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Midha T, Kolomeisky AB, Igoshin OA. Insights into Error Control Mechanisms in Biological Processes: Copolymerization and Enzyme-Kinetics Revisited. J Phys Chem B 2024; 128:5612-5622. [PMID: 38814670 DOI: 10.1021/acs.jpcb.4c02173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
The high fidelity observed in biological information processing ranging from replication to translation has stimulated significant research efforts to clarify the underlying microscopic picture. Theoretically, several approaches to analyze the error rates have been proposed. The copolymerization theory describes the addition and removal of monomers at the growing tip of a copolymer, leading to a closed set of nonlinear equations. On the other hand, enzyme-kinetics approaches formulate linear equations of biochemical networks, describing transitions between discrete chemical states. However, it is still unclear whether the error values computed by the two approaches agree. Moreover, there are conflicting interpretations on whether the error is under thermodynamic or kinetic discrimination control. In this work, we examine the error rate in persistent copying biochemical processes by specifically analyzing both theoretical approaches. The initial disagreement of the results between the two theories motivated us to rederive the formula for the error rate in the kinetic model. The error computed with the new method resulted in excellent agreement between both theoretical approaches and with Monte Carlo simulations. Furthermore, our theoretical analysis shows that the kinetic discrimination controls the error, even when the energy difference between adding the right and wrong products is very small. Our theoretical investigation gives important insights into the physical-chemical properties of complex biological processes by providing the quantitative framework to evaluate them.
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Affiliation(s)
- Tripti Midha
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Anatoly B Kolomeisky
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Oleg A Igoshin
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Bioengineering, Rice University, Houston, Texas 77005, United States
- Department of Biosciences, Rice University, Houston, Texas 77005, United States
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2
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Qureshi B, Juritz J, Poulton JM, Beersing-Vasquez A, Ouldridge TE. A universal method for analyzing copolymer growth. J Chem Phys 2023; 158:104906. [PMID: 36922142 DOI: 10.1063/5.0133489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/12/2023] Open
Abstract
Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerization has been studied theoretically in a number of contexts, often by considering a Markov process in which monomers are added or removed from the growing tip of a long copolymer. To date, the analysis of the most general models of this class has necessitated simulation. We present a general method for analyzing such processes without resorting to simulation. Our method can be applied to models with an arbitrary network of sub-steps prior to addition or removal of a monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the approach allows for a dependency of addition and removal reactions on the neighboring site in the copolymer and thermodynamically self-consistent models in which all steps are assumed to be microscopically reversible. Using our approach, thermodynamic quantities such as chemical work; kinetic quantities such as time taken to grow; and statistical quantities such as the distribution of monomer types in the growing copolymer can be directly derived either analytically or numerically from the model definition.
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Affiliation(s)
- Benjamin Qureshi
- Department of Bioengineering and Centre for Synthetic Biology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Jordan Juritz
- Department of Bioengineering and Centre for Synthetic Biology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Jenny M Poulton
- Foundation for Fundamental Research on Matter (FOM), Institute for Atomic and Molecular Physics (AMOLF), 1098 XE Amsterdam, The Netherlands
| | | | - Thomas E Ouldridge
- Department of Bioengineering and Centre for Synthetic Biology, Imperial College London, London SW7 2AZ, United Kingdom
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3
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Juritz J, Poulton JM, Ouldridge TE. Minimal mechanism for cyclic templating of length-controlled copolymers under isothermal conditions. J Chem Phys 2022; 156:074103. [DOI: 10.1063/5.0077865] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jordan Juritz
- Department of Bioengineering and Centre for Synthetic Biology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Jenny M. Poulton
- Foundation for Fundamental Research on Matter (FOM), Institute for Atomic and Molecular Physics (AMOLF), 1098 XE Amsterdam, The Netherlands
| | - Thomas E. Ouldridge
- Department of Bioengineering and Centre for Synthetic Biology, Imperial College London, London SW7 2AZ, United Kingdom
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4
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A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers. Proc Natl Acad Sci U S A 2021; 118:2102881118. [PMID: 34518221 DOI: 10.1073/pnas.2102881118] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/22/2021] [Indexed: 12/18/2022] Open
Abstract
Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.
