BIOPHYSICAL THEORY AND MODELING |
Bistable behaviour in a model of the lac operon in Escherichia coli with variable growth rate
Moises Santillan 1*
1 Cinvestav-IPN
* To whom correspondence should be addressed. E-mail: moises.santillan{at}mac.com.
Submitted on July 23, 2007
Revised on September 4, 2007
Accepted on 16 November 2007
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Abstract |
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This work is a continuation of another study previously published in (Biophys. J. 92: 3830-3842). Both the former and the present works are advocated to investigating the bistable behaviour of the lac operon in Escherichia coli from a mathematical modelling point of view. In the previous paper we developed a detailed mathematical model that accounts for all of the known regulatory mechanisms in this system, and studied what the effect of inducing the operon with lactose, instead of an artificial inducer, is. In this paper, the model is improved to account, in a more detailed way, for the interaction of the repressor molecules with the three lac operators. Besides, a recently discovered cooperative interaction between the CAP molecule ---an activator of the lactose operon--- and Operator 3, which influences DNA folding, is also included in this new version of the model. Finally the growth rate dependence on the rate of energy entering the bacteria ---in the form of transported glucose molecules and of metabolized lactose molecules--- is also considered. A large number of numerical experiments is carried out with this improved model. The results are discussed in regard to the bistable behaviour of the lactose operon. Special attention is paid to the effect that having a variable growth rate has on the system dynamics.
Key Words:
computational biology, gene regulatory networks, mathematical model, multistability, systems biology
