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Borsley S, Leigh DA, Roberts BMW. Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction. Angew Chem Int Ed Engl 2024; 63:e202400495. [PMID: 38568047 DOI: 10.1002/anie.202400495] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Indexed: 05/03/2024]
Abstract
Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.
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Affiliation(s)
- Stefan Borsley
- Department of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, United Kingdom
| | - David A Leigh
- Department of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, United Kingdom
| | - Benjamin M W Roberts
- Department of Chemistry, The University of Manchester, Oxford Road, M13 9PL, Manchester, United Kingdom
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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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Di Terlizzi I, Gironella M, Herraez-Aguilar D, Betz T, Monroy F, Baiesi M, Ritort F. Variance sum rule for entropy production. Science 2024; 383:971-976. [PMID: 38422150 DOI: 10.1126/science.adh1823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Accepted: 01/09/2024] [Indexed: 03/02/2024]
Abstract
Entropy production is the hallmark of nonequilibrium physics, quantifying irreversibility, dissipation, and the efficiency of energy transduction processes. Despite many efforts, its measurement at the nanoscale remains challenging. We introduce a variance sum rule (VSR) for displacement and force variances that permits us to measure the entropy production rate σ in nonequilibrium steady states. We first illustrate it for directly measurable forces, such as an active Brownian particle in an optical trap. We then apply the VSR to flickering experiments in human red blood cells. We find that σ is spatially heterogeneous with a finite correlation length, and its average value agrees with calorimetry measurements. The VSR paves the way to derive σ using force spectroscopy and time-resolved imaging in living and active matter.
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Affiliation(s)
- I Di Terlizzi
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - M Gironella
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Department of Medical Biochemistry and Cell Biology, Institute of Biomedicine, The Sahlgrenska Academy, University of Gothenburg, 40530 Gothenburg, Sweden
| | - D Herraez-Aguilar
- Facultad de Ciencias Experimentales, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1,800, 28223 Pozuelo de Alarcón, Madrid, Spain
| | - T Betz
- Third Institute of Physics, Georg August Universität Göttingen, Göttingen, Germany
- Cluster of Excellence "Multiscale Bioimaging: from Molecular Machines to Networks of Excitable Cells" (MBExC), University of Göttingen, Göttingen, Germany
| | - F Monroy
- Departamento de Química Física, Facultad de Química, Universidad Complutense, 28040 Madrid, Spain
- Translational Biophysics, Instituto de Investigación Sanitaria Hospital Doce de Octubre (IMAS12), Av. Andalucía, 28041 Madrid, Spain
| | - M Baiesi
- Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
- INFN, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - F Ritort
- Small Biosystems Lab, Condensed Matter Physics Department, Universitat de Barcelona, C/ Marti i Franques 1, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia (IN2UB), Universitat de Barcelona, 08028 Barcelona, Spain
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4
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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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5
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Albaugh A, Fu RS, Gu G, Gingrich TR. Limits on the Precision of Catenane Molecular Motors: Insights from Thermodynamics and Molecular Dynamics Simulations. J Chem Theory Comput 2024; 20:1-6. [PMID: 38127444 DOI: 10.1021/acs.jctc.3c01201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2023]
Abstract
Thermodynamic uncertainty relations (TURs) relate precision to the dissipation rate, yet the inequalities can be far from saturation. Indeed, in catenane molecular motor simulations, we record precision far below the TUR limit. We further show that this inefficiency can be anticipated by four physical parameters: the thermodynamic driving force, fuel decomposition rate, coupling between fuel decomposition and motor motion, and rate of undriven motor motion. The physical insights might assist in designing molecular motors in the future.
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Affiliation(s)
- Alex Albaugh
- Department of Chemical Engineering and Materials Science, Wayne State University, 5050 Anthony Wayne Drive, Detroit, Michigan 48202, United States
| | - Rueih-Sheng Fu
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Geyao Gu
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Todd R Gingrich
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
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6
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Sangchai T, Al Shehimy S, Penocchio E, Ragazzon G. Artificial Molecular Ratchets: Tools Enabling Endergonic Processes. Angew Chem Int Ed Engl 2023; 62:e202309501. [PMID: 37545196 DOI: 10.1002/anie.202309501] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 08/03/2023] [Accepted: 08/04/2023] [Indexed: 08/08/2023]
Abstract
Non-equilibrium chemical systems underpin multiple domains of contemporary interest, including supramolecular chemistry, molecular machines, systems chemistry, prebiotic chemistry, and energy transduction. Experimental chemists are now pioneering the realization of artificial systems that can harvest energy away from equilibrium. In this tutorial Review, we provide an overview of artificial molecular ratchets: the chemical mechanisms enabling energy absorption from the environment. By focusing on the mechanism type-rather than the application domain or energy source-we offer a unifying picture of seemingly disparate phenomena, which we hope will foster progress in this fascinating domain of science.
