Markov Model for Ion Channels

This online document helps the absolute beginners to persue the future direction in coding and modeling Markov Models for ion channels. We have discussed the general theory of Markov Model and the Ergodicity for Monte Carlo simulation. The different Numerical Methods has been explored through implementation of simultaneous differential equations and algebric equation method. Usually, differential equations are efficient to implement nonlinear dynamics (chaotic state) and algebraic methods are good for regular and linear models.

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Following are the major techniques implemented

  • Analytical Solutions : Manual implementation of condition of equilibrium and detailed balance.
  • Numerical Methods:
    • Simultaneous Ordinary Differential Equations: Solving differential equation by implementation of numerical methods.
    • Algebraic Method: Translation of differential equations into an algebraic problem as linear equation of matrices and vector.
  • Monte Carlo Simulation: Random generation of states based on wighted probability distribution and calculation fraction of states at equilibrium.

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By Namuna Panday, Ph. D. Department of Anestheology, UCLA, Los Angeles, CA, USA