Importance of Considering the Isotonic System Hypothesis When Modelling the Self-Control of Gene Expression Regulatory Modules in Living Cells

Systems Biology is one of the modern tools, which uses advanced mathematical simulation models for in-silico design microorganisms that possess desired characteristics. The deterministic models developed to simulate the cell metabolism biochemistry, are based on a hypothetical (reduced) reaction mechanism, of known kinetics and stoichiometry. A central part of such models concerns the adequate simulation of the protein synthesis homeostatic self-regulation present in any gene expression regulatory module (GERM) that produces enzymes controlling the whole cell metabolism with negative feedback loops and rapid adjustments of the enzymatic activity. However, classical formulations by using the default Constant Volume Whole-Cell (CVWC) continuous variable ordinary differential (ODE) dynamic models do not explicitly consider the cell volume exponential increase during the cell growth leading to biased and distorted conclusions on GERM regulatory performances. This paper exemplifies the overwhelming importance of using a holistic variable-volume whole-cell (VVWC) modelling framework with explicitly including constraints accounting for the cell-volume growth while preserving a constant osmotic pressure and membrane integrity. To point-out the discrepancy between the two simulation approaches, the comparison is made in the case of a simple generic GERM from the E. coli cell, by mimicking the cell homeostasis and its response to dynamic perturbations.