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Lukyanets SP, Kliushnichenko OV. Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle. Phys Rev E 2024; 109:054103. [PMID: 38907458 DOI: 10.1103/physreve.109.054103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 04/08/2024] [Indexed: 06/24/2024]
Abstract
We consider a nonequilibrium transition that leads to the formation of nonlinear steady-state structures due to the gas flow scattering on a partially penetrable obstacle. The resulting nonequilibrium steady state (NESS) corresponds to a two-domain gas structure attained at certain critical parameters. We use a simple mean-field model of the driven lattice gas with ring topology to demonstrate that this transition is accompanied by the emergence of local invariants related to a complex composed of the obstacle and its nearest gas surrounding, which we refer to as obstacle edges. These invariants are independent of the main system parameters and behave as local first integrals, at least qualitatively. As a result, the complex becomes insensitive to the noise of external driving field within the overcritical domain. The emerged invariants describe the conservation of the number of particles inside the obstacle and strong temporal synchronization or correlation of gas states at obstacle edges. Such synchronization guarantees the equality to zero of the total edge current at any time. The robustness against external drive fluctuations is shown to be accompanied by strong spatial localization of induced gas fluctuations near the domain wall separating the depleted and dense gas phases. Such a behavior can be associated with nonequilibrium protection effect and synchronization of edges. The transition rates between different NESSs are shown to be different. The relaxation rates from one NESS to another take complex and real values in the sub- and overcritical regimes, respectively. The mechanism of these transitions is governed by the generation of shock waves at the back side of the obstacle. In the subcritical regime, these solitary waves are generated sequentially many times, while only a single excitation is sufficient to rearrange the system state in the overcritical regime.
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Affiliation(s)
- S P Lukyanets
- Department of Theoretical Physics, Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kyiv, Ukraine
| | - O V Kliushnichenko
- Department of Theoretical Physics, Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kyiv, Ukraine
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2
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Pal B, Gupta AK. Reservoir crowding in a resource-constrained exclusion process with a dynamic defect. Phys Rev E 2022; 106:044130. [PMID: 36397510 DOI: 10.1103/physreve.106.044130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
To understand the complicated transport processes that occur in biological and physical systems, we investigate a constrained totally asymmetric simple exclusion process with a stochastic defect particle. The defect particle might randomly emerge or vanish, resulting in a dynamic defect, and slows down the flow of moving particles when attached to the lattice. Using a mean-field technique, we examine the steady-state characteristics and boundary-layer analysis is provided to comprehend the properties of finite system. In a simplification, our theoretical method unifies three different parameter used to define the defect dynamics into one parameter termed the obstruction factor. It is found that the defect kinetics lead to emergence of phases where the current is defect restricted. The system shows nine phases overall, including bulk-induced and boundary-induced shock phases, with the phase schema showing no more than eight phases depending on the dynamics. We found that variation of obstruction does not lead to qualitative transition in the system, whereas the change in constraint on total particles affect the system qualitatively. All the theoretical outcomes have been validated using extensive Monte Carlo simulations.
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Affiliation(s)
- Bipasha Pal
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India
| | - Arvind Kumar Gupta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, Punjab, India
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3
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Gedeon T, Humphries AR, Mackey MC, Walther HO, Wang Z. Operon dynamics with state dependent transcription and/or translation delays. J Math Biol 2021; 84:2. [PMID: 34905089 DOI: 10.1007/s00285-021-01693-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Revised: 06/18/2021] [Accepted: 11/16/2021] [Indexed: 11/29/2022]
Abstract
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons with state-dependent delays. The paper provides justification and derivation of the model, detailed analysis of the appropriate setting of the corresponding dynamical system, and extensive numerical analysis of its dynamics. Comparison with constant delay models shows significant differences in dynamics that include existence of stable periodic orbits in inducible systems and multistability in repressible systems. A combination of parameter space exploration, numerics, analysis of steady state linearization and bifurcation theory indicates the likely presence of Shilnikov-type homoclinic bifurcations in the repressible operon model.
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Affiliation(s)
- Tomáš Gedeon
- Department of Mathematics, Montana State University, Bozeman, MT, 59717, USA
| | - Antony R Humphries
- Departments of Mathematics and Statistics, and, Physiology, McGill University, Montreal, QC, H3A 0B9, Canada
| | - Michael C Mackey
- Departments of Physiology, Physics, and, Mathematics and Statistics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, H3G 1Y6, Canada
| | - Hans-Otto Walther
- Mathematisches Institut, Universität Giessen, Arndtstrasse 2, 35392, Giessen, Germany
| | - Zhao Wang
- Department of Mathematics and Statistics, McGill University, Montreal, QC, H3A 0B9, Canada.
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4
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Gedeon T, Davis L, Weber K, Thorenson J. Trade-offs among transcription elongation rate, number, and duration of ubiquitous pauses on highly transcribed bacterial genes. J Bioinform Comput Biol 2021; 19:2150020. [PMID: 34353243 DOI: 10.1142/s0219720021500207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we study the limitations imposed on the transcription process by the presence of short ubiquitous pauses and crowding. These effects are especially pronounced in highly transcribed genes such as ribosomal genes (rrn) in fast growing bacteria. Our model indicates that the quantity and duration of pauses reported for protein-coding genes is incompatible with the average elongation rate observed in rrn genes. When maximal elongation rate is high, pause-induced traffic jams occur, increasing promoter occlusion, thereby lowering the initiation rate. This lowers average transcription rate and increases average transcription time. Increasing maximal elongation rate in the model is insufficient to match the experimentally observed average elongation rate in rrn genes. This suggests that there may be rrn-specific modifications to RNAP, which then experience fewer pauses, or pauses of shorter duration than those in protein-coding genes. We identify model parameter triples (maximal elongation rate, mean pause duration time, number of pauses) which are compatible with experimentally observed elongation rates. Average transcription time and average transcription rate are the model outputs investigated as proxies for cell fitness. These fitness functions are optimized for different parameter choices, opening up a possibility of differential control of these aspects of the elongation process, with potential evolutionary consequences. As an example, a gene's average transcription time may be crucial to fitness when the surrounding medium is prone to abrupt changes. This paper demonstrates that a functional relationship among the model parameters can be estimated using a standard statistical analysis, and this functional relationship describes the various trade-offs that must be made in order for the gene to control the elongation process and achieve a desired average transcription time. It also demonstrates the robustness of the system when a range of maximal elongation rates can be balanced with transcriptional pause data in order to maintain a desired fitness.
