A biologically inspired two-species exclusion model: effects of RNA polymerase motor traffic on simultaneous DNA replication

We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles ($P$) represents RNAP motors while the other ($R$) represents replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of only two $R$ particles are allowed to enter the lattice from two opposite ends whereas the unrestricted number of $P$ particles constitute a totally asymmetric simple exclusion process (TASEP) in a segment in the middle of the lattice. Consequently, the lattice consists of three segments; the encounters of the $P$ particles with the $R$ particles are confined within the middle segment (segment $2$) whereas only the $R$ particles can occupy the sites in the segments $1$ and $3$. The model captures three distinct pathways for resolving the co-directional as well as head-collision between the $P$ and $R$ particles. Using Monte Carlo simulations and heuristic analytical arguments that combine exact results for the TASEP with mean-field approximations, we predict the possible outcomes of the conflict between the traffic of RNAP motors ($P$ particles engaged in transcription) and the replication forks ($R$ particles). The outcomes, of course, depend on the dynamical phase of the TASEP of $P$ particles. In principle, the model can be adapted to the experimental conditions to account for the data quantitatively.