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Transcription is a key process in gene expression, in which RNA polymerasesproduce a complementary RNA copy from a DNA template. RNA polymerization isfrequently interrupted by backtracking, a process in which polymerases performa random walk along the DNA template. Recovery of polymerases from thetranscriptionally-inactive backtracked state is determined by a kineticcompetition between 1D diffusion and RNA cleavage. Here we describe backtrackrecovery as a continuous-time random walk, where the time for a polymerase torecover from a backtrack of a given depth is described as a first-passage timeof a random walker to reach an absorbing state. We represent RNA cleavage as astochastic resetting process, and derive exact expressions for the recoverytime distributions and mean recovery times from a given initial backtrack depthfor both continuous and discrete-lattice descriptions of the random walk. Weshow that recovery time statistics do not depend on the discreteness of the DNAlattice when the rate of 1D diffusion is large compared to the rate ofcleavage.

Stochastic resetting in backtrack recovery by RNA polymerases