Modelling Bistable Genetic Regulatory Circuits Under Variable Volume Framework

G. Maria

Abstract
Adequate modelling of Genetic Regulatory Circuits (GRC) allows a deeper understanding of the regulatory and control mechanism of gene expression in living cells, but also in-silico design of synthetic cell-systems exhibiting desired mini-functions (i.e. motifs, such as bistable-switches, oscillators, amplitude filters, etc.), with various practical applications in medical, industrial, or environmental fields. Modular lumped dynamic models have been reported as being valuable tools to adequately reproducing a wide-range of cell nonlinear dynamics, such as saturation, inhibition, sigmoidals, multiple steady-states, stable oscillations. In the present work, the analysis of a bistable-switch formed by two gene-expression modules is performed in a variable-volume and isotonic modelling framework, by mimicking the E. coli cell growth. A combination of lumped models, of Hill-type activation – repression, with including quick buffering reversible reactions using dimeric intermediates, is proved to offer a more flexible representation of the bistable genetic-switch than the classical lumped power-law approach. Intermediate species, of adjustable levels, allow a fine-tuning of GRC properties, in terms of stability strength, responsiveness and selectivity to external stimuli, regulatory efficiency and species connectivity in the gene-expression modules, under stationary and dynamic perturbations.

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Keywords
Bistable switch, genetic regulatory circuits, dynamic models, variable volume