Dynamics of Stochastic Sequence-Level Models of Transcription and Translation in Prokaryotes

Abstract

In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is completed. Also, from one transcript, several translation events occur in parallel. To study how events in transcription elongation affect translation elongation and fluctuations in protein levels, we propose a delayed stochastic model of prokaryotic transcription and translation at the nucleotide and codon level that includes the promoter open complex formation and alternative pathways to elongation, namely pausing, arrests, editing, pyrophosphorolysis, RNA polymerase traffic, and premature termination. Stepwise translation can start after the ribosome binding site is formed and accounts for variable codon translation rates, ribosome traffic, back-translocation, drop-off, and trans-translation. The recent development of measurement techniques in genetics promises better un-derstanding of the functioning of biological systems. To attain the most out of these techniques, new methods are needed of interpreting the data, since most existent me-thods have been developed to analyze population level measurements, rather than ex-tracting information from single cell dynamics. For example, one needs accurate estima-tion of the measurement noise from single cell measurements of gene expression. We use recently developed methods to measure gene expression in vivo in individual cells, at the single RNA and protein molecule levels. Such measurements of gene expression, attained in various conditions, as well as the proposed modeling strategy, are used to study and model the dynamics of gene expression at the single event level and to esti-mate noise sources in the processes. First, the model is shown to accurately match the measurements of sequence-dependent translation elongation dynamics. Next, the degree of coupling between fluc-tuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation is characterized. Finally, sequence-specific transcriptional pauses are found to have an effect on protein noise levels. For parameter values within realistic intervals, transcription and translation are found to be tightly coupled in Escherichia coli, as the noise in protein levels is mostly determined by the underlying noise in RNA levels. Sequence-dependent events in transcription elongation, e.g. pauses, are found to cause tangible effects in the degree of fluctuations in protein levels, implying that these are evolvable. /Kir11