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Affiliation(s)
- Tomáš Gedeon
- Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400, USA
| | - Lisa Davis
- Department of Mathematical Sciences, Montana State University, P.O. Box 172400, Bozeman, MT 59717-2400, USA
| | - Katelyn Weber
- Department of Statistics, London School of Economics and Political Science, London, UK
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Yadav V, Ullah Irshad I, Kumar H, Sharma AK. Quantitative Modeling of Protein Synthesis Using Ribosome Profiling Data. Front Mol Biosci 2021; 8:688700. [PMID: 34262940 PMCID: PMC8274658 DOI: 10.3389/fmolb.2021.688700] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 05/25/2021] [Indexed: 12/12/2022] Open
Abstract
Quantitative prediction on protein synthesis requires accurate translation initiation and codon translation rates. Ribosome profiling data, which provide steady-state distribution of relative ribosome occupancies along a transcript, can be used to extract these rate parameters. Various methods have been developed in the past few years to measure translation-initiation and codon translation rates from ribosome profiling data. In the review, we provide a detailed analysis of the key methods employed to extract the translation rate parameters from ribosome profiling data. We further discuss how these approaches were used to decipher the role of various structural and sequence-based features of mRNA molecules in the regulation of gene expression. The utilization of these accurate rate parameters in computational modeling of protein synthesis may provide new insights into the kinetic control of the process of gene expression.
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Affiliation(s)
- Vandana Yadav
- Department of Physics, Indian Institute of Technology Madras, Chennai, India
| | | | - Hemant Kumar
- School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar, India
| | - Ajeet K Sharma
- Department of Physics, Indian Institute of Technology Jammu, Jammu, India
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6
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Garg S, Dhiman I. Particle creation and annihilation in a dynamically disordered totally asymmetric simple exclusion process. Phys Rev E 2021; 103:052120. [PMID: 34134211 DOI: 10.1103/physreve.103.052120] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2020] [Accepted: 05/03/2021] [Indexed: 11/07/2022]
Abstract
We study a single-channel dynamically disordered totally asymmetric simple exclusion process with bulk particle attachment and detachment. The continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The effects of various parameters, namely particle attachment rate, defect binding and unbinding rates, and binding constant, have been investigated. An increase in the attachment rate of particles reduces the number of steady-state phases, whereas a variation in defect binding and unbinding rates shifts the phase boundaries. One of the important consequences of introducing particle nonconserving dynamics is the appearance of shock in the steady state. The shock dynamics have been thoroughly examined and the defect strength is found to have a significant effect on the shock position. The mean-field solutions are validated using extensive Monte Carlo simulations.
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Affiliation(s)
- Shaweta Garg
- School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147001, Punjab, India
| | - Isha Dhiman
- School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147001, Punjab, India
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7
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Song Xiao, Chen X, Liu Y. Bidirectional Totally Asymmetric Simple Exclusion Process with a Bottleneck and Different Hopping Rates. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2021. [DOI: 10.1134/s1990793120060317] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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8
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Lips D, Ryabov A, Maass P. Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process. Phys Rev E 2019; 100:052121. [PMID: 31869987 DOI: 10.1103/physreve.100.052121] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Indexed: 06/10/2023]
Abstract
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
- Centro de Física Teórica e Computacional, Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande P-1749-016 Lisboa, Portugal
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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9
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Ghosh S, Dutta A, Patra S, Sato J, Nishinari K, Chowdhury D. Biologically motivated asymmetric exclusion process: Interplay of congestion in RNA polymerase traffic and slippage of nascent transcript. Phys Rev E 2019; 99:052122. [PMID: 31212543 DOI: 10.1103/physreve.99.052122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2018] [Indexed: 02/03/2023]
Abstract
We develop a theoretical framework, based on an 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 an 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 develop 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 a longer period in 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.
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Affiliation(s)
- Soumendu Ghosh
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
| | - Annwesha Dutta
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
| | | | - Jun Sato
- Research Center for Advanced Science and Technology, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8904, Japan
| | - Katsuhiro Nishinari
- Research Center for Advanced Science and Technology, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8904, Japan
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10
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Wang YQ, Wang JX, Li WH, Zhou CF, Jia B. Analytical and simulation studies of driven diffusive system with asymmetric heterogeneous interactions. Sci Rep 2018; 8:16287. [PMID: 30389975 PMCID: PMC6214950 DOI: 10.1038/s41598-018-34579-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Accepted: 10/18/2018] [Indexed: 11/22/2022] Open
Abstract
Totally asymmetric simple exclusion process (namely, TASEP) is one of the most vital driven diffusive systems, which depicts stochastic dynamics of self-driven particles unidirectional updating along one-dimensional discrete lattices controlled by hard-core exclusions. Different with pre-existing results, driven diffusive system composed by multiple TASEPs with asymmetric heterogeneous interactions under two-dimensional periodic boundaries is investigated. By using detailed balance principle, particle configurations are extensively studied to obtain universal laws of characteristic order parameters of such stochastic dynamic system. By performing analytical analyses and Monte-Carlo simulations, local densities are found to be monotone increase with global density and spatially homogeneous to site locations. Oppositely, local currents are found to be non-monotonically increasing against global density and proportional to forward rate. Additionally, by calculating different cases of topologies, changing transition rates are found to have greater effects on particle configurations in adjacent subsystems. By intuitively comparing with pre-existing results, the improvement of our work also shows that introducing and considering totally heterogeneous interactions can improve the total current in such multiple TASEPs and optimize the overall transport of such driven-diffusive system. Our research will be helpful to understand microscopic dynamics and non-equilibrium dynamical behaviors of interacting particle systems.
