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Origin of Bistability in the lac Operon

M. Santillán ^* , M. C. Mackey   and E. S. Zeron 

^* Unidad Monterrey, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional, Monterrey, México; Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, México DF, México; Centre for Nonlinear Dynamics in Physiology and Medicine, Departments of Physiology, Physics, and Mathematics, McGill University, Montreal, Canada; and Departamento de Matemáticas, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional, México DF, México

Correspondence: Address reprint requests to M. Santillán, E-mail: moises.santillan{at}mac.com.

Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.

This article has been cited by other articles:

				M. Santillan Bistable Behavior in a Model of the lac Operon in Escherichia coli with Variable Growth Rate Biophys. J., March 15, 2008; 94(6): 2065 - 2081. [Abstract] [Full Text] [PDF]