Discontinuous Galerkin calculations for a nonlinear PDE model of DNA transcription with short, transient and frequent pausing

Abstract

A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic information from DNA either to mRNA or to rRNA. The transcription process is punctuated by short, frequent RNAP pauses which are incorporated into the model as traffic lights. These pauses cause a delay in the average transcription process. The DG solution of the nonlinear model is used to calculate the delay and to determine the effect of the pauses on the average transcription time. Numerical error measurements between the DG solution and the true solution (derived by the method of characteristics) are given for a simple model problem. It shows an excellent agreement in a neighborhood away from the shocks as well as O(Δx) convergence for the delay calculation. Preliminary parameter studies indicate that in a system with multiple pauses both the location and time duration of the pauses can significantly affect the average delay experienced by an RNAP.