Torres Valderrama Aldemar, Witteveen Jeroen, Navarro Maria, Blom Joke
CWI, Amsterdam, Science Park 123, 1098 XG, Amsterdam, The Netherlands.
Department of Neurology and Neurosurgery, Brain Center Rudolf Magnus, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX, Utrecht, The Netherlands.
J Math Neurosci. 2015 Dec;5(1):3. doi: 10.1186/2190-8567-5-3. Epub 2015 Jan 12.
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.
我们研究了概率不确定性在神经细胞动作电位机制中的传播。通过使用霍奇金 - 赫胥黎（H-H）模型和稀疏网格上的随机配置方法，我们获得了跨膜电位和门控变量确定性动力学的精确概率解释。利用索伯尔指数，在H-H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，并且具有直接的生物物理学解释。我们讨论了H-H模型的这一有趣特性如何能够在不确定性量化分析中极大地减少概率自由度，在数值模拟中节省CPU时间，并为生理学和数学神经科学中其他重要的确定性模型的概率推广开辟可能性。
