1
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Degünther J, van der Meer J, Seifert U. General theory for localizing the where and when of entropy production meets single-molecule experiments. Proc Natl Acad Sci U S A 2024; 121:e2405371121. [PMID: 39121164 DOI: 10.1073/pnas.2405371121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 07/11/2024] [Indexed: 08/11/2024] Open
Abstract
The laws of thermodynamics apply to biophysical systems on the nanoscale as described by the framework of stochastic thermodynamics. This theory provides universal, exact relations for quantities like work, which have been verified in experiments where a fully resolved description allows direct access to such quantities. Complementary studies consider partially hidden, coarse-grained descriptions, in which the mean entropy production typically is not directly accessible but can be bounded in terms of observable quantities. Going beyond the mean, we introduce a fluctuating entropy production that applies to individual trajectories in a coarse-grained description under time-dependent driving. Thus, this concept is applicable to the broad and experimentally significant class of driven systems in which not all relevant states can be resolved. We provide a paradigmatic example by studying an experimentally verified protein unfolding process. As a consequence, the entire distribution of the coarse-grained entropy production rather than merely its mean retains spatial and temporal information about the microscopic process. In particular, we obtain a bound on the distribution of the physical entropy production of individual unfolding events.
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Affiliation(s)
- Julius Degünther
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart 70550, Germany
| | - Jann van der Meer
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart 70550, Germany
| | - Udo Seifert
- II. Institut für Theoretische Physik, Universität Stuttgart, Stuttgart 70550, Germany
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2
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Yasuda K. Irreversibility of stochastic state transitions in Langevin systems with odd elasticity. Phys Rev E 2024; 109:064116. [PMID: 39020984 DOI: 10.1103/physreve.109.064116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2023] [Accepted: 05/13/2024] [Indexed: 07/20/2024]
Abstract
Active microscopic objects, such as an enzyme molecule, are modeled by the Langevin system with the odd elasticity, in which energy injection from the substrate to the enzyme is described by the antisymmetric part of the elastic matrix. By applying the Onsager-Machlup integral and large deviation theory to the Langevin system with odd elasticity, we can calculate the cumulant generating function of the irreversibility of the state transition. For an N-component system, we obtain a formal expression of the cumulant generating function and demonstrate that the oddness λ, which quantifies the antisymmetric part of the elastic matrix, leads to higher-order cumulants that do not appear in a passive elastic system. To demonstrate the effect of the oddness under the concrete parameter, we analyze the simplest two-component system and obtain the optimal transition path and cumulant generating function. The cumulants obtained from expansion of the cumulant generating function increase monotonically with the oddness. This implies that the oddness causes the uncertainty of stochastic state transitions.
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3
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Grelier M, Sivak DA, Ehrich J. Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor. Phys Rev E 2024; 109:034115. [PMID: 38632770 DOI: 10.1103/physreve.109.034115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 01/30/2024] [Indexed: 04/19/2024]
Abstract
Molecular motors fulfill critical functions within all living beings. Understanding their underlying working principles is therefore of great interest. Here we develop a simple model inspired by the two-component biomolecular motor F_{o}-F_{1} ATP synthase. We analyze its energetics and characterize information flows between the machine's components. At maximum output power we find that information transduction plays a minor role for free-energy transduction. However, when the two components are coupled to different environments (e.g., when in contact with heat baths at different temperatures), we show that information flow becomes a resource worth exploiting to maximize free-energy transduction. Our findings suggest that real-world powerful and efficient information engines could be found in machines whose components are subjected to fluctuations of different strength, since in this situation the benefit gained from using information for work extraction can outweigh the costs of information generation.
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Affiliation(s)
- Mathis Grelier
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
- PULS Group, Department of Physics, FAU Erlangen-Nürnberg, IZNF, 91058 Erlangen, Germany
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
| | - Jannik Ehrich
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
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4
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Kasuga K, Yoshimori A. Nonintegral form of the reciprocal relation associated with violation of the fluctuation response relation. Phys Rev E 2023; 108:034109. [PMID: 37849163 DOI: 10.1103/physreve.108.034109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 08/15/2023] [Indexed: 10/19/2023]
Abstract
We extend Onsager's reciprocal relation to systems in a nonequilibrium steady state. While Onsager's reciprocal relation concerns the kinetic (Onsager) coefficient, the extended reciprocal relation concerns violation of the fluctuation response relation (FRR) for mechanical and thermal perturbations. This extended relation holds at each frequency when the extent of the FRR violation is expressed in a frequency domain. This nonintegral form distinguishes the extended relation from previous relations expressed by integration over a frequency. To obtain this relation, we consider one-particle one-dimensional systems described by an overdamped Langevin equation with a force driving the system away from equilibrium. We assume a special property of the potential in the system. From this Langevin equation, we obtain the Fokker-Planck (FP) equation describing the time evolution of the distribution function of the particle. Using the FP equation, we calculate the responses of the particle velocity and heat current by applying time-dependent perturbations of the driving force and temperature. We express the extent of the FRR violation in terms of these responses with time correlation functions and expand them in powers of the FP operator. This reciprocal relation is valid far from equilibrium. One can also confirm this reciprocal relation through experiments with systems such as colloidal suspensions because the FRR violation can be experimentally observed.
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Affiliation(s)
- Kotaro Kasuga
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
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5
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Watanabe RR, Kiper BT, Zarco-Zavala M, Hara M, Kobayashi R, Ueno H, García-Trejo JJ, Li CB, Noji H. Rotary properties of hybrid F 1-ATPases consisting of subunits from different species. iScience 2023; 26:106626. [PMID: 37192978 PMCID: PMC10182284 DOI: 10.1016/j.isci.2023.106626] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Revised: 02/14/2023] [Accepted: 04/03/2023] [Indexed: 05/18/2023] Open
Abstract
F1-ATPase (F1) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of FoF1-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and β, F1 shows diversity in the maximum catalytic turnover rate Vmax and the number of rotary steps per turn. To study the design principle of F1, we prepared eight hybrid F1s composed of subunits from two of three genuine F1s: thermophilic Bacillus PS3 (TF1), bovine mitochondria (bMF1), and Paracoccus denitrificans (PdF1), differing in the Vmax and the number of rotary steps. The Vmax of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of β and the couplings between α-β. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.
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Affiliation(s)
- Ryo R. Watanabe
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Busra Tas Kiper
- Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
| | - Mariel Zarco-Zavala
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Mayu Hara
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Ryohei Kobayashi
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - Hiroshi Ueno
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
| | - José J. García-Trejo
- Department of Biology, Chemistry Faculty, National Autonomous University of Mexico, Mexico 04510, Mexico
| | - Chun-Biu Li
- Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
- Corresponding author
| | - Hiroyuki Noji
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan
- Corresponding author
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6
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Minoguchi M, Sasa SI. Divergent Stiffness of One-Dimensional Growing Interfaces. PHYSICAL REVIEW LETTERS 2023; 130:197101. [PMID: 37243631 DOI: 10.1103/physrevlett.130.197101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 01/12/2023] [Accepted: 04/13/2023] [Indexed: 05/29/2023]
Abstract
When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness.