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Affiliation(s)
- Thitiporn Sangchai
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - Shaymaa Al Shehimy
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - Emanuele Penocchio
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, USA
| | - Giulio Ragazzon
- University of Strasbourg, CNRS, Institut de Science et d'Ingénierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, 67000, Strasbourg, France
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7
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García-Martínez A, Zinovjev K, Ruiz-Pernía JJ, Tuñón I. Conformational Changes and ATP Hydrolysis in Zika Helicase: The Molecular Basis of a Biomolecular Motor Unveiled by Multiscale Simulations. J Am Chem Soc 2023; 145:24809-24819. [PMID: 37921592 PMCID: PMC10852352 DOI: 10.1021/jacs.3c09015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Revised: 09/30/2023] [Accepted: 10/17/2023] [Indexed: 11/04/2023]
Abstract
We computationally study the Zika NS3 helicase, a biological motor, using ATP hydrolysis energy for nucleic acid remodeling. Through molecular mechanics and hybrid quantum mechanics/molecular mechanics simulations, we explore the conformational landscape of motif V, a conserved loop connecting the active sites for ATP hydrolysis and nucleic acid binding. ATP hydrolysis, initiated by a meta-phosphate group formation, involves the nucleophilic attack of a water molecule activated by Glu286 proton abstraction. Motif V hydrogen bonds to this water via the Gly415 backbone NH group, assisting hydrolysis. Posthydrolysis, free energy is released when the inorganic phosphate moves away from the coordination shell of the magnesium ion, inducing a significant shift in the conformational landscape of motif V to establish a hydrogen bond between the Gly415 NH group and Glu285. According to our simulations, the Zika NS3 helicase acts as a ratchet biological motor with motif V transitions steered by Gly415's γ-phosphate sensing in the ATPase site.
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Affiliation(s)
| | - Kirill Zinovjev
- Departamento de Química Física, Universidad de Valencia, 46100 Bujassot, Spain
| | | | - Iñaki Tuñón
- Departamento de Química Física, Universidad de Valencia, 46100 Bujassot, Spain
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8
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Ellis GFR. Efficient, Formal, Material, and Final Causes in Biology and Technology. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1301. [PMID: 37761600 PMCID: PMC10529506 DOI: 10.3390/e25091301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 08/24/2023] [Accepted: 08/28/2023] [Indexed: 09/29/2023]
Abstract
This paper considers how a classification of causal effects as comprising efficient, formal, material, and final causation can provide a useful understanding of how emergence takes place in biology and technology, with formal, material, and final causation all including cases of downward causation; they each occur in both synchronic and diachronic forms. Taken together, they underlie why all emergent levels in the hierarchy of emergence have causal powers (which is Noble's principle of biological relativity) and so why causal closure only occurs when the upwards and downwards interactions between all emergent levels are taken into account, contra to claims that some underlying physics level is by itself causality complete. A key feature is that stochasticity at the molecular level plays an important role in enabling agency to emerge, underlying the possibility of final causation occurring in these contexts.
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Affiliation(s)
- George F R Ellis
- Mathematics Department, The New Institute, University of Cape Town, 20354 Hamburg, Germany
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9
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Leblanc JA, Sugiyama MG, Antonescu CN, Brown AI. Quantitative modeling of EGF receptor ligand discrimination via internalization proofreading. Phys Biol 2023; 20:056008. [PMID: 37557183 DOI: 10.1088/1478-3975/aceecd] [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: 05/11/2023] [Accepted: 08/09/2023] [Indexed: 08/11/2023]
Abstract
The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.
