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Martinez-Corral R, Nam KM, DePace AH, Gunawardena J. The Hill function is the universal Hopfield barrier for sharpness of input-output responses. Proc Natl Acad Sci U S A 2024; 121:e2318329121. [PMID: 38787881 PMCID: PMC11145184 DOI: 10.1073/pnas.2318329121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 04/25/2024] [Indexed: 05/26/2024] Open
Abstract
The Hill functions, [Formula: see text], have been widely used in biology for over a century but, with the exception of [Formula: see text], they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, coregulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalizes most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, [Formula: see text], for any equilibrium model with [Formula: see text] input binding sites. [Formula: see text] exhibits a cusp which approaches, but never exceeds, the sharpness of [Formula: see text], but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers, and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, [Formula: see text], whose structure may be of mathematical interest, and suggest the importance of characterizing Hopfield barriers for other forms of cellular information processing.
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Affiliation(s)
| | - Kee-Myoung Nam
- Department of Systems Biology, Harvard Medical School, Boston, MA02115
| | - Angela H. DePace
- Department of Systems Biology, Harvard Medical School, Boston, MA02115
- HHMI, Boston, MA02115
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2
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Tsuruyama T. Harnessing Information Thermodynamics: Conversion of DNA Information into Mechanical Work in RNA Transcription and Nanopore Sequencing. ENTROPY (BASEL, SWITZERLAND) 2024; 26:324. [PMID: 38667878 PMCID: PMC11049638 DOI: 10.3390/e26040324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Revised: 04/04/2024] [Accepted: 04/08/2024] [Indexed: 04/28/2024]
Abstract
Recent advancements in information thermodynamics have revealed that information can be directly converted into mechanical work. Specifically, RNA transcription and nanopore sequencing serve as prime examples of this conversion, by reading information from a DNA template. This paper introduces an information thermodynamic model in which these molecular motors can move along the DNA template by converting the information read from the template DNA into their own motion. This process is a stochastic one, characterized by significant fluctuations in forward movement and is described by the Fokker-Planck equation, based on drift velocity and diffusion coefficients. In the current study, it is hypothesized that by utilizing the sequence information of the template DNA as mutual information, the fluctuations can be reduced, thereby biasing the forward movement on DNA and, consequently, reducing reading errors. Further research into the conversion of biological information by molecular motors could unveil new applications, insights, and important findings regarding the characteristics of information processing in biology.
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Affiliation(s)
- Tatsuaki Tsuruyama
- Department of Discovery Medicine, Graduate School of Medicine, Kyoto University, Kyoto 606-8501, Japan; ; Tel.: +81-75-366-7417
- Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
- Department of Clinical Laboratory, Graduate School of Health Sciences, Kyoto Tachibana University, Kyoto 607-8175, Japan
- Kitano Medical Institute, Kitano Hospita, Osaka 530-8480, Japan
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3
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Martinez-Corral R, Nam KM, DePace AH, Gunawardena J. The Hill function is the universal Hopfield barrier for sharpness of input-output responses. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.03.27.587054. [PMID: 38585761 PMCID: PMC10996692 DOI: 10.1101/2024.03.27.587054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/09/2024]
Abstract
The Hill functions, ℋ h ( x ) = x h / 1 + x h , have been widely used in biology for over a century but, with the exception of ℋ 1 , they have had no justification other than as a convenient fit to empirical data. Here, we show that they are the universal limit for the sharpness of any input-output response arising from a Markov process model at thermodynamic equilibrium. Models may represent arbitrary molecular complexity, with multiple ligands, internal states, conformations, co-regulators, etc, under core assumptions that are detailed in the paper. The model output may be any linear combination of steady-state probabilities, with components other than the chosen input ligand held constant. This formulation generalises most of the responses in the literature. We use a coarse-graining method in the graph-theoretic linear framework to show that two sharpness measures for input-output responses fall within an effectively bounded region of the positive quadrant, Ω m ⊂ ℝ + 2 , for any equilibrium model with m input binding sites. Ω m exhibits a cusp which approaches, but never exceeds, the sharpness of ℋ m but the region and the cusp can be exceeded when models are taken away from thermodynamic equilibrium. Such fundamental thermodynamic limits are called Hopfield barriers and our results provide a biophysical justification for the Hill functions as the universal Hopfield barriers for sharpness. Our results also introduce an object, Ω m , whose structure may be of mathematical interest, and suggest the importance of characterising Hopfield barriers for other forms of cellular information processing.
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Affiliation(s)
| | - Kee-Myoung Nam
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Angela H. DePace
- Howard Hughes Medical Institute, Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
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4
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Ryabov A, Tasinkevych M. Diffusion coefficient and power spectrum of active particles with a microscopically reversible mechanism of self-propelling. J Chem Phys 2022; 157:104108. [DOI: 10.1063/5.0101520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Catalytically active macromolecules are envisioned as key building blocks in development of artificial nanomotors. However, theory and experiments report conflicting findings regarding their dynamics. The lack of consensus is mostly caused by a limited understanding of specifics of self-propulsion mechanisms at the nanoscale. Here, we study a generic model of a self-propelled nanoparticle that does not rely on a particular mechanism. Instead, its main assumption is the fundamental symmetry of microscopic dynamics of chemical reactions: the principle of microscopic reversibility. Significant consequences of this assumption arise if we subject the particle to an action of an external time-periodic force. The particle diffusion coefficient is then enhanced compared to the unbiased dynamics. The enhancement can be controlled by the force amplitude and frequency. We also derive the power spectrum of particle trajectories. Among new effects stemming from the microscopic reversibility are the enhancement of the spectrum at all frequencies and sigmoid-shaped transitions and a peak at characteristic frequencies of rotational diffusion and external forcing. The microscopic reversibility is a generic property of a broad class of chemical reactions, therefore we expect that the presented results will motivate new experimental studies aimed at testing of our predictions. This could provide new insights into dynamics of catalytic macromolecules.