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Affiliation(s)
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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7
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Leighton MP, Sivak DA. Inferring Subsystem Efficiencies in Bipartite Molecular Machines. PHYSICAL REVIEW LETTERS 2023; 130:178401. [PMID: 37172234 DOI: 10.1103/physrevlett.130.178401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2022] [Accepted: 03/20/2023] [Indexed: 05/14/2023]
Abstract
Molecular machines composed of coupled subsystems transduce free energy between different external reservoirs, in the process internally transducing energy and information. While subsystem efficiencies of these molecular machines have been measured in isolation, less is known about how they behave in their natural setting when coupled together and acting in concert. Here, we derive upper and lower bounds on the subsystem efficiencies of a bipartite molecular machine. We demonstrate their utility by estimating the efficiencies of the F_{o} and F_{1} subunits of ATP synthase and that of kinesin pulling a diffusive cargo.
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Affiliation(s)
- Matthew P Leighton
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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8
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Ertel B, van der Meer J, Seifert U. Waiting Time Distributions in Hybrid Models of Motor-Bead Assays: A Concept and Tool for Inference. Int J Mol Sci 2023; 24:ijms24087610. [PMID: 37108771 PMCID: PMC10145242 DOI: 10.3390/ijms24087610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 04/12/2023] [Accepted: 04/17/2023] [Indexed: 04/29/2023] Open
Abstract
In single-molecule experiments, the dynamics of molecular motors are often observed indirectly by measuring the trajectory of an attached bead in a motor-bead assay. In this work, we propose a method to extract the step size and stalling force for a molecular motor without relying on external control parameters. We discuss this method for a generic hybrid model that describes bead and motor via continuous and discrete degrees of freedom, respectively. Our deductions are solely based on the observation of waiting times and transition statistics of the observable bead trajectory. Thus, the method is non-invasive, operationally accessible in experiments and can, in principle, be applied to any model describing the dynamics of molecular motors. We briefly discuss the relation of our results to recent advances in stochastic thermodynamics on inference from observable transitions. Our results are confirmed by extensive numerical simulations for parameters values of an experimentally realized F1-ATPase assay.
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Affiliation(s)
- Benjamin Ertel
- II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany
| | - Jann van der Meer
- 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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9
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Foster PJ, Bae J, Lemma B, Zheng J, Ireland W, Chandrakar P, Boros R, Dogic Z, Needleman DJ, Vlassak JJ. Dissipation and energy propagation across scales in an active cytoskeletal material. Proc Natl Acad Sci U S A 2023; 120:e2207662120. [PMID: 37000847 PMCID: PMC10083585 DOI: 10.1073/pnas.2207662120] [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: 05/09/2022] [Accepted: 02/22/2023] [Indexed: 04/03/2023] Open
Abstract
Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.
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Affiliation(s)
- Peter J. Foster
- Physics of Living Systems, Department of Physics, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Physics, Brandeis University, Waltham, MA02454
| | - Jinhye Bae
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
- Department of NanoEngineering, University of California San Diego, La Jolla, CA92093
| | - Bezia Lemma
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, Harvard University, Cambridge, MA02138
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Juanjuan Zheng
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
| | - William Ireland
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
| | - Pooja Chandrakar
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Rémi Boros
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA02454
- Department of Physics, University of California, Santa Barbara, CA93106
| | - Daniel J. Needleman
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
- Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA02138
- Center for Computational Biology, Flatiron Institute, New York, NY10010
| | - Joost J. Vlassak
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA02138
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10
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Riccardi M, Martin OJF. Electromagnetic Forces and Torques: From Dielectrophoresis to Optical Tweezers. Chem Rev 2023; 123:1680-1711. [PMID: 36719985 PMCID: PMC9951227 DOI: 10.1021/acs.chemrev.2c00576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2022] [Indexed: 02/02/2023]
Abstract
Electromagnetic forces and torques enable many key technologies, including optical tweezers or dielectrophoresis. Interestingly, both techniques rely on the same physical process: the interaction of an oscillating electric field with a particle of matter. This work provides a unified framework to understand this interaction both when considering fields oscillating at low frequencies─dielectrophoresis─and high frequencies─optical tweezers. We draw useful parallels between these two techniques, discuss the different and often unstated assumptions they are based upon, and illustrate key applications in the fields of physical and analytical chemistry, biosensing, and colloidal science.
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Affiliation(s)
- Marco Riccardi
- Nanophotonics and Metrology Laboratory, Swiss Federal Institute of Technology Lausanne (EPFL), EPFL-STI-NAM, Station 11, CH-1015Lausanne, Switzerland
| | - Olivier J. F. Martin
- Nanophotonics and Metrology Laboratory, Swiss Federal Institute of Technology Lausanne (EPFL), EPFL-STI-NAM, Station 11, CH-1015Lausanne, Switzerland
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11
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Takahashi K, Nakamura T, Akutagawa T. Dynamic supramolecular cations in conductive and magnetic [Ni(dmit)2] crystals. Coord Chem Rev 2023. [DOI: 10.1016/j.ccr.2022.214881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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12
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Rassolov G, Tociu L, Fodor E, Vaikuntanathan S. From predicting to learning dissipation from pair correlations of active liquids. J Chem Phys 2022; 157:054901. [DOI: 10.1063/5.0097863] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. Towards designing such materials, an important challenge is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on these challenges. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations which, unlike most existing approaches, is applicable even for strongly interacting particles and far from equilibrium, to predict dissipation in these systems. Based on this theory, we reveal analytically a robust relation between dissipation and structure which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out-of-equilibrium.
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Affiliation(s)
| | - Laura Tociu
- The University of Chicago, United States of America
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13
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Amano S, Esposito M, Kreidt E, Leigh DA, Penocchio E, Roberts BMW. Insights from an information thermodynamics analysis of a synthetic molecular motor. Nat Chem 2022; 14:530-537. [PMID: 35301472 DOI: 10.1038/s41557-022-00899-z] [Citation(s) in RCA: 38] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Accepted: 01/28/2022] [Indexed: 12/11/2022]
Abstract
Information is physical, a realization that has transformed the physics of measurement and communication. However, the flow between information, energy and mechanics in chemical systems remains largely unexplored. Here we analyse a minimalist autonomous chemically driven molecular motor in terms of information thermodynamics, a framework that quantitatively relates information to other thermodynamic parameters. The treatment reveals how directional motion is generated by free energy transfer from chemical to mechanical (conformational and/or co-conformational) processes by 'energy flow' and 'information flow'. It provides a thermodynamic level of understanding of molecular motors that is general, complements previous analyses based on kinetics and has practical implications for machine design. In line with kinetic analysis, we find that power strokes do not affect the directionality of chemically driven machines. However, we find that power strokes can modulate motor velocity, the efficiency of free energy transfer and the number of fuel molecules consumed per cycle. This may help explain the role of such (co-)conformational changes in biomachines and illustrates the interplay between energy and information in chemical systems.
