Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism (2015)

We investigate the propagation of probabilistic uncertainty through the ac- tion potential mechanism in nerve cells. Using the Hodgkin–Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an accurate probabilistic in- terpretation 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 generalisa- tion of other deterministic models of great importance in physiology and mathemati- cal neuroscience.