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Affiliation(s)
- Artem Ryabov
- Faculty of Mathematics and Physics, Department of Macromolecular Physics, Charles University, Czech Republic
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5
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Nam KM, Martinez-Corral R, Gunawardena J. The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems. Interface Focus 2022; 12:20220013. [PMID: 35860006 PMCID: PMC9184966 DOI: 10.1098/rsfs.2022.0013] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 04/25/2022] [Indexed: 12/25/2022] Open
Abstract
The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices represent biochemical species or molecular states, edges represent reactions or transitions and labels represent rates. The graph yields a linear dynamics for molecular concentrations or state probabilities, with the graph Laplacian as the operator, and the labels encode the nonlinear interactions between system and environment. The labels can be specified by vertices of other graphs or by conservation laws or, when the environment consists of thermodynamic reservoirs, they may be constants. In the latter case, the graphs correspond to infinitesimal generators of Markov processes. The key advantage of the framework has been that steady states are determined as rational algebraic functions of the labels by the Matrix-Tree theorems of graph theory. When the system is at thermodynamic equilibrium, this prescription recovers equilibrium statistical mechanics but it continues to hold for non-equilibrium steady states. The framework goes beyond other graph-based approaches in treating the graph as a mathematical object, for which general theorems can be formulated that accommodate biomolecular complexity. It has been particularly effective at analysing enzyme-catalysed modification systems and input-output responses.
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Affiliation(s)
- Kee-Myoung Nam
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
| | | | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
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6
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Albaugh A, Gingrich TR. Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics. Nat Commun 2022; 13:2204. [PMID: 35459863 PMCID: PMC9033874 DOI: 10.1038/s41467-022-29393-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 02/23/2022] [Indexed: 01/26/2023] Open
Abstract
Most computer simulations of molecular dynamics take place under equilibrium conditions-in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.
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Affiliation(s)
- Alex Albaugh
- grid.16753.360000 0001 2299 3507Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 USA
| | - Todd R. Gingrich
- grid.16753.360000 0001 2299 3507Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 USA
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7
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Nitschke W, Schoepp‐Cothenet B, Duval S, Zuchan K, Farr O, Baymann F, Panico F, Minguzzi A, Branscomb E, Russell MJ. Aqueous electrochemistry: The toolbox for life's emergence from redox disequilibria. ELECTROCHEMICAL SCIENCE ADVANCES 2022. [DOI: 10.1002/elsa.202100192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Affiliation(s)
| | | | - Simon Duval
- CNRS, BIP (UMR 7281), Aix Marseille Univ Marseille France
| | - Kilian Zuchan
- CNRS, BIP (UMR 7281), Aix Marseille Univ Marseille France
| | - Orion Farr
- CNRS, BIP (UMR 7281), Aix Marseille Univ Marseille France
- Aix Marseille Univ CINaM (UMR 7325) Luminy France
| | - Frauke Baymann
- CNRS, BIP (UMR 7281), Aix Marseille Univ Marseille France
| | - Francesco Panico
- Dipartimento di Chimica Università degli Studi di Milano Milan Italy
| | | | - Elbert Branscomb
- Department of Physics Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana Illinois USA
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8
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Speck T. Efficiency of isothermal active matter engines: Strong driving beats weak driving. Phys Rev E 2022; 105:L012601. [PMID: 35193264 DOI: 10.1103/physreve.105.l012601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
We study microscopic engines that use a single active particle as their "working medium." Part of the energy required to drive the directed motion of the particle can be recovered as work, even at a constant temperature. A wide class of synthetic active particles can be captured by schematically accounting for the chemical degrees of freedom that power the directed motion without having to resolve the exact microscopic mechanism. We derive analytical results for the quasistatic thermodynamic efficiency, i.e., the fraction of available chemical energy that can be recovered as mechanical work. While this efficiency is vanishingly small for colloidal particles, it increases as the dissipation is increased beyond the linear-response regime and goes through a maximum at large propulsion speeds. Our results demonstrate that driving beyond the linear-response regime has nontrivial consequences for the efficiency of active engines.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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9
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Saito T. Projection of strong coupling interaction with thermal bath in a polymer. Phys Rev E 2022; 105:014501. [PMID: 35193307 DOI: 10.1103/physreve.105.014501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 12/06/2021] [Indexed: 11/07/2022]
Abstract
We investigate modifications of a stochastic polymer picture through a shift in the boundary between the system and an external environment. A conventional bead-and-spring model serving as the coarse-graining model is given by the Langevin equation for all the monomers subject to white noise. However, stochastic motion for only a tagged monomer is observed to occur in the presence of colored noise. The qualitative change in the observations arises from the boundary shift decided by the observer. The Langevin dynamics analyses interpret the colored noise as the emergence of the polymeric elastic force, resulting in additional heat in the tagged monomer observation. Being distinguished from coarse-graining based on scale separation, the projection of comparable internal degrees of freedom is also discussed in light of the fluctuation theorem and the stochastic polymer thermodynamics.
