title: Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.
abstract: The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.
authors.affiliation: Department of Applied Mathematics, University of Waterloo, Waterloo, Canada. mscott@math.uwaterloo.ca
authors.forename: M
authors.initials: M
authors.lastname: Scott
mesh_terms: D000465:Algorithms; D000818:Animals; D001704:Biopolymers / Q000378:metabolism*; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D001704:Biopolymers