The hair cells of the vertebrate inner ear convert mechanical stimuli to electrical signals. Two adaptation mechanisms are known to modify the ionic current flowing through the transduction channels of the hair bundles: a rapid process involves calcium ions binding to the channels; and a slower adaptation is associated with the movement of myosin motors. We present a mathematical model of the hair cell which demonstrates that the combination of these two mechanisms can produce `self-tuned critical oscillations', i.e. maintain the hair bundle at the threshold of an oscillatory instability. The characteristic frequency depends on the geometry of the bundle and on the calcium dynamics, but is independent of channel kinetics. Poised on the verge of vibrating, the hair bundle acts as an active amplifier. However, if the hair cell is sufficiently perturbed, other dynamical regimes can occur. These include slow relaxation oscillations which resemble the hair bundle motion observed in some experimental preparations.
Full simulation on the dynamics of auditory synaptic fusion: Strong clustering of calcium channel might be the origin of the coherent release in the auditory hair cells
Amplitude death of coupled hair bundles with stochastic channel noise
毛细胞在脊椎动物中进行听觉传导。在低等脊椎动物如青蛙和海龟中，由于毛细胞的活跃机制，毛束（静纤毛）可以自发地振荡或静止。最近，已经提出了振幅死亡现象[K.- H. Ahn，J. R. Soc. Interface，{ \bf 10}，20130525（2013）]作为蛙毛细胞束中听觉转导的机制，其中振荡的突然停止由于不同毛束之间的耦合而出现。由于通道的构型变化的随机性质，离子通道的门控本质上是随机的。由于通道门控引起的噪声的强度可以与发束的热布朗噪声相当。因此，我们进行随机模拟的弹性耦合的头发束。尽管杂散噪声波动，由于其随机动力学，我们的模拟表明，从集体振荡到振幅死亡的过渡，束间耦合强度的增加。在其随机动力学中，耦合发束振幅死亡状态的形成可以看作是随着耦合强度的增加，发束位移波动的突然抑制。在随机动力学中可以清楚地看到通过振幅死亡现象而提高的信噪比。我们的数值计算结果表明，多个转导通道每毛束是一个重要因素的振幅死亡现象，因为这种现象可能会消失，为少数转导通道，由于强大的门控噪声。