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Affiliation(s)
- Shuntaro Amano
- Department of Chemistry, University of Manchester, Manchester, UK
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City, Luxembourg
| | - Elisabeth Kreidt
- Department of Chemistry, University of Manchester, Manchester, UK
| | - David A Leigh
- Department of Chemistry, University of Manchester, Manchester, UK.
| | - Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City, Luxembourg.
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14
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Gradziuk G, Torregrosa G, Broedersz CP. Irreversibility in linear systems with colored noise. Phys Rev E 2022; 105:024118. [PMID: 35291095 DOI: 10.1103/physreve.105.024118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 02/01/2022] [Indexed: 06/14/2023]
Abstract
Time irreversibility is a distinctive feature of nonequilibrium dynamics and several measures of irreversibility have been introduced to assess the distance from thermal equilibrium of a stochastically driven system. While the dynamical noise is often approximated as white, in many real applications the time correlations of the random forces can actually be significantly long-lived compared to the relaxation times of the driven system. We analyze the effects of temporal correlations in the noise on commonly used measures of irreversibility and demonstrate how the theoretical framework for white-noise-driven systems naturally generalizes to the case of colored noise. Specifically, we express the autocorrelation function, the area enclosing rates, and mean phase space velocity in terms of solutions of a Lyapunov equation and in terms of their white-noise limit values.
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Affiliation(s)
- Grzegorz Gradziuk
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Gabriel Torregrosa
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
| | - Chase P Broedersz
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany and Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081 HV Amsterdam, The Netherlands
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15
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Gao Q, Chun HM, Horowitz JM. Thermodynamic constraints on the nonequilibrium response of one-dimensional diffusions. Phys Rev E 2022; 105:L012102. [PMID: 35193184 DOI: 10.1103/physreve.105.l012102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 12/21/2021] [Indexed: 11/07/2022]
Abstract
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.
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Affiliation(s)
- Qi Gao
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hyun-Myung Chun
- Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Jordan M Horowitz
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Department of Biophysics, University of Michigan, Ann Arbor, Michigan 48109, USA.,Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48104, USA
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16
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Yasuda K, Komura S. Nonreciprocality of a micromachine driven by a catalytic chemical reaction. Phys Rev E 2021; 103:062113. [PMID: 34271630 DOI: 10.1103/physreve.103.062113] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Accepted: 04/20/2021] [Indexed: 11/06/2022]
Abstract
We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechanochemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechanochemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical timescales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called "nonreciprocality" and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two timescales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.
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Affiliation(s)
- Kento Yasuda
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan
| | - Shigeyuki Komura
- Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University, Tokyo 192-0397, Japan
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17
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Physical bioenergetics: Energy fluxes, budgets, and constraints in cells. Proc Natl Acad Sci U S A 2021; 118:2026786118. [PMID: 34140336 DOI: 10.1073/pnas.2026786118] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.
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18
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Nakayama Y, Toyabe S. Optimal Rectification without Forward-Current Suppression by Biological Molecular Motor. PHYSICAL REVIEW LETTERS 2021; 126:208101. [PMID: 34110213 DOI: 10.1103/physrevlett.126.208101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 04/23/2021] [Indexed: 06/12/2023]
Abstract
We experimentally show that biological molecular motor F_{1}-ATPase (F_{1}) implements an optimal rectification mechanism. The rectification mechanism hardly suppresses the synthesis of adenosine triphosphate by F_{1}, which is F_{1}'s physiological role, while inhibiting the unfavorable hydrolysis of adenosine triphosphate. This optimal rectification contrasts highly with that of a simple ratchet model, where the inhibition of the backward current is inevitably accompanied by the suppression of the forward current. Our detailed analysis of single-molecule trajectories demonstrates a novel but simple rectification mechanism of F_{1} with parallel landscapes and asymmetric transition rates.
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Affiliation(s)
- Yohei Nakayama
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba 6-6-05, Sendai 980-8579, Japan
| | - Shoichi Toyabe
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Aoba 6-6-05, Sendai 980-8579, Japan
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19
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Large SJ, Ehrich J, Sivak DA. Free-energy transduction within autonomous systems. Phys Rev E 2021; 103:022140. [PMID: 33735999 DOI: 10.1103/physreve.103.022140] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Accepted: 02/04/2021] [Indexed: 11/07/2022]
Abstract
The excess work required to drive a stochastic system out of thermodynamic equilibrium through a time-dependent external perturbation is directly related to the amount of entropy produced during the driving process, allowing excess work and entropy production to be used interchangeably to quantify dissipation. Given the common intuition of biological molecular machines as internally communicating work between components, it is tempting to extend this correspondence to the driving of one component of an autonomous system by another; however, no such relation between the internal excess work and entropy production exists. Here we introduce the "transduced additional free-energy rate" between strongly coupled subsystems of an autonomous system, which is analogous to the excess power in systems driven by an external control parameter that receives no feedback from the system. We prove that this is a relevant measure of dissipation-in that it equals the steady-state entropy production rate due to the downstream subsystem-and demonstrate its advantages with a simple model system.
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Affiliation(s)
- Steven J Large
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
| | - Jannik Ehrich
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, BC, V5A 1S6 Canada
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20
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Keta YE, Fodor É, van Wijland F, Cates ME, Jack RL. Collective motion in large deviations of active particles. Phys Rev E 2021; 103:022603. [PMID: 33736055 DOI: 10.1103/physreve.103.022603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
We analyze collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyze the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.
