Exponentially slow transitions on a Markov chain: The frequency of Calcium Sparks

European Journal of Applied Mathematics

Volumn 16, Issue 4, 2005, Pages 427-446

  Hinch, Robert ^a   Chapman, S Jon ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28344442016     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792505006194     Document Type: Article

References (31)

1. BERS, D. M. (1993) Excitation Contraction Coupling and Cardiac Contractile Force. Kluwer Academic.
2. CHENG, H., LEDERER, W. J. & CANNELL, M. B. (1993) Calcium sparks - elementary events underlying excitation-contraction coupling in heart muscle. Science 262, 740-744.
3. i waves in cardiac myocytes. Am. J. Physiol. 270, C148-C159.
4. COOMBES, S., HINCH, R. & TIMOFEEVA, Y. (2004) Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release. Prog. Biophys. Mot. Biol. 85, 197-216.
5. 2+ release. Biophys. J. 82, 2918-2945.
6. GRIMMETT, G. & STIRZAKER, D. (2001) Probability and Random Processes (3rd ed.). Oxford University Press.
7. HINCH, E. J. (1991) Perturbation Methods. Cambridge University Press.
8. HINCH, R. (2004) A mathematical analysis of the generation and termination of calcium sparks. Biophys. J. 86(3), 1293-1307.
9. 2+ release in cardiac ventricular myocytes. Biophys. J. 87, 3723-3736.
10. HANGGI, Nonlinear fluctuations: The problem of deterministic limit and reconstruction of stochastic dynamics, Phys. Rev. A 25 (1982) 1130-1136.
11. 2+ sparks. Biophys. J. 75, 595-600.
12. KRAMERS, H. A. (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica VII, 284-304.
13. HANGGI, P., GRABERT, H., TALKNER, P. & THOMAS, H. (1984) Bistable systems: Master equation versus Fokker-Planck modelling. Phys. Rev. A 29(1), 371-378.
14. WARD, M. J. (1998) Analysing multiscale phenomena using singular perturbation methods, Proceedings of Symposia in Applied Mathematics, AMS Short Courses, pp. 151-184.
15. MOYAL, J. E. (1949) Stochastic processes and statistical physics. J. Roy. Stat. Soc. (London) B11, 150-172.
16. HANGGI, P. & THOMAS, H. (1982) Stochastic pricesses: Time evolution, symmetries and linear response. Phys. Rep. 25, 1130-1136.
17. KNESSL, C., MANGEL, M., MATKOWSKY, B. J., SCHUSS, Z. & TIER.C. (1984) Asymptotic solutionm of the Kramers-Moyal equation and first passage times for Markov jump processes. Phys. Rev. A 29, 3359-3369.
18. KNESSL, C., MATKOWSKY, B. J., SCHUSS, Z. & TIER,C. (1985) An asymptotic theory of large deviations for Markov jump processes. SIAM J. Appl. Math. 46, 1006-1028.
19. MAIER, R. S. & STEIN, D. L. (1993) Effect of focusing of caustics on exit phenomena in systems lacking detailed balance. Phys. Rev. Lett. 71(12), 1783-1786.
20. MATKOWSKY, B. J. & SCHUSS, Z. (1981) Eigenvalues of the Fokker-Planck operator and the approach to equilibrium for diffusion fields. SIAM J. Appl. Maths. 40(2), 242-254.
21. NEWELL, G. F. (1971) Application of Queuing Theory. Chapman & Hall.
22. REYNA, L. G. & WARD, M. J. (1995) On the exponentially slow motion of a viscous shock. Comm. Pure Appl. Math. 48, 79-120.
23. REYNA, L. G. & WARD, M. J. (1995) Metastable internal layer dynamics for the viscous Cahn-Hilliard equation. Methods & Appl. Anal. 2, 285-306.
24. 2+ release in the cardiac diad. Biophys. J. 83, 59-78.
25. 2+channel gating in the cardiac diad. Biophys. J. 73, 97-111.
26. STERN, M. D. (1992) Theory of excitation-coupling in cardiac muscle. Biophys. J. 63, 469-489.
27. STERN, M. D., SONG, L. S., CHENG, H., SHAM, J. S. K., YANG, H. T., BOHELER, K. R. & RIOS, E. (1999) Local control models of cardiac excitation-contraction coupling: a possible role for allosteric interactions between ryanodine receptors. J. Gen. Physiol. 113, 469-489.
28. 2+ release channel. Biophys. J. 71, 2996-3012.
29. VAN KAMPEN, N. G. (1961) A power series expansion of the Master equation. Can. J. Phys. 39, 551-567.
30. VAN KAMPEN, N. G. (1981) Stochastic Processes in Physics and Chemistry. North-Holland.
31. WINSLOW, R. L., HINCH, R. & GREENTEIN, J. L. (2005) Mechanisms and models of cardiac excitation-contraction coupling. In: Synapses and Muscles. Springer-Verlag.