Marina Chugunova | Applied Math, University of Waterloo
Application of Markov Chains and Stochastic Differential Equations for the Hodgkin-Huxley Model
The Nobel Prize winners of 1963, Alan Hodgkin and Andrew Huxley developed a deterministic mathematical model that describes the electrical dynamics of the excitable neuron membrane. The Hodgkin-Huxley equations, however, do not include recently discovered channel noise, which corresponds to a randomness in the process of opening and closing of ion channels.
In this presentation, we discuss methods that allow to include stochastic effect. These methods are reviewed in the article "Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons" by Joshua Goldwyn, Nikita Imennov, Michael Famulare, and Eric Shea-Brown.