Theoretical analysis of transcription process with polymerase stalling

Experimental evidence shows that in gene transcription RNA polymerase has the possibility to be stalled at a certain position of the transcription template. This may be due to the template damage or protein barriers. Once stalled, polymerase may backtrack along the template to the previous nucleotide to wait for the repair of the damaged site, simply bypass the barrier or damaged site and consequently synthesize an incorrect messenger RNA, or degrade and detach from the template. Thus, the effective transcription rate (the rate to synthesize correct product mRNA) and the transcription effectiveness (the ratio of the effective transcription rate to the effective transcription initiation rate) are both influenced by polymerase stalling events. So far, no theoretical model has been given to discuss the gene transcription process including polymerase stalling. In this study, based on the totally asymmetric simple exclusion process, the transcription process including polymerase stalling is analyzed theoretically. The dependence of the effective transcription rate, effective transcription initiation rate, and transcription effectiveness on the transcription initiation rate, termination rate, as well as the backtracking rate, bypass rate, and detachment (degradation) rate when stalling, are discussed in detail. The results showed that backtracking restart after polymerase stalling is an ideal mechanism to increase both the effective transcription rate and the transcription effectiveness. Without backtracking, detachment of stalled polymerase can also help to increase the effective transcription rate and transcription effectiveness. Generally, the increase of the bypass rate of the stalled polymerase will lead to the decrease of the effective transcription rate and transcription effectiveness. However, when both detachment rate and backtracking rate of the stalled polymerase vanish, the effective transcription rate may also be increased by the bypass mechanism.