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Affiliation(s)
- Takuya Saito
- Department of Physical Sciences, Aoyama Gakuin University, Chuo-ku, Sagamihara 252-5258, Japan
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10
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Speck T. Modeling of biomolecular machines in non-equilibrium steady states. J Chem Phys 2021; 155:230901. [PMID: 34937348 DOI: 10.1063/5.0070922] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium, such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with tens of thousands or even millions of degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared toward the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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11
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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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12
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DNA-Topology Simplification by Topoisomerases. Molecules 2021; 26:molecules26113375. [PMID: 34204901 PMCID: PMC8199745 DOI: 10.3390/molecules26113375] [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: 03/25/2021] [Revised: 05/20/2021] [Accepted: 05/26/2021] [Indexed: 11/17/2022] Open
Abstract
The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.
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13
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Dutta A, Schütz GM, Chowdhury D. Stochastic thermodynamics and modes of operation of a ribosome: A network theoretic perspective. Phys Rev E 2021; 101:032402. [PMID: 32289926 DOI: 10.1103/physreve.101.032402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 02/14/2020] [Indexed: 12/29/2022]
Abstract
The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as "translation" of the genetic message encoded in the sequence of mRNA transcript. In each successful chemomechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle, and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemomechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.
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Affiliation(s)
- Annwesha Dutta
- Department of Physics, Indian Institute of Technology, Kanpur 208016, India
| | - Gunter M Schütz
- Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany
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14
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Gaspard P. Stochastic approach to entropy production in chemical chaos. CHAOS (WOODBURY, N.Y.) 2020; 30:113103. [PMID: 33261359 DOI: 10.1063/5.0025350] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time average of the entropy production rate can be decomposed into the contributions of the cycles obtained from the stoichiometric matrix in both stochastic processes and deterministic systems. These methods are applied to a complex reaction network constructed on the basis of Rössler's reinjection principle and featuring chemical chaos.
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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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15
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Biddle JW, Gunawardena J. Reversal symmetries for cyclic paths away from thermodynamic equilibrium. Phys Rev E 2020; 101:062125. [PMID: 32688527 DOI: 10.1103/physreve.101.062125] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Accepted: 04/21/2020] [Indexed: 11/07/2022]
Abstract
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if expenditure of energy changes the rate of even a single transition to yield a nonequilibrium steady state, such time-reversal symmetry undergoes a widespread breakdown, far beyond the point at which the energy is expended. An explosion of interdependency also arises, with steady-state probabilities of system states depending in a complicated manner on the rate of every transition in the system. Nevertheless, in the midst of this global nonequilibrium complexity, we find that cyclic paths have reversibility properties that remain local, and which can exhibit symmetry, no matter how far the system is from thermodynamic equilibrium. Specifically, given any cycle of reversible transitions, the ratio of the frequencies with which the cycle occurs in one direction versus the other is determined, in the long-time limit, only by the thermodynamic force on the cycle itself, without requiring knowledge of transition rates elsewhere in the system. In particular, if there is no net energy expenditure on the cycle, then, over long times, the cycle occurrence frequencies are the same in either direction.
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Affiliation(s)
- John W Biddle
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States
| | - Jeremy Gunawardena
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States
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16
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Strasberg P, Esposito M. Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force. Phys Rev E 2020; 101:050101. [PMID: 32575212 DOI: 10.1103/physreve.101.050101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 04/22/2020] [Indexed: 11/07/2022]
Abstract
The nonequilibrium thermodynamics of an open (classical or quantum) system in strong contact with a single heat bath can be conveniently described in terms of the Hamiltonian of mean force. However, the conventional formulation is limited by the necessity to measure differences in equilibrium properties of the system-bath composite. We make use of the freedom involved in defining thermodynamic quantities, which leaves the thermodynamics unchanged, to show that the Hamiltonian of mean force can be inferred from measurements on the system alone, up to that irrelevant freedom. In doing so, we refute a key criticism expressed in the works by P. Talkner and P. Hänggi [Phys. Rev. E 94, 022143 (2016)10.1103/PhysRevE.94.022143 and arXiv:1911.11660]. We also discuss the remaining part of the criticism.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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17
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Abstract
In the 1930s, Lars Onsager published his famous 'reciprocal relations' describing free energy conversion processes. Importantly, these relations were derived on the assumption that the fluxes of the processes involved in the conversion were proportional to the forces (free energy gradients) driving them. For chemical reactions, however, this condition holds only for systems operating close to equilibrium-indeed very close; nominally requiring driving forces to be smaller than k B T. Fairly soon thereafter, however, it was quite inexplicably observed that in at least some biological conversions both the reciprocal relations and linear flux-force dependency appeared to be obeyed no matter how far from equilibrium the system was being driven. No successful explanation of how this 'paradoxical' behaviour could occur has emerged and it has remained a mystery. We here argue, however, that this anomalous behaviour is simply a gift of water, of its viscosity in particular; a gift, moreover, without which life almost certainly could not have emerged. And a gift whose appreciation we primarily owe to recent work by Prof. R. Dean Astumian who, as providence has kindly seen to it, was led to the relevant insights by the later work of Onsager himself.
