Stochastic sequence-level model of coupled transcription and translation in prokaryotes

Abstract

Background: In prokaryotes, transcription and translation are dynamically coupled, as the latter starts before the former is complete. 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.

Results: First, we show that the model accurately matches measurements of sequence-dependent translation elongation dynamics. Next, we characterize the degree of coupling between fluctuations in RNA and protein levels, and its dependence on the rates of transcription and translation initiation. Finally, modeling sequence-specific transcriptional pauses, we find that these affect protein noise levels.

Conclusions: 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.

Figure 1

Kinetics of RNA polymerases on the DNA strand. (A) Example of the kinetics of multiple RNAp molecules on the DNA template over 400 s. Note that, on several occasions, the RNAp molecules pause and that one RNAp never overtakes another on the DNA template. (B) Distribution of time intervals between consecutive transcription initiation and (C) completion events. Data is from 57 000 initiation events.

Figure 2

Kinetics of ribosomes on an RNA strand. (A) Example of the kinetics of several ribosomes along an mRNA template that suffered an arrest at nucleotide 1850, from the moment the ribosome binding site is formed to the degradation of the mRNA. The continuous gray region in the bottom left corresponds to the untranscribed sequence of the mRNA. (B) Distribution of time intervals between consecutive translation initiation events. (C) Distribution (grey bars) of time intervals between consecutive translation completion events given the presence of a sequence dependent arrest site at nucleotide 1850. The solid black line shows the distribution of time intervals between consecutive translation completion events without the sequence-dependent arrest site, normalized to the same scale. Data is from 600 000 initiation events.

Figure 3

Appearance of radioactivity in β-galactosidase. Appearance of radioactivity incorporated from the three different mRNA strands, at different times after initiation of translation elongation in the models (lines) and in the measurements (crosses, triangles and circles) [17]. Values of radioactivity are normalized such that the maximum corresponds to 23 radioactive methionines.

Figure 4

Noise in mRNA as a function of the transcription initiation rate. Noise (CV²) in mRNA levels for varying effective transcription initiation rates. The mRNA degradation rate is set so that the mean mRNA levels at steady state are identical in all cases.

Figure 5

Noise in protein levels for varying transcription and translation initiation rates. Noise (CV²) in protein levels for varying effective transcription initiation rates and three different rates of translation initiation. mRNA and protein degradation rates are set so that the mean mRNA and mean protein levels at steady state are identical in all cases.

Figure 6

Normalized maximum correlation between RNA and protein time series. The higher the rate of translation initiation (and thus higher protein degradation to keep the mean the same), the more correlated the fluctuations in protein and RNA levels become, as measured by the normalized maximum correlation. This is because the protein levels follow any fluctuations in the RNA levels faster. Similarly, increasing the rate of transcription initiation, while maintaining the rate of translation initiation constant, decreases the correlation between fluctuations in protein and RNA levels.