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

Abstract

We develope a theoretical framework, based on exclusion process, that is motivated by a biological phenomenon called transcript slippage (TS). In this model a discrete lattice repesents a DNA strand while each of the particles that hop on it unidirectionally, from site to site, represents a RNA polymerase (RNAP). While walking like a molecular motor along a DNA track in a step-by-step manner, a RNAP simultaneously synthesizes a RNA chain; in each forward step it elongates the nascent RNA molecule by one unit, using the DNA track also as the template. At some special "slippery" position on the DNA, which we represent as a defect on the lattice, a RNAP can lose its grip on the nascent RNA and the latter's consequent slippage results in a final product that is either longer or shorter than the corresponding DNA template. We develope an exclusion model for RNAP traffic where the kinetics of the system at the defect site captures key features of TS events. We demonstrate the interplay of the crowding of RNAPs and TS. A RNAP has to wait at the defect site for longer period in a more congested RNAP traffic, thereby increasing the likelihood of its suffering a larger number of TS events. The qualitative trends of some of our results for a simple special case of our model are consistent with experimental observations. The general theoretical framework presented here will be useful for guiding future experimental queries and for analysis of the experimental data with more detailed versions of the same model.

On the phase transition in the sublattice TASEP with stochastic blockage

“….89) Remark 5 15. The limit (5.89) of the scaled variance which arises from the the boundary layer contribution alone is equal to the scaled total variance (3.5) established in Theorem 3.2, thus showing that the origin of the divergence of compressibility C comes from the unbounded fluctuations of the domain wall position in the thermodynamic limit.…”

“…Non-equilibrium phase transitions in one-dimensional driven diffusive systems caused by a single static defect bond have a long history of study [1,2,3,4,5,6,7] and continue to intrigue not only from a statistical physics and probabilistic perspective [8,9,10,11,12] but also because of their recently recognized significance for biological transport by molecular motors [13,14,15,16]. The general picture is that at a critical density ρ c of driven particles there is a defect-induced nonequilibrium phase transition from a spatially homogeneous "free-flow" phase for ρ < ρ c to a "congested phase" for ρ > ρ c with two coexisting low density and high-density segments, corresponding to the formation of a macroscopic "traffic jam" upstream of the blockage bond.…”

Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

“…A special version of ASEP, in which particles on a lattice can hop unidirectionally, is referred to as a totally asymmetric simple exclusion process (TASEP). Researchers have applied TASEPs to traffic flows of self-driven particles, as in biological transport [4][5][6][7], vehicular traffic [8,9], and pedestrian flow [10][11][12]. Recently, one-lane TASEPs with varying hopping probabilities [13,14] and multi-lane TASEPs with interactions between lanes [15][16][17][18][19][20][21] have begun to be investigated.…”

“…Appendix A: Exclusion of the other solution of Eq. (6) In this Appendix, we discuss the exclusion of the other solution of Eq. ( 6); specifically,…”

On the phase transition in the sublattice TASEP with stochastic blockage

“…Non-equilibrium phase transitions in one-dimensional driven diffusive systems caused by a single static defect bond have a long history of study [1][2][3][4][5][6][7] and continue to intrigue not only from a statistical physics and probabilistic perspective [8][9][10][11][12] but also because of their recently recognized significance for biological transport by molecular motors [13][14][15][16]. The general picture is that at a critical density ρ c of driven particles there is a defect-induced nonequilibrium phase transition from a spatially homogeneous 'free-flow' phase for ρ < ρ c to a 'congested phase' for ρ > ρ c with two coexisting low density and high-density segments, corresponding to the formation of a macroscopic 'traffic jam' upstream of the blockage bond.…”