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RNA polymerase motors on DNA track: effects of traffic congestion on RNA synthesis

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 ssDNA. In some 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 because of the similarities between the collective dynamics of the RNAPs on ssDNA track and that of vehicles in highway traffic. In this paper 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 ssDNA track. We also suggest novel experiments for testing our theoretical predictions.