Abstract
BackgroundIn Saccharomyces cerevisiæ, structural bistability generates a bimodal expression of the galactose uptake genes (GAL) when exposed to low and high glucose concentrations. This indicates that yeast cells can decide between using either the limited amount of glucose or growing on galactose under changing environmental conditions. A crucial requirement for any plausible mechanistic model of this system is that it reproduces the robustness of the bistable response observed in vivo against inter-individual parametric variability and fluctuating environmental conditions.ResultsWe show how a control-theoretic analysis of the robustness of a model of the GAL regulatory network may be used to establish the model’s plausibility in characterizing the persistent memory of different carbon sources, without the need for extensive simulations. Chemical Reaction Network Theory is used to establish that the proposed network model is compatible with structural bistability. The robustness of each of the two operative conditions against fluctuations of the species concentrations is demonstrated by studying the Domains of Attraction of the corresponding equilibrium points. Finally, we use a global robustness analysis method based on Semi-Definite Programming to evaluate the modification of the bistable steady states induced by multiple parametric variations throughout bounded regions of the parameter space.ConclusionsOur analysis provides convincing evidence for the robustness, and hence plausibility, of the GAL regulatory network model. The proposed workflow also demonstrates the power of analytical methods from control theory to provide a direct quantitative characterization of the dynamics of multistable biomolecular regulatory systems without recourse to extensive computer simulations.
Highlights
In Saccharomyces cerevisiæ, structural bistability generates a bimodal expression of the galactose uptake genes (GAL) when exposed to low and high glucose concentrations
For intermediate levels of the input, the two populations settled on different steady states, confirming the multistable nature of the system. These and other experimental results have revealed that the GAL system exhibits bistable dynamics and that such bistability generates a persistent memory of the type of carbon source consumed by the cell in the past
In order to represent a plausible mechanistic description of a biological phenomenon, the model must replicate an essential feature of biological systems, that is robustness against inter-individual parametric variability and in vivo fluctuating environmental conditions [9,10,11,12]
Summary
In Saccharomyces cerevisiæ, structural bistability generates a bimodal expression of the galactose uptake genes (GAL) when exposed to low and high glucose concentrations. This indicates that yeast cells can decide between using either the limited amount of glucose or growing on galactose under changing environmental conditions. Afterwards, we focus on the study of the robustness of bistability both against fluctuations of the concentrations of the molecular species, caused by endogenous stochastic noise or by exogenous perturbations, and in the face of parametric uncertainties The principle underpinning these analyses is that the quality of a model cannot be solely evaluated by its capability to reproduce a particular set of experimental measurements. In order to represent a plausible mechanistic description of a biological phenomenon, the model must replicate an essential feature of biological systems, that is robustness against inter-individual parametric variability and in vivo fluctuating environmental conditions [9,10,11,12]
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