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5
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Duru JM, Pârvulescu OC, Dobre T, Răducanu CE. Stochastic modelling of cellulose hydrolysis with Gauss and Weibull distributed transition probabilities. Sci Rep 2021; 11:9466. [PMID: 33947888 PMCID: PMC8097066 DOI: 10.1038/s41598-021-88873-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2020] [Accepted: 04/12/2021] [Indexed: 11/09/2022] Open
Abstract
Two Markov-type stochastic models were developed to describe the kinetics of acid hydrolysis of cellulose. One of them involved a Gauss (normal) distribution of probabilities of chemical bond breaking, the other a Weibull distribution. It was considered that the random breaking of cellulose was based on the cleavage of a parent macromolecule into two descendants. Model equations and kinetics of acid hydrolysis of cellulose consisting of 10 and 100 units of cellobiose were presented. The effects of acid concentration and temperature on the kinetics of hydrolysis process were taken into account. The results obtained applying both stochastic models were in a reasonable agreement with those obtained using a deterministic kinetic model. These stochastic models can accurately describe the kinetics of acid hydrolysis and cover the drawbacks of some deterministic kinetic models, e.g., large number of model equations and parameters, modification of parameter values by changing the process conditions.
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Affiliation(s)
- Joseph Mcgreg Duru
- Chemical and Biochemical Engineering Department, University POLITEHNICA of Bucharest, 1-6 Gheorghe Polizu, 011061, Bucharest, Romania
| | - Oana Cristina Pârvulescu
- Chemical and Biochemical Engineering Department, University POLITEHNICA of Bucharest, 1-6 Gheorghe Polizu, 011061, Bucharest, Romania.
| | - Tănase Dobre
- Chemical and Biochemical Engineering Department, University POLITEHNICA of Bucharest, 1-6 Gheorghe Polizu, 011061, Bucharest, Romania
| | - Cristian Eugen Răducanu
- Chemical and Biochemical Engineering Department, University POLITEHNICA of Bucharest, 1-6 Gheorghe Polizu, 011061, Bucharest, Romania
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6
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Gaspard P. Template-directed growth of copolymers. CHAOS (WOODBURY, N.Y.) 2020; 30:043114. [PMID: 32357651 DOI: 10.1063/1.5145100] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
The theory of multistate template-directed reversible copolymerization is developed by extending the method based on iterated function systems to matrices, taking into account the possibility of multiple activation states instead of a single one for the growth process. In this extended theory, the mean growth velocity is obtained with an iterated matrix function system and the probabilities of copolymer sequences are given by matrix products defined along the template. The theory allows us to understand the effects of template heterogeneity, which include a fractal distribution of local growth velocities far enough from equilibrium, and a regime of sublinear growth in time close to equilibrium.
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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7
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Chiuchiù D, Ferrare J, Pigolotti S. Assembly of heteropolymers via a network of reaction coordinates. Phys Rev E 2019; 100:062502. [PMID: 31962425 DOI: 10.1103/physreve.100.062502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Indexed: 06/10/2023]
Abstract
In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.
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Affiliation(s)
- Davide Chiuchiù
- Biological Complexity Unit, Okinawa Institute for Science and Technology, 1919-1 Tancha, Onna, Kunigami-gun, Okinawa 904-0412, Japan
| | - James Ferrare
- Biological Complexity Unit, Okinawa Institute for Science and Technology, 1919-1 Tancha, Onna, Kunigami-gun, Okinawa 904-0412, Japan
- Tulane University, 6823 St. Charles Avenue, New Orleans, Lousiana 70118, USA
| | - Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute for Science and Technology, 1919-1 Tancha, Onna, Kunigami-gun, Okinawa 904-0412, Japan
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Chiuchiú D, Tu Y, Pigolotti S. Error-Speed Correlations in Biopolymer Synthesis. PHYSICAL REVIEW LETTERS 2019; 123:038101. [PMID: 31386470 PMCID: PMC7402413 DOI: 10.1103/physrevlett.123.038101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2019] [Indexed: 06/10/2023]
Abstract
Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical processes aided by enzymes. The performance of these enzymes is usually characterized in terms of their average error rate and speed. However, because of thermal fluctuations in these single-molecule processes, both error and speed are inherently stochastic quantities. In this Letter, we study fluctuations of error and speed in biopolymer synthesis and show that they are in general correlated. This means that, under equal conditions, polymers that are synthesized faster due to a fluctuation tend to have either better or worse errors than the average. The error-correction mechanism implemented by the enzyme determines which of the two cases holds. For example, discrimination in the forward reaction rates tends to grant smaller errors to polymers with faster synthesis. The opposite occurs for discrimination in monomer rejection rates. Our results provide an experimentally feasible way to identify error-correction mechanisms by measuring the error-speed correlations.
