A Continuum Model and Numerical Simulations for Transcription of a Crowded Gene -- the rrn Operon
- Thursday, September 14, 2017 from 3:10pm to 4:00pm
- Wilson Hall, 1-144 - view map
Dr. Lisa Davis (MSU Mathematical Sciences) will present:
In fast-transcribing prokaryotic genes, such as an rrn gene, 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; however, some studies indicate that elongation is faster in the presence of multiple RNAPs than elongation by a single polymerase. Over the course of the project, we have considered several mathematical models. I will give a brief overview of the essential biological quantities of interest, and the remainder of the talk will focus on a continuum model taking the form of a nonlinear conservation law PDE where transcriptional pausing is incorporating into the flux term with a discontinuous velocity function. The velocity relation is parametrized according to the user-specified (or randomly generated) spatial locations and time duration of the pauses. We discuss various algorithms that were used for model simulation for a series of parameter studies. The most recent results were obtained using a python implementation of the well-known Clawpack software which uses a finite volume method with a Riemann solver specially suited for this type of flux function. The basic ideas behind a Riemann solver will be defined. A specific PDE formulation that allows easy extraction of important biological quantities is discussed, and some Clawpack functionalities relevant to the project will be discussed in the talk also.