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Affiliation(s)
- Yann-Edwin Keta
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
- Département de Physique, École normale supérieure de Lyon, 69364 Lyon Cedex 07, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Frédéric van Wijland
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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21
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Hou R, Wang Z. Thermodynamic marking of F OF 1 ATP synthase. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2021; 1862:148369. [PMID: 33454313 DOI: 10.1016/j.bbabio.2021.148369] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Received: 08/07/2020] [Revised: 12/02/2020] [Accepted: 01/05/2021] [Indexed: 11/29/2022]
Abstract
FOF1 ATP synthase is a ~100% efficient molecular machine for energy conversion in biology, and holds great lessons for man-made energy technology and nanotechnology. In light of formidable biocomplexity of the FOF1 machinery, its modeling from pure physical principles remains difficult and rare. Here we construct a thermodynamic model of FOF1 from experimentally accessible quantities plus a single entropy production that generally has vanishingly small values (<1kB). Based on the physical inputs, this model captures FOF1 performance observed over an exhaustively wide range of proton-motive force and nucleotide concentrations. The model predicts a distinct 1/8kBT slope for ATP synthesis rate versus proton-motive force, which is verified by experimental data and represents a profound thermodynamic marking of this amazingly efficient machine operating near a universal limit of the 2nd law of thermodynamics. The model further predicts two symmetries of heat productions, which are testable by available experimental techniques and offer quantitative constraints on FOF1's possible mechanisms behind its ~100% efficiency.
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Affiliation(s)
- Ruizheng Hou
- Department of Applied Physics, School of Science, Xi'an University of Technology, Xi'an, Shaan Xi 710048, China.
| | - Zhisong Wang
- Department of Physics and NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117542, Singapore
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22
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Koyuk T, Seifert U. Thermodynamic Uncertainty Relation for Time-Dependent Driving. PHYSICAL REVIEW LETTERS 2020; 125:260604. [PMID: 33449796 DOI: 10.1103/physrevlett.125.260604] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Accepted: 12/09/2020] [Indexed: 05/10/2023]
Abstract
Thermodynamic uncertainty relations yield a lower bound on entropy production in terms of the mean and fluctuations of a current. We derive their general form for systems under arbitrary time-dependent driving from arbitrary initial states and extend these relations beyond currents to state variables. The quality of the bound is discussed for various types of observables for an interacting pair of colloidal particles in a moving laser trap and for the dynamical unfolding of a small protein. Since the input for evaluating these bounds does not require specific knowledge of the system or its coupling to the time-dependent control, they should become widely applicable tools for thermodynamic inference in time-dependently driven systems.
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Affiliation(s)
- Timur Koyuk
- 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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23
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Otsubo S, Ito S, Dechant A, Sagawa T. Estimating entropy production by machine learning of short-time fluctuating currents. Phys Rev E 2020; 101:062106. [PMID: 32688599 DOI: 10.1103/physreve.101.062106] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 05/05/2020] [Indexed: 11/07/2022]
Abstract
Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the stochastic dynamics, it would be promising to apply the TURs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics. Here we investigate a theoretical framework for estimation of the entropy production rate using the TURs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics. Specifically, we derive a TUR for the short-time region and prove that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen. This formulation naturally includes a generalization of the TURs with the partial entropy production of subsystems under autonomous interaction, which reveals the hierarchical structure of the estimation. We then construct estimators on the basis of the short-time TUR and machine learning techniques such as the gradient ascent. By performing numerical experiments, we demonstrate that our learning protocol performs well even in nonlinear Langevin dynamics. We also discuss the case of Markov jump processes, where the exact estimation is shown to be impossible in general. Our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium, including biological systems.
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Affiliation(s)
- Shun Otsubo
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
| | - Sosuke Ito
- Universal Biology Institute, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0031, Japan.,JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
| | - Andreas Dechant
- WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan
| | - Takahiro Sagawa
- Department of Applied Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
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24
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Okazaki KI, Nakamura A, Iino R. Chemical-State-Dependent Free Energy Profile from Single-Molecule Trajectories of Biomolecular Motors: Application to Processive Chitinase. J Phys Chem B 2020; 124:6475-6487. [DOI: 10.1021/acs.jpcb.0c02698] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Affiliation(s)
- Kei-ichi Okazaki
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, 444-8585, Japan
| | - Akihiko Nakamura
- Department of Life and Coordination-Complex Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, 444-8787, Japan
- Department of Applied Life Sciences, Faculty of Agriculture, Shizuoka University, Shizuoka, 422-8529, Japan
| | - Ryota Iino
- Department of Life and Coordination-Complex Molecular Science, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki, 444-8787, Japan
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25
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Lathouwers E, Lucero JNE, Sivak DA. Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors. J Phys Chem Lett 2020; 11:5273-5278. [PMID: 32501698 DOI: 10.1021/acs.jpclett.0c01055] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Living systems at the molecular scale are composed of many constituents with strong and heterogeneous interactions, operating far from equilibrium, and subject to strong fluctuations. These conditions pose significant challenges to efficient, precise, and rapid free energy transduction, yet nature has evolved numerous molecular machines that do just this. Using a simple model of the ingenious rotary machine FoF1-ATP synthase, we investigate the interplay between nonequilibrium driving forces, thermal fluctuations, and interactions between strongly coupled subsystems. This model reveals design principles for effective free energy transduction. Most notably, while tight coupling is intuitively appealing, we find that output power is maximized at intermediate-strength coupling, which permits lubrication by stochastic fluctuations with only minimal slippage.
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Affiliation(s)
- Emma Lathouwers
- Department of Physics, Simon Fraser University, Burnaby, BC V5A1S6 Canada
| | - Joseph N E Lucero
- Department of Physics, Simon Fraser University, Burnaby, BC V5A1S6 Canada
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, BC V5A1S6 Canada
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26
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Fritz JH, Nguyen B, Seifert U. Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator. J Chem Phys 2020; 152:235101. [PMID: 32571070 DOI: 10.1063/5.0006115] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Biomolecular processes are typically modeled using chemical reaction networks coupled to infinitely large chemical reservoirs. A difference in chemical potential between these reservoirs can drive the system into a non-equilibrium steady-state (NESS). In reality, these processes take place in finite systems containing a finite number of molecules. In such systems, a NESS can be reached with the help of an externally driven pump for which we introduce a simple model. The crucial parameters are the pumping rate and the finite size of the chemical reservoir. We apply this model to a simple biochemical oscillator, the Brusselator, and quantify the performance using the number of coherent oscillations. As a surprising result, we find that higher precision can be achieved with finite-size reservoirs even though the corresponding current fluctuations are larger than in the ideal infinite case.
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Affiliation(s)
- Jonas H Fritz
- 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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27
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Tanaka M, Kawakami T, Okaniwa T, Nakayama Y, Toyabe S, Ueno H, Muneyuki E. Tight Chemomechanical Coupling of the F 1 Motor Relies on Structural Stability. Biophys J 2020; 119:48-54. [PMID: 32531205 DOI: 10.1016/j.bpj.2020.04.039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2019] [Revised: 03/31/2020] [Accepted: 04/06/2020] [Indexed: 11/19/2022] Open
Abstract
The F1 motor is a rotating molecular motor that ensures a tight chemomechanical coupling between ATP hydrolysis/synthesis reactions and rotation steps. However, the mechanism underlying this tight coupling remains to be elucidated. In this study, we used electrorotation in single-molecule experiments using an F1βE190D mutant to demonstrate that the stall torque was significantly smaller than the wild-type F1, indicating a loose coupling of this mutant, despite showing similar stepping torque as the wild-type. Experiments on the ATPase activity after heat treatment and gel filtration of the α3β3-subcomplex revealed the unstable structure of the βE190D mutant. Our results suggest that the tight chemomechanical coupling of the F1 motor relies on the structural stability of F1. We also discuss the difference between the stepping torque and the stall torque.