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Affiliation(s)
- Davide Chiuchiú
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Yuhai Tu
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Simone Pigolotti
- Biological Complexity Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
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9
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Li QS, Zheng PD, Shu YG, Ou-Yang ZC, Li M. Template-specific fidelity of DNA replication with high-order neighbor effects: A first-passage approach. Phys Rev E 2019; 100:012131. [PMID: 31499764 DOI: 10.1103/physreve.100.012131] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Indexed: 06/10/2023]
Abstract
DNA replication fidelity is a critical issue in molecular biology. Biochemical experiments have provided key insights on the mechanism of fidelity control by DNA polymerases in the past decades, whereas systematic theoretical studies on this issue began only recently. Because of the underlying difficulties of mathematical treatment, comprehensive surveys on the template-specific replication kinetics are still rare. Here we propose a first-passage approach to address this problem, in particular the positional fidelity, for complicated processes with high-order neighbor effects. Under biologically relevant conditions, we derived approximate analytical expressions of the positional fidelity which show intuitively how some key kinetic pathways are coordinated to guarantee the high fidelity, as well as the high velocity, of the replication processes. It is also shown that the fidelity at any template position is dominantly determined by the nearest-neighbor template sequences, which is consistent with the idea that replication mutations are randomly distributed in the genome.
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Affiliation(s)
- Qiu-Shi Li
- School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, People's Republic of China
| | - Pei-Dong Zheng
- School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, People's Republic of China
| | - Yao-Gen Shu
- Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, PO Box 2735, Beijing 100190, People's Republic of China
| | - Zhong-Can Ou-Yang
- Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, PO Box 2735, Beijing 100190, People's Republic of China
| | - Ming Li
- School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing 100049, People's Republic of China
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10
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Gaspard P. Multistate reversible copolymerization of non-Markovian chains under low conversion conditions. J Chem Phys 2019; 150:164903. [DOI: 10.1063/1.5088942] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U. L. B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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11
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Nonequilibrium correlations in minimal dynamical models of polymer copying. Proc Natl Acad Sci U S A 2019; 116:1946-1951. [PMID: 30659156 DOI: 10.1073/pnas.1808775116] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Living systems produce "persistent" copies of information-carrying polymers, in which template and copy sequences remain correlated after physically decoupling. We identify a general measure of the thermodynamic efficiency with which these nonequilibrium states are created and analyze the accuracy and efficiency of a family of dynamical models that produce persistent copies. For the weakest chemical driving, when polymer growth occurs in equilibrium, both the copy accuracy and, more surprisingly, the efficiency vanish. At higher driving strengths, accuracy and efficiency both increase, with efficiency showing one or more peaks at moderate driving. Correlations generated within the copy sequence, as well as between template and copy, store additional free energy in the copied polymer and limit the single-site accuracy for a given chemical work input. Our results provide insight into the design of natural self-replicating systems and can aid the design of synthetic replicators.
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12
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Blokhuis A, Lacoste D. Length and sequence relaxation of copolymers under recombination reactions. J Chem Phys 2018; 147:094905. [PMID: 28886641 DOI: 10.1063/1.5001021] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
We describe the kinetics and thermodynamics of copolymers undergoing recombination reactions, which are important for prebiotic chemistry. We use two approaches: the first one, based on chemical rate equations and the mass-action law describes the infinite size limit, while the second one, based on the chemical master equation, describes systems of finite size. We compare the predictions of both approaches for the relaxation of thermodynamic quantities towards equilibrium. We find that for some choice of initial conditions, the entropy of the sequence distribution can be lowered at the expense of increasing the entropy of the length distribution. We consider mainly energetically neutral reactions, except for one simple case of non-neutral reactions.
