A traffic flow model for bio-polymerization processes.

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.