Approximation of Stochastic Models in Systems Biology

Understanding the underlying mechanisms at the molecular level requires the analysis of stochastic models that take into account the discreteness of reactions and molecules. The chemical master equation (CME) provides an appropriate description for such models, but its numerical solution is in many cases computationally expensive or even infeasible as the number of reachable states is huge.

We present the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a ''window'' in the state space. In subsequent steps, the window follows the direction in which the system is most likely to evolve until the time period of interest has elapsed.

In order to show the effectiveness of our approach, we apply it to various examples. The experimental results show that the proposed method can be efficiently applied to models that previously could not be solved numerically.