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Affiliation(s)
- Alex Blokhuis
- Gulliver Laboratory, UMR CNRS 7083, PSL Research University, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
| | - David Lacoste
- Gulliver Laboratory, UMR CNRS 7083, PSL Research University, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
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13
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14
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Szymanski R, Sosnowski S, Cypryk M. Steady State and Equilibrium in Reversible Copolymerization at Constant Comonomer Concentrations. MACROMOL THEOR SIMUL 2017. [DOI: 10.1002/mats.201700039] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- R. Szymanski
- Centre of Molecular and Macromolecular Studies; Polish Academy of Sciences; Sienkiewicza 112 90-363 Lodz Poland
| | - S. Sosnowski
- Centre of Molecular and Macromolecular Studies; Polish Academy of Sciences; Sienkiewicza 112 90-363 Lodz Poland
| | - M. Cypryk
- Centre of Molecular and Macromolecular Studies; Polish Academy of Sciences; Sienkiewicza 112 90-363 Lodz Poland
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15
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems; Université Libre de Bruxelles; Code Postal 231 Campus Plaine B-1050 Brussels Belgium
| | - David Andrieux
- Center for Nonlinear Phenomena and Complex Systems; Université Libre de Bruxelles; Code Postal 231 Campus Plaine B-1050 Brussels Belgium
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16
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Bogod I, Rahav S. Kinetic discrimination of a polymerase in the presence of obstacles. Phys Rev E 2017; 95:042408. [PMID: 28505806 DOI: 10.1103/physreve.95.042408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Indexed: 11/07/2022]
Abstract
One of the causes of high fidelity of copying in biological systems is kinetic discrimination. In this mechanism larger dissipation and copying velocity result in improved copying accuracy. We consider a model of a polymerase which simultaneously copies a single-stranded RNA and opens a single- to double-stranded junction serving as an obstacle. The presence of the obstacle slows down the motor, resulting in a change of its fidelity, which can be used to gain information about the motor and junction dynamics. We find that the motor's fidelity does not depend on details of the motor-junction interaction, such as whether the interaction is passive or active. Analysis of the copying fidelity can still be used as a tool for investigating the junction kinetics.
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Affiliation(s)
- Ilana Bogod
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Saar Rahav
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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17
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Ouldridge TE, Rein Ten Wolde P. Fundamental Costs in the Production and Destruction of Persistent Polymer Copies. PHYSICAL REVIEW LETTERS 2017; 118:158103. [PMID: 28452507 DOI: 10.1103/physrevlett.118.158103] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Indexed: 05/18/2023]
Abstract
Producing a polymer copy of a polymer template is central to biology, and effective copies must persist after template separation. We show that this separation has three fundamental thermodynamic effects. First, polymer-template interactions do not contribute to overall reaction thermodynamics and hence cannot drive the process. Second, the equilibrium state of the copied polymer is template independent and so additional work is required to provide specificity. Finally, the mixing of copies from distinct templates makes correlations between template and copy sequences unexploitable, combining with copying inaccuracy to reduce the free energy stored in a polymer ensemble. These basic principles set limits on the underlying costs and resource requirements, and suggest design principles, for autonomous copying and replication in biological and synthetic systems.
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Affiliation(s)
- Thomas E Ouldridge
- Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom
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18
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Song YS, Shu YG, Zhou X, Ou-Yang ZC, Li M. Proofreading of DNA polymerase: a new kinetic model with higher-order terminal effects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:025101. [PMID: 27842005 DOI: 10.1088/0953-8984/29/2/025101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The fidelity of DNA replication by DNA polymerase (DNAP) has long been an important issue in biology. While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP which consists of both a polymerase site and an exonuclease (proofreading) site, there were quite a few theoretical studies on the fidelity issue. The first model which explicitly considered both sites was proposed in the 1970s and the basic idea was widely accepted by later models. However, all these models did not systematically investigate the dominant factor on DNAP fidelity, i.e. the higher-order terminal effects through which the polymerization pathway and the proofreading pathway coordinate to achieve high fidelity. In this paper, we propose a new and comprehensive kinetic model of DNAP based on some recent experimental observations, which includes previous models as special cases. We present a rigorous and unified treatment of the corresponding steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs, which are in good agreements with previous intuitive estimates given by experimentalists.
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Affiliation(s)
- Yong-Shun Song
- School of Physical Sciences, University of Chinese Academy of Sciences, No 19A Yuquan Road, Beijing 100049, People's Republic of China
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19
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Gaspard P. Template-Directed Copolymerization, Random Walks along Disordered Tracks, and Fractals. PHYSICAL REVIEW LETTERS 2016; 117:238101. [PMID: 27982621 DOI: 10.1103/physrevlett.117.238101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2016] [Indexed: 06/06/2023]
Abstract
In biology, template-directed copolymerization is the fundamental mechanism responsible for the synthesis of DNA, RNA, and proteins. More than 50 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of information processing in DNA replication, transcription, and translation remain poorly understood. Challenging issues are the facts that DNA or RNA sequences constitute disordered media for the motion of polymerases or ribosomes while errors occur in copying the template. Here, it is shown that these issues can be addressed and sequence heterogeneity effects can be quantitatively understood within a framework revealing universal aspects of information processing at the molecular scale. In steady growth regimes, the local velocities of polymerases or ribosomes along the template are distributed as the continuous or fractal invariant set of a so-called iterated function system, which determines the copying error probabilities. The growth may become sublinear in time with a scaling exponent that can also be deduced from the iterated function system.
