Acta mathematica scientia, Series B >
MARKOV CHAIN INVERSION APPROACH TO IDENTIFY THE TRANSITION RATES OF ION CHANNELS
Received date: 2011-12-28
Revised date: 2012-02-08
Online 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).
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.
Key words： Markov chain; transition rate; inversion; lifetime distribution
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 . DOI: 10.1016/S0252-9602(12)60135-0
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