Analytic solutions for stochastic models of transcription

Abstract

The spatio-temporal organization of one RNA polymerase (RNAP) along a DNA strand is explored by studying a kinetic stochastic model for transcription process, the first step in gene expression. An explicit expression for the probability density of one RNAP was found and compared with stochastic simulation results from the corresponding detailed stochastic model. The explicit solution predicts that the movement of RNAP in large genes (genes of a few hundred nucleotides or more) is advective. It provides a justification for the use of delays in gene expression modeling, especially in delay-stochastic models. The kinetic model for the elongation stage of transcription was extended to two bodies, and the related Fokker-Planck equation was developed. This equation describes the evolution of the joint probability density for two RNAPs along the DNA track.