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Affiliation(s)
- Mana Tanaka
- Department of Physics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan
| | - Tomohiro Kawakami
- Department of Physics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan
| | - Tomoaki Okaniwa
- Department of Physics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan
| | - Yohei Nakayama
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Shoichi Toyabe
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Hiroshi Ueno
- Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan.
| | - Eiro Muneyuki
- Department of Physics, Faculty of Science and Engineering, Chuo University, Tokyo, Japan.
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28
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Ariga T, Tomishige M, Mizuno D. Experimental and theoretical energetics of walking molecular motors under fluctuating environments. Biophys Rev 2020; 12:503-510. [PMID: 32173796 DOI: 10.1007/s12551-020-00684-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Accepted: 03/02/2020] [Indexed: 01/10/2023] Open
Abstract
Molecular motors are nonequilibrium open systems that convert chemical energy to mechanical work. Their energetics are essential for various dynamic processes in cells, but largely remain unknown because fluctuations typically arising in small systems prevent investigation of the nonequilibrium behavior of the motors in terms of thermodynamics. Recently, Harada and Sasa proposed a novel equality to measure the dissipation of nonequilibrium small systems. By utilizing this equality, we have investigated the nonequilibrium energetics of the single-molecule walking motor kinesin-1. The dissipation from kinesin movement was measured through the motion of an attached probe particle and its response to external forces, indicating that large hidden dissipation exists. In this short review, aiming to readers who are not familiar with nonequilibrium physics, we briefly introduce the theoretical basis of the dissipation measurement as well as our recent experimental results and mathematical model analysis and discuss the physiological implications of the hidden dissipation in kinesin. In addition, further perspectives on the efficiency of motors are added by considering their actual working environment: living cells.
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Affiliation(s)
- Takayuki Ariga
- Graduate School of Medicine, Yamaguchi University, Ube, Japan.
| | - Michio Tomishige
- Department of Physics and Mathematics, Aoyama Gakuin University, Sagamihara, Japan
| | - Daisuke Mizuno
- Department of Physics, Kyushu University, Fukuoka, Japan
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29
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Efficiencies of molecular motors: a comprehensible overview. Biophys Rev 2020; 12:419-423. [PMID: 32170586 DOI: 10.1007/s12551-020-00672-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 02/27/2020] [Indexed: 12/17/2022] Open
Abstract
Many biological molecular motors can operate specifically and robustly at the highly fluctuating nano-scale. How these molecules achieve such remarkable functions is an intriguing question that requires various notions and quantifications of efficiency associated with the operations and energy transduction of these nano-machines. Here we give a short review of some important concepts of motor efficiencies, including the thermodynamic, Stokes, and generalized and transport efficiencies, as well as some implications provided by the thermodynamic uncertainty relations recently developed in nonequilibrium physics.
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30
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Structural basis for power stroke vs. Brownian ratchet mechanisms of motor proteins. Proc Natl Acad Sci U S A 2019; 116:19777-19785. [PMID: 31506355 DOI: 10.1073/pnas.1818589116] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F1-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism.
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31
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Nishizaka T, Masaike T, Nakane D. Insights into the mechanism of ATP-driven rotary motors from direct torque measurement. Biophys Rev 2019; 11:653-657. [PMID: 31321734 DOI: 10.1007/s12551-019-00564-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2019] [Accepted: 06/20/2019] [Indexed: 11/29/2022] Open
Abstract
Motor proteins are molecular machines that convert chemical energy into mechanical work. In addition to existing studies performed on the linear motors found in eukaryotic cells, researchers in biophysics have also focused on rotary motors such as F1-ATPase. Detailed studies on the rotary F1-ATPase motor have correlated all chemical states to specific mechanical events at the single-molecule level. Recent studies showed that there exists another ATP-driven protein motor in life: the rotary machinery that rotates archaeal flagella (archaella). Rotation speed, stepwise movement, and variable directionality of the motor of Halobacterium salinarum were described in previous studies. Here we review recent experimental work discerning the molecular mechanism underlying how the archaellar motor protein FlaI drives rotation by generation of motor torque. In combination, those studies found that rotation slows as the viscous drag of markers increases, but torque remains constant at 160 pN·nm independent of rotation speed. Unexpectedly, the estimated work done in a single rotation is twice the expected energy that would come from hydrolysis of six ATP molecules in the FlaI hexamer. To reconcile the apparent contradiction, a new and general model for the mechanism of ATP-driven rotary motors is discussed.
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Affiliation(s)
- Takayuki Nishizaka
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-8588, Japan.
| | - Tomoko Masaike
- Department of Applied Biological Science, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda City, Chiba, 278-8510, Japan
| | - Daisuke Nakane
- Department of Physics, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo, 171-8588, Japan
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32
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Wang Z, Hou R, Loh IY. Track-walking molecular motors: a new generation beyond bridge-burning designs. NANOSCALE 2019; 11:9240-9263. [PMID: 31062798 DOI: 10.1039/c9nr00033j] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Track-walking molecular motors are the core bottom-up mechanism for nanometre-resolved translational movements - a fundamental technological capability at the root of numerous applications ranging from nanoscale assembly lines and chemical synthesis to molecular robots and shape-changing materials. Over the last 10 years, artificial molecular walkers (or nanowalkers) have evolved from the 1st generation of bridge-burning designs to the 2nd generation capable of truly sustainable movements. Invention of non-bridge-burning nanowalkers was slow at first, but has picked up speed since 2012, and is now close to breaking major barriers for wide-spread development. Here we review the 2nd generation of artificial nanowalkers, which are mostly made of DNA molecules and draw energy from light illumination or from chemical fuels for entirely autonomous operation. They are typically symmetric dimeric motors walking on entirely periodic tracks, yet the motors possess an inherent direction for large-scale amplification of the action of many motor copies. These translational motors encompass the function of rotational molecular motors on circular or linear tracks, and may involve molecular shuttles as 'engine' motifs. Some rules of thumb are provided to help readers design similar motors from DNA or other molecular building blocks. Opportunities and challenges for future development are discussed, especially in the areas of molecular robotics and active materials based on the advanced motors.
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Affiliation(s)
- Zhisong Wang
- Department of Physics, National University of Singapore, Singapore 117542, Singapore.
