Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase which usually happens when the polymerase tries to incorporate a mismatched nucleoside triphosphate. Previous models have made assumptions for easier calculations. One of the key assumptions made is that there is no trailing polymerase behind the backtracking polymerase or the trailing polymerase remains stationary when the leading polymerase backtracks. We derive analytic solutions for a stochastic model that allows for locally interacting RNAPs to explicitly show how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide a related method for computing the statistics of the times to error correction or incorporation given an initial local RNAP configuration. Our model and the associated results provide the components needed in more complete multi-RNAP descriptions. For example, all RNAPs along a transcript may be considered using exclusion processes such as the TASEP model that has been used to describe mRNA. In the many-body picture, one would be able to address multiple, simultaneously stalled RNAPs on how their interactions affect their probabilities of correction or incorporating an error. A competition between transcription fidelity and RNA production rate would be expected to arise
and will be the subject of future investigation.