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Affiliation(s)
- Yu-Qing Wang
- School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China. .,MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, China.
| | - Ji-Xin Wang
- School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China
| | - Wan-He Li
- School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China
| | - Chao-Fan Zhou
- School of Physical Sciences, University of Science and Technology of China, Hefei, 230026, China
| | - Bin Jia
- MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, China.
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11
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Lips D, Ryabov A, Maass P. Brownian Asymmetric Simple Exclusion Process. PHYSICAL REVIEW LETTERS 2018; 121:160601. [PMID: 30387631 DOI: 10.1103/physrevlett.121.160601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Indexed: 06/08/2023]
Abstract
We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude 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 noninteracting 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 nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.
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Affiliation(s)
- Dominik Lips
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
| | - Artem Ryabov
- Charles University, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, CZ-18000 Praha 8, Czech Republic
| | - Philipp Maass
- Universität Osnabrück, Fachbereich Physik, Barbarastraße 7, D-49076 Osnabrück, Germany
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12
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Szavits-Nossan J, Romano MC, Ciandrini L. Power series solution of the inhomogeneous exclusion process. Phys Rev E 2018; 97:052139. [PMID: 29906846 DOI: 10.1103/physreve.97.052139] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2018] [Indexed: 11/07/2022]
Abstract
We develop a power series method for the nonequilibrium steady state of the inhomogeneous one-dimensional totally asymmetric simple exclusion process (TASEP) in contact with two particle reservoirs and with site-dependent hopping rates in the bulk. The power series is performed in the entrance or exit rates governing particle exchange with the reservoirs, and the corresponding particle current is computed analytically up to the cubic term in the entry or exit rate, respectively. We also show how to compute higher-order terms using combinatorial objects known as Young tableaux. Our results address the long outstanding problem of finding the exact nonequilibrium steady state of the inhomogeneous TASEP. The findings are particularly relevant to the modeling of mRNA translation in which the rate of translation initiation, corresponding to the entrance rate in the TASEP, is typically small.
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Affiliation(s)
- Juraj Szavits-Nossan
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - M Carmen Romano
- SUPA, Institute for Complex Systems and Mathematical Biology, Department of Physics, Aberdeen AB24 3UE, United Kingdom and Institute of Medical Sciences, University of Aberdeen, Foresterhill, Aberdeen AB24 3FX, United Kingdom
| | - Luca Ciandrini
- DIMNP, Université de Montpellier, CNRS, Montpellier, France and L2C, Université de Montpellier, CNRS, Montpellier, France
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13
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Mishra B, Chowdhury D. Interference of two codirectional exclusion processes in the presence of a static bottleneck: A biologically motivated model. Phys Rev E 2017; 95:062117. [PMID: 28709297 DOI: 10.1103/physreve.95.062117] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2017] [Indexed: 12/15/2022]
Abstract
We develop a two-species exclusion process with a distinct pair of entry and exit sites for each species of rigid rods. The relatively slower forward stepping of the rods in an extended bottleneck region, located in between the two entry sites, controls the extent of interference of the codirectional flow of the two species of rods. The relative positions of the sites of entry of the two species of rods with respect to the location of the bottleneck are motivated by a biological phenomenon. However, the primary focus of the study here is to explore the effects of the interference of the flow of the two species of rods on their spatiotemporal organization and the regulations of this interference by the extended bottleneck. By a combination of mean-field theory and computer simulation, we calculate the flux of both species of rods and their density profiles as well as the composite phase diagrams of the system. If the bottleneck is sufficiently stringent, then some of the phases become practically unrealizable, although not ruled out on the basis of any fundamental physical principle. Moreover, the extent of suppression of flow of the downstream entrants by the flow of the upstream entrants can also be regulated by the strength of the bottleneck. We speculate on the possible implications of the results in the context of the biological phenomenon that motivated the formulation of the theoretical model.
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Affiliation(s)
- Bhavya Mishra
- Department of Physics, Indian Institute of Technology Kanpur, 208016, India
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14
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Soh H, Baek Y, Ha M, Jeong H. Effects of a local defect on one-dimensional nonlinear surface growth. Phys Rev E 2017; 95:042123. [PMID: 28505796 DOI: 10.1103/physreve.95.042123] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Indexed: 11/07/2022]
Abstract
The slow-bond problem is a long-standing question about the minimal strength ε_{c} of a local defect with global effects on the Kardar-Parisi-Zhang (KPZ) universality class. A consensus on the issue has been delayed due to the discrepancy between various analytical predictions claiming ε_{c}=0 and numerical observations claiming ε_{c}>0. We revisit the problem via finite-size scaling analyses of the slow-bond effects, which are tested for different boundary conditions through extensive Monte Carlo simulations. Our results provide evidence that the previously reported nonzero ε_{c} is an artifact of a crossover phenomenon which logarithmically converges to zero as the system size goes to infinity.
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Affiliation(s)
- Hyungjoon Soh
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Yongjoo Baek
- Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Meesoon Ha
- Department of Physics Education, Chosun University, Gwangju 61452, Korea
| | - Hawoong Jeong
- Department of Physics and Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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15
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Cirillo ENM, Krehel O, Muntean A, van Santen R. Lattice model of reduced jamming by a barrier. Phys Rev E 2016; 94:042115. [PMID: 27841483 DOI: 10.1103/physreve.94.042115] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Indexed: 11/07/2022]
Abstract
We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.
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Affiliation(s)
- Emilio N M Cirillo
- Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, I-00161, Roma, Italy
| | - Oleh Krehel
- ICMS-Institute of Complex Molecular Systems, Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | - Adrian Muntean
- Department of Mathematics and Computer Science, Karlstad University, Sweden
| | - Rutger van Santen
- ICMS-Institute for Complex Molecular Systems, Faculty of Chemical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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16
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Foulaadvand ME, Maass P. Phase transitions and optimal transport in stochastic roundabout traffic. Phys Rev E 2016; 94:012304. [PMID: 27575145 DOI: 10.1103/physreve.94.012304] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Indexed: 11/07/2022]
Abstract
We study traffic in a roundabout model, where the dynamics along the interior lane of the roundabout are described by the totally asymmetric simple exclusion process (TASEP). Vehicles can enter the interior lane or exit from it via S intersecting streets with given rates, and locally modified dynamics at the junctions take into account that collisions of entering vehicles with vehicles approaching the entrance point from the interior lane should be avoided. A route matrix specifies the probabilities for vehicles to arrive from and to exit to certain intersecting streets. By subdividing the interior lane into segments between consecutive intersecting streets with effective entrance and exit rates, a classification of the stationary roundabout traffic in terms of TASEP multiphases is given, where each segment can be in either the low-density, high-density, or maximum current TASEP phase. A general methodology is developed, which allows one to calculate the multiphases and optimal throughput conditions based on a mean-field treatment. Explicit analytical results from this treatment are derived for equivalent interesting streets. The results are shown to be in good agreement with kinetic Monte Carlo simulations.
