On the Distribution of Transcription Times

Abstract

A previously studied model of prokaryotic transcription [Roussel and Zhu, Bull. Math. Biol. 68 (2006) 1681--1713] is revisited. The first four moments of the distribution of transcription times are obtained analytically and analyzed. A Gaussian is found to be a poor approximation to this distribution for short transcription units at typical values of the rate constants, but a good approximation for long transcription units. An approximate form of the distribution is obtained in which the slow steps are treated exactly and the fast steps are lumped together into a single lag term. This approximate form might be particularly useful as a function to be fit to experimental transcription time distributions. Multi-polymerase effects are also studied by simulation. We find that the analytic model generally predicts the behavior of the multi-polymerase simulations, often quantitatively, provided termination is not rate-limiting.

Keywords

• gene transcription
• stochastic model