Mathematical modeling for transcription of DNA with pausing : stochastic model with torque, and diffusive transport model
Heberling, Tamra Lindsey.
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In fast-transcribing prokaryotic genes, like an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been observed to cause RNAP traffic jams; yet some studies indicate that elongation seems to be faster in the presence of multiple RNAPs than elongation by a single RNAP. We propose that an interaction between RNAPs via the torque produced by RNAP on helically twisted DNA can explain this apparent paradox. We have incorporated the torque mechanism into a stochastic model and simulated transcription both with and without torque. Simulation results illustrate that the torque causes shorter pause durations and fewer collisions between polymerases. Our results suggest that the torsional interaction of RNAPs is an important mechanism in maintaining fast transcription times, and that transcription should be viewed as a cooperative group effort by multiple polymerases. In an effort to further understand transcription, we investigate the Brownian ratchet model for nucleotide translocation. We model elongation as diffusive particle transport in a tilted periodic potential. To incorporate the RNAP pauses, a second periodic potential is added to the first. We present a formula for the mean escape time from a tilted, periodic potential composed of multiple periodic functions as the product of the mean escape time from each individual periodic function. This formula is extended to an arbitrary finite number of periodic functions. Two examples using truncated Fourier series are presented and analyzed.