Modeling Stochastic Gating Of Ion Channels

By collecting data in fixing cuttlefish axon potential experiment,Hodgkin and Huxley come up with biological membrane dynamics model,that is to say,H-H model,which is foundational model in all excitable membrane.Henceforth,in order to improve H-H model,lots of study are devoted,for example,simplifications and extensions of H-H model,I-F model,stochastic H-H model and so on.H-H model have explained integral behavior to lots of ion channels,and action potentials will be elicited if outside stimulus exceed threshold.With profound study,it is found that a few ion channels can also elicit subthreshold spontaneous action potentials without outside stimulus.Using molecular dynamics methods can treat with a few molecular subthreshold spontaneous firing if every ion channel is independent and identical,but,really,biological membrane ion channels are international, especially,near ion channels each other.If one ion channel is open,penetrating certain ion,there is small potential,which will affect around ion channels'stats,and make near ion channels open.Similarly,if one ion channel is close,it can also control around ion channels open.In this paper,we consider subthreshold spontaneous action potentials elicited by ion channel fluctuations with stochastic Markov theory.Firstly,if near ion channels have same firing,stochastic H-H model and corresponding master equation are concluded from independent ion channels earth other.Seeing results of numerical simulation, if ion channels numbers differ in a set of ion channels,subthreshold spontaneous action potentials's frequency will vary,and the variance is irregular.Secondly if near ion channels have certain interaction,the covariance coefficient and corresponding master are deduced based independent ion channels.