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33
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Sumi T, Klumpp S. Is F 1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip. NANO LETTERS 2019; 19:3370-3378. [PMID: 31017791 DOI: 10.1021/acs.nanolett.9b01181] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We present a chemomechanical network model of the rotary molecular motor F1-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F1-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.
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Affiliation(s)
| | - Stefan Klumpp
- Institute for the Dynamics of Complex Systems , University of Göttingen , Friedrich-Hund-Platz 1 , 37077 Göttingen , Germany
- Department Theory and Bio-Systems , Max Planck Institute of Colloids and Interfaces , 14424 Potsdam , Germany
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34
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Evaluation of the Duty Ratio of the Bacterial Flagellar Motor by Dynamic Load Control. Biophys J 2019; 116:1952-1959. [PMID: 31053259 DOI: 10.1016/j.bpj.2019.04.004] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2018] [Revised: 03/29/2019] [Accepted: 04/05/2019] [Indexed: 01/01/2023] Open
Abstract
The bacterial flagellar motor is one of the most complex and sophisticated nanomachineries in nature. A duty ratio D is a fraction of time that the stator and the rotor interact and is a fundamental property to characterize the motor but remains to be determined. It is known that the stator units of the motor bind to and dissociate from the motor dynamically to control the motor torque depending on the load on the motor. At low load, at which the kinetics such as proton translocation speed limits the rotation rate, the dependency of the rotation rate on the number of stator units N implies D: the dependency becomes larger for smaller D. Contradicting observations supporting both the small and large D have been reported. A dilemma is that it is difficult to explore a broad range of N at low load because the stator units easily dissociate, and N is limited to one or two at vanishing load. Here, we develop an electrorotation method to dynamically control the load on the flagellar motor of Salmonella with a calibrated magnitude of the torque. By instantly reducing the load for keeping N high, we observed that the speed at low load depends on N, implying a small duty ratio. We recovered the torque-speed curves of individual motors and evaluated the duty ratio to be 0.14 ± 0.04 from the correlation between the torque at high load and the rotation rate at low load.
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35
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Fodor É, Mehandia V, Comelles J, Thiagarajan R, Gov NS, Visco P, van Wijland F, Riveline D. Spatial Fluctuations at Vertices of Epithelial Layers: Quantification of Regulation by Rho Pathway. Biophys J 2019; 114:939-946. [PMID: 29490253 DOI: 10.1016/j.bpj.2017.12.026] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2017] [Revised: 12/19/2017] [Accepted: 12/20/2017] [Indexed: 01/14/2023] Open
Abstract
In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin, and cross-linkers. Such an approach deliberately avoids consideration of the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway, which is composed of multiple layers of coupled activators and inhibitors. Here, we investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, and the persistence time and length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.
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Affiliation(s)
- Étienne Fodor
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom; Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, Paris cedex 13, France
| | - Vishwajeet Mehandia
- Laboratory of Cell Physics, ISIS/IGBMC, Université de Strasbourg and CNRS (UMR 7006), Strasbourg, France; Development and Stem Cells Program, IGBMC, CNRS (UMR 7104), INSERM (U964), Université de Strasbourg, Illkirch, France; School of Mechanical, Materials and Energy Engineering, Indian Institute of Technology, Ropar, India
| | - Jordi Comelles
- Laboratory of Cell Physics, ISIS/IGBMC, Université de Strasbourg and CNRS (UMR 7006), Strasbourg, France; Development and Stem Cells Program, IGBMC, CNRS (UMR 7104), INSERM (U964), Université de Strasbourg, Illkirch, France
| | - Raghavan Thiagarajan
- Laboratory of Cell Physics, ISIS/IGBMC, Université de Strasbourg and CNRS (UMR 7006), Strasbourg, France; Development and Stem Cells Program, IGBMC, CNRS (UMR 7104), INSERM (U964), Université de Strasbourg, Illkirch, France
| | - Nir S Gov
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Paolo Visco
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, Paris cedex 13, France
| | - Frédéric van Wijland
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, Paris cedex 13, France
| | - Daniel Riveline
- Laboratory of Cell Physics, ISIS/IGBMC, Université de Strasbourg and CNRS (UMR 7006), Strasbourg, France; Development and Stem Cells Program, IGBMC, CNRS (UMR 7104), INSERM (U964), Université de Strasbourg, Illkirch, France.
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36
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Nemoto T, Fodor É, Cates ME, Jack RL, Tailleur J. Optimizing active work: Dynamical phase transitions, collective motion, and jamming. Phys Rev E 2019; 99:022605. [PMID: 30934223 DOI: 10.1103/physreve.99.022605] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Indexed: 06/09/2023]
Abstract
Active work measures how far the local self-forcing of active particles translates into real motion. Using population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes.
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Affiliation(s)
- Takahiro Nemoto
- Philippe Meyer Institute for Theoretical Physics, Physics Department, École Normale Supérieure & PSL Research University, 24 rue Lhomond, 75231 Paris Cedex 05, France
| | - Étienne Fodor
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Michael E Cates
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert L Jack
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Julien Tailleur
- Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS/P7, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France
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37
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Wang Z. Generic maps of optimality reveal two chemomechanical coupling regimes for motor proteins: from F 1-ATPase and kinesin to myosin and cytoplasmic dynein. Integr Biol (Camb) 2019; 10:34-47. [PMID: 29296987 DOI: 10.1039/c7ib00142h] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Many motor proteins achieve high efficiency for chemomechanical conversion, and single-molecule force-resisting experiments are a major tool to detect the chemomechanical coupling of efficient motors. Here, we introduce several quantitative relations that involve only parameters extracted from force-resisting experiments and offer new benchmarks beyond mere efficiency to judge the chemomechanical optimality or deficit of evolutionary remote motors on the same footing. The relations are verified by the experimental data from F1-ATPase, kinesin-1, myosin V and cytoplasmic dynein, which are representative members of four motor protein families. A double-fitting procedure yields the chemomechanical parameters that can be cross-checked for consistency. Using the extracted parameters, two generic maps of chemomechanical optimality are constructed on which motors across families can be quantitatively compared. The maps reveal two chemomechanical coupling regimes, one conducive to high efficiency and high directionality, and the other advantageous to force generation. Surprisingly, an F1 rotor and a kinesin-1 walker belong to the first regime despite their obvious evolutionary gap, while myosin V and cytoplasmic dynein follow the second regime. This analysis also predicts the symmetries of directional biases and heat productions for the motors, which impose constraints on their chemomechanical coupling and are open to future experimental tests. The verified relations, six in total, present a unified fitting framework to analyze force-resisting experiments. The generic maps of optimality, to which many more motors can be added in future, provide a rigorous method for a systematic cross-family comparison of motors to expose their evolutionary connections and mechanistic similarities.
