Abstract
This paper presents a comparison of computational algorithms to simulate action potentials using stochastic sodium channels. Four algorithms are compared in single-node models: Strassberg and DeFelice (1993) (SD), Rubinstein (1995) (R), Chow and White (1996) (CW), and Fox (1997) (F). Neural responses are simulated to a simple and a preconditioned monophasic current pulse. Three exact algorithms implementing Markov jumping processes (SD, R, CW) resulted in similar responses, while the approximation algorithm using Langevin's equation (F) showed quite different responses from those in the exact algorithms. The computational time was measured as well: 1(F), 7(CW), 32(SD), 39(R) relative to that of the F algorithm. Furthermore, it is shown that as the sampling step for integration of the transmembrane potential increases, neural responses in all algorithms tended to be different from those in dense sampling steps, however, the CW algorithm was robust even at a sparse sampling step. It is concluded that the most computationally efficient algorithm having appropriate properties of neural excitability is the CW algorithm. © 2002 Biomedical Engineering Society.
PAC2002: 8716Uv, 8716Ac, 0250Ga, 0250Ey, 0260Jh
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Chow, C. C., and J. A. White. Spontaneous action potentials due to channel fluctuations. Biophys. J. 71:3013–3021, 1996.
Clay, J. R., and L. J. DeFelice. Relationship between membrane excitability and single channel open-close kinetics. Biophys. J. 42:151–157, 1983.
Colquhoun, D., and A. G. Hawkes. Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc. R. Soc. London, Ser. B 199:231–262, 1977.
Colquhoun, D., and A. G. Hawkes. On the stochastic properties of single ion channels. Proc. R. Soc. London, Ser. B 211:205–235, 1981.
Fox, R. F. Stochastic versions of the Hodgkin-Huxley equations. Biophys. J. 72:2069–2074, 1997.
Gillespie, D. T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81:2340–2361, 1977.
Hodgkin, A. L., and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London) 117:500–544, 1952.
Lecar, H., and R. Nossal. Theory of threshold fluctuations in nerves. Biophys. J. 11:1048–1067, 1971.
Matsuoka, A. J., J. T. Rubinstein, P. J. Abbas, and C. A. Miller. The effects of interpulse intervals on stochastic properties of electrical stimulation: Models and measurements. IEEE Trans. Biomed. Eng. 48:416–424, 2001.
Neher, E., and C. F. Stevens. Conductance fluctuations and ionic pores in membranes. Annu. Rev. Biophys. Bioeng. 6:249–273, 1977.
Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed. Singapore: McGraw-Hill, 1985.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. New York: Cambridge University Press, 1993.
Rubinstein, J. T. Threshold fluctuations in an N sodium channel model of the node of ranvier. Biophys. J. 68:779–785, 1995.
Sigworth, F. J. The variance of sodium current fluctuations at the node of ranvier. J. Physiol. (London) 307:97–129, 1980.
Skaugen, E., and L. Walloe. Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta. Physiol. Scand. 49:343–363, 1979.
Strassberg, A. F., and L. J. DeFelice. Limitation of the Hodgkin-Huxley formalism: Effects of single channel kinetics on transmembrane voltage dynamics. Neural Comput. 5:843–855, 1993.
van Kampen, N. G. Stochastic Processes in Physics and Chemistry, 2nd ed. Amsterdam: Elsevier, 1992.
Verveen, A. A. Fluctuation in Excitability. Amsterdam: Drukkerij, Holland N.V., 1961.
White, J. A., J. T. Rubinstein, and A. R. Kay. Channel noise in neurons. Trends Neurosci. 23:131–137, 2000.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mino, H., Rubinstein, J.T. & White, J.A. Comparison of Algorithms for the Simulation of Action Potentials with Stochastic Sodium Channels. Annals of Biomedical Engineering 30, 578–587 (2002). https://doi.org/10.1114/1.1475343
Issue Date:
DOI: https://doi.org/10.1114/1.1475343