Continuum and Stochastic Models for Describing Transcription of the rrn Operon


Dr. Lisa Davis, Department of Mathematical Sciences, Montana State University

Abstract: Bacteria are known for their ability to efficiently regulate their growth rate in response to changes in environment.  The regulation of growth rate is coupled with ribosome production, and ribosome production rates depend on both transcription of rrn genes and translation of ribosomal mRNA by ribosomes themselves.  In the current presentation, we focus on efforts to describe one portion of this coupled system.  In fast-transcribing prokaryotic genes, such as an rrn operon, many RNA polymerases (RNAPs) transcribe the DNA simultaneously.  Active elongation of RNAPs involves periods of fast forward motion that are often interrupted by pauses.  In some literature, this has been observed to cause RNAP traffic jams.  However, other studies indicate that elongation is faster in the presence of multiple RNAPs than elongation by a single polymerase.  Several types of mathematical models have been proposed to capture the essential behaviors of this phenomena.  I will give a brief overview of the essential biological quantities of interest, and the remainder of the talk will focus on two mathematical models we have proposed for characterizing this process.  The first is a continuum model taking the form of a nonlinear conservation law PDE where transcriptional pausing is incorporated into the flux term with a piecewise continuous density-velocity relationship.  The velocity relation is parametrized according to the user-specified (or randomly generated) spatial locations and time duration of the pauses.  The second model is a stochastic one that is based on the classical TASEP model but with added complexity to account for the interactions among neighboring RNAPs that can influence local elongation velocities.  I'll mention the algorithms that were used for model simulation for a series of parameter studies. If time permits, I'll discuss future directions where sensitivity with respect to model parameters is crucial for developing a better understanding of the validity of these models.  In addition, we would like to combine the lessons learned from previous models into the development of a specific second order PDE formulation which allows for a richer, more adaptive density-velocity relationship.

Bio: Dr. Davis’s research interests are in the areas of computational mathematics, sensitivity analysis and mathematical modeling of biological systems.  She studies efficient and robust computational algorithms for solving problems in various areas of applied mathematics.  She has a background in finite element methods as well as finite volume methods for numerical simulation of systems governed by partial differential equations.  Her research has received national funding from the NSF, DEPSCoR and AFOSR.  Her most recent work is in the area of model construction and numerical simulation for bio-polymerization models.  She is currently the PI on a grant focused on broadening the career pathways for doctoral students in Mathematics and Statistics through interdisciplinary research projects, internship opportunities and targeted course work and professional development called MT PEAKS. She is also the PI on a recent NSF grant focused on developing mathematical models of the ribosome assembly process.

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