Mixed molecular motor traffic on nucleic acid tracks: models of transcriptional interference and regulation of gene expression

RNA polymerase (RNAP) is molecular machine that polymerizes a RNA molecule, a linear heteropolymer, using a single stranded DNA (ssDNA) as the corresponding template; the sequence of monomers of the RNA is dictated by that of monomers on the ssDNA template. While polymerizing a RNA, the RNAP walks step-by-step on the ssDNA template in a specific direction. Thus, a RNAP can be regarded also as a molecular motor and the sites of start and stop of its walk on the DNA mark the two ends of the genetic message that it transcribes into RNA. Interference of transcription of two overlapping genes is believed to regulate the levels of their expression, i.e., the overall rate of the corresponding RNA synthesis, through suppressive effect of one on the other. Here we model this process as a mixed traffic of two groups of RNAP motors that are characterized by two distinct pairs of start and stop sites. Each group polymerizes identical copies of a RNA while the RNAs polymerized by the two groups are different. These models, which may also be viewed as two interfering totally asymmetric simple exclusion processes, account for all modes of transcriptional interference in spite of their extreme simplicity. A combination of mean-field theory and computer simulation of these models demonstrate the physical origin of the switch-like regulation of the two interfering genes in both co-directional and contra-directional traffic of the two groups of RNAP motors.