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Affiliation(s)
- E. Branscomb
- Carl R. Woese Institute for Genomic Biology, and Department of Physics, University of Illinois, 3113 IGB MC 195, 128 W. Gregory Dr., Urbana, IL 61801, USA
| | - M. J. Russell
- NASA Astrobiology Institute, Ames Research Center, Mountain View, CA, USA
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18
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Astumian RD. Kinetic asymmetry allows macromolecular catalysts to drive an information ratchet. Nat Commun 2019; 10:3837. [PMID: 31444340 PMCID: PMC6707331 DOI: 10.1038/s41467-019-11402-7] [Citation(s) in RCA: 99] [Impact Index Per Article: 19.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2019] [Accepted: 07/11/2019] [Indexed: 11/09/2022] Open
Abstract
Molecular machines carry out their function by equilibrium mechanical motions in environments that are far from thermodynamic equilibrium. The mechanically equilibrated character of the trajectories of the macromolecule has allowed development of a powerful theoretical description, reminiscent of Onsager’s trajectory thermodynamics, that is based on the principle of microscopic reversibility. Unlike the situation at thermodynamic equilibrium, kinetic parameters play a dominant role in determining steady-state concentrations away from thermodynamic equilibrium, and kinetic asymmetry provides a mechanism by which chemical free-energy released by catalysis can drive directed motion, molecular adaptation, and self-assembly. Several examples drawn from the recent literature, including a catenane-based chemically driven molecular rotor and a synthetic molecular assembler or pump, are discussed. The mechanism by which macromolecular catalysts use energy from exergonic reactions to move, adapt, and assemble has been unclear. In this Perspective article, R. Dean Astumian shows that in addition to disequilibrium of the catalyzed reaction, kinetic asymmetry is the essential feature required to drive non-equilibrium response by an information ratchet mechanism.
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Affiliation(s)
- R Dean Astumian
- Department of Physics, University of Maine, Orono, ME, 04469-5709, USA.
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19
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Ziraldo R, Hanke A, Levene SD. Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA. Nucleic Acids Res 2019; 47:69-84. [PMID: 30476194 PMCID: PMC6326819 DOI: 10.1093/nar/gky1174] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Accepted: 11/02/2018] [Indexed: 11/13/2022] Open
Abstract
The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.
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Affiliation(s)
- Riccardo Ziraldo
- Department of Bioengineering, University of Texas at Dallas, TX 75080, USA
| | - Andreas Hanke
- Department of Physics and Astronomy, University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
| | - Stephen D Levene
- Department of Bioengineering, University of Texas at Dallas, TX 75080, USA.,Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA.,Department of Physics, University of Texas at Dallas, Richardson, TX 75080, USA
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20
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Ehrmann A, Nguyen B, Seifert U. Interlinked GTPase cascades provide a motif for both robust switches and oscillators. J R Soc Interface 2019; 16:20190198. [PMID: 31387482 DOI: 10.1098/rsif.2019.0198] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
GTPases regulate a wide range of cellular processes, such as intracellular vesicular transport, signal transduction and protein translation. These hydrolase enzymes operate as biochemical switches by toggling between an active guanosine triphosphate (GTP)-bound state and an inactive guanosine diphosphate (GDP)-bound state. We compare two network motifs, a single-species switch and an interlinked cascade that consists of two species coupled through positive and negative feedback loops. We find that interlinked cascades are closer to the ideal all-or-none switch and are more robust against fluctuating signals. While the single-species switch can only achieve bistability, interlinked cascades can be converted into oscillators by tuning the cofactor concentrations, which catalyse the activity of the cascade. These regimes can only be achieved with sufficient chemical driving provided by GTP hydrolysis. In this study, we present a thermodynamically consistent model that can achieve bistability and oscillations with the same feedback motif.
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Affiliation(s)
- Andreas Ehrmann
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Basile Nguyen
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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21
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Strasberg P, Winter A. Stochastic thermodynamics with arbitrary interventions. Phys Rev E 2019; 100:022135. [PMID: 31574732 DOI: 10.1103/physreve.100.022135] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2019] [Indexed: 06/10/2023]
Abstract
We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.g., feedback control operations) which are allowed to depend on the entire measurement record. For this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities-internal energy, heat, work, and entropy-along a single "trajectory" for a causal model. The first law at the trajectory level and the second law on average is verified. We highlight the special case of Bayesian or "bare" measurements (incomplete information, but no average disturbance) which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in Jarzynski-type experiments. An analysis of a recent Maxwell demon experiment using real-time feedback control is also given. As a mathematical tool, we prove a classical version of Stinespring's dilation theorem, which might be of independent interest.
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Affiliation(s)
- Philipp Strasberg
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Andreas Winter
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
- ICREA - Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010 Barcelona, Spain
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22
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Mechanisms for achieving high speed and efficiency in biomolecular machines. Proc Natl Acad Sci U S A 2019; 116:5902-5907. [PMID: 30850521 DOI: 10.1073/pnas.1812149116] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
How does a biomolecular machine achieve high speed at high efficiency? We explore optimization principles using a simple two-state dynamical model. With this model, we establish physical principles-such as the optimal way to distribute free-energy changes and barriers across the machine cycle-and connect them to biological mechanisms. We find that a machine can achieve high speed without sacrificing efficiency by varying its conformational free energy to directly link the downhill, chemical energy to the uphill, mechanical work and by splitting a large work step into more numerous, smaller substeps. Experimental evidence suggests that these mechanisms are commonly used by biomolecular machines. This model is useful for exploring questions of evolution and optimization in molecular machines.
