Modeling reaction noise with a desired accuracy by using the X level approach reaction noise estimator (XARNES) method.

A novel computational method for modeling reaction noise characteristics has been suggested. The method can be classified as a moment closure method. The approach is based on the concept of correlation forms which are used for describing spatially extended many body problems where particle numbers change in space and time. In here, it was shown how the formalism of spatially extended correlation forms can be adapted to study well mixed reaction systems. Stochastic fluctuations in particle numbers are described by selectively capturing correlation effects up to the desired order, ξ. The method is referred to as the ξ-level Approximation Reaction Noise Estimator method (XARNES). For example, the ξ=1 description is equivalent to the mean field theory (first-order effects), the ξ=2 case corresponds to the previously developed PARNES method (pair effects), etc. The main idea is that inclusion of higher order correlation effects should lead to better (more accurate) results. Several models were used to test the method, two versions of a simple complex formation model, the Michaelis-Menten model of enzymatic kinetics, the smallest bistable reaction network, a gene expression network with negative feedback, and a random large network. It was explicitly demonstrated that increase in ξ indeed improves accuracy in all cases investigated. The approach has been implemented as automatic software using the Mathematica programming language. The user only needs to input reaction rates, stoichiometry coefficients, and the desired level of computation ξ.