Quasi Steady-State Approximations (QSSAs) in the CME-based stochastic framework

The Chemical Master Equation (CME) provides an accurate stochastic description of complex biochemical processes in terms of probability distribution of the underlying chemical population. In contrast to deterministicmethods, CMEs are therefore considered fruitful stochastic methods for the analysis of biochemical reactions. In the deterministic framework, reactions are usually described by directly expressing the time-evolution of the concentration for each of the involved species, thus leading to having to handle an Ordinary Differential Equation (ODE) system, often of great dimension. To face the analysis of complex processes, the practice to exploit Quasi-Steady State Approximations (QSSAs) has been introduced in literature with the aim of reducing the dimensionality of the system, thus speeding numerical simulations. In this work, we perform a preliminary investigation of the applicability of QSSAs to the stochastic method based on CMEs. To this end, the CME description is applied to the original chemical network, as well as to the standard and total QSS Approximations. The contribution confirms by simulations the effectiveness and superiority of the latter approximation with respect to the former one, also from a stochastic point of view.