DocumentCode :
508168
Title :
Identifying Kinetic Constants by the Intrinsic Properties of Markov Chain
Author :
Xiang, Xuyan ; Deng, Yingchun ; Yang, Xiangqun
Author_Institution :
Coll. of Math. & Comput. Sci., Hunan Univ. of Arts & Sci., Changde, China
Volume :
5
fYear :
2009
fDate :
14-16 Aug. 2009
Firstpage :
148
Lastpage :
153
Abstract :
The process underlying the opening and closing of ion channels in biological can be modelled kinetically as a time-homogeneous Markov chain. How to identify the kinetic constants (transition rates) that measure the ´speed´ to jump from one state to another plays a very important role in ion channels. Maximum likelihood method is widely employed for estimating the kinetic constants. However it leads to the non-identifiability since the joint probability distributions could be the same to models with different generator matrices, and the estimation could be very rough since it involves the estimating of some latent variables. Here we develop a totally different approach to supply a gap. Our algorithms employ the intrinsic properties of the Markov process and all calculations are simply reduced to the estimation of their PDFs (probability density functions) of lifetime and death-time of observable states. Once we have them, all subsequent calculations are then automatic and exact. In the current paper, four classical mechanisms: star-graph, line,star-graph branch and (reversible) cyclic chain, are considered to single-ion channels. It is found that all kinetic constants are uniquely determined by the PDFs of their lifetime and death-time for partially (a few) observable states. Numerical examples are included to demonstrate the application of our approach to data.
Keywords :
Markov processes; bioelectric phenomena; biomembrane transport; cellular biophysics; maximum likelihood estimation; probability; Markov chain intrinsic properties; ion channel closing; ion channel kinetic constants; ion channel opening; ion channel transition rates; line mechanism; observable state death time; observable state lifetime; probability density function estimation; reversible cyclic chain mechanism; single ion channels; star graph branch mechanism; star graph mechanism; time homogeneous Markov chain; Biological system modeling; Kinetic theory; Life estimation; Lifetime estimation; Markov processes; Maximum likelihood estimation; Probability density function; Probability distribution; State estimation; Velocity measurement;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Natural Computation, 2009. ICNC '09. Fifth International Conference on
Conference_Location :
Tianjin
Print_ISBN :
978-0-7695-3736-8
Type :
conf
DOI :
10.1109/ICNC.2009.521
Filename :
5365760
Link To Document :
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