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Yildirim2003_Lac_Operon

ABSTRACT: This a model from the article: Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data. Yildirim N, Mackey MC Biophys. J. 2003 12719218 , Abstract: A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics. The model reproduces the time profile of beta-galactosidase activity as shown in Fig 3 of the paper. The delay functions for transcription (M) and translation (B and P) have been implemented by introducing intermediates ( I1, I2 and I3) in the reaction scheme which then give their respective products (I1-> M, I2 ->B and I3 ->P) after an appropriate length of time. The steady state values, attained upon simulation of model equations, for Allolactose (A), mRNA (M), beta-galactosidase (B), Lactose (L), and Permease (P) match with those predicted by the paper. The model was successfully tested on Jarnac, MathSBML and COPASI This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team. For more information see the terms of use . To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

SUBMITTER: Nicolas Le Novère

PROVIDER: BIOMD0000000065 | BioModels | 2024-09-02

REPOSITORIES: BioModels

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	BIOMD0000000065?filename=BIOMD0000000065-biopax2.owl	Owl
	BIOMD0000000065?filename=BIOMD0000000065-biopax3.owl	Owl
	BIOMD0000000065?filename=BIOMD0000000065.m	Other
	BIOMD0000000065?filename=BIOMD0000000065.pdf	Pdf
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Publications

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.

Yildirim Necmettin N Mackey Michael C MC

Biophysical journal 20030501 5

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the ...[more]

PMID: 12719218

Publication: 1/2

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