A unified master-equations-based setting for the analysis of chemical reactions

An important research topic in the eld of Systems Biology is the detection of ecient methods for modeling complex cellular mechanisms. Recently it has been pointed out the importance of the noise role in the dynamics of biological processes. Generally speaking, the role of stochastic uctuations is particularly important in the dynamics of biochemical reactions in which are involved a low number of molecules. These assumptions lead to the statement that the time-evolution of the number of copies of the involved players is well described by the probabilistic approach given by the so-called Chemical Master Equations (CME). For a general set of chemical reactions a multi-dimensional Markov-chain model is written, describing the molecular behavior of all the chemical species therein involved. The related multi-dimensional CME model, describing the time-evolution of the probabilistic concen- trations for any species, is then derived. Some structural properties of the CME model are pointed out, allowing a computationally cheap management of some classical analytic tasks such as the determination of the equilibrium distributions and the simulation of the underlying stochastic processes related to the molecular behavior of the whole chemical reaction.