{The chemical master equation is considered an accurate description of general chemical systems, and especially so for gene regulatory networks and protein-protein interaction networks. However, solving chemical master equations directly is considered computationally intensive. This paper discusses an efficient way of solving the chemical master equation for some prototypical problems in systems biology. Comparisons between this new approach and some traditional approaches, especially Monte-Carlo algorithms, are also presented, and show that under certain conditions the new approach performs better than Monte-Carlo algorithms. (C) 2009 Published by Elsevier Ltd}