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Register a new userA Biologically Motivated Asymmetric Exclusion Process: interplay of congestion in RNA polymerase traffic and slippage of nascent transcript
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Added by
Debashish Chowdhury
Publication date
2018
fields
Physics
and research's language is
English
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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 represents 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 latters 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 detail
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Totally asymmetric simple exclusion process (TASEP) was originally introduced as a model for the traffic-like collective movement of ribosomes on a messenger RNA (mRNA) that serves as the track for the motor-like forward stepping of individual ribosomes. In each step, a ribosome elongates a protein by a single unit using the track also as a template for protein synthesis. But, pre-fabricated, functionally competent, ribosomes are not available to begin synthesis of protein; a subunit directionally scans the mRNA in search of the pre-designated site where it is supposed to bind with the other subunit and begin the synthesis of the corresponding protein. However, because of `leaky scanning, a fraction of the scanning subunits miss the target site and continue their search beyond the first target. Sometimes such scanners successfully identify the site that marks the site for initiation of the synthesis of a different protein. In this paper, we develop an exclusion model, with three interconvertible species of hard rods, to capture some of the key features of these biological phenomena and study the effects of the interference of the flow of the different species of rods on the same lattice. More specifically, we identify the meantime for the initiation of protein synthesis as appropriate mean {it first-passage} time that we calculate analytically using the formalism of backward master equations. In spite of the approximations made, our analytical predictions are in reasonably good agreement with the numerical data that we obtain by performing Monte Carlo simulations. We also compare our results with a few experimental facts reported in the literature and propose new experiments for testing some of our new quantitative predictions.
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with an amplitude large compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking and exchange symmetry effect. The latter leads to a current equal to that of non-interacting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of non-equilibrium steady states to occur. Our results show that the particle size can be of crucial importance for non-equilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.
We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, the dynamics is governed by equations that usually describe food search of the paradigmatic Physarum polycephalum. In this work we assume that the two paths undergo damping whose relative strength is periodically modulated in time and analyse the dynamics in the presence of stochastic forces simulating Gaussian noise. We identify different responses depending on the modulation frequency and on the noise amplitude. At frequencies smaller than the mean dissipation rate, the system tends to switch to the path which minimizes dissipation. Synchronous switching occurs at an optimal noise amplitude which depends on the modulation frequency. This behaviour disappears at larger frequencies, where the dynamics can be described by the time-averaged equations. Here, we find metastable patterns that exhibit the features of noise-induced resonances.
We study the nonequilibrium steady states in asymmetric exclusion processes (TASEP) with open boundary conditions having spatially inhomogeneous hopping rates. Assuming spatially smoothly varying hopping rates with a few (or no) discontinuities, we show that the steady states are in general classified by the steady state currents in direct analogy with open TASEPs having uniform hopping rates. We calculate the steady state density profiles, which are now space-dependent. We also obtain the phase diagrams in the plane of the control parameters, which though have phase boundaries that are in general curved lines, have the same topology as their counterparts for conventional open TASEPs, independent of the form of the hopping rate functions. This reveals a type of universality, not encountered in critical phenomena.
We revisit the totally asymmetric simple exclusion process with open boundaries (TASEP), focussing on the recent discovery by de Gier and Essler that the model has a dynamical transition along a nontrivial line in the phase diagram. This line coincides neither with any change in the steady-state properties of the TASEP, nor the corresponding line predicted by domain wall theory. We provide numerical evidence that the TASEP indeed has a dynamical transition along the de Gier-Essler line, finding that the most convincing evidence was obtained from Density Matrix Renormalisation Group (DMRG) calculations. By contrast, we find that the dynamical transition is rather hard to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss in general terms scenarios that admit a distinction between static and dynamic phase behaviour.
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