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Affiliation(s)
- M Ebrahim Foulaadvand
- Department of Physics, University of Zanjan, P.O. Box 45196-313, Zanjan, Iran.,School of Nanosciences, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
| | - Philipp Maass
- Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany
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17
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Abstract
Using the dynamic mean-field approximation of the totally asymmetric simple exclusion process (TASEP), we investigate the effect of small changes in the initiation, elongation, and termination rates along the mRNA strand on the steady-state protein translation rate. We show that the sensitivity of mRNA translation is equal to the sensitivity of the maximal eigenvalue of a symmetric, nonnegative, tridiagonal, and irreducible matrix. This leads to new analytical results as well as efficient numerical schemes that are applicable for large-scale models. Our results show that in the usual endogenous case, when initiation is more rate-limiting than elongation, the sensitivity of the translation rate to small mutations rapidly increases towards the 5′ end of the ORF. When the initiation rate is high, as may be the case for highly expressed and/or heterologous optimized genes, the maximal sensitivity is with respect to the elongation rates at the middle of the mRNA strand. We also show that the maximal possible effect of a small increase/decrease in any of the rates along the mRNA is an increase/decrease of the same magnitude in the translation rate. These results are in agreement with previous molecular evolutionary and synthetic biology experimental studies.
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18
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Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases. J Theor Biol 2015; 372:65-73. [PMID: 25744205 DOI: 10.1016/j.jtbi.2015.02.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2014] [Revised: 02/14/2015] [Accepted: 02/23/2015] [Indexed: 11/20/2022]
Abstract
Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a "wild-type" state to a given "terminally differentiated," "resistant," or "cancerous" state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be "nonlinear" (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times.
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19
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Baek Y, Ha M, Jeong H. Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062111. [PMID: 25615048 DOI: 10.1103/physreve.90.062111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2014] [Indexed: 06/04/2023]
Abstract
We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory, which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent 1/2 even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.
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Affiliation(s)
- Yongjoo Baek
- Natural Science Research Institute, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
| | - Meesoon Ha
- Department of Physics Education, Chosun University, Gwangju 501-759, Korea
| | - Hawoong Jeong
- Department of Physics and Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea and APCTP, Pohang, Gyeongbuk 790-784, Korea
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20
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Cook LJ, Dong JJ, LaFleur A. Interplay between finite resources and a local defect in an asymmetric simple exclusion process. Phys Rev E 2013; 88:042127. [PMID: 24229136 DOI: 10.1103/physreve.88.042127] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Revised: 08/21/2013] [Indexed: 11/07/2022]
Abstract
When particle flux is regulated by multiple factors such as particle supply and varying transport rate, it is important to identify the respective dominant regimes. We extend the well-studied totally asymmetric simple exclusion model to investigate the interplay between a controlled entrance and a local defect site. The model mimics cellular transport phenomena where there is typically a finite particle pool and nonuniform moving rates due to biochemical kinetics. Our simulations reveal regions where, despite an increasing particle supply, the current remains constant while particles redistribute in the system. Exploiting a domain wall approach with mean-field approximation, we provide a theoretical ground for our findings. The results in steady-state current and density profiles provide quantitative insights into the regulation of the transcription and translation process in bacterial protein synthesis.
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Affiliation(s)
- L Jonathan Cook
- Department of Physics and Engineering, Washington and Lee University, Lexington, Virginia 24450, USA
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21
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Davis L, Gedeon T, Gedeon J, Thorenson J. A traffic flow model for bio-polymerization processes. J Math Biol 2013; 68:667-700. [PMID: 23404039 DOI: 10.1007/s00285-013-0651-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2012] [Revised: 11/27/2012] [Indexed: 11/25/2022]
Abstract
Bio-polymerization processes like transcription and translation are central to proper function of a cell. The speed at which the bio-polymer grows is affected both by the number of pauses of elongation machinery, as well the number of bio-polymers due to crowding effects. In order to quantify these effects in fast transcribing ribosome genes, we rigorously show that a classical traffic flow model is the limit of a mean occupancy ODE model. We compare the simulation of this model to a stochastic model and evaluate the combined effect of the polymerase density and the existence of pauses on the instantaneous transcription rate of ribosomal genes.
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Affiliation(s)
- Lisa Davis
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717-2400, USA
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22
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Jiang R, Wang YQ, Kolomeisky AB, Huang W, Hu MB, Wu QS. Phase diagram structures in a periodic one-dimensional exclusion process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012107. [PMID: 23410283 DOI: 10.1103/physreve.87.012107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2012] [Revised: 11/18/2012] [Indexed: 06/01/2023]
Abstract
This paper studies a periodic one-dimensional exclusion process composed of a driven part and a biased diffusive part in a mesoscopic limit. It is shown that, depending on the biased diffusion parameter δ, rich phase diagram structures appear in which diverse phases have been exhibited and the density profile in the diffusive part is qualitatively different. This is because the domain wall is behaving differently. Our analytical results are in good agreement with Monte Carlo simulations.
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Affiliation(s)
- Rui Jiang
- State Key Laboratory of Fire Science and School of Engineering Science, University of Science and Technology of China, Hefei 230026, China.