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23
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Strasberg P, Esposito M. Non-Markovianity and negative entropy production rates. Phys Rev E 2019; 99:012120. [PMID: 30780330 DOI: 10.1103/physreve.99.012120] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Indexed: 11/07/2022]
Abstract
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.
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Affiliation(s)
- Philipp Strasberg
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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24
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Fischer A, Chatterjee A, Speck T. Aggregation and sedimentation of active Brownian particles at constant affinity. J Chem Phys 2019; 150:064910. [PMID: 30769983 DOI: 10.1063/1.5081115] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Andreas Fischer
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
- Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
| | - Arkya Chatterjee
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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25
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Rao R, Esposito M. Conservation laws and work fluctuation relations in chemical reaction networks. J Chem Phys 2018; 149:245101. [DOI: 10.1063/1.5042253] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Riccardo Rao
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, G.D. Luxembourg
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26
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Ariga T, Tomishige M, Mizuno D. Nonequilibrium Energetics of Molecular Motor Kinesin. PHYSICAL REVIEW LETTERS 2018; 121:218101. [PMID: 30517811 DOI: 10.1103/physrevlett.121.218101] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Revised: 07/18/2018] [Indexed: 06/09/2023]
Abstract
Nonequilibrium energetics of single molecule translational motor kinesin was investigated by measuring heat dissipation from the violation of the fluctuation-response relation of a probe attached to the motor using optical tweezers. The sum of the dissipation and work did not amount to the input free energy change, indicating large hidden dissipation exists. Possible sources of the hidden dissipation were explored by analyzing the Langevin dynamics of the probe, which incorporates the two-state Markov stepper as a kinesin model. We conclude that internal dissipation is dominant.
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Affiliation(s)
- Takayuki Ariga
- Graduate School of Medicine, Yamaguchi University, Yamaguchi 755-8505, Japan
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
| | - Michio Tomishige
- Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan
| | - Daisuke Mizuno
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
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27
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Tsuruyama T. Entropy in Cell Biology: Information Thermodynamics of a Binary Code and Szilard Engine Chain Model of Signal Transduction. ENTROPY 2018; 20:e20080617. [PMID: 33265706 PMCID: PMC7513144 DOI: 10.3390/e20080617] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/24/2018] [Revised: 08/06/2018] [Accepted: 08/13/2018] [Indexed: 11/16/2022]
Abstract
A model of signal transduction from the perspective of informational thermodynamics has been reported in recent studies, and several important achievements have been obtained. The first achievement is that signal transduction can be modelled as a binary code system, in which two forms of signalling molecules are utilised in individual steps. The second is that the average entropy production rate is consistent during the signal transduction cascade when the signal event number is maximised in the model. The third is that a Szilard engine can be a single-step model in the signal transduction. This article reviews these achievements and further introduces a new chain of Szilard engines as a biological reaction cascade (BRC) model. In conclusion, the presented model provides a way of computing the channel capacity of a BRC.
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Affiliation(s)
- Tatsuaki Tsuruyama
- Department of Discovery Medicine, Pathology Division, Graduate School of Medicine, Kyoto University, Yoshida-Konoe-cho, Sakyo-ku, Kyoto 606-8315, Japan
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28
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Information Thermodynamics of the Cell Signal Transduction as a Szilard Engine. ENTROPY 2018; 20:e20040224. [PMID: 33265315 PMCID: PMC7512737 DOI: 10.3390/e20040224] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Revised: 03/20/2018] [Accepted: 03/22/2018] [Indexed: 01/17/2023]
Abstract
A cell signaling system is in a non-equilibrium state, and it includes multistep biochemical signaling cascades (BSCs), which involve phosphorylation of signaling molecules, such as mitogen-activated protein kinase (MAPK) pathways. In this study, the author considered signal transduction description using information thermodynamic theory. The ideal BSCs can be considered one type of the Szilard engine, and the presumed feedback controller, Maxwell’s demon, can extract the work during signal transduction. In this model, the mutual entropy and chemical potential of the signal molecules can be redefined by the extracted chemical work in a mechanicochemical model, Szilard engine, of BSC. In conclusion, signal transduction is computable using the information thermodynamic method.
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29
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Ouldridge TE. The importance of thermodynamics for molecular systems, and the importance of molecular systems for thermodynamics. NATURAL COMPUTING 2018; 17:3-29. [PMID: 29576756 PMCID: PMC5856891 DOI: 10.1007/s11047-017-9646-x] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Improved understanding of molecular systems has only emphasised the sophistication of networks within the cell. Simultaneously, the advance of nucleic acid nanotechnology, a platform within which reactions can be exquisitely controlled, has made the development of artificial architectures and devices possible. Vital to this progress has been a solid foundation in the thermodynamics of molecular systems. In this pedagogical review and perspective, we discuss how thermodynamics determines both the overall potential of molecular networks, and the minute details of design. We then argue that, in turn, the need to understand molecular systems is helping to drive the development of theories of thermodynamics at the microscopic scale.
