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Analysis of the lactose metabolism in E. coli using sum-of-squares decomposition

Ahmadzadeh, Ali and Halasz, Adam and Prajna, Stephen and Jadbabaie, Ali and Kumar, Vijay (2005) Analysis of the lactose metabolism in E. coli using sum-of-squares decomposition. In: IEEE Conference on Decision and Control, 44th, and 2005 European Control Conference. CDC-ECC '05. IEEE , Piscataway, NJ, pp. 879-884. ISBN 0780395670 http://resolver.caltech.edu/CaltechAUTHORS:AHMcdc-ecc05

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Abstract

We provide a system-theoretic analysis of the mathematical model of lactose induction in E.coli which predicts the level of lactose induction into the cell for specified values of external lactose. Depending on the levels of external lactose and other parameters, the Lac operon is known to have a low steady state in which it is said to be turned off and high steady state where it is said to be turned on. Furthermore, the model has been shown experimentally to exhibit a bi-stable behavior. Using ideas from Lyapunov stability theory and sum-of-squares decomposition, we characterize the reachable state space for different sets of initial conditions, calculating estimates of the regions of attraction of the biologically relevant equilibria of this system. The changes in the basins of attraction with changes in model parameters can be used to provide biological insight. Specifically, we explain the crucial role played by a small basal transcription rate in the Lac operon. We show that if the basal rate is below a threshold, the region of attraction of the low steady state grows significantly, indicating that system is trapped in the (off) mode, showing the importance of the basal rate of transcription.


Item Type:Book Section
Additional Information:© Copyright 2005 IEEE. Reprinted with permission. Publication Date: 12-15 Dec. 2005. We gratefully acknowledge the support of ONR grant YIP-542371, NSF grants ECS-0347285, CNS-0410514, and CCF-0432025, and DARPA grant Biocomp AF F30602-01-2-0563. A. Halasz is supported by an NIH-NLM Individual Biomedical Informatics Fellowship, award 1-F37-LM-008343-1.
Record Number:CaltechAUTHORS:AHMcdc-ecc05
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:AHMcdc-ecc05
Alternative URL:http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=33412&arnumber=1582268&count=1407&index=155
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10818
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:14 Jun 2008
Last Modified:26 Dec 2012 10:05

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