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Center for Nonlinear Studies |
In fast-transcribing prokaryotic genes, such as an rrn gene, 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. Over the course of this research project, we have considered several mathematical models to capture the essential behaviors known to this phenomena. I will give a brief overview of the essential biological quantities of interest, and the remainder of the talk will focus on an overview of two mathematical models that have been proposed. 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 there's time, 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.
Host: Dr. Kyle Hickmann