Modeling the Stochastic Gating of Ion Channels

  • Gregory D. Smith
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 20)


In previous chapters we have seen several kinetic diagrams representing various molecular states and transitions between these states due to conformational changes and the binding or unbinding of ligands. Up to this point we have assumed a large number of molecules and written rate equations consistent with these transition-state diagrams. But how should we interpret a transition-state diagram when we are considering only a single molecule or a small number of molecules? The short answer to this question is that transition rates can be interpreted as transition probabilities per unit time.


Open Channel Stochastic Excitability Transition Probability Matrix Membrane Voltage Macroscopic Current 
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Suggestions for Further Reading

  1. Handbook of stochastic methods for physics, chemistry, and the natural sciences, G.W. Gardiner. This is an accessible introduction to stochastic methods including Markov systems, stochastic differential equations, Fokker-Planck equations, and master equations (Gardiner 1997).Google Scholar
  2. Spontaneous action potentials due to channel fluctuations, C.C. Chow and J.A. White. A theoretical and numerical analysis of the Hodgkin-Huxley equations when stochastic ion channel dynamics are included (Chow and White 1996).Google Scholar
  3. Stochastic versions of the Hodgkin-Huxley equations, R.F. Fox. A presentation of master equation and Langevin descriptions of the Hodgkin-Huxley equations with stochastic ion channel dynamics (Fox 1997).Google Scholar
  4. Channel noise in neurons, J.A. White, J.T. Rubinstein, and A.R. Kay. A good review of stochastic gating of voltage-dependent ion channels and channel noise in neurons (White et al. 2000).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Gregory D. Smith

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