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23
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Shi QH, Jiang R, Hu MB, Wu QS. Phase transitions induced by competition of two driven parts in a periodic system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041131. [PMID: 22680442 DOI: 10.1103/physreve.85.041131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2012] [Revised: 03/11/2012] [Indexed: 06/01/2023]
Abstract
This paper studies a periodic driven diffusive system, which separates into two equal-sized parts with different values of hopping rates. Competition of the two different driven parts leads to various bulk-driven phase transitions, including shock and antishock. More interestingly, for the symmetric scenario, one can observe shock and antishock simultaneously in the system. We have explained the coexistence of shock and antishock via the effective boundary reservoir density. Theoretical analysis has been carried out to characterize the emerging nonequilibrium steady states, which is in good agreement with Monte Carlo simulations.
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Affiliation(s)
- Qi-Hong Shi
- State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China
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24
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Ezaki T, Nishinari K. Positive congestion effect on a totally asymmetric simple exclusion process with an adsorption lane. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061149. [PMID: 22304082 DOI: 10.1103/physreve.84.061149] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2011] [Indexed: 05/31/2023]
Abstract
We propose a type of asymmetric simple exclusion process by introducing an adsorption lane. In the system, each particle can be adsorbed by the adsorption lane only once per travel. The adsorption and desorption probabilities control the density of adsorption sites and the number of adsorbed particles. The ratio of the adsorbed particles shows reversal dynamics for congestion of the system, which is called the "positive congestion effect." We analyze this phenomenon by simulations and an approximation and successfully derive its critical condition. The spatial distribution of particles controlled by the adsorption and desorption probabilities is also investigated through balance equations of particles.
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Affiliation(s)
- Takahiro Ezaki
- Department of Aeronautics and Astronautics, School of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
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25
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Sharma AK, Chowdhury D. Stochastic theory of protein synthesis and polysome: Ribosome profile on a single mRNA transcript. J Theor Biol 2011; 289:36-46. [DOI: 10.1016/j.jtbi.2011.08.023] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2011] [Revised: 08/18/2011] [Accepted: 08/19/2011] [Indexed: 12/31/2022]
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26
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Brackley CA, Romano MC, Thiel M. The dynamics of supply and demand in mRNA translation. PLoS Comput Biol 2011; 7:e1002203. [PMID: 22022250 PMCID: PMC3192816 DOI: 10.1371/journal.pcbi.1002203] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2010] [Accepted: 08/04/2011] [Indexed: 11/30/2022] Open
Abstract
We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking “competition” effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system. In this paper we show that the rate at which proteins are produced can be controlled at the elongation stage of mRNA translation. Regulation of translation initiation has been a focus of much study, but the subsequent effect of changes in the initiation rate on the overall translation rate, and the role of slow and fast codon usage in mRNA sequences is still not fully understood. We consider a model of elongation in which the dynamics of tRNA use and recharging are considered for real mRNA sequences. We find that the balance between the demand for, and supply of tRNAs is crucial in determining translation rates. Particularly interesting “competition” effects are observed when the simultaneous translation of multiple mRNA is considered. We show indeed that, via the choice of slow or fast codons, it is in principle possible to control how variation of the supply and demand for tRNA resources changes the rate of protein production from different mRNAs.
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Affiliation(s)
- Chris A Brackley
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen, United Kingdom.
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27
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Ohta Y, Kodama T, Ihara S. Cellular-automaton model of the cooperative dynamics of RNA polymerase II during transcription in human cells. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041922. [PMID: 22181190 DOI: 10.1103/physreve.84.041922] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2011] [Revised: 05/30/2011] [Indexed: 05/31/2023]
Abstract
RNA polymerase II (RNAPII) is the responsible motor protein for transcription. Here we report the formulation and results of a cellular automaton model of the RNAPII dynamics of gene transcription that takes account the effect of the velocity change according to the gene position, such as occurs in introns and exons. We describe RNAPII dynamics in terms of the properties in the time domain, such as elapsed time, residence time, and time intervals. We found that the RNAPII molecules move as a free-flow state, though regions of reduced velocity do exist such as exons, as far as the time interval between nearest RNAPII molecules is larger than the time required for an RNAPII passing the exclusion length in the velocity reduction region. On the other hand, if the reduction is strong enough to reach a certain threshold, at the maximally reductive velocity region, a transition occurs from the RNAPII free-flow state to the states with congested and repetitive flows. We analytically obtained the conditions for these flow states and the transition threshold. From simulations of high-density RNAPII in the SAMD4A gene with the strong blockade, we confirmed the transition from free flow to the repetitive and congested flows, suggesting that the transition may serve as a regulatory mechanism of gene expression. By fitting the experimentally observed RNAPII density profile of the SAMD4A gene during the course of transcription of the normal and altered gene (in knock-down cells) with or without roadblock, we found that the RNAPII density flow is a free state. However, even in this free state, there is a long-range correlation between RNAPII molecules, ranging from 1 to 20 min, with the corresponding distance from 3 to 80 kbp, during transcription in normal cells. This long-range correlation probably relates to the higher-order DNA loop structure.
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Affiliation(s)
- Yoshihiro Ohta
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo 153-8904, Japan
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28
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Reuveni S, Eliazar I, Yechiali U. Asymmetric inclusion process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041101. [PMID: 22181081 DOI: 10.1103/physreve.84.041101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Revised: 08/28/2011] [Indexed: 05/31/2023]
Abstract
We introduce and explore the asymmetric inclusion process (ASIP), an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process (ASEP). In both processes, random events cause particles to propagate unidirectionally along a one-dimensional lattice of n sites. In the ASEP, particles are subject to exclusion interactions, whereas in the ASIP, particles are subject to inclusion interactions that coalesce them into inseparable clusters. We study the dynamics of the ASIP, derive evolution equations for the mean and probability generating function (PGF) of the sites' occupancy vector, obtain explicit results for the above mean at steady state, and describe an iterative scheme for the computation of the PGF at steady state. We further obtain explicit results for the load distribution in steady state, with the load being the total number of particles present in all lattice sites. Finally, we address the problem of load optimization, and solve it under various criteria. The ASIP model establishes bridges between statistical physics and queueing theory as it represents a tandem array of queueing systems with (unlimited) batch service, and a tandem array of growth-collapse processes.