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Affiliation(s)
- Thomas E. Ouldridge
- Department of Bioengineering, Imperial College London, South Kensington Campus, London, SW7 2AZ UK
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30
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Nguyen B, Hartich D, Seifert U, Rios PDL. Thermodynamic Bounds on the Ultra- and Infra-affinity of Hsp70 for Its Substrates. Biophys J 2017; 113:362-370. [PMID: 28746847 DOI: 10.1016/j.bpj.2017.06.010] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2017] [Revised: 05/31/2017] [Accepted: 06/09/2017] [Indexed: 12/16/2022] Open
Abstract
The 70 kDa heat shock protein Hsp70 has several essential functions in living systems, such as protecting cells against protein aggregation, assisting protein folding, remodeling protein complexes, and driving translocation into organelles. These functions require high affinity for nonspecific amino acid sequences that are ubiquitous in proteins. It has been recently shown that this high affinity, called ultra-affinity, depends on a process driven out of equilibrium by ATP hydrolysis. Here, we establish the thermodynamic bounds for ultra-affinity, and further show that the same reaction scheme can in principle be used both to strengthen and to weaken affinities (leading in this case to infra-affinity). We show that cofactors are essential to achieve affinity beyond the equilibrium range. Finally, biological implications are discussed.
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Affiliation(s)
- Basile Nguyen
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany; Laboratory of Statistical Biophysics, Institute of Physics, School of Basic Science and Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
| | - David Hartich
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart, Germany
| | - Paolo De Los Rios
- Laboratory of Statistical Biophysics, Institute of Physics, School of Basic Science and Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
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31
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Strasberg P, Esposito M. Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining. Phys Rev E 2017; 95:062101. [PMID: 28709214 DOI: 10.1103/physreve.95.062101] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2017] [Indexed: 05/10/2023]
Abstract
We consider a classical and possibly driven composite system X⊗Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X⊗Y. This setup can be equivalently seen as a system X strongly coupled to a non-Markovian reservoir Y⊗R. We demonstrate that only in the limit where the dynamics of Y is much faster than X, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between X and its environment. Away from the limit where Y evolves much faster than X, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir.
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Affiliation(s)
- Philipp Strasberg
- Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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32
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Miller HJD, Anders J. Entropy production and time asymmetry in the presence of strong interactions. Phys Rev E 2017; 95:062123. [PMID: 28709224 DOI: 10.1103/physreve.95.062123] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2017] [Indexed: 06/07/2023]
Abstract
It is known that the equilibrium properties of open classical systems that are strongly coupled to a heat bath are described by a set of thermodynamic potentials related to the system's Hamiltonian of mean force. By adapting this framework to a more general class of nonequilibrium states, we show that the equilibrium properties of the bath can be well defined, even when the system is arbitrarily far from equilibrium and correlated with the bath. These states, which retain a notion of temperature, take the form of conditional equilibrium distributions. For out-of-equilibrium processes we show that the average entropy production quantifies the extent to which the system and bath state is driven away from the conditional equilibrium distribution. In addition, we show that the stochastic entropy production satisfies a generalized Crooks relation and can be used to quantify time asymmetry of correlated nonequilibrium processes. These results naturally extend the familiar properties of entropy production in weakly coupled systems to the strong coupling regime. Experimental measurements of the entropy production at strong coupling could be pursued using optomechanics or trapped-ion systems, which allow strong coupling to be engineered.
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Affiliation(s)
- H J D Miller
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, England, United Kingdom
| | - J Anders
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, England, United Kingdom
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33
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34
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Loutchko D, Eisbach M, Mikhailov AS. Stochastic thermodynamics of a chemical nanomachine: The channeling enzyme tryptophan synthase. J Chem Phys 2017; 146:025101. [DOI: 10.1063/1.4973544] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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35
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McGrath T, Jones NS, Ten Wolde PR, Ouldridge TE. Biochemical Machines for the Interconversion of Mutual Information and Work. PHYSICAL REVIEW LETTERS 2017; 118:028101. [PMID: 28128612 DOI: 10.1103/physrevlett.118.028101] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2016] [Indexed: 05/18/2023]
Abstract
We propose a physically realizable information-driven device consisting of an enzyme in a chemical bath, interacting with pairs of molecules prepared in correlated states. These correlations persist without direct interaction and thus store free energy equal to the mutual information. The enzyme can harness this free energy, and that stored in the individual molecular states, to do chemical work. Alternatively, the enzyme can use the chemical driving to create mutual information. A modified system can function without external intervention, approaching biological systems more closely.
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Affiliation(s)
- Thomas McGrath
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Nick S Jones
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | | | - Thomas E Ouldridge
- Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom
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36
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Altaner B, Polettini M, Esposito M. Fluctuation-Dissipation Relations Far from Equilibrium. PHYSICAL REVIEW LETTERS 2016; 117:180601. [PMID: 27835007 DOI: 10.1103/physrevlett.117.180601] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2016] [Indexed: 06/06/2023]
Abstract
Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current's spontaneous fluctuations with its response to perturbations of the conjugate thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects the microscopic transitions that contribute to the current. We discuss the physical requirements for the validity of our result and apply it to nanosized electronic devices.
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Affiliation(s)
- Bernhard Altaner
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Matteo Polettini
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg 1511, Luxembourg
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37
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Speck T. Thermodynamic formalism and linear response theory for nonequilibrium steady states. Phys Rev E 2016; 94:022131. [PMID: 27627270 DOI: 10.1103/physreve.94.022131] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2016] [Indexed: 11/07/2022]
Abstract
We study the linear response in systems driven away from thermal equilibrium into a nonequilibrium steady state with nonvanishing entropy production rate. A simple derivation of a general response formula is presented under the condition that the generating function describes a transformation that (to lowest order) preserves normalization and thus describes a physical stochastic process. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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38
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Chaudhuri D. Entropy production by active particles: Coupling of odd and even functions of velocity. Phys Rev E 2016; 94:032603. [PMID: 27739815 DOI: 10.1103/physreve.94.032603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2016] [Indexed: 06/06/2023]
Abstract
Nonequilibrium stochastic dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems. Numerical simulation is used to find probability distribution of entropy production, which shows good agreement with the detailed fluctuation theorem.
