PNNL

Abstract

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.