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Affiliation(s)
- Shlomi Reuveni
- School of Chemistry, Tel-Aviv University, Tel-Aviv IL-69978, Israel
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29
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Liu M, Tuo X, Wang R, Jiang R. Recent developments in totally asymmetric simple exclusion processes with local inhomogeneity. CHINESE SCIENCE BULLETIN-CHINESE 2011. [DOI: 10.1007/s11434-011-4449-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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30
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Brackley CA, Romano MC, Thiel M. Slow sites in an exclusion process with limited resources. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051920. [PMID: 21230513 DOI: 10.1103/physreve.82.051920] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2010] [Revised: 09/23/2010] [Indexed: 05/30/2023]
Abstract
We introduce slow bottleneck sites into a recent extension of the totally asymmetric exclusion process where hopping rates are allowed to vary dynamically with the availability of resources. In the context of messenger RNA (mRNA) translation in biology, this refers to the availability of amino acid-transfer-RNA (aa-tRNA) complexes which act as the source of amino acids for protein production. We study a simple designer mRNA with a single defect codon in the center. As well as the familiar queuing behavior we also observe a regime within the queuing phase where the queue becomes less severe as the aa-tRNAs become depleted.
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Affiliation(s)
- Chris A Brackley
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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31
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Embley B, Parmeggiani A, Kern N. Understanding totally asymmetric simple-exclusion-process transport on networks: generic analysis via effective rates and explicit vertices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041128. [PMID: 19905294 DOI: 10.1103/physreve.80.041128] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2009] [Indexed: 05/28/2023]
Abstract
In this paper we rationalize relevant features of totally asymmetric simple-exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle-hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.
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Affiliation(s)
- Ben Embley
- School of Chemical Engineering and Analytical Science, The University of Manchester, PO Box 88, Sackville Street, Manchester M60 1QD, United Kingdom.
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32
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Tailleur J, Evans MR, Kafri Y. Nonequilibrium phase transitions in the extraction of membrane tubes by molecular motors. PHYSICAL REVIEW LETTERS 2009; 102:118109. [PMID: 19392247 DOI: 10.1103/physrevlett.102.118109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2008] [Indexed: 05/27/2023]
Abstract
The extraction of membrane tubes by molecular motors is known to play an important role for the transport properties of eukaryotic cells. By studying a generic class of models for the tube extraction, we discover a rich phase diagram. In particular we show that the density of motors along the tube can exhibit shocks, inverse shocks, and plateaux, depending on parameters which could in principle be probed experimentally. In addition the phase diagram exhibits interesting reentrant behavior.
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Affiliation(s)
- J Tailleur
- SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland
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33
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Foulaadvand ME, Kolomeisky AB, Teymouri H. Asymmetric exclusion processes with disorder: effect of correlations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061116. [PMID: 19256811 DOI: 10.1103/physreve.78.061116] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2008] [Revised: 10/16/2008] [Indexed: 05/27/2023]
Abstract
Multiparticle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three nonequilibrium phases that are determined by the dynamic behavior at the entrance, at the exit and at the slowest defect bond in the bulk of the system. Specifically, we consider dynamics of asymmetric exclusion process with two identical defect bonds as a function of distance between them. Two approximate theoretical methods that treat the system as a sequence of segments with exact description of dynamics inside the segments and neglect correlations between them, are presented. In addition, a numerical iterative procedure for calculating dynamic properties of asymmetric exclusion systems is developed. Our theoretical predictions are compared with extensive Monte Carlo computer simulations. It is shown that correlations play an important role in the particle dynamics. When two defect bonds are far away from each other the strongest correlations are found at these bonds. However, bringing defect bonds closer leads to the shift of correlations to the region between them. Our analysis indicates that it is possible to develop a successful theoretical description of asymmetric exclusion processes with disorder by properly taking into account the correlations.
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34
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Dong JJ, Schmittmann B, Zia RKP. Inhomogeneous exclusion processes with extended objects: the effect of defect locations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:051113. [PMID: 18233629 DOI: 10.1103/physreve.76.051113] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/12/2007] [Indexed: 05/25/2023]
Abstract
We study the effects of local inhomogeneities, i.e., slow sites of hopping rate q<1, in a totally asymmetric simple exclusion process for particles of size l>or=1 (in units of the lattice spacing). We compare the simulation results of l=1 and l>1 and notice that the existence of local defects has qualitatively similar effects on the steady state. We focus on the stationary current as well as the density profiles. If there is only a single slow site in the system, we observe a significant dependence of the current on the location of the slow site for both l=1 and l>1 cases. When two slow sites are introduced, more intriguing phenomena emerge, e.g., dramatic decreases in the current when the two are close together. In addition, we study the asymptotic behavior when q-->0. We also explore the associated density profiles and compare our findings to an earlier study using a simple mean-field theory. We then outline the biological significance of these effects.
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Affiliation(s)
- J J Dong
- Center for Stochastic Processes in Science and Engineering, Department of Physics, Virginia Tech, Blacksburg, Virginia 24061-0435, USA.
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35
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Nowak SA, Fok PW, Chou T. Dynamic boundaries in asymmetric exclusion processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031135. [PMID: 17930227 DOI: 10.1103/physreve.76.031135] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2007] [Indexed: 05/25/2023]
Abstract
We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left-hand boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right-hand boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady-state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of nonequilibrium phases of the system, fluctuating boundary layers, and particle densities in the laboratory frame versus the frame of the fluctuating wall.
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Affiliation(s)
- Sarah A Nowak
- Department of Biomathematics, UCLA, Los Angeles, California 90095-1766, USA
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36
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Ebrahim Foulaadvand M, Chaaboki S, Saalehi M. Characteristics of the asymmetric simple exclusion process in the presence of quenched spatial disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011127. [PMID: 17358130 DOI: 10.1103/physreve.75.011127] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2006] [Revised: 11/10/2006] [Indexed: 05/14/2023]
Abstract
We investigate the effect of quenched spatial disordered hopping rates on the characteristics of the asymmetric simple exclusion process with open boundaries both numerically and by extensive simulations. Disorder averages of the bulk density and current are obtained in terms of various input and output rates. We study the binary and uniform distributions of disorder. It is verified that the effect of spatial inhomogeneity is generically to enlarge the size of the maximal-current phase. This is in accordance with the mean-field results obtained by Harris and Stinchcombe [Phys. Rev. E 70, 016108 (2004)]. Furthermore, we obtain the dependence of the current and the bulk density on the characteristics of the disorder distribution function. It is shown that the impact of disorder crucially depends on the particle input and out rates. In some situations, disorder can constructively enhance the current.