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Affiliation(s)
- Jaleesa A Leblanc
- Department of Physics, Toronto Metropolitan University, Toronto, Ontario, Canada
| | - Michael G Sugiyama
- Department of Chemistry and Biology, Toronto Metropolitan University, Toronto, Ontario, Canada
| | - Costin N Antonescu
- Department of Chemistry and Biology, Toronto Metropolitan University, Toronto, Ontario, Canada
| | - Aidan I Brown
- Department of Physics, Toronto Metropolitan University, Toronto, Ontario, Canada
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10
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Vilfan A, Šarlah A. Theoretical efficiency limits and speed-efficiency trade-off in myosin motors. PLoS Comput Biol 2023; 19:e1011310. [PMID: 37478158 PMCID: PMC10395908 DOI: 10.1371/journal.pcbi.1011310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 06/26/2023] [Indexed: 07/23/2023] Open
Abstract
Muscle myosin is a non-processive molecular motor generates mechanical work when cooperating in large ensembles. During its cyle, each individual motor keeps attaching and detaching from the actin filament. The random nature of attachment and detachment inevitably leads to losses and imposes theoretical limits on the energetic efficiency. Here, we numerically determine the theoretical efficiency limit of a classical myosin model with a given number of mechano-chemical states. All parameters that are not bounded by physical limits (like rate limiting steps) are determined by numerical efficiency optimization. We show that the efficiency is limited by the number of states, the stiffness and the rate-limiting kinetic steps. There is a trade-off between speed and efficiency. Slow motors are optimal when most of the available free energy is allocated to the working stroke and the stiffness of their elastic element is high. Fast motors, on the other hand, work better with a lower and asymmetric stiffness and allocate a larger fraction of free energy to the release of ADP. Overall, many features found in myosins coincide with the findings from the model optimization: there are at least 3 bound states, the largest part of the working stroke takes place during the first transition, the ADP affinity is adapted differently in slow and fast myosins and there is an asymmetry in elastic elements.
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Affiliation(s)
- Andrej Vilfan
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen, Germany
- J. Stefan Institute, Ljubljana, Slovenia
| | - Andreja Šarlah
- Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
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11
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Bilancioni M, Esposito M, Penocchio E. A [3]-catenane non-autonomous molecular motor model: Geometric phase, no-pumping theorem, and energy transduction. J Chem Phys 2023; 158:224104. [PMID: 37310874 DOI: 10.1063/5.0151625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 05/17/2023] [Indexed: 06/15/2023] Open
Abstract
We study a model of a synthetic molecular motor-a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one-subjected to time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space, which corrects previous erroneous results. We also analyze the performance of the motor subjected to step-wise driving protocols in the absence and presence of an applied load. Optimization strategies for generating large currents and maximizing free energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization.
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Affiliation(s)
- Massimo Bilancioni
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
| | - Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg City 1511, Luxembourg
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
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12
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Sanchez R, Mackenzie SA. On the thermodynamics of DNA methylation process. Sci Rep 2023; 13:8914. [PMID: 37264042 DOI: 10.1038/s41598-023-35166-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 05/13/2023] [Indexed: 06/03/2023] Open
Abstract
DNA methylation is an epigenetic mechanism that plays important roles in various biological processes including transcriptional and post-transcriptional regulation, genomic imprinting, aging, and stress response to environmental changes and disease. Consistent with thermodynamic principles acting within living systems and the application of maximum entropy principle, we propose a theoretical framework to understand and decode the DNA methylation process. A central tenet of this argument is that the probability density function of DNA methylation information-divergence summarizes the statistical biophysics underlying spontaneous methylation background and implicitly bears on the channel capacity of molecular machines conforming to Shannon's capacity theorem. On this theoretical basis, contributions from the molecular machine (enzyme) logical operations to Gibb entropy (S) and Helmholtz free energy (F) are intrinsic. Application to the estimations of S on datasets from Arabidopsis thaliana suggests that, as a thermodynamic state variable, individual methylome entropy is completely determined by the current state of the system, which in biological terms translates to a correspondence between estimated entropy values and observable phenotypic state. In patients with different types of cancer, results suggest that a significant information loss occurs in the transition from differentiated (healthy) tissues to cancer cells. This type of analysis may have important implications for early-stage diagnostics. The analysis of entropy fluctuations on experimental datasets revealed existence of restrictions on the magnitude of genome-wide methylation changes originating by organismal response to environmental changes. Only dysfunctional stages observed in the Arabidopsis mutant met1 and in cancer cells do not conform to these rules.
