Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression.

The quantitative modeling of gene transcription and translation requires a treatment of two key features: stochastic fluctuations due to the limited copy numbers of key molecules (genes, RNA polymerases, ribosomes), and delayed output due to the time required for biopolymer synthesis. Recently proposed algorithms allow for efficient simulations of such systems. However, it is critical to know whether the results of delay stochastic simulations agree with those from more detailed models of the transcription and translation processes. We present a generalization of previous delay stochastic simulation algorithms which allows both for multiple delays and for distributions of delay times. We show that delay stochastic simulations closely approximate simulations of a detailed transcription model except when two-body effects (e.g. collisions between polymerases on a template strand) are important. Finally, we study a delay stochastic model of prokaryotic transcription and translation which reproduces observations from a recent experimental study in which a single gene was expressed under the control of a repressed lac promoter in E. coli cells. This demonstrates our ability to quantitatively model gene expression using these new methods.