Stochastic Dynamics Of Single Ion Channel

The conduction mechanism of neuronal electrical signals is an important research field in electrophysiology.It is basic for studying the working mechanism of the brain and the formation and conduction of various perceptions.However,for ion channel,it is very difficult to observe the mesoscopic system,which needs to be studied by mathematical means and methods.First of all,for the single ion channel dynamics whose switching rate is constant,an ana-lytical steady state solution of the stochastic model describing the integrated dynamics of the membrane voltage and the gating of a single channel is presented.It is found that the voltage density function experiences bifurcation in the parameter space,and the threshold is deter-mined by the comparison between the rates of the voltage evolution and which of the channel gating.As an application,the entropy production rate associated with the gating currents is calculated,its variation tendency in parameter space is consistent to which of the number of transitions counted from the sample pathes.The analysis in this paper identify the values of parameters that justify the formation of the voltage pulse and the efficient energy costing,which associates with the singularity of the voltage density functions.Secondly,through a stochastic model that mimics the kinetics of spontaneous gating of a potassium channel,we present a theoretical method to calculate the free energy dissipations associated with the K+current and the leakage current.On physical perspective,the essential role of the system is K+-attery charging the leakage battery.A part of power will inevitably be dissipated among the process.So the efficiency of energy transference is calculated.Finally,we con-struct a stochastic model to describe the re-polarizing dynamics of a single potassium channel clamped by a constant current.The stationary probability density functions(PDFs)of the pro-cess are got numerically.These PDFs will bifurcate between continuity and singularity at two boundaries under certain parametric conditions.The reasons are explained and the paramet-ric threshold for the bifurcation behaviors are estimated.Then the re-polarizing effects of the single potassium channel are shown by the sample pathes,the stationary mean voltages,and corresponding voltage fluctuations.Also,we calculate the energy dissipations to show the cost-performance relationship.Maybe more important phenomenon is the inevitably existing energy transference in the system.In conclusion,in this paper,we clarify the related physical mechanism,define its ex-tension,establish a strict stochastic process model,and analyze a series of properties of the model,such as non-equilibrium steady state distribution,entropy generation,etc.At the same time,we design a random algorithm for the system,and use it as a tool to explore the char-acteristics of the system.Through this thesis,we try to provide new means of modeling and analyzing for the theoretical research of mesoscopic and complex biological systems.In this way,the dynamic mechanism of ion channels will be understood better.