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Affiliation(s)
- Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India and Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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39
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Wei G, Xi W, Nussinov R, Ma B. Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell. Chem Rev 2016; 116:6516-51. [PMID: 26807783 PMCID: PMC6407618 DOI: 10.1021/acs.chemrev.5b00562] [Citation(s) in RCA: 253] [Impact Index Per Article: 31.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.
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Affiliation(s)
- Guanghong Wei
- State Key Laboratory of Surface Physics, Key Laboratory for Computational Physical Sciences (MOE), and Department of Physics, Fudan University, Shanghai, P. R. China
| | - Wenhui Xi
- State Key Laboratory of Surface Physics, Key Laboratory for Computational Physical Sciences (MOE), and Department of Physics, Fudan University, Shanghai, P. R. China
| | - Ruth Nussinov
- Basic Science Program, Leidos Biomedical Research, Inc. Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702, USA
- Sackler Inst. of Molecular Medicine Department of Human Genetics and Molecular Medicine Sackler School of Medicine, Tel Aviv University, Tel Aviv 69978, Israel
| | - Buyong Ma
- Basic Science Program, Leidos Biomedical Research, Inc. Cancer and Inflammation Program, National Cancer Institute, Frederick, Maryland 21702, USA
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40
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Wagoner JA, Dill KA. Molecular Motors: Power Strokes Outperform Brownian Ratchets. J Phys Chem B 2016; 120:6327-36. [DOI: 10.1021/acs.jpcb.6b02776] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Jason A. Wagoner
- Laufer
Center for Physical and Quantitative Biology, Stony Brook University, Stony
Brook, New York 11794, United States
| | - Ken A. Dill
- Laufer
Center for Physical and Quantitative Biology, and Departments of Physics
and Astronomy and Chemistry, Stony Brook University, Stony Brook, New York 11794, United States
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41
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Seifert U. First and Second Law of Thermodynamics at Strong Coupling. PHYSICAL REVIEW LETTERS 2016; 116:020601. [PMID: 26824534 DOI: 10.1103/physrevlett.116.020601] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2015] [Indexed: 06/05/2023]
Abstract
For a small driven system coupled strongly to a heat bath, internal energy and exchanged heat are identified such that they obey the usual additive form of the first law. By identifying this exchanged heat with the entropy change of the bath, the total entropy production is shown to obey an integral fluctuation theorem on the trajectory level implying the second law in the form of a Clausius inequalilty on the ensemble level. In this Hamiltonian approach, the assumption of an initially uncorrelated state is not required. The conditions under which the proposed identification of heat is unique and experimentally accessible are clarified.
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Affiliation(s)
- Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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42
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Horowitz JM. Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium. J Chem Phys 2015; 143:044111. [DOI: 10.1063/1.4927395] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jordan M. Horowitz
- Department of Physics, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA
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43
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Cao Y, Gong Z, Quan HT. Thermodynamics of information processing based on enzyme kinetics: An exactly solvable model of an information pump. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062117. [PMID: 26172671 DOI: 10.1103/physreve.91.062117] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2015] [Indexed: 06/04/2023]
Abstract
Motivated by the recent proposed models of the information engine [Proc. Natl. Acad. Sci. USA 109, 11641 (2012)] and the information refrigerator [Phys. Rev. Lett. 111, 030602 (2013)], we propose a minimal model of the information pump and the information eraser based on enzyme kinetics. This device can either pump molecules against the chemical potential gradient by consuming the information to be encoded in the bit stream or (partially) erase the information initially encoded in the bit stream by consuming the Gibbs free energy. The dynamics of this model is solved exactly, and the "phase diagram" of the operation regimes is determined. The efficiency and the power of the information machine is analyzed. The validity of the second law of thermodynamics within our model is clarified. Our model offers a simple paradigm for the investigating of the thermodynamics of information processing involving the chemical potential in small systems.
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Affiliation(s)
- Yuansheng Cao
- School of Physics, Peking University, Beijing 100871, China
| | - Zongping Gong
- School of Physics, Peking University, Beijing 100871, China
| | - H T Quan
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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44
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Esposito M, Parrondo JMR. Stochastic thermodynamics of hidden pumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052114. [PMID: 26066126 DOI: 10.1103/physreve.91.052114] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/04/2023]
Abstract
We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed.
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Affiliation(s)
- Massimiliano Esposito
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Juan M R Parrondo
- Departamento de Fisica Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
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45
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Zimmermann E, Seifert U. Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022709. [PMID: 25768533 DOI: 10.1103/physreve.91.022709] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
Many single-molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F(1)-ATPase and the kinesin motor.
