Totally asymmetric exclusion process with site-wise dynamic disorder

Abstract

We propose an extension of the totally asymmetric simple exclusion process (TASEP) in which particles hopping along a lattice can be blocked by obstacles that dynamically attach/detach from lattice sites. The model can be thought as TASEP with site-wise dynamic disorder. We consider two versions of defect dynamics: (i) defects can bind to any site, irrespective of particle occupation, (ii) defects only bind to sites which are not occupied by particles (particle-obstacle exclusion). In case (i) there is a symmetric, parabolic-like relationship between the current and particle density, as in the standard TASEP. Case (ii) leads to a skewed relationship for slow defect dynamics. We also show that the presence of defects induces particle clustering, despite the translation invariance of the system. For open boundaries the same three phases as for the standard TASEP are observed, albeit the position of phase boundaries is affected by the presence of obstacles. We develop a simple mean-field theory that captures the model's quantitative behaviour for periodic and open boundary conditions and yields good estimates for the current-density relationship, mean cluster sizes and phase boundaries. Lastly, we discuss an application of the model to the biological process of gene transcription.

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

“…The model reproduces key features of transcription including cooperative nucleosome destabilization [ 23 , 24 , 66 ], polymerase convoy formation [ 63 ], and transcriptional bursting [ 56 ]. Further, the model provides significant insight into the physics of jamming transitions in the presence of dynamic defects [ 34 ].…”

“…RNAPII automatically moves through nucleosomes at a manually specified, slower rate rather than letting the wrapping dynamics dictate the advancement), the representative cases focused on low nucleosome density with slow rebinding, and they interpreted the results by mapping them on to a hypothetical two state model [ 25 ]. Waclaw et al investigated a general dynamic defect TASEP with single site hopping particles and single site defects focusing primarily on closed loop cases with soft exclusion effects that allow nucleosome and polymerase co-occupancy with some coverage of the open boundary case [ 34 ].…”

“…Previous studies investigating the flux-density-hop rate ( J-ρ-v ) relationship of TASEPs with dynamic defects have focused primarily on weak or fast fluctuating perturbations and have utilized mean field approaches that cannot account for the long range particle-particle and particle-defect correlations [ 25 , 34 , 35 – 36 ]. Most notably, Waclaw et al studied a variety of single site dynamic defect TASEPs with periodic and open boundaries with constrained and unconstrained defect binding [ 34 ]. However, most of their theoretical results were derived for the mathematically simpler case with periodic boundaries in which the bulk particle density remains constant.…”

Bayesian inference of PolII dynamics over the exclusion process

“…While the ASEP was originally proposed to model biopolymerization on DNA [21], this and related models have been applied to diverse problems, e.g., protein translation [22][23][24], molecular motors [25], pedestrian and vehicle traffic [26]. Recently proposed applications to transcription incorporate disordered dynamics [27]. ASEP's theoretical appeal is due to its analytical results representative of a large class of models [28,29] and a convenient mean-field treatment that yields the exact stationary solution [30].…”

Current-density relation in the exclusion process with dynamic obstacles

“…In our previous paper [39] we used computer simulations to show that the parabolic form of Eq. ( 1) holds approximately for the ddTASEP, whereby the effective particle speed u = 4J max was found to be smaller than the intrinsic speed v. We also applied a simple mean-field approximation to derive the current-density relation for high binding and unbinding rates.…”