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Affiliation(s)
- Zhisong Wang
- Department of Physics, National University of Singapore, Singapore 117542, Singapore.
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38
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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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39
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Gnesotto FS, Mura F, Gladrow J, Broedersz CP. Broken detailed balance and non-equilibrium dynamics in living systems: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:066601. [PMID: 29504517 DOI: 10.1088/1361-6633/aab3ed] [Citation(s) in RCA: 116] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.
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Affiliation(s)
- F S Gnesotto
- Arnold-Sommerfeld-Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universität München, D-80333 München, Germany
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40
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Elastic coupling power stroke mechanism of the F 1-ATPase molecular motor. Proc Natl Acad Sci U S A 2018; 115:5750-5755. [PMID: 29760063 PMCID: PMC5984535 DOI: 10.1073/pnas.1803147115] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The angular velocity profile of the 120° F1-ATPase power stroke was resolved as a function of temperature from 16.3 to 44.6 °C using a ΔμATP = -31.25 kBT at a time resolution of 10 μs. Angular velocities during the first 60° of the power stroke (phase 1) varied inversely with temperature, resulting in negative activation energies with a parabolic dependence. This is direct evidence that phase 1 rotation derives from elastic energy (spring constant, κ = 50 kBT·rad-2). Phase 2 of the power stroke had an enthalpic component indicating that additional energy input occurred to enable the γ-subunit to overcome energy stored by the spring after rotating beyond its 34° equilibrium position. The correlation between the probability distribution of ATP binding to the empty catalytic site and the negative Ea values of the power stroke during phase 1 suggests that this additional energy is derived from the binding of ATP to the empty catalytic site. A second torsion spring (κ = 150 kBT·rad-2; equilibrium position, 90°) was also evident that mitigated the enthalpic cost of phase 2 rotation. The maximum ΔGǂ was 22.6 kBT, and maximum efficiency was 72%. An elastic coupling mechanism is proposed that uses the coiled-coil domain of the γ-subunit rotor as a torsion spring during phase 1, and then as a crankshaft driven by ATP-binding-dependent conformational changes during phase 2 to drive the power stroke.
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41
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Wang SW. Inferring energy dissipation from violation of the fluctuation-dissipation theorem. Phys Rev E 2018; 97:052125. [PMID: 29906903 DOI: 10.1103/physreve.97.052125] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2017] [Indexed: 06/08/2023]
Abstract
The Harada-Sasa equality elegantly connects the energy dissipation rate of a moving object with its measurable violation of the Fluctuation-Dissipation Theorem (FDT). Although proven for Langevin processes, its validity remains unclear for discrete Markov systems whose forward and backward transition rates respond asymmetrically to external perturbation. A typical example is a motor protein called kinesin. Here we show generally that the FDT violation persists surprisingly in the high-frequency limit due to the asymmetry, resulting in a divergent FDT violation integral and thus a complete breakdown of the Harada-Sasa equality. A renormalized FDT violation integral still well predicts the dissipation rate when each discrete transition produces a small entropy in the environment. Our study also suggests a way to infer this perturbation asymmetry based on the measurable high-frequency-limit FDT violation.
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Affiliation(s)
- Shou-Wen Wang
- Beijing Computational Science Research Center, Beijing, 100094, China and Department of Engineering Physics, Tsinghua University, Beijing, 100086, China
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42
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Tamiya Y, Watanabe R, Noji H, Li CB, Komatsuzaki T. Effects of non-equilibrium angle fluctuation on F 1-ATPase kinetics induced by temperature increase. Phys Chem Chem Phys 2018; 20:1872-1880. [PMID: 29292807 DOI: 10.1039/c7cp06256g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
F1-ATPase (F1) is an efficient rotary protein motor, whose reactivity is modulated by the rotary angle to utilize thermal fluctuation. In order to elucidate how its kinetics are affected by the change in the fluctuation, we have extended the reaction-diffusion formalism [R. Watanabe et al., Biophys. J., 2013, 105, 2385] applicable to a wider range of temperatures based on experimental data analysis of F1 derived from thermophilic Bacillus under high ATP concentration conditions. Our simulation shows that the rotary angle distribution manifests a stronger non-equilibrium feature as the temperature increases, because ATP hydrolysis and Pi release are more accelerated compared with the timescale of rotary angle relaxation. This effect causes the rate coefficient obtained from dwell time fitting to deviate from the Arrhenius relation in Pi release, which has been assumed in the previous activation thermodynamic quantities estimation using linear Arrhenius fitting. Larger negative correlation is also found between hydrolysis and Pi release waiting time in a catalytic dwell with the increase in temperature. This loss of independence between the two successive reactions at the catalytic dwell sheds doubt on the conventional dwell time fitting to obtain rate coefficients with a double exponential function at temperatures higher than 65 °C, which is close to the physiological temperature of the thermophilic Bacillus.
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Affiliation(s)
- Yuji Tamiya
- Department of Mathematics, Hokkaido University, Sapporo 001-0020, Japan
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43
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Dai L, Flechsig H, Yu J. Deciphering Intrinsic Inter-subunit Couplings that Lead to Sequential Hydrolysis of F 1-ATPase Ring. Biophys J 2017; 113:1440-1453. [PMID: 28978438 PMCID: PMC5627347 DOI: 10.1016/j.bpj.2017.08.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 07/31/2017] [Accepted: 08/04/2017] [Indexed: 11/05/2022] Open
Abstract
Rotary sequential hydrolysis of the metabolic machine F1-ATPase is a prominent manifestation of high coordination among multiple chemical sites in ring-shaped molecular machines, and it is also functionally essential for F1 to tightly couple chemical reactions and central γ-shaft rotation. High-speed AFM experiments have identified that sequential hydrolysis is maintained in the F1 stator ring even in the absence of the γ-rotor. To explore the origins of intrinsic sequential performance, we computationally investigated essential inter-subunit couplings on the hexameric ring of mitochondrial and bacterial F1. We first reproduced in stochastic Monte Carlo simulations the experimentally determined sequential hydrolysis schemes by kinetically imposing inter-subunit couplings and following subsequent tri-site ATP hydrolysis cycles on the F1 ring. We found that the key couplings to support the sequential hydrolysis are those that accelerate neighbor-site ADP and Pi release upon a certain ATP binding or hydrolysis reaction. The kinetically identified couplings were then examined in atomistic molecular dynamics simulations at a coarse-grained level to reveal the underlying structural mechanisms. To do that, we enforced targeted conformational changes of ATP binding or hydrolysis to one chemical site on the F1 ring and monitored the ensuing conformational responses of the neighboring sites using structure-based simulations. Notably, we found asymmetrical neighbor-site opening that facilitates ADP release upon enforced ATP binding. We also captured a complete charge-hopping process of the Pi release subsequent to enforced ATP hydrolysis in the neighbor site, confirming recent single-molecule analyses with regard to the role of ATP hydrolysis in F1. Our studies therefore elucidate both the coordinated chemical kinetics and structural dynamics mechanisms underpinning the sequential operation of the F1 ring.
