Extended Repression Mechanisms in Modelling Bistable Genetic Switches of Adjustable Characteristics within a Variable Cell Volume Modelling Framework

G. Maria

Abstract
Genetic switches (GS) are a category of genetic regulatory circuits (GRC) responsible for the control and adaptation of cell metabolism to environmental changes. When mechanistic dynamic models of continuous variables are employed, a large variety of extended/reduced mathematical formulations have been proposed over the last decades, trying to simplify the regulatory network representation without risking missing the essential features of the real system. These models include the main GS species, which are: the DNA, mRNA, protein (enzyme) product, repressor, inducer / activator, RNA polymerase, and various individual or lumped metabolites. This study presents a comparison between Hill-type reduced models from literature and proposed non-Hill type extensions that replace the Hill coefficients by complex repression mechanisms. These complexes include elementary steps of the cross-repression control in inducible GS by means of rapid reversible reactions involving DNA/mRNA and dimeric transcription factors (TFs). Investigation is made under a variable-volume whole-cell (VVWC) holistic modelling framework, by placing the GS in a growing E. coli cell of known characteristics, and by mimicking the GS response to exogenous/endogenous gene expression activators/repressors. Comparison is made in terms of GS regulation indices, by analysing the influence of some system parameters (level of inducer, transcription factor, target protein, and Hill-type induction/repression nonlinearity) on the GS efficiency, and the close relationship between GS complexity and its stability.

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Keywords
Bistable genetic switch, dynamic modelling, variable volume, whole-cell, repression complexes, Hill kinetics