# First Passage Time in Computation by Tape-Copying Turing Machines: Slippage of Nascent Tape

## TL;DR

This paper models RNA polymerase as a tape-copying Turing machine to analyze the stochastic timing and slippage events during transcription, providing insights into transcriptional errors caused by slippage.

## Contribution

It introduces a formal stochastic model of transcriptional slippage using first-passage time analysis in a tape-copying Turing machine framework.

## Key findings

- Derived statistical characteristics of first-passage times for slippage events.
- Quantified probabilities of lengthening or shortening of transcripts due to slippage.
- Potential applications in analyzing transcriptional error data.

## Abstract

Transcription of the genetic message encoded chemically in the sequence of the DNA template is carried out by a molecular machine called RNA polymerase (RNAP). Backward or forward slippage of the nascent RNA with respect to the DNA template strand give rise to a transcript that is, respectively, longer or shorter than the corresponding template. We model a RNAP as a "Tape-copying Turing machine" (TCTM) where the DNA template is the input tape while the nascent RNA strand is the output tape. Although the TCTM always steps forward the process is assumed to be stochastic that has a probability of occurrence per unit time. The time taken by a TCTM for each single successful forward stepping on the input tape, during which the output tape suffers lengthening or shortening by $n$ units because of backward or forward slippage, is a random variable; we report some of the statistical characteristics of this time by using the formalism for calculation of the distributions of {\it first-passage time}. The results are likely to find applications in the analysis of experimental data on "programmed" transcriptional error caused by transcriptional slippage which is a mode of "recoding" of genetic information.