Stochastic versions of the Hodgkin-Huxley equations

Biophysical Journal

Volumn 72, Issue 5, 1997, Pages 2068-2074

  Fox, Ronald F ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; CALCULATION; MATHEMATICAL ANALYSIS; NERVE CELL; NOISE; STOCHASTIC MODEL;

EID: 0030893069     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0006-3495(97)78850-7     Document Type: Article

References (24)

1. Arnold, L. 1974. Stochastic Differential Equations. John Wiley and Sons, New York.
2. Bertram, R., and A. Sherman. 1996. Population dynamics of synaptic release sites. SIAM J. Appl. Math. (in press).
3. Bertram, R., A. Sherman, and E. F. Stanley. 1996. Single-domain/Bound calcium hypothesis of transmitter release and facilitation. J. Neurophysiol. 75:1919-1931.
4. Chow, C. C., and J. A. White. 1996. Spontaneous action potentials due to channel fluctuations. Biophys. J. 71:3013-3021.
5. Collins, J. J., C. C. Chow, and T. T. Imhoff. 1995a. Aperiodic stochastic resonance in excitable systems. Phys. Rev. E. 52:R3321-R3324.
6. Collins, J. J., C. C. Chow, and T. T. Imhoff. 1995b. Stochastic resonance without tuning. Nature. 376:236-238.
7. DeFelice, L. J., and A. Isaac. 1992. Chaotic states in a random world: relationship between the non-linear differential equations of excitability and the stochastic properties of ion channels. J. Statist. Phys. 70: 339-354.
8. Fox, R. F. 1992. Second-order algorithm for the numerical integration of colored-noise problems. Phys. Rev. A. 43:2649-2654.
9. Fox, R. F., and Yan-nan Lu. 1994. Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys. Rev. E. 49:3421-3431.
10. Hille, B. 1992. Ionic Channels of Excitable Membranes, 2nd Ed. Sinauer Associates, Sunderland, MA.
11. Hodgkin, A. L., and A. F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (Lond.). 10:500-544.
12. Honeycutt, R. 1990. Higher order algorithms for the numerical simulation of stochastic differential equations. Ph.D. dissertation. Georgia Institute of Technology, Atlanta.
13. Katz, B. 1966. Nerve, Muscle and Synapse. McGraw-Hill, New York.
14. Knuth, D. E. 1969. The Art of Computer Programming, Vol. 2. Addison-Wesley, Reading, MA.
15. Lecar, H., and R. Nossal. 1971a. Theory of threshold fluctuations in nerves. I. Relationships mbetween electrical noise and fluctuations in axon firing. Biophys. J. 11:1048-1067;
16. Lecar, H., and R. Nossal. 1971b. Theory of threshold fluctuations in nerves. II. Analysis of various sources of membrane noise. Biophys. J. 11:1068-1084.
17. Longtin, A. 1993. Stochastic resonance in neuron models. J. Statist. Phys. 70:309-327.
18. Mannella, R., and V. Palleschi. 1989. Fast and precise algorithm for computer simulation of stochastic differential equations. Phys. Rev. A. 40:3381-3386.
19. Neher, E., and B. Sakmann. 1976. Single-channel currents recorded from membrane of denervated frog muscle fibers. Nature. 260:779-802.
20. Nossal, R., and H. Lecar. 1991. Molecular and Cell Biophysics. Addison-Wesley, Redwood City, CA.
21. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1988. Numerical recipes in C. Cambridge University Press, New York.
22. Rubinstein, J. T. 1995. Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophys. J. 68:779-785.
23. Skaugen, E., and L. Walløe. 1979. Firing behavior in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta Physiol. Scand. 107:343-363.
24. Strassberg, A., and L. J. DeFelice. 1993. Limitations of the Hodgkin-Huxley formalism: effects of single channel kinetics on transmembrane voltage dynamics. Neural Computation. 5:843-855.