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Affiliation(s)
- Robersy Sanchez
- Department of Biology, The Pennsylvania State University, 361 Frear North Bldg, University Park, PA, 16802, USA.
| | - Sally A Mackenzie
- Departments of Biology and Plant Science, The Pennsylvania State University, 362 Frear North Bldg, University Park, PA, 16802, USA.
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13
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Ray KK, Kinz-Thompson CD, Fei J, Wang B, Lin Q, Gonzalez RL. Entropic control of the free-energy landscape of an archetypal biomolecular machine. Proc Natl Acad Sci U S A 2023; 120:e2220591120. [PMID: 37186858 PMCID: PMC10214133 DOI: 10.1073/pnas.2220591120] [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: 12/04/2022] [Accepted: 04/17/2023] [Indexed: 05/17/2023] Open
Abstract
Biomolecular machines are complex macromolecular assemblies that utilize thermal and chemical energy to perform essential, multistep, cellular processes. Despite possessing different architectures and functions, an essential feature of the mechanisms of action of all such machines is that they require dynamic rearrangements of structural components. Surprisingly, biomolecular machines generally possess only a limited set of such motions, suggesting that these dynamics must be repurposed to drive different mechanistic steps. Although ligands that interact with these machines are known to drive such repurposing, the physical and structural mechanisms through which ligands achieve this remain unknown. Using temperature-dependent, single-molecule measurements analyzed with a time-resolution-enhancing algorithm, here, we dissect the free-energy landscape of an archetypal biomolecular machine, the bacterial ribosome, to reveal how its dynamics are repurposed to drive distinct steps during ribosome-catalyzed protein synthesis. Specifically, we show that the free-energy landscape of the ribosome encompasses a network of allosterically coupled structural elements that coordinates the motions of these elements. Moreover, we reveal that ribosomal ligands which participate in disparate steps of the protein synthesis pathway repurpose this network by differentially modulating the structural flexibility of the ribosomal complex (i.e., the entropic component of the free-energy landscape). We propose that such ligand-dependent entropic control of free-energy landscapes has evolved as a general strategy through which ligands may regulate the functions of all biomolecular machines. Such entropic control is therefore an important driver in the evolution of naturally occurring biomolecular machines and a critical consideration for the design of synthetic molecular machines.
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Affiliation(s)
- Korak Kumar Ray
- Department of Chemistry, Columbia University, New York, NY10027
| | | | - Jingyi Fei
- Department of Chemistry, Columbia University, New York, NY10027
| | - Bin Wang
- Department of Mechanical Engineering, Columbia University, New York, NY10027
| | - Qiao Lin
- Department of Mechanical Engineering, Columbia University, New York, NY10027
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14
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Terai K, Yuly JL, Zhang P, Beratan DN. Correlated particle transport enables biological free energy transduction. Biophys J 2023; 122:1762-1771. [PMID: 37056051 PMCID: PMC10209040 DOI: 10.1016/j.bpj.2023.04.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Revised: 02/17/2023] [Accepted: 04/07/2023] [Indexed: 04/15/2023] Open
Abstract
Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. We show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).
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Affiliation(s)
- Kiriko Terai
- Department of Chemistry, Duke University, Durham, North Carolina
| | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersy
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina
| | - David N Beratan
- Department of Chemistry, Duke University, Durham, North Carolina; Department of Physics, Duke University, Durham, North Carolina; Department of Biochemistry, Duke University, Durham, North Carolina.
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15
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Semaan MT, Crutchfield JP. First and second laws of information processing by nonequilibrium dynamical states. Phys Rev E 2023; 107:054132. [PMID: 37329111 DOI: 10.1103/physreve.107.054132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 05/04/2023] [Indexed: 06/18/2023]
Abstract
The averaged steady-state surprisal links a driven stochastic system's information processing to its nonequilibrium thermodynamic response. By explicitly accounting for the effects of nonequilibrium steady states, a decomposition of the surprisal results in an information processing first law that extends and tightens-to strict equalities-various information processing second laws. Applying stochastic thermodynamics' integral fluctuation theorems then shows that the decomposition reduces to the second laws under appropriate limits. In unifying them, the first law paves the way to identifying the mechanisms by which nonequilibrium steady-state systems leverage information-bearing degrees of freedom to extract heat. To illustrate, we analyze an autonomous Maxwellian information ratchet that tunably violates detailed balance in its effective dynamics. This demonstrates how the presence of nonequilibrium steady states qualitatively alters an information engine's allowed functionality.
