Mass fluctuation kinetics : analysis and computation of equilibria and local dynamics

Abstract

The mass fluctuation kinetics (MFK) model is a set of coupled first-order differential equations describing the temporal evolution of means, variances and covariances of species concentrations in systems of chemical reactions. It generalizes classical mass action kinetics (MAK) in which fluctuations around the mean are ignored. This thesis begins with the motivating background theory for the development of MFK. The model equations follow from the time-evolution of the molecule number moment generating function obtained from the chemical master equation (CME). A closed-form expression for the MFK Jacobian matrix that describes small deviations from equilibrium is derived. An MFK software toolbox prototype, developed in MATLAB (and available at http://www.mit.edu/~azunre/MFK), applies this Jacobian in the context of single substrate enzyme kinetics to exploring the local dynamics of MFK equilibria. MFK means and covariances are observed to be locally decoupled at the equilibrium in the large volume thermodynamic limit, providing an alternative explanation for why MAK is an accurate approximation for system behavior there. Increasing discreteness of system behavior with decreasing system volume, a characteristic that the MAK model cannot capture, is captured by the MFK model via the growth of its variance. This ability is limited to a threshold beyond which MFK ceases to be a useful approximation for system behavior. Systematic extensions to higher order moments to correct for this are suggested.