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37
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Lakatos G, O'Brien J, Chou T. Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/10/002] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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38
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Lakatos G, Chou T, Kolomeisky A. Steady-state properties of a totally asymmetric exclusion process with periodic structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:011103. [PMID: 15697576 DOI: 10.1103/physreve.71.011103] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2003] [Revised: 08/16/2004] [Indexed: 05/24/2023]
Abstract
We study the steady-state behavior of totally asymmetric simple exclusion processes (TASEPs) that contain periodically varying movement rates. In this model, particles move to the right at one of two rates: p(2) if the particle occupies one of a periodically arranged set of lattice sites; p(1) otherwise. Approximate mean field approaches are used to study the steady-state currents and bulk densities of this model. These mean field methods are found to provide results in good agreement with data derived from Monte Carlo simulations. Finally, the condition for particle-hole symmetry in the TASEP with periodically varying movement rates is specified, and the changes in the locations of the boundary-limited to maximal-current transition lines due to symmetry violation are investigated.
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Affiliation(s)
- Greg Lakatos
- Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada.
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39
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Klumpp S, Lipowsky R. Asymmetric simple exclusion processes with diffusive bottlenecks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066104. [PMID: 15697431 DOI: 10.1103/physreve.70.066104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2004] [Indexed: 05/24/2023]
Abstract
One-dimensional asymmetric simple exclusion processes (ASEPs) that are coupled to external reservoirs via diffusive transport are studied. These ASEPs consist of active compartments characterized by directed movements of the particles and diffusive compartments in which the particles undergo unbiased diffusion. Phase diagrams are obtained by a self-consistent mean field approach and by Monte Carlo simulations. The diffusive compartments act as diffusive bottlenecks if the velocity of the driven compartments or ASEPs is sufficiently large. A diffusive bottleneck at the boundary of the system leads to the absence of a maximal current phase, while a diffusive bottleneck in the interior of the system leads to a new phase characterized by different densities in the two active compartments adjacent to the diffusive one and to a maximal current defined by the bottleneck.
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Affiliation(s)
- Stefan Klumpp
- Max-Planck-Institut für Kolloid- und Grenzflächenforschung, 14424 Potsdam-Golm, Germany.
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40
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Chou T. Water alignment, dipolar interactions, and multiple proton occupancy during water-wire proton transport. Biophys J 2004; 86:2827-36. [PMID: 15111400 PMCID: PMC1304152 DOI: 10.1016/s0006-3495(04)74335-0] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
Abstract
A discrete multistate kinetic model for water-wire proton transport is constructed and analyzed using Monte Carlo simulations. In the model, each water molecule can be in one of three states: oxygen lone-pairs pointing leftward, pointing rightward, or protonated (H(3)O(+)). Specific rules for transitions among these states are defined as protons hop across successive water oxygens. Our model also includes water-channel interactions that preferentially align the water dipoles, nearest-neighbor dipolar coupling interactions, and Coulombic repulsion. Extensive Monte Carlo simulations were performed and the observed qualitative physical behaviors discussed. We find the parameters that allow the model to exhibit superlinear and sublinear current-voltage relationships, and show why alignment fields, whether generated by interactions with the pore interior or by membrane potentials, always decrease the proton current. The simulations also reveal a "lubrication" mechanism that suppresses water dipole interactions when the channel is multiply occupied by protons. This effect can account for an observed sublinear-to-superlinear transition in the current-voltage relationship.
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Affiliation(s)
- Tom Chou
- Department of Biomathematics and the Institute for Pure and Applied Mathematics, Los Angeles, California 90095-1766, USA.
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41
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Chou T, Lakatos G. Clustered bottlenecks in mRNA translation and protein synthesis. PHYSICAL REVIEW LETTERS 2004; 93:198101. [PMID: 15600884 DOI: 10.1103/physrevlett.93.198101] [Citation(s) in RCA: 88] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2003] [Indexed: 05/24/2023]
Abstract
Using a model based on the totally asymmetric exclusion process, we investigate the effects of slow codons along messenger RNA. Ribosome density profiles near neighboring clusters of slow codons interact, enhancing suppression of ribosome throughput when such bottlenecks are closely spaced. Increasing the slow codon cluster size beyond approximately 3-4 codons does not significantly reduce the ribosome current. Our results are verified by both extensive Monte Carlo simulations and numerical calculation, and provide a biologically motivated explanation for the experimentally observed clustering of low-usage codons.
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Affiliation(s)
- Tom Chou
- Department of Biomathematics, UCLA, Los Angeles, California 90095, USA
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42
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Parmeggiani A, Franosch T, Frey E. Totally asymmetric simple exclusion process with Langmuir kinetics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046101. [PMID: 15600454 DOI: 10.1103/physreve.70.046101] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2003] [Revised: 03/26/2004] [Indexed: 05/24/2023]
Abstract
We discuss a class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting nonconserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high and low density phases, two and three phase coexistence regions, and a boundary independent "Meissner" phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert W functions. It allows one to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.
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Affiliation(s)
- A Parmeggiani
- Hahn-Meitner Institut, Abteilung Theorie, Glienicker Strasse 100, D-14109 Berlin, Germany.
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43
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Shaw LB, Sethna JP, Lee KH. Mean-field approaches to the totally asymmetric exclusion process with quenched disorder and large particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:021901. [PMID: 15447509 DOI: 10.1103/physreve.70.021901] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2004] [Indexed: 05/24/2023]
Abstract
The process of protein synthesis in biological systems resembles a one-dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to quenched disorder in the particle hopping rates. We study the totally asymmetric exclusion process with large particles and quenched disorder via several mean-field approaches and compare the mean-field results with Monte Carlo simulations. Mean-field equations obtained from the literature are found to be reasonably effective in describing this system. A numerical technique is developed for computing the particle current rapidly. The mean-field approach is extended to include two-point correlations between adjacent sites. The two-point results are found to match Monte Carlo simulations more closely.