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Affiliation(s)
- Mikhael T Semaan
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
- Science Research Initiative, College of Science, University of Utah, Salt Lake City, Utah 84112, USA
| | - James P Crutchfield
- Complexity Sciences Center and Department of Physics and Astronomy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA
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16
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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: 0] [Impact Index Per Article: 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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17
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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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18
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Penocchio E, Ragazzon G. Kinetic Barrier Diagrams to Visualize and Engineer Molecular Nonequilibrium Systems. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2023; 19:e2206188. [PMID: 36703505 DOI: 10.1002/smll.202206188] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2022] [Revised: 12/11/2022] [Indexed: 06/18/2023]
Abstract
Molecular nonequilibrium systems hold great promises for the nanotechnology of the future. Yet, their development is slowed by the absence of an informative representation. Indeed, while potential energy surfaces comprise in principle all the information, they hide the dynamic interplay of multiple reaction pathways underlying nonequilibrium systems, i.e., the degree of kinetic asymmetry. To offer an insightful visual representation of kinetic asymmetry, we extended an approach pertaining to catalytic networks, the energy span model, by focusing on system dynamics - rather than thermodynamics. Our approach encompasses both chemically and photochemically driven systems, ranging from unimolecular motors to simple self-assembly schemes. The obtained diagrams give immediate access to information needed to guide experiments, such as states' population, rate of machine operation, maximum work output, and effects of design changes. The proposed kinetic barrier diagrams offer a unifying graphical tool for disparate nonequilibrium phenomena.
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Affiliation(s)
- Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, Luxembourg, L-1511, Luxembourg
- Department of Chemistry, Northwestern University, Evanston, IL, 60208, USA
| | - Giulio Ragazzon
- University of Strasbourg, CNRS, Institut de Science et d'Ingégnierie Supramoléculaires (ISIS) UMR 7006, 8 allée Gaspard Monge, Strasbourg, F-67000, France
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19
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Singhania A, Chatterjee S, Kalita S, Saha S, Chettri P, Gayen FR, Saha B, Sahoo P, Bandyopadhyay A, Ghosh S. An Inbuilt Electronic Pawl Gates Orbital Information Processing and Controls the Rotation of a Double Ratchet Rotary Motor. ACS APPLIED MATERIALS & INTERFACES 2023; 15:15595-15604. [PMID: 36926805 DOI: 10.1021/acsami.3c01103] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
A direct external input energy source (e.g., light, chemical reaction, redox potential, etc.) is compulsory to supply energy to rotary motors for accomplishing rotation around the axis. The stator leads the direction of rotation, and a sustainable rotation requires two mutual input energy supplies (e.g., light and heat, light and pH or metal ion, etc.); however, there are some exceptions (e.g., covalent single bond rotors and/or motors). On the contrary, our experiment suggested that double ratchet rotary motors (DRMs) can harvest power from available thermal noise, kT, for sustainable rotation around the axis. Under a scanning tunneling microscope, we have imaged live thermal noise movement as a dynamic orbital density and resolved the density diagram up to the second derivative. A second input energy can synchronize multiple rotors to afford a measurable output. Therefore, we hypothesized that rotation control in a DRM must be evolved from an orbital-level information transport channel between the two coupled rotors but was not limited to the second input energy. A DRM comprises a Brownian rotor and a power stroke rotor coupled to a -C≡C- stator, where the transport of information through coupled orbitals between the two rotors is termed the vibrational information flow chain (VIFC). We test this hypothesis by studying the DRM's density functional theory calculation and variable-temperature 1H nuclear magnetic resonance. Additionally, we introduced inbuilt pawl-like functional moieties into a DRM to create different electronic environments by changing proton intercalation interactions, which gated information processing through the VIFC. The results show the VIFC can critically impact the motor's noise harvesting, resulting in variable rotational motions in DRMs.
