System representation of stochastic models of first-order chemical reactions

A new approach for the computation of probability distributions of molecule populations for coupled first-order chemical reactions is introduced. The approach is based on system theory, where the system states are type of molecules (molecule species) and the signals are probabilities. The transfer functions of the defined systems can be applied to both closed and open reaction systems. The use of block diagrams offers a clear, visual, and convenient way to decompose a complicated reaction system into simpler sub-systems and vice versa. Since the state of the system is the molecule species instead of molecule population, with this method one can study chemical reactions involving any number of molecules. The proposed methodology is applied to an enzyme catalyst reaction. Also, a special form of reaction topology, a first order reaction chain, is studied, and the analytic solution for it is derived.