具有通道噪声的可激系统中快慢分析的失效
Breakdown of fast-slow analysis in an excitable system with channel noise
摘要：
我们考虑一个随机版本的可兴奋系统的基础上的Morris-Lecar模型的神经元，其中的噪声来源于随机钠和钾离子通道的开放和关闭。可以通过使用涉及快速电压变量和缓慢恢复变量的时间尺度的分离来分析确定性模型中的神经兴奋性，所述缓慢恢复变量表示开放钾通道的分数。在随机设置中，自发激发由离子通道噪声启动。如果恢复变量在起始期间是恒定的，则可以使用Kramer速率理论计算自发活动速率。在随机模型中，这一假设的有效性进行检查使用系统的扰动分析。我们发现，在大多数物理相关的情况下，这个假设打破了，需要一个替代Kramers理论的可激发系统与一个确定性的不动点。我们还表明，退出时间问题可以制定在一个可兴奋的系统，通过考虑随机过程的最大似然轨迹。
英文摘要：
We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron, in which the noise originates from stochastic Sodium and Potassium ion channels opening and closing. One can analyze neural excitability in the deterministic model by using a separation of time scales involving a fast voltage variable and a slow recovery variable, which represents the fraction of open Potassium channels. In the stochastic setting, spontaneous excitation is initiated by ion channel noise. If the recovery variable is constant during initiation, the spontaneous activity rate can be calculated using Kramer's rate theory. The validity of this assumption in the stochastic model is examined using a systematic perturbation analysis. We find that in most physically relevant cases, this assumption breaks down, requiring an alternative to Kramers theory for excitable systems with one deterministic fixed point. We also show that an exit time problem can be formulated in an excitable system by considering maximum likelihood trajectories of the stochastic process.
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