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Affiliation(s)
- Anup Singhania
- Natural Product Chemistry Group, Chemical Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Satadru Chatterjee
- Natural Product Chemistry Group, Chemical Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
| | - Sudeshna Kalita
- Natural Product Chemistry Group, Chemical Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Supriya Saha
- Advanced Computation & Data Sciences Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
- Green Engineered Materials and Additive Manufacturing Division, CSIR-AMPRI, 462026 Bhopal, Madhya Pradesh, India
| | - Prerna Chettri
- Natural Product Chemistry Group, Chemical Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Firdaus Rahaman Gayen
- Advanced Materials Group, Material Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Biswajit Saha
- Advanced Materials Group, Material Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
| | - Pathik Sahoo
- International Center for Materials and Nanoarchitectronics (MANA) and Research Center for Advanced Measurement and Characterization (RCAMC), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 3050047, Japan
| | - Anirban Bandyopadhyay
- International Center for Materials and Nanoarchitectronics (MANA) and Research Center for Advanced Measurement and Characterization (RCAMC), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 3050047, Japan
| | - Subrata Ghosh
- Natural Product Chemistry Group, Chemical Sciences & Technology Division, CSIR-North East Institute of Science & Technology, Jorhat 785006, Assam, India
- Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India
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20
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Karan C, Chaudhuri D. Cooperation and competition in the collective drive by motor proteins: mean active force, fluctuations, and self-load. SOFT MATTER 2023; 19:1834-1843. [PMID: 36789956 DOI: 10.1039/d2sm01183b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We consider the dynamics of a bio-filament under the collective drive of motor proteins. They are attached irreversibly to a substrate and undergo stochastic attachment-detachment with the filament to produce a directed force on it. We establish the dependence of the mean directed force and force correlations on the parameters describing the individual motor proteins using analytical theory and direct numerical simulations. The effective Langevin description for the filament motion gives mean-squared displacement, asymptotic diffusion constant, and mobility leading to an effective temperature. Finally, we show how competition between motor protein extensions generates a self-load, describable in terms of the effective temperature, affecting the filament motion.
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Affiliation(s)
- Chitrak Karan
- Institute of Physics, Sachivalaya Marg, Sainik School, Bhubaneswar, 751005, India.
- Homi Bhaba National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India.
| | - Debasish Chaudhuri
- Institute of Physics, Sachivalaya Marg, Sainik School, Bhubaneswar, 751005, India.
- Homi Bhaba National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India.
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21
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Surveying membrane landscapes: a new look at the bacterial cell surface. Nat Rev Microbiol 2023:10.1038/s41579-023-00862-w. [PMID: 36828896 DOI: 10.1038/s41579-023-00862-w] [Citation(s) in RCA: 14] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/30/2023] [Indexed: 02/26/2023]
Abstract
Recent studies applying advanced imaging techniques are changing the way we understand bacterial cell surfaces, bringing new knowledge on everything from single-cell heterogeneity in bacterial populations to their drug sensitivity and mechanisms of antimicrobial resistance. In both Gram-positive and Gram-negative bacteria, the outermost surface of the bacterial cell is being imaged at nanoscale; as a result, topographical maps of bacterial cell surfaces can be constructed, revealing distinct zones and specific features that might uniquely identify each cell in a population. Functionally defined assembly precincts for protein insertion into the membrane have been mapped at nanoscale, and equivalent lipid-assembly precincts are suggested from discrete lipopolysaccharide patches. As we review here, particularly for Gram-negative bacteria, the applications of various modalities of nanoscale imaging are reawakening our curiosity about what is conceptually a 3D cell surface landscape: what it looks like, how it is made and how it provides resilience to respond to environmental impacts.
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22
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Hou D, Xu Y, Yan J, Zeng Q, Wang Z, Chen Y. Intracellularly Self-Assembled 2D Materials Induce Apoptotic Cell Death by Impeding Cytosolic Transport. ACS NANO 2023; 17:3055-3063. [PMID: 36688625 DOI: 10.1021/acsnano.2c11876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Using a photochemically isomerizable cucurbit[6]uril derivative as a building block, we succeeded in generating a large number of oversized 2D materials within the cytosol of a living cell via controlled self-assembly. Fluorescence recovery after a photobleaching assay indicated that the resulting 2D material pieces posed discernible hindrance to not only diffusive spreading but also motor-driven motion of intracellular components in the cytosol, which eventually induced apoptotic cell death. Such behavior was seldom observed in previous 2D material-bearing cells prepared by endocytosis, as the total lateral size constituted by the endocytosed 2D materials per cell failed to exceed a threshold level, leading to a tortuosity of transport path inadequate to impede cytosolic transport in an appreciable manner. By varying the initial concentration of the building block, the existence of such a threshold was experimentally demonstrated from the relationship between the flow cytometry side scatter of the treated cells and corresponding cell viability. With the otherwise well-regulated cytosolic transport dynamics of living cells being physically altered, therapeutics with a new mechanism of action that counteracts drug resistance or intracellular platforms that advance our understanding of subcellular pathology of certain intractable diseases are in sight.
