BIOPHYSICAL THEORY AND MODELING |
Markov Chain Modeling of Pyelonephritis-Associated Pili Expression in Uropathogenic Escherichia coli
Baiyu Zhou 1, David Beckwith 1, Laura Jarboe 1 and James C. Liao 1*
1 UCLA
* To whom correspondence should be addressed. E-mail: liaoj{at}ucla.edu.
Submitted on August 31, 2004
Revised on January 2, 2005
Accepted on 24 January 2005
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Abstract |
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Pyelonephritis-associate pili (Pap) expression in uropathogenic Escherichia coli is regulated by a complex phase variation mechanism involving the competition between Leucine-responsive regulatory protein (Lrp) and DNA adenine methylase (Dam). Population dynamics of pap gene expression has been studied extensively and the detailed molecular mechanism has been largely elucidated, providing sufficient information for mathematical modeling. Although the Gillespie algorithm is suited for modeling of stochastic systems such as pap operon, it becomes computationally expensive when detailed molecular steps are explicitly modeled in a population. Here we developed a Markov Chain model to simplify the computation. Our model is analytically derived from the molecular mechanism. The model presented here is able to reproduce results presented using the Gillespie method (Jarboe et al., 2004), but since the regulatory information is incorporated before simulation, our model runs more efficiently and allows investigation of additional regulatory features. The model predictions are consistent with experimental data obtained in this work and in the literature. The results show that pap expression in uropathogenic E. coli is initial state dependent, as previously reported. However, without environment stimuli, the pap-expressing fraction in a population will reach an equilibrium level after about 50-100 generations. The transient time before reaching equilibrium is determined by PapI stability and Lrp and Dam copy numbers per cell. This work demonstrates that the Markov Chain model captures the essence of the complex molecular mechanism and greatly simplifies the computation.
Key Words:
Markov Chain, Stochastic model, pap operon, uropathogenic Escherichia coli
