We investigate the propagation of probabilistic uncertainty through the action potential mechanism in nerve cells. Using the Hodgkin-Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an accurate probabilistic interpretation of the deterministic dynamics of the transmembrane potential and gating variables. Using Sobol indices, out of the 11 uncertain parameters in the H-H model, we unravel two main uncertainty sources, which account for more than 90 % of the fluctuations in neuronal responses, and have a direct biophysical interpretation. We discuss how this interesting feature of the H-H model allows one to reduce greatly the probabilistic degrees of freedom in uncertainty quantification analyses, saving CPU time in numerical simulations and opening possibilities for probabilistic generalisation of other deterministic models of great importance in physiology and mathematical neuroscience.

中文翻译：

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通过动作电位机制在神经冲动中不确定性的传播。

我们通过神经细胞中的动作电位机制研究了概率不确定性的传播。使用Hodgkin-Huxley（HH）模型和稀疏网格上的随机搭配，我们获得了跨膜电位和门控变量确定性动力学的准确概率解释。使用Sobol指数，从HH模型的11个不确定参数中，我们揭示了两个主要的不确定性来源，它们占神经元反应波动的90％以上，并具有直接的生物物理解释。我们讨论了HH模型的这一有趣功能如何使不确定性量化分析中的概率自由度大大降低，