Clausznitzer Diana, Lindner Benjamin, Jülicher Frank, Martin Pascal
Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Apr;77(4 Pt 1):041901. doi: 10.1103/PhysRevE.77.041901. Epub 2008 Apr 1.
Hair cells perform the mechanoelectrical transduction of sound signals in the auditory and vestibular systems of vertebrates. The part of the hair cell essential for this transduction is the so-called hair bundle. In vitro experiments on hair cells from the sacculus of the American bullfrog have shown that the hair bundle comprises active elements capable of producing periodic deflections like a relaxation oscillator. Recently, a continuous nonlinear stochastic model of the hair bundle motion [Nadrowski, Proc. Natl. Acad. Sci. U.S.A. 101, 12195 (2004)] has been shown to reproduce the experimental data in stochastic simulations faithfully. Here, we demonstrate that a binary filtering of the hair bundle's deflection (experimental data and continuous hair bundle model) does not change significantly the spectral statistics of the spontaneous as well as the periodically driven hair bundle motion. We map the continuous hair bundle model to the FitzHugh-Nagumo model of neural excitability and discuss the bifurcations between different regimes of the system in terms of the latter model. Linearizing the nullclines and assuming perfect time-scale separation between the variables we can map the FitzHugh-Nagumo system to a simple two-state model in which each of the states corresponds to the two possible values of the binary-filtered hair bundle trajectory. For the two-state model, analytical expressions for the power spectrum and the susceptibility can be calculated [Lindner and Schimansky-Geier, Phys. Rev. E 61, 6103 (2000)] and show the same features as seen in the experimental data as well as in simulations of the continuous hair bundle model.
毛细胞在脊椎动物的听觉和前庭系统中执行声音信号的机械电转换。对于这种转换至关重要的毛细胞部分是所谓的毛束。对美国牛蛙球囊毛细胞的体外实验表明，毛束包含能够像弛豫振荡器一样产生周期性偏转的活性元件。最近，毛束运动的连续非线性随机模型[纳德罗夫斯基，《美国国家科学院院刊》101, 12195 (2004)]已被证明在随机模拟中能如实地再现实验数据。在此，我们证明对毛束偏转（实验数据和连续毛束模型）进行二值滤波不会显著改变自发以及周期性驱动的毛束运动的频谱统计。我们将连续毛束模型映射到神经兴奋性的菲茨休 - 纳古莫模型，并根据后一种模型讨论系统不同状态之间的分岔。使零倾线线性化并假设变量之间存在完美的时间尺度分离，我们可以将菲茨休 - 纳古莫系统映射到一个简单的双态模型，其中每个状态对应于二值滤波后的毛束轨迹的两个可能值。对于双态模型，可以计算功率谱和磁化率的解析表达式[林德纳和希曼斯基 - 盖尔，《物理评论E》61, 6103 (2000)]，并且这些表达式显示出与实验数据以及连续毛束模型模拟中所见相同的特征。
