Abstract
Gene regulation is an essential process for cell development, having a profound effect in dictating cell functions. Bacterial genes are often regulated through inducible systems like the Lac operon which plays an important role in cell metabolism. An accurate model of its regulation can reveal the dynamics of gene expression. In this paper, a mathematical model of this system is constructed by focusing on regulation by the Lac repressor. The results show, as expected, that the concentration of lactose approaches zero while glucose concentration approaches the initial concentration of lactose by the action of β-galactosidase, expressed by the Lac operon. Addition of PD control improves stability of the system, with the phase margin increasing from 45° to 90°. Modeling the dynamics of gene expression in inducible operons like Lac operon can be essential for its applications in the production of recombinant proteins and its potential usage in gene therapy.
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