Speaker
Description
The focus of the presentation is the development, numerical simulation and parameter analysis of a model of the transcription of ribosomal RNA in highly transcribed genes. The well-known nonlinear Lighthill-Whitham-Richards (LWR) equation is used to model the transcription process. The numerical treatment for model simulations includes introducing a low complexity time accurate method by adding a simple linear time filter to both explicit and implicit finite difference schemes. Time filters were first introduced in 1966 and subsequently analyzed and expanded by many scholars. The work presented here is motivated by a time filter proposed by Guzel and Layton in 2018. The new filtered methods require a minimal modification of the code for the original unfiltered schemes, avoiding extra computational expense. Convergence results demonstrate that the unfiltered semi-implicit scheme outperforms the fully explicit scheme, and combining the filtering scheme with each of the fully explicit and semi-implicit schemes further increases computational accuracy. Finally biologically relevant transcription data can be extracted from the model simulations. One can calculate transcription time results for individual RNAPs transcribing the DNA strand, and average transcription time results over a specified period of time can be calculated. Simulation results are shown for two benchmark regimes of the LWR model, a shock wave example and a rarefaction wave case.
