MCMC estimation of Markov models for ion channels

Biophysical Journal

Volumn 100, Issue 8, 2011, Pages 1919-1929

  Siekmann, Ivo ^a   Wagner II, Larry E ^c   Yule, David ^c   Fox, Colin ^d   Bryant, David ^d   Crampin, Edmund J ^a,b   Sneyd, James ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c UNIVERSITY OF ROCHESTER MEDICAL CENTER   (United States)

^d UNIVERSITY OF OTAGO   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79959753998     PISSN: 00063495     EISSN: 15420086     Source Type: Journal    
DOI: 10.1016/j.bpj.2011.02.059     Document Type: Article

References (39)

1. Neher, E., and B. Sakmann. 1976. Single-channel currents recorded from membrane of denervated frog muscle fibers. Nature. 260:799-802.
2. Colquhoun, D., and A. G. Hawkes. 1981. On the stochastic properties of single ion channels. Proc. R. Soc. Lond. B Biol. Sci. 211:205-235. (Pubitemid 11151113)
3. Qin, F., A. Auerbach, and F. Sachs. 1996. Idealization of single-channel currents using the segmental K-means method. Biophys. J. 70:MP432.
4. Qin, F., A. Auerbach, and F. Sachs. 1997. Maximum likelihood estimation of aggregated Markov processes. Proc. R. Soc. Lond. B Biol. Sci. 264:375-383. (Pubitemid 27144045)
5. Colquhoun, D., A. G. Hawkes, and K. Srodzinski. 1996. Joint distributions of apparent open and shut times of single-ion channels and maximum likelihood fitting of mechanisms. Philos. Trans. R. Soc. Lond. A. 354:2555-2590.
6. Gamerman, D., and H. F. Lopes. 2006. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, 2nd Ed. Texts in Statistical Science., Vol. 68. Taylor & Francis, Boca Raton, FL.
7. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter, editors. 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall, London, UK.
8. Ball, F. G., Y. Cai, A. O'Hagan. 1999. Bayesian inference for ionchannel gating mechanisms directly from single-channel recordings, using Markov chain Monte Carlo. Proc. R. Soc. Lond. A. 455:2879-2932.
9. Sachs, F., J. Neil, and N. Barkakati. 1982. The automated analysis of data from single ionic channels. Pflugers Arch. 395:331-340. (Pubitemid 13167908)
10. Roux, B., and R. Sauvé. 1985. A general solution to the time interval omission problem applied to single channel analysis. Biophys. J. 48:149-158. (Pubitemid 15028684)
11. Blatz, A. L., and K. L. Magleby. 1986. Correcting single channel data for missed events. Biophys. J. 49:967-980.
12. Ball, F. G., and M. S. P. Sansom. 1988. Aggregated Markov processes incorporating time interval omission. Adv. Appl. Probab. 20:546-572.
13. Milne, R. K., G. F. Yeo, B. W. Madsen. 1988. Stochastic modeling of a single ion channel: an alternating renewal approach with application to limited time resolution. Proc. R. Soc. Lond. B Biol. Sci. 233:247-292.
14. Yeo, G. F., R. K. Milne, B. W. Madsen. 1988. Statistical inference from single channel records: two-state Markov model with limited time resolution. Proc. R. Soc. Lond. B Biol. Sci. 235:63-94.
15. Crouzy, S. C., and F. J. Sigworth. 1990. Yet another approach to the dwell-time omission problem of single-channel analysis. Biophys. J. 58:731-743. (Pubitemid 20312930)
16. Magleby, K. L., and D. S. Weiss. 1990. Estimating kinetic parameters for single channels with simulation. A general method that resolves the missed event problem and accounts for noise. Biophys. J. 58:1411-1426.
17. Hawkes, A. G., A. Jalali, and D. Colquhoun. 1990. The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected. Philos. Trans. R. Soc. Lond. A. 332:511-583.
18. Hawkes, A. G., A. Jalali, and D. Colquhoun. 1992. Asymptotic distributions of apparent open times and shut times in a single channel record allowing for the omission of brief events. Philos. Trans. R. Soc. Lond. B Biol. Sci. 337:383-404.
19. Rosales, R., J. A. Stark, S. B. Hladky. 2001. Bayesian restoration of ion channel records using hidden Markov models. Biophys. J. 80:1088-1103. (Pubitemid 32182138)
20. Rosales, R. A. 2004. MCMC for hidden Markov models incorporating aggregation of states and filtering. Bull. Math. Biol. 66:1173-1199. (Pubitemid 39033603)
21. Rosales, R. A., M. Fill, and A. L. Escobar. 2004. Calcium regulation of single ryanodine receptor channel gating analyzed using HMM/MCMC statistical methods. J. Gen. Physiol. 123:533-553. (Pubitemid 38590857)
22. + channel. Biophys. J. 96:3987-3996.
23. Gin, E., M. Falcke, J. Sneyd. 2009. Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors. J. Theor. Biol. 257:460-474.
24. Wagner, II, L. E., S. K. Joseph, and D. I. Yule. 2008. Regulation of single inositol 1, 4, 5-trisphosphate receptor channel activity by protein kinase A phosphorylation. J. Physiol. (Lond.). 586:3577-3596.
25. Gin, E., L. E. Wagner, II, J. Sneyd. 2009. Inositol trisphosphate receptor and ion channel models based on single-channel data. Chaos. 19:037104.
26. Ball, F. G., and M. S. P. Sansom. 1989. Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings. Proc. R. Soc. Lond. B Biol. Sci. 236:385-416. (Pubitemid 19135590)
27. Fredkin, D. R., and J. A. Rice. 1992. Bayesian restoration of singlechannel patch clamp recordings. Biometrics. 48:427-448.
28. Fredkin, D. R., and J. A. Rice. 1992. Maximum likelihood estimation and identification directly from single-channel recordings. Proc. Biol. Sci. 249:125-132.
29. De Gunst, M. C. M., H. R. Künsch, and J. G. Schouten. 2001. Statistical analysis of ion channel data using hidden Markov models with correlated state-dependent noise and filtering. J. Am. Stat. Assoc. 96:794-804.
30. Venkataramanan, L., and F. J. Sigworth. 2002. Applying hidden Markov models to the analysis of single ion channel activity. Biophys. J. 82:1930-1942. (Pubitemid 34280808)
31. The, Y.-K., and J. Timmer. 2006. Analysis of single ion channel data incorporating time-interval omission and sampling. J. Roy. Soc. Interface. 3:87-97. (Pubitemid 46682207)
32. Raiffa, H., and R. Schlaifer. 1961. Applied Statistical Decision Theory. Harvard University Graduate School of Business Administration, Boston, MA.
33. Gelfand, A. E., and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85:398-409.
34. Carter, C. K., and R. Kohn. 1994. On Gibbs sampling for state space models. Biometrika. 81:541-553.
35. Metropolis, N., A. W. Rosenbluth, E. Teller. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087-1092.
36. Hastings, W. K. 1970. Monte-Carlo sampling methods using Markov chains and their applications. Biometrika. 57:97-109.
37. Gillespie, D. T. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22:403-434.
38. Bruno, W. J., J. Yang, and J. E. Pearson. 2005. Using independent opento-closed transitions to simplify aggregated Markov models of ion channel gating kinetics. Proc. Natl. Acad. Sci. USA. 102:6326-6331. (Pubitemid 40617442)
39. Green, P. J. 1995. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika. 82:711-732.