Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis

Abstract

RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mechano-chemical cycle of individual RNAPs during the elongation of the mRNA. By a combination of analytical and numerical techniques, we calculate the rates of mRNA synthesis and the average density profile of the RNAPs on the DNA track. We also introduce, and compute, two new measures of fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of intrinsic noise in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP. We suggest appropriate experimental systems and techniques for testing our theoretical predictions.

Interacting particles in disordered flashing ratchets

“…This has led to many interesting collective effects in models of elastically coupled motors [15,16,17,1,3,4] and excluded volume interactions [18,19,20,21,22,23,24,25,26,27,28,29]. Of particular interest to the present work is the model of a discrete flashing ratchet considered in [30,31] in which large scale properties of a system of hard-core particles moving in a ratchet potential defined on a discrete lattice was studied.…”

Transcriptional bursts: A unified model of machines and mechanisms

“…But, these models capture the en- tire processes of RNA production by a single effective rate constant. In contrast, models developed to understand the operational mechanisms of RNAP motors [17,21,22,23,24,25,26,27,28] explicitly describe the different stages of transcription, namely, initiation, elongation and termination, but (except for ref.[28]) do not address the question of temporal fluctuations in transcription. The main aim of this letter is to combine the key features of these two types of models within a single unified theoretical framework.…”

“…More specifically, we extend our recent model of RNAP traffic [28] by allowing the gene to switch between the this model can predict the contributions of the processes (i)-(iv) on transcriptional noise; estimation of the contributions made by the processes (ii)-(iv) was beyond the scope of all the earlier models of transcriptional noise. Carrying out computer simulations of this model we obtain the time series of the transcriptional events.…”

“…More specifically, we extend our recent model of RNAP traffic [28] by allowing the gene to switch between the…”

“…Initiation and termination of transcription are captured by the same prescription which have been used in our earlier work reported in ref. [28]; the corresponding rate constants being ω α and ω β , respectively.…”