Slow nucleosome dynamics set the transcriptional speed limit and induce RNA polymerase II traffic jams and bursts

Nucleosomes are recognized as key regulators of transcription. However, the relationship between slow nucleosome unwrapping dynamics and bulk transcriptional properties has not been thoroughly explored. Here, an agent-based model that we call the dynamic defect Totally Asymmetric Simple Exclusion Process (ddTASEP) was constructed to investigate the effects of nucleosome-induced pausing on transcriptional dynamics. Pausing due to slow nucleosome dynamics induced RNAPII convoy formation, which would cooperatively prevent nucleosome rebinding leading to bursts of transcription. The mean first passage time (MFPT) and the variance of first passage time (VFPT) were analytically expressed in terms of the nucleosome rate constants, allowing for the direct quantification of the effects of nucleosome-induced pausing on pioneering polymerase dynamics. The mean first passage elongation rate γ(hc, ho) is inversely proportional to the MFPT and can be considered to be a new axis of the ddTASEP phase diagram, orthogonal to the classical αβ-plane (where α and β are the initiation and termination rates). Subsequently, we showed that, for β = 1, there is a novel jamming transition in the αγ-plane that separates the ddTASEP dynamics into initiation-limited and nucleosome pausing-limited regions. We propose analytical estimates for the RNAPII density ρ, average elongation rate v, and transcription flux J and verified them numerically. We demonstrate that the intra-burst RNAPII waiting times tin follow the time-headway distribution of a max flux TASEP and that the average inter-burst interval tIBI¯ correlates with the index of dispersion De. In the limit γ→0, the average burst size reaches a maximum set by the closing rate hc. When α≪1, the burst sizes are geometrically distributed, allowing large bursts even while the average burst size NB¯ is small. Last, preliminary results on the relative effects of static and dynamic defects are presented to show that dynamic defects can induce equal or greater pausing than static bottle necks.Author summary: To perform specific functions, cells must express specific genes by copying the information in DNA into RNA via transcription. Structural proteins called nucleosomes are spaced every 200 base pairs along the length of a strand of DNA and play a crucial function in the regulation of gene activity by tightly binding DNA strands and condensing them into heterochromatin, preventing transcription by RNA polymerase II (RNAPII). Even on active genes where nucleosomes are loosely attached to DNA strands, the wrapping and unwrapping of nucleosomes pause transcription as RNAPII passes by. Previous mathematical models of transcription have compared this biological process to traffic on a one lane highway without obstructions. In contrast, our proposed model simulates transcription like traffic in a grid system where nucleosomes can be thought of as pedestrians or other vehicles crossing the road at regularly spaced intersections. Just as side street traffic and pedestrian crossings can cause cars to form convoys and cause jams limiting the max speed in an area, nucleosomes can cause RNAPII to form convoys that lead to bursts of mRNA production and limit the average polymerase flux through the gene.