Spontaneous noise reduction in a strongly cooperative reaction model

Noise characteristics of a simple multiparticle reaction model were investigated. The model can describe strongly cooperative reactions and is defined as follows. Particles A react in clusters of size k and each reaction forms a product molecule P. The back reaction is also allowed, and each cluster can dissociate into k reactants A. To describe a situation where the reaction is part of a pathway, the system is made open by assuming that particles A are injected and that particles P decay. This is a continuation study. The model is studied by using the same technique as employed previously, the pair approach reaction noise estimator (PARNES) method. Several new issues have been addressed. (i) In the previous work closeness to the Poisson distribution was used as a noise measure. In this work a more traditional noise measure, the ratio of the variance and the mean, was used to analyze stochastic features of the problem. (ii) The dependence of the new noise measure on k has been analyzed in detail, with an emphasis of investigating reactions with large k values. (iii) The previous study focused on understanding time-dependent issues, while this study focuses on describing the equilibrium state of the system. (iv) An exact solution (published elsewhere), available for closed system only, was used to re-investigate the validity of the PARNES method for describing reactions with large k. It was found that the PARNES method cannot describe fine details of the noise characteristics of such reactions.