Multiparticle reaction noise characteristics

Abstract

A simple multiparticle reaction model was studied where reactants A react with (a possibly large) stoichiometric coefficient k. Each reaction forms a product molecule P, and every product molecule can be split into k A particles through the back reaction. To study the fluctuations in particle numbers a novel approach has been developed; to be referred to as the Pair approach based Reaction Noise EStimator (PARNES) method. The PARNES method is based on the full Kirkwood superposition approximation implemented at the pair level. Kirkwood's method has been adapted to study stochastic properties of an arbitrary reaction network in a perfectly mixed reaction volume. PARNES works well for large particle numbers. It provides qualitative description when particle numbers are low. The PARNES method can easily augment mean field calculations. Extension of the method beyond the pair approach level is straightforward. Both stationary and non-stationary properties of the model were investigated, and the findings of this work point to two possible scenarios of intracellular noise control. When k is increased, the fluctuations in the number of product molecules become smaller (sub-Poissonian) in a stationary state, and relaxation to a stationary state becomes faster.