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université libre de Bruxelles (ULB), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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20
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Gaspard P. Kinetics and thermodynamics of living copolymerization processes. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2016; 374:rsta.2016.0147. [PMID: 27698043 PMCID: PMC5052731 DOI: 10.1098/rsta.2016.0147] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/01/2016] [Indexed: 05/06/2023]
Abstract
Theoretical advances are reported on the kinetics and thermodynamics of free and template-directed living copolymerizations. Until recently, the kinetic theory of these processes had only been established in the fully irreversible regime, in which the attachment rates are only considered. However, the entropy production is infinite in this regime and the approach to thermodynamic equilibrium cannot be investigated. For this purpose, the detachment rates should also be included. Inspite of this complication, the kinetics can be exactly solved in the regimes of steady growth and depolymerization. In this way, analytical expressions are obtained for the mean growth velocity, the statistical properties of the copolymer sequences, as well as the thermodynamic entropy production. The results apply to DNA replication, transcription and translation, allowing us to understand important aspects of molecular evolution.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, 1050 Brussels, Belgium
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21
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Gaspard P. Kinetics and thermodynamics of exonuclease-deficient DNA polymerases. Phys Rev E 2016; 93:042419. [PMID: 27176340 DOI: 10.1103/physreve.93.042419] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Indexed: 05/02/2023]
Abstract
A kinetic theory is developed for exonuclease-deficient DNA polymerases, based on the experimental observation that the rates depend not only on the newly incorporated nucleotide, but also on the previous one, leading to the growth of Markovian DNA sequences from a Bernoullian template. The dependencies on nucleotide concentrations and template sequence are explicitly taken into account. In this framework, the kinetic and thermodynamic properties of DNA replication, in particular, the mean growth velocity, the error probability, and the entropy production are calculated analytically in terms of the rate constants and the concentrations. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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22
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Gaspard P. Kinetics and thermodynamics of DNA polymerases with exonuclease proofreading. Phys Rev E 2016; 93:042420. [PMID: 27176341 DOI: 10.1103/physreve.93.042420] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Indexed: 05/02/2023]
Abstract
Kinetic theory and thermodynamics are applied to DNA polymerases with exonuclease activity, taking into account the dependence of the rates on the previously incorporated nucleotide. The replication fidelity is shown to increase significantly thanks to this dependence at the basis of the mechanism of exonuclease proofreading. In particular, this dependence can provide up to a 100-fold lowering of the error probability under physiological conditions. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.
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Affiliation(s)
- Pierre Gaspard
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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Szymanski R, Sosnowski S, Cypryk M. Evolution of Chain Microstructure and Kinetics of Reaching Equilibrium in Living Reversible Copolymerization. MACROMOL THEOR SIMUL 2016. [DOI: 10.1002/mats.201500047] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Ryszard Szymanski
- Center of Molecular and Macromolecular Studies; Sienkiewicza 112 Lodz 90-363 Poland
| | - Stanislaw Sosnowski
- Center of Molecular and Macromolecular Studies; Sienkiewicza 112 Lodz 90-363 Poland
| | - Marek Cypryk
- Center of Molecular and Macromolecular Studies; Sienkiewicza 112 Lodz 90-363 Poland
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Shu YG, Song YS, Ou-Yang ZC, Li M. A general theory of kinetics and thermodynamics of steady-state copolymerization. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:235105. [PMID: 25992648 DOI: 10.1088/0953-8984/27/23/235105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Kinetics of steady-state copolymerization has been investigated since the 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in the 1980s, a penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to solve analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in a unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.
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Affiliation(s)
- Yao-Gen Shu
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, PO Box 2735, Beijing 100190, People's Republic of China. School of Physics, University of Chinese Academy of Sciences, No 19A Yuquan Road, Beijing 100049, People's Republic of China
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