MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

doi:10.1016/S0252-9602(12)60135-0

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1703-1718.doi: 10.1016/S0252-9602(12)60135-0

MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

向绪言¹|邓迎春^1,2|杨向群^1,2

1.College of Mathematics, Hunan University of Arts and Science, Changde 415000, China|2.College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China

收稿日期:2011-12-28 修回日期:2012-02-08 出版日期:2012-09-20 发布日期:2012-09-20
基金资助:
Supported by National Natural Science Foundation of China (10871054; 11171101), Provincial Natural Science Foundation of Hunan (09JJ6016) and Scientific Research Fund of Hunan Provincial Education Department (10B073).

MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

XIANG Xu-Yan¹, DENG Ying-Chun^1,2, YANG Xiang-Qun^1,2

1.College of Mathematics, Hunan University of Arts and Science, Changde 415000, China|2.College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China

Received:2011-12-28 Revised:2012-02-08 Online:2012-09-20 Published:2012-09-20
Supported by:
Supported by National Natural Science Foundation of China (10871054; 11171101), Provincial Natural Science Foundation of Hunan (09JJ6016) and Scientific Research Fund of Hunan Provincial Education Department (10B073).

摘要/Abstract

摘要：

We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain. A Markov chain inversion approach is developed to perform a difficult inversion to identify the transition rates from the parameters characterizing the lifetime distributions at a small number of states, although it is straightforward to derive the lifetime distribution. The general explicit equations relating the parameters of the lifetime distribution to the tran-sition rates are derived and transition rates are then obtained as roots to this system of equations. The concrete solutions are proposed to the basic and regular schemes such as linear, star-graph branch and loop. Useful conclusions and solutions to realistic schemes are also included to show its efficiency.

关键词: Markov chain, transition rate, inversion, lifetime distribution

Abstract:

Key words: Markov chain, transition rate, inversion, lifetime distribution

中图分类号:

60J10

向绪言, 邓迎春, 杨向群. MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS[J]. 数学物理学报(英文版), 2012, 32(5): 1703-1718.

XIANG Xu-Yan, DENG Ying-Chun, YANG Xiang-Qun. MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS[J]. Acta mathematica scientia,Series B, 2012, 32(5): 1703-1718.

参考文献

[1] Jiang Y X, Lee A, Chen J Y, Cadene M, Chait B T, MacKinnon R. Crystal structure and mechanism of a calcium-gated potassium channel. Nature, 2002, 417: 515–522

[2] Purohit P, Mitra A, Auerbach A. A stepwise mechanism for acetylcholine receptor channel gating. Nature, 2007, 446: 930–933

[3] Tombola F, Pathak M M, Isacoff E Y. How does voltage open an ion channel? Annu Rev Cell Dev Biol, 2006, 22: 23–52

[4] Chakrapani S, Bailey T D, Auerbach A. Gating dynamics of the acetylcholine receptor extracellular do-main. J Gen Physiol, 2004, 123: 341–356

[5] Celentano J J, Hawkesy A G. Use of the covariance matrix in directly fitting kinetic parameters: application to GABAA receptors. Biophys J, 2004, 87: 276–294

[6] Gil Z, Magleby K L, Silberberg S D. Two-dimensional kinetic analysis suggests nonsequential gating of mechanosensitive channels in Xenopus oocytes. Biophys J, 2001, 81: 2082–2099

[7] Colquhoun D, Hawkes A G. On the stochastic properties of bursts of single ion channels opening and of clusters of brusts. Philos Trans R Soc Lond Biol Sci, 1982, 300: 1–59

[8] Colquhoun D, Hawkes A G, Srodzinski K. Joint distributions of apparent open times and shut times of single ion channels and the maximum likelihood fitting of mechanisms. Pro R Soc Lond A, 1996, 354: 2555–2590

[9] Qin F, Auerbach A, Sachs F. Estimating single-channel kinetic parameters from idealized patch-clamp data containing missed events. Biophy J, 1996, 70: 264–280

[10] Sakemann B, Neher E. Single-Channel Recording. 2nd ed. New York: Springer, 2009

[11] Auerbach A. Gating of acetylcholine receptor channels-Brownian motion across a broad transition state. PNAS, 2005, 102: 1408–1412

[12] Fulinski A, Grzywna Z, Mellor I, Siwy Z, Usherwood P N R. Non-Markovian character of ionic current fluctuations in membrane channels. Phys Rev E, 1998, 58: 919–924

[13] Ball F G, Milne R K, Yeo G F. Marked continuous-time markov chain modelling of burst behaviour for single ion channels. J Appl Math Deci Sci, 2007, 11: 48138–48151

[14] Larget B. A canonical representation for aggregated Markov processes. J Appl Prob, 1998, 35: 313–324

[15] Ball F G, Milne R K, Yeo G F. Aggregated semi-Markov processes incorporating time interval omission. Adv Appl Prob, 1991, 23(4): 772–797

[16] Ball F G, Milne R K, Yeo G F. Multivariate semi-Markov analysis of burst properties of multiconductance single ion channels. J Appl Prob, 2002, 39: 179–196

[17] Ball F G, Milne R K, Yeo G F. A unified approach to burst properties of multiconductance single ion channels. Math Medi Biol, 2004, 21(3): 205–245

[18] Chakrapani S, Cordero-Morales J F, Perozo E. A quantitative description of KcsA gating II: single channel currents. J Gen Physiol, 2007, 130: 479–496

[19] Shelley C, Magleby K L. Linking exponential components to kinetic states in markov models for single-channel gating. J Gen Physiol, 2008, 132: 295–312

[20] Colquhoun D, Sigworth F J. Fitting and statistical analysis of single channel records//Sakmann B, Neher E, eds. Single-Channel Recording. New York: Plenum Press, 1995: 483–587

[21] French R J, Wonderlin W F. Software for acquisition and analysis of ion channel data: choices, tasks, and strategies. Methods Enzymol, 1992, 207: 711–728

[22] Heinemann S H. Guide to data acquisition and analysis//Sakmann B, Neher E, eds. Single-Channel Recording. New York: Plenum Press, 1995: 53–91

[23] Jackson M B. Stationary single channel analysis. Methods Enzymol, 1992, 207: 729–746

[24] Jewell N P. Mixtures of exponential distributions. Ann Statist, 1982, 10: 479–484

MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS

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