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Affiliation(s)
- Eva Zimmermann
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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46
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Thomas DG, Jaramillo-Riveri S, Baxter DJ, Cannon WR. Comparison of Optimal Thermodynamic Models of the Tricarboxylic Acid Cycle from Heterotrophs, Cyanobacteria, and Green Sulfur Bacteria. J Phys Chem B 2014; 118:14745-60. [PMID: 25495377 DOI: 10.1021/jp5075913] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We have applied a new stochastic simulation approach to predict the metabolite levels, material flux, and thermodynamic profiles of the oxidative TCA cycles found in E. coli and Synechococcus sp. PCC 7002, and in the reductive TCA cycle typical of chemolithoautotrophs and phototrophic green sulfur bacteria such as Chlorobaculum tepidum. The simulation approach is based on modeling states using statistical thermodynamics and employs an assumption similar to that used in transition state theory. The ability to evaluate the thermodynamics of metabolic pathways allows one to understand the relationship between coupling of energy and material gradients in the environment and the self-organization of stable biological systems, and it is shown that each cycle operates in the direction expected due to its environmental niche. The simulations predict changes in metabolite levels and flux in response to changes in cofactor concentrations that would be hard to predict without an elaborate model based on the law of mass action. In fact, we show that a thermodynamically unfavorable reaction can still have flux in the forward direction when it is part of a reaction network. The ability to predict metabolite levels, energy flow, and material flux should be significant for understanding the dynamics of natural systems and for understanding principles for engineering organisms for production of specialty chemicals.
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Affiliation(s)
- Dennis G Thomas
- Knowledge Discovery and Informatics Group, National Security Directorate, ‡Computational Biology and Bioinformatics Group, Fundamental and Computational Sciences Directorate, and §Molecular Sciences Computing Division, Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , Richland, Washington 99352, United States
| | - Sebastian Jaramillo-Riveri
- Knowledge Discovery and Informatics Group, National Security Directorate, ‡Computational Biology and Bioinformatics Group, Fundamental and Computational Sciences Directorate, and §Molecular Sciences Computing Division, Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , Richland, Washington 99352, United States
| | - Douglas J Baxter
- Knowledge Discovery and Informatics Group, National Security Directorate, ‡Computational Biology and Bioinformatics Group, Fundamental and Computational Sciences Directorate, and §Molecular Sciences Computing Division, Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , Richland, Washington 99352, United States
| | - William R Cannon
- Knowledge Discovery and Informatics Group, National Security Directorate, ‡Computational Biology and Bioinformatics Group, Fundamental and Computational Sciences Directorate, and §Molecular Sciences Computing Division, Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory , Richland, Washington 99352, United States
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47
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Barato AC, Seifert U. Stochastic thermodynamics with information reservoirs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042150. [PMID: 25375481 DOI: 10.1103/physreve.90.042150] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Indexed: 05/10/2023]
Abstract
We generalize stochastic thermodynamics to include information reservoirs. Such information reservoirs, which can be modeled as a sequence of bits, modify the second law. For example, work extraction from a system in contact with a single heat bath becomes possible if the system also interacts with an information reservoir. We obtain an inequality, and the corresponding fluctuation theorem, generalizing the standard entropy production of stochastic thermodynamics. From this inequality we can derive an information processing entropy production, which gives the second law in the presence of information reservoirs. We also develop a systematic linear response theory for information processing machines. For a unicyclic machine powered by an information reservoir, the efficiency at maximum power can deviate from the standard value of 1/2. For the case where energy is consumed to erase the tape, the efficiency at maximum erasure rate is found to be 1/2.
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Affiliation(s)
- Andre C Barato
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
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48
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Wu W, Wang J. Potential and flux field landscape theory. II. Non-equilibrium thermodynamics of spatially inhomogeneous stochastic dynamical systems. J Chem Phys 2014; 141:105104. [DOI: 10.1063/1.4894389] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- Wei Wu
- Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794, USA
| | - Jin Wang
- Department of Physics and Astronomy and Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794, USA
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun, China
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49
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Chaudhuri D. Active Brownian particles: entropy production and fluctuation response. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022131. [PMID: 25215712 DOI: 10.1103/physreve.90.022131] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2014] [Indexed: 06/03/2023]
Abstract
Within the Rayleigh-Helmholtz model of active Brownian particles, activity is due to a nonlinear velocity-dependent force. In the presence of external trapping potential or constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey fluctuation theorems for entropy production. Using the simulation, we further show that the steady-state response function obeys a modified fluctuation-dissipation relation.
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Affiliation(s)
- Debasish Chaudhuri
- Indian Institute of Technology Hyderabad, Yeddumailaram 502205, Andhra Pradesh, India
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50
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Golubeva N, Imparato A. Efficiency at maximum power of motor traffic on networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062118. [PMID: 25019736 DOI: 10.1103/physreve.89.062118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2014] [Indexed: 06/03/2023]
Abstract
We study motor traffic on Bethe networks subject to hard-core exclusion for both tightly coupled one-state machines and loosely coupled two-state machines that perform work against a constant load. In both cases we find an interaction-induced enhancement of the efficiency at maximum power (EMP) as compared to noninteracting motors. The EMP enhancement occurs for a wide range of network and single-motor parameters and is due to a change in the characteristic load-velocity relation caused by phase transitions in the system. Using a quantitative measure of the trade-off between the EMP enhancement and the corresponding loss in the maximum output power we identify parameter regimes where motor traffic systems operate efficiently at maximum power without a significant decrease in the maximum power output due to jamming effects.
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Affiliation(s)
- N Golubeva
- Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, Building 1520, DK-8000 Aarhus C, Denmark
| | - A Imparato
- Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, Building 1520, DK-8000 Aarhus C, Denmark
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