Chemical master equation reduction methods

We study invariant manifold methods for reducing chemical master equations using the Michaelis-Menten mechanism as an example. We try Fraser's functional iteration method first, but find that it is difficult to use for master equations of high dimension. Using the insights gained from Fraser's method, we develop a technique to produce reduced chemical master equations directly from the eigenvectors of the state-to-state transition rate matrix. The dimension of the original chemical master equation grows quadratically with number of molecules, while the dimension of the reduced one we obtain is linear in the number of molecules. Additionally, a simple, effective way is developed to generate initial conditions for the reduced models.