Stochastic behaviour of ion channels in varying conditions

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 14, Issue 2, 1997, Pages 125-149

  Merlushkin, Anton ^a,b   Hawkes, Alan G ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b Credit Suisse USA   (United States)

Author keywords

First latency; Inhomogeneous process; Ion channel; Markov process; Semi markov process; Time interval omission

Indexed keywords

IONS; PROBABILITY DISTRIBUTIONS; STOCHASTIC SYSTEMS;

CONDITION; FINITE NUMBER; FIRST LATENCY; INHOMOGENEOUS PROCESS; ION CHANNEL; SEMI MARKOV PROCESS; SINGLE-ION CHANNELS; STOCHASTIC BEHAVIOR; TIME INTERVAL; TIME-INTERVAL OMISSION;

MARKOV PROCESSES;

ION CHANNEL; NICOTINIC RECEPTOR;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CHANNEL GATING; KINETICS; MATHEMATICS; METABOLISM; MUSCLE; PROBABILITY; STATISTICS; SYSTEM ANALYSIS;

ANIMALS; ION CHANNEL GATING; ION CHANNELS; KINETICS; MARKOV CHAINS; MATHEMATICS; MODELS, BIOLOGICAL; MUSCLES; PROBABILITY THEORY; RECEPTORS, NICOTINIC; STOCHASTIC PROCESSES;

EID: 0031160518     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/14.2.125     Document Type: Article

References (15)

1. BALL, F., & SANSOM, M., 1988. Aggregated Markov processes incorporating time interval omission. Adv. Appl. Prob. 20, 546-72.
2. BALL, F., MILNE, R. K., & YEO, G. F., 1991. Aggregated semi-Markov processes incorporating time interval omission. Adv. Appl. Prob. 23, 772-97.
3. ÇINLAR, E., 1975. Introduction to Stochastic Processes. Englewood Cliffs, NJ: Prentice-Hall.
4. COLQUHOUN, D., & HAWKES, A. G., 1982. On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Phil. Trans. R. Soc. Lond. B 300, 1-59.
5. COLQUHOUN, D., & HAWKES, A. G., 1995. The principles of the stochastic interpretation of ion-channel mechanisms. In: Single-Channel Recording (2nd edn), Chapter 18, (B. Sakmann & E. Neher, eds.), pp. 397-482. New York: Plenum Press.
6. COLQUHOUN, D., HAWKES, A. G., MERLUSHKIN, A., & EDMONDS, B., 1997. Properties of single ion channel currents elicited by a pulse of agonist concentration or voltage. To appear in Phil. Trans. R. Soc. Lond. A 355.
7. HAMILL, O. P., MARTY, A., NEHER, E., SAKMANN, B., & SIGWORTH, F. J., 1981. Single-channel currents recorded from membrane of denervated frog muscle fibres. Pflügers Archiv: Europ. J. Physiol. 391, 85-100.
8. HAWKES, A. G., JALALI, A., & COLQUHOUN, D., 1990. The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected. Phil. Trans. R. Soc. Lond. A 332, 511-38.
9. HAWKES, A. G., JALALI, A., & COLQUHOUN, D., 1992. Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. Phil. Trans. R. Soc. Lond. B 337, 383-404.
10. JALALI, A., & HAWKES, A. G., 1992. Generalised eigenproblems arising in aggregated Markov processes allowing for time interval omission. Adv. Appl. Prob. 24, 302-21.
11. MERLUSHKIN, A. I. 1996. Some Problems Arising in Stochastic Modelling of Ion Channels due to Time Interval Omission. Ph.D. thesis, University of Wales.
12. MERLUSHKIN, A., & HAWKES, A. G., 1995a. Stochastic behaviour of an apparent aggregated process following a jump in the generator of the underlying Markov process. Working paper 12, University of Wales Swansea, European Business Management School.
13. MERLUSHKIN, A., & HAWKES, A. G., 1995b. Stochastic description of the response of ion channels to a pulse of agonist. Working paper 8, University of Wales Swansea, European Business Management School.
14. NEHER, E., & SAKMANN, B., 1976. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature 260, 799-802.
15. ROUX, B., & SAUVÉ, R., 1985. A general solution to the time interval omission problem applied to single channel analysis. Biophys. J. 48, 149-58.