Origin and dynamics of a bottleneck-induced shock in a two-channel exclusion process

Interaction vs inhomogeneity in a periodic TASEP

“…For more clarity, in figure A1 we display the admissible region in the plane I vs 1/η, along with some instances of the correlatordensity relation (A. 19), obtained for different values of v. We note in particular that, excluding the borderline case I = 0, η = 1, the regions corresponding to v < 1 or v > 1 are respectively characterized by η > 1 or η < 1. Remembering the correlator definition (A.9), this physically means that we have, respectively, a larger or smaller probability to find an empty node, if we know that one of its neighbours is occupied.…”

“…Since the rates w depend on the position, equation (19) establishes a constraint to the spatial variations of the density ρ, such as to impose that the value of the current J remains fixed. Now, let us observe that, if all the hopping rates are multiplied by the same factor, say λ, the current gets multiplied by the same factor, in formulae…”

“…Among other interesting issues, that of spatial inhomogeneity of hopping rates has been frequently considered in the literature [10][11][12][13][14][15][16][17][18][19]. In case of periodic boundary conditions, it turns out that several different types of inhomogeneities (a unique slower rate [10][11][12], randomly distributed rates [13,14], smoothly varying rates [15][16][17]) give rise to the same kind of phenomena, namely, steady states featuring domain walls (or shocks), which separate regions at different densities.…”

Abortive Initiation as a Bottleneck for Transcription in the Early Drosophila Embryo

“…The proposed abortive k-TASEP model is a special case of an inhomogeneous k-TASEP model with only one slow site located at the first site of the lattice. The inhomogeneous TASEP model has attracted significant interest in recent years, and some important analytical and numerical results have been obtained for point particles (see Cook et al, 2013, Poker et al, 2015, Dhiman and Gupta, 2016, Xiao et al, 2016, as well as for extended particles Shaw et al (2003Shaw et al ( , 2004b, Dong et al (2007), Klumpp and Hwa (2008), Dong et al (2009), Zia et al (2011), Brackley et al (2011). The standard way to treat a problem with an individual slow site like ours would consist in using mean-field approximations for the sublattices to the left and to the right of the slow site and stitching the two solutions together by the flux conservation equation on the slow site Kolomeisky (1998), Shaw et al (2004a).…”

Biologically motivated asymmetric exclusion process: Interplay of congestion in RNA polymerase traffic and slippage of nascent transcript

“…One of the key properties of the NESS is the non-vanishing particle flux which is defined as the number of particles passing through a site per unit time. The effects of different types of defects and inhomogeneities on the flux and the density profile of the particles have been investigated extensively over the last three decades [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. We treat the 'slippage prone site', where TS occurs, as a special type of 'defect' in a TASEP-based model of RNAP traffic.…”