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Affiliation(s)
- Delong Hou
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
| | - Yong Xu
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
| | - Jun Yan
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
| | - Qi Zeng
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
| | - Zhonghui Wang
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
| | - Yi Chen
- College of Biomass Science and Engineering, Sichuan University, Chengdu 610065, People's Republic of China
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23
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Ragazzon G, Malferrari M, Arduini A, Secchi A, Rapino S, Silvi S, Credi A. Autonomous Non-Equilibrium Self-Assembly and Molecular Movements Powered by Electrical Energy. Angew Chem Int Ed Engl 2023; 62:e202214265. [PMID: 36422473 PMCID: PMC10107654 DOI: 10.1002/anie.202214265] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Revised: 11/07/2022] [Accepted: 11/22/2022] [Indexed: 11/25/2022]
Abstract
The ability to exploit energy autonomously is one of the hallmarks of life. Mastering such processes in artificial nanosystems can open technological opportunities. In the last decades, light- and chemically driven autonomous systems have been developed in relation to conformational motion and self-assembly, mostly in relation to molecular motors. In contrast, despite electrical energy being an attractive energy source to power nanosystems, its autonomous harnessing has received little attention. Herein we consider an operation mode that allows the autonomous exploitation of electrical energy by a self-assembling system. Threading and dethreading motions of a pseudorotaxane take place autonomously in solution, powered by the current flowing between the electrodes of a scanning electrochemical microscope. The underlying autonomous energy ratchet mechanism drives the self-assembly steps away from equilibrium with a higher energy efficiency compared to other autonomous systems. The strategy is general and might be extended to other redox-driven systems.
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Affiliation(s)
- Giulio Ragazzon
- Institut de Science et d'Ingégnierie Supramoléculaires (ISIS) UMR 7006, University of Strasbourg, CNRS, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - Marco Malferrari
- Dipartimento di Chimica "Giacomo Ciamician", Università di Bologna, via Selmi 2, 40126, Bologna, Italy
| | - Arturo Arduini
- Dipartimento di Scienze Chimiche, della Vita e della Sostenibilità Ambientale, Università di Parma, Parco Area delle Scienze 17/A, 43124, Parma, Italy
| | - Andrea Secchi
- Dipartimento di Scienze Chimiche, della Vita e della Sostenibilità Ambientale, Università di Parma, Parco Area delle Scienze 17/A, 43124, Parma, Italy
| | - Stefania Rapino
- Dipartimento di Chimica "Giacomo Ciamician", Università di Bologna, via Selmi 2, 40126, Bologna, Italy
| | - Serena Silvi
- Dipartimento di Chimica "Giacomo Ciamician", Università di Bologna, via Selmi 2, 40126, Bologna, Italy.,CLAN-Center for Light-Activated Nanostructures (CLAN), Università di Bologna and Consiglio Nazionale delle Ricerche, via Gobetti 101, 40129, Bologna, Italy
| | - Alberto Credi
- CLAN-Center for Light-Activated Nanostructures (CLAN), Università di Bologna and Consiglio Nazionale delle Ricerche, via Gobetti 101, 40129, Bologna, Italy.,Dipartimento di Chimica Industriale "Toso Montanari", Università di Bologna, viale del Risorgimento 4, 40136, Bologna, Italy
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24
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Zhang Z, Du V, Lu Z. Energy landscape design principle for optimal energy harnessing by catalytic molecular machines. Phys Rev E 2023; 107:L012102. [PMID: 36797891 DOI: 10.1103/physreve.107.l012102] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 12/27/2022] [Indexed: 06/18/2023]
Abstract
Under temperature oscillation, cyclic molecular machines such as catalysts and enzymes could harness energy from the oscillatory bath and use it to drive other processes. Using an alternative geometrical approach, under fast temperature oscillation, we derive a general design principle for obtaining the optimal catalytic energy landscape that can harness energy from a temperature-oscillatory bath and use it to invert a spontaneous reaction. By driving the reaction against the spontaneous direction, the catalysts convert low free-energy product molecules to high free-energy reactant molecules. The design principle, derived for arbitrary cyclic catalysts, is expressed as a simple quadratic objective function that only depends on the reaction activation energies, and is independent of the temperature protocol. Since the reaction activation energies are directly accessible by experimental measurements, the objective function can be directly used to guide the search for optimal energy-harvesting catalysts.