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Affiliation(s)
- Leah B Shaw
- Department of Physics, Cornell University, Ithaca, New York 14853-2501, USA.
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44
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Shaw LB, Kolomeisky AB, Lee KH. Local inhomogeneity in asymmetric simple exclusion processes with extended objects. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/6/010] [Citation(s) in RCA: 102] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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45
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Ha M, Timonen J, den Nijs M. Queuing transitions in the asymmetric simple exclusion process. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056122. [PMID: 14682861 DOI: 10.1103/physreve.68.056122] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2003] [Indexed: 05/24/2023]
Abstract
Stochastic driven flow along a channel can be modeled by the asymmetric simple exclusion process. We confirm numerically the presence of a dynamic queuing phase transition at a nonzero obstruction strength, and establish its scaling properties. Below the transition, the traffic jam is macroscopic in the sense that the length of the queue scales linearly with system size. Above the transition, only a power-law shaped queue remains. Its density profile scales as deltarho approximately x(-nu) with nu=1/3, and x is the distance from the obstacle. We construct a heuristic argument, indicating that the exponent nu=1/3 is universal and independent of the dynamic exponent of the underlying dynamic process. Fast bonds create only power-law shaped depletion queues, and with an exponent that could be equal to nu=2/3, but the numerical results yield consistently somewhat smaller values nu approximately 0.63(3). The implications of these results to faceting of growing interfaces and localization of directed polymers in random media, both in the presence of a columnar defect are pointed out as well.
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Affiliation(s)
- Meesoon Ha
- Department of Physics, University of Washington, P.O. Box 351560, Seattle, WA 98195-1560, USA
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46
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Myllys M, Maunuksela J, Merikoski J, Timonen J, Horváth VK, Ha M, den Nijs M. Effect of a columnar defect on the shape of slow-combustion fronts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:051103. [PMID: 14682784 DOI: 10.1103/physreve.68.051103] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2003] [Indexed: 05/24/2023]
Abstract
We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with enhanced or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for enhanced vs reduced driving in the defect clearly demonstrates the existence of a Kardar-Parisi-Zhang-type nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough enhanced driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a nonzero enhanced driving in agreement with the simulated behavior of the ASEP model.
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Affiliation(s)
- M Myllys
- Department of Physics, University of Jyväskylä, P.O. Box 35, Jyväskylä FIN-40014, Finland
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47
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Shaw LB, Zia RKP, Lee KH. Totally asymmetric exclusion process with extended objects: a model for protein synthesis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:021910. [PMID: 14525009 DOI: 10.1103/physreve.68.021910] [Citation(s) in RCA: 155] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2003] [Indexed: 05/23/2023]
Abstract
The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent, covering more than one lattice site. We expand the well studied totally asymmetric exclusion process, in which particles typically cover a single lattice site, to include cases with extended objects. Exact solutions can be determined for a uniform closed system. We analyze the uniform open system through two approaches. First, a continuum limit produces a modified diffusion equation for particle density profiles. Second, an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase. Finally, we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with Monte Carlo simulations.
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Affiliation(s)
- Leah B Shaw
- Department of Physics, Cornell University, Ithaca, New York 14853-2501, USA.
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48
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Abstract
We explore and quantify the physical and biochemical mechanisms that may be relevant in the regulation of translation. After elongation and detachment from the 3' termination site of mRNA, parts of the ribosome machinery can diffuse back to the initiation site, especially if it is held nearby, enhancing overall translation rates. The elongation steps of the mRNA-bound ribosomes are modeled using exact and asymptotic results of the totally asymmetric exclusion process. Since the ribosome injection rates of the totally asymmetric exclusion process depend on the local concentrations at the initiation site, a source of ribosomes emanating from the termination end can feed back to the initiation site, leading to a self-consistent set of equations for the steady-state ribosome throughput. Additional mRNA binding factors can also promote loop formation, or cyclization, bringing the initiation and termination sites into close proximity. The probability distribution of the distance between the initiation and termination sites is described using simple noninteracting polymer models. We find that the initiation, or initial ribosome adsorption binding required for maximal throughput, can vary dramatically depending on certain values of the bulk ribosome concentration and diffusion constant. If cooperative interactions among the loop-promoting proteins and the initiation/termination sites are considered, the throughput can be further regulated in a nonmonotonic manner. Experiments that can potentially test the hypothesized physical mechanisms are discussed.
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Affiliation(s)
- Tom Chou
- Department of Biomathematics, University of California at Los Angeles, Los Angeles, California 90095-1766, USA.
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49
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Parmeggiani A, Franosch T, Frey E. Phase coexistence in driven one-dimensional transport. PHYSICAL REVIEW LETTERS 2003; 90:086601. [PMID: 12633448 DOI: 10.1103/physrevlett.90.086601] [Citation(s) in RCA: 173] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2002] [Indexed: 05/24/2023]
Abstract
We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.
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Affiliation(s)
- A Parmeggiani
- Hahn-Meitner Institut, Abteilung Theorie, Glienicker Strasse 100, D-14109 Berlin, Germany
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50
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Fouladvand ME, Lee HW. Exactly solvable two-way traffic model with ordered sequential update. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:6465-79. [PMID: 11970562 DOI: 10.1103/physreve.60.6465] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/1999] [Indexed: 04/18/2023]
Abstract
Within the formalism of the matrix product ansatz, we study a two-species asymmetric exclusion process with backward and forward site-ordered sequential updates. This model, which was originally introduced with the random sequential update [J. Phys. A 30, 8497 (1997)], describes a two-way traffic flow with a dynamic impurity and shows a phase transition between the free flow and the traffic jam. We investigate characteristics of this jamming and examine similarities and differences between our results and those with a random sequential update.
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Affiliation(s)
- M E Fouladvand
- Department of Physics, Sharif University of Technology, P.O. Box 11365-9161, Tehran, Iran.
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