Modelling stochasticity in multi-stable and oscillatory biological networks far from equilibrium

Abstract

Random nature of chemical reactions and low copy numbers of participating chemical species originate fluctuations in naturally open biological systems. These inevitable fluctuations drive these open biological systems even in the presence of perturbations to self-organised, dissipative structures far from thermodynamic equilibrium in the presence of inward and outward flows of material, energy and information. Far from equilibrium, biological systems exhibit much complex dynamical behaviour such as multi-stability, oscillations, chaos and fractals and this review focus on the important stochastic modelling issues and approaches relevant to modelling these complex systems with examples. For example, 2MA method provides a robust way to look at the evolution of first two moments and Keizer’s theory provides a mechanistic, statistical framework for modelling fluctuations for large volume systems. Always analytical methods like Chemical Master Equation, Chemical Langevin Equation, Fokker-Plank equation provide more insights into system behaviour as they consider the effect of randomness and the real particle behaviour. Nevertheless, these modelling methods or experimental methods are not yet developed enough to see a meososcopic system’s dynamic behaviour in all parameter ranges in one picture. More efficient, and accurate, modelling and simulation methods which consider the real thermodynamic and mechanistic behaviour of systems are necessarily needed for better understanding of dynamics in meososcopic complex biosystems.