[Amath-seminars] Talk by Lisa Davis Thursday 2/9 at 1:30pm

Randall J LeVeque rjl at uw.edu
Wed Feb 8 13:51:19 PST 2017

Our visitor Lisa Davis will be giving a talk on her work in the NARC
Seminar tomorrow at 1:30pm.

All are welcome!

Speaker: Lisa Davis, Montana State University

Title: Mathematical Models and Computation for Transcription of a
Crowded Gene -- the rrn Operon

Time and Date: 1:30pm on Thursday Feb. 9, 2017

Place: Lewis 208


In fast-transcribing prokaryotic genes, such as 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
theorized to cause RNAP traffic jams. However, some studies indicate that
elongation can be faster in the presence of multiple RNAPs than elongation
by a single polymerase, but the mechanism of this interaction among the
RNAPs is not known. Two mathematical models of the transcription phenomena
will be discussed. The first is a nonlinear PDE model that was used as a
first attempt to model simple forms of traffic flow over 60 years ago. The
PDE takes the form of a nonlinear scalar conservation law, and
transcriptional pauses are modeled as discontinuities in the flow velocity
term. Obtaining biologically relevant quantities and analyzing the data
allows us to carry out simple parameter studies and to answer questions
related to the organism’s overall “fitness.” A stochastic model will be
discussed also. This model considers the torque imposed by RNAP motion on
helically twisted DNA and transmitted to the neighboring polymerases. We
theorize that it may play a central role in the observed cooperative
behavior of polymerases. We have incorporated the torque mechanism into a
basic stochastic model and simulated transcription both with and without
torque, including the transcriptional pausing phenomena in both cases. The
underlying stochastic model is an implementation of the commonly used
Totally Asymmetric Simple Exclusion Process (TASEP) framework, and the
torque mechanism is incorporated by modelling the DNA strand between two
neighboring RNAPs as an elastic rod. Simulation results indicate that the
torque mechanism causes shorter pause durations and fewer collisions
between polymerases. Transcription times in the torque model qualitatively
agree with experimental data better than those of the underlying TASEP
model without the torque effects. Using torque as the interacting mechanism
of polymerases also leads to significantly fewer collisions and fewer
traffic jams of polymerases. 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.


Dr. Lisa G. Davis

Professor of Mathematics

Graduate Program Committee
Dept. of Mathematical Sciences
Montana State University
2-214 Wilson Hall
Bozeman, MT 59717-2400
Office: (406) 994-5347
Fax: (406) 994-1789
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