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Affiliation(s)
- Liqiang Dai
- Complex System Research Division, Beijing Computational Science Research Center, Beijing, China
| | - Holger Flechsig
- Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Hiroshima, Japan
| | - Jin Yu
- Complex System Research Division, Beijing Computational Science Research Center, Beijing, China.
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44
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Hwang W, Hyeon C. Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States. J Phys Chem Lett 2017; 8:250-256. [PMID: 27983853 DOI: 10.1021/acs.jpclett.6b02657] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Theoretical analysis, which maps single-molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1, whose dynamics is confined on one-dimensional tracks, is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers a thermodynamic basis to understand the heat-enhanced self-diffusion of exothermic enzymes.
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Affiliation(s)
- Wonseok Hwang
- Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
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45
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Wang SW, Kawaguchi K, Sasa SI, Tang LH. Entropy Production of Nanosystems with Time Scale Separation. PHYSICAL REVIEW LETTERS 2016; 117:070601. [PMID: 27563943 DOI: 10.1103/physrevlett.117.070601] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2016] [Indexed: 06/06/2023]
Abstract
Energy flows in biomolecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a solvable Langevin model, that the seemingly hidden entropy production is measurable through the violation spectrum of the fluctuation-response relation of a slow observable. For general Markov systems with time scale separation, we prove that the violation spectrum exhibits a characteristic plateau in the intermediate frequency region. Despite its vanishing height, the plateau can account for energy dissipation over a broad time scale. Our findings suggest a general possibility to probe hidden entropy production in nanosystems without direct observation of fast variables.
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Affiliation(s)
- Shou-Wen Wang
- Beijing Computational Science Research Center, Beijing 100094, China
- Department of Engineering Physics, Tsinghua University, Beijing 100086, China
| | - Kyogo Kawaguchi
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA
| | - Shin-Ichi Sasa
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Lei-Han Tang
- Beijing Computational Science Research Center, Beijing 100094, China
- Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, China
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46
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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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47
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Goychuk I. Molecular machines operating on the nanoscale: from classical to quantum. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2016; 7:328-50. [PMID: 27335728 PMCID: PMC4901870 DOI: 10.3762/bjnano.7.31] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2015] [Accepted: 01/29/2016] [Indexed: 05/18/2023]
Abstract
The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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48
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Chapman B, Loiselle D. Thermodynamics and kinetics of the FoF1-ATPase: application of the probability isotherm. ROYAL SOCIETY OPEN SCIENCE 2016; 3:150379. [PMID: 26998316 PMCID: PMC4785967 DOI: 10.1098/rsos.150379] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Accepted: 01/08/2016] [Indexed: 06/05/2023]
Abstract
We use the results of recent publications as vehicles with which to discuss the thermodynamics of the proton-driven mitochondrial F o F1-ATP synthase, focusing particularly on the possibility that there may be dissociation between rotatory steps and ATP synthesis/hydrolysis. Such stoichiometric 'slippage' has been invoked in the literature to explain observed non-ideal behaviour. Numerical solution of the Rate Isotherm (the kinetic equivalent of the more fundamental Probability Isotherm) suggests that such 'slippage' is an unlikely explanation; instead, we suggest that the experimental results may be more consistent with damage to the enzyme caused by its isolation from the biomembrane and its experimental fixation, resulting in non-physiological friction within the enzyme's rotary mechanism. We emphasize the unavoidable constraint of the Second Law as instantiated by the obligatory dissipation of Gibbs Free Energy if the synthase is to operate at anything other than thermodynamic equilibrium. We use further numerical solution of the Rate Isotherm to demonstrate that there is no necessary association of low thermodynamic efficiency with high metabolic rates in a bio-world in which the dominating mechanism of metabolic control is multifactorial enzyme activation.
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Affiliation(s)
- Brian Chapman
- Honorary Principal Research Fellow, School of Applied and Biomedical Science, Faculty of Science and Technology, Federation University Australia, Victoria, Australia
| | - Denis Loiselle
- Department of Physiology and the Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
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49
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ATP hydrolysis assists phosphate release and promotes reaction ordering in F1-ATPase. Nat Commun 2015; 6:10223. [PMID: 26678797 PMCID: PMC4703894 DOI: 10.1038/ncomms10223] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2015] [Accepted: 11/16/2015] [Indexed: 12/28/2022] Open
Abstract
F1-ATPase (F1) is a rotary motor protein that can efficiently convert chemical energy to mechanical work of rotation via fine coordination of its conformational motions and reaction sequences. Compared with reactant binding and product release, the ATP hydrolysis has relatively little contributions to the torque and chemical energy generation. To scrutinize possible roles of ATP hydrolysis, we investigate the detailed statistics of the catalytic dwells from high-speed single wild-type F1 observations. Here we report a small rotation during the catalytic dwell triggered by the ATP hydrolysis that is indiscernible in previous studies. Moreover, we find in freely rotating F1 that ATP hydrolysis is followed by the release of inorganic phosphate with low synthesis rates. Finally, we propose functional roles of the ATP hydrolysis as a key to kinetically unlock the subsequent phosphate release and promote the correct reaction ordering.
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50
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Maxwell's demon in biochemical signal transduction with feedback loop. Nat Commun 2015; 6:7498. [PMID: 26099556 PMCID: PMC4557369 DOI: 10.1038/ncomms8498] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2014] [Accepted: 05/12/2015] [Indexed: 11/17/2022] Open
Abstract
Signal transduction in living cells is vital to maintain life itself, where information transfer in noisy environment plays a significant role. In a rather different context, the recent intensive research on ‘Maxwell's demon'—a feedback controller that utilizes information of individual molecules—have led to a unified theory of information and thermodynamics. Here we combine these two streams of research, and show that the second law of thermodynamics with information reveals the fundamental limit of the robustness of signal transduction against environmental fluctuations. Especially, we find that the degree of robustness is quantitatively characterized by an informational quantity called transfer entropy. Our information-thermodynamic approach is applicable to biological communication inside cells, in which there is no explicit channel coding in contrast to artificial communication. Our result could open up a novel biophysical approach to understand information processing in living systems on the basis of the fundamental information–thermodynamics link. The connection between information and thermodynamics is embodied in the figure of Maxwell's demon, a feedback controller. Here, the authors apply thermodynamics of information to signal transduction in chemotaxis of E. coli, predicting that its robustness is quantified by transfer entropy.
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