毛束施加一个负向力。通过增强毛束运动，该力部分补偿了耳蜗内液体的粘性阻尼。对一个六态动力学模型的线性稳定性分析揭示了生理范围内参数值的霍普夫分岔。这些分岔标志着系统行为从阻尼振荡响应转变为自发极限环振荡的条件。通过改变毛束中静纤毛的数量以及Ca2+结合的速率常数，我们计算出了一个代表性感受器器官——鸡的耳蜗——在观察到的听觉敏感性范围内的分岔频率。使用分岔前参数值的模拟展示了具有显著压缩非线性的频率选择性放大。由于转导通道普遍存在于毛细胞中，这种主动通道模型描述了一种可能适用于所有物种和毛细胞类型的听觉放大机制。
