  It is increasingly realized that taking stochastic effects into account is
important in order to study biological cells. However, the corresponding
mathematical formulation, the chemical master equation (CME), suffers from the
curse of dimensionality and thus solving it directly is not feasible for most
realistic problems. In this paper we propose a dynamical low-rank algorithm for
the CME that reduces the dimensionality of the problem by dividing the reaction
network into partitions. Only reactions that cross partitions are subject to an
approximation error (everything else is computed exactly). This approach,
compared to the commonly used stochastic simulation algorithm (SSA, a Monte
Carlo method), has the advantage that it is completely noise-free. This is
particularly important if one is interested in resolving the tails of the
probability distribution. We show that in some cases (e.g. for the lambda
phage) the proposed method can drastically reduce memory consumption and run
time and provide better accuracy than SSA.
