R. Bundschuh, F. Hayot, and C. Jayaprakash, Biophys. J. 84 (2003), 1606-1615
Computer simulations of large genetic networks are often extremely time consuming since in addition to the biologically interesting translation and transcription reactions many less interesting reactions like DNA-binding and dimerizations have to be simulated. It is desirable to use the fact that the latter occur on much faster time scales than the former to eliminate the fast and uninteresting reactions and obtain effective models of the slow reactions only. We use a specific example to show that traditional methods of eliminating fast reactions reproduce the correct average behavior of a genetic network but fail to capture the fluctuations that such a network exhibits due to the small number of molecules. We identify the inclusion of fast varying variables in the effective description as the cause for the failure of the traditional schemes. We suggest a different effective description of our network, which entails the introduction of an additional species not present in the original network. We show that this description allows for a very efficient simulation of the reduced system while retaining the correct fluctuations of the full system. This approach ought to be applicable to a wide range of genetic networks.