Robustness model validation of bistability in biomolecular systems

Bistability is a key system-level dynamical property to understand the basic mechanisms underpinning some cellular functions, like persistent memory, switch-like biochemical responses and irreversible cell differentiation. These processes are guaranteed by evolved molecular modules, involving genes, proteins and metabolites, which implement transitions between distinct operative conditions in response to exogenous and endogenous signals. In many cases, such a coordinated control action leads to a change in the dynamic behaviour of the cell, which persists even after the activating signal (e.g., the concentration of a certain molecular species) has returned to the initial concentration. A propaedeutical step to the construction of biomodels for this class of systems, is the analysis of the structure of the underlying biochemical reaction network; in particular, a necessary requirement is that the topology of this network is compatible with the assumed bistable Bistablebehaviour. Subsequently, one can face the question of whether the same performance is guaranteed even in the presence of endogenous and exogenous perturbations, i.e., whether the model is robustly bistable Bistablein the face of, e.g., parametric uncertainty (deriving from interindividual variability) or fluctuating environmental conditions (due to the intrinsic stochastic nature of cellular processes). The present chapter focusses on the presentation of methodological approaches for the characterization of bistability in biological systems; such methods are important as tools to assess the plausibility of mathematical models of biosystems that exhibit bimodal experimental behaviour, without recurring to large-scale computational simulations.