A traffic flow model for bio-polymerization processes

Abstract

Bio-polymerization processes like transcription and translation are central to proper function of a cell. The speed at which the bio-polymer grows is affected both by the number of pauses of elongation machinery, as well the number of bio-polymers due to crowding effects. In order to quantify these effects in fast transcribing ribosome genes, we rigorously show that a classical traffic flow model is the limit of a mean occupancy ODE model. We compare the simulation of this model to a stochastic model and evaluate the combined effect of the polymerase density and the existence of pauses on the instantaneous transcription rate of ribosomal genes.

Discontinuous Galerkin Calculations for a Nonlinear PDE Model of DNA Transcription with Short, Transient and Frequent Pausing

“…one draw from a random variable) is certainly insufficient to make any conclusions about overall behavior of such a system. A preliminary result is reported in [6] where multiple realizations of the pauses are used for model simulations, and average delays are reported over a range of values of instantaneous transcription rates. In that case, the average delay calculations exhibit a high amount of variability for the multiple realizations.…”

“…It is known from empirical observation that during the transcription process, a polymerase frequently pauses along the DNA strand causing a transcriptional delay and affecting the instantaneous transcription speed, see [6,12,13,17]. One goal of the current research is to use numerical simulations of the PDE model described in Section 3 (with various selections of pause data) in order to quantify the effect of pauses and subsequent delays on the overall transcription rate of the ribosomal RNA.…”

“…For details related to the biological literature, the interested reader is referred to [6] where the authors discuss several aspects of the motivating questions from the biological system and give computational results for the general model given above. In that work, the focus is the justification of the nonlinear model as a viable mathematical model and the numerical results are described in terms of their implications for the biological mechanisms related to physical phenomena of transcriptional pausing.…”

“…One of the three models is a continuum model taking the form of a hyperbolic conservation law with a nonlinear flux component. This paper serves as a companion to that work, and it details the Discontinuous Galerkin finite element methods used for the simulation results of the PDE model used in [6].…”

“…To sustain the high cellular demand on ribosome RNA synthesis, the density of polymerases on the rrn operon is very high. In [6], three types of models are considered in order to quantify the combined effect of high polymerase density and ubiquitous pauses on the transcription rate of ribosomal RNA. One of the three models is a continuum model taking the form of a hyperbolic conservation law with a nonlinear flux component.…”