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Affiliation(s)
- Zhongmin Zhang
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
| | - Vincent Du
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
| | - Zhiyue Lu
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, USA
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25
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Abstract
F1-ATPase is a rotary molecular motor that in vivo is subject to strong nonequilibrium driving forces. There is great interest in understanding the operational principles governing its high efficiency of free-energy transduction. Here we use a near-equilibrium framework to design a nontrivial control protocol to minimize dissipation in rotating F1 to synthesize adenosine triphosphate. We find that the designed protocol requires much less work than a naive (constant-velocity) protocol across a wide range of protocol durations. Our analysis points to a possible mechanism for energetically efficient driving of F1 in vivo and provides insight into free-energy transduction for a broader class of biomolecular and synthetic machines.
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Affiliation(s)
- Deepak Gupta
- Department of Physics, Simon Fraser University, BurnabyV5A 1S6, British Columbia, Canada
- Institute for Theoretical Physics, Technical University of Berlin, Hardenbergstr. 36, BerlinD-10623, Germany
| | - Steven J Large
- Department of Physics, Simon Fraser University, BurnabyV5A 1S6, British Columbia, Canada
| | - Shoichi Toyabe
- Department of Applied Physics, Tohoku University, Aoba 6-6-05, Sendai980-8579, Japan
| | - David A Sivak
- Department of Physics, Simon Fraser University, BurnabyV5A 1S6, British Columbia, Canada
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26
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Ariga K. Molecular Machines and Microrobots: Nanoarchitectonics Developments and On-Water Performances. MICROMACHINES 2022; 14:mi14010025. [PMID: 36677086 PMCID: PMC9860627 DOI: 10.3390/mi14010025] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 12/16/2022] [Accepted: 12/21/2022] [Indexed: 05/14/2023]
Abstract
This review will focus on micromachines and microrobots, which are objects at the micro-level with similar machine functions, as well as nano-level objects such as molecular machines and nanomachines. The paper will initially review recent examples of molecular machines and microrobots that are not limited to interfaces, noting the diversity of their functions. Next, examples of molecular machines and micromachines/micro-robots functioning at the air-water interface will be discussed. The behaviors of molecular machines are influenced significantly by the specific characteristics of the air-water interface. By placing molecular machines at the air-water interface, the scientific horizon and depth of molecular machine research will increase dramatically. On the other hand, for microrobotics, more practical and advanced systems have been reported, such as the development of microrobots and microswimmers for environmental remediations and biomedical applications. The research currently being conducted on the surface of water may provide significant basic knowledge for future practical uses of molecular machines and microrobots.
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Affiliation(s)
- Katsuhiko Ariga
- International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan;
- Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan
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27
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Amano S, Esposito M, Kreidt E, Leigh DA, Penocchio E, Roberts BMW. Using Catalysis to Drive Chemistry Away from Equilibrium: Relating Kinetic Asymmetry, Power Strokes, and the Curtin–Hammett Principle in Brownian Ratchets. J Am Chem Soc 2022; 144:20153-20164. [DOI: 10.1021/jacs.2c08723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shuntaro Amano
- Department of Chemistry, University of Manchester, Oxford Road, ManchesterM13 9PL, United Kingdom
- Institute of Supramolecular Science and Engineering (ISIS), University of Strasbourg, 67000Strasbourg, France
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, avenue de la Faïencerie, 1511Luxembourg City, G.D. Luxembourg
| | - Elisabeth Kreidt
- Department of Chemistry, University of Manchester, Oxford Road, ManchesterM13 9PL, United Kingdom
- Department of Chemistry and Chemical Biology, University of Dortmund, Otto-Hahn-Str. 6, 44227Dortmund, Germany
| | - David A. Leigh
- Department of Chemistry, University of Manchester, Oxford Road, ManchesterM13 9PL, United Kingdom
| | - Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, avenue de la Faïencerie, 1511Luxembourg City, G.D. Luxembourg
- Department of Chemistry, Northwestern University, Evanston, Illinois60208, United States
| | - Benjamin M. W. Roberts
- Department of Chemistry, University of Manchester, Oxford Road, ManchesterM13 9PL, United Kingdom
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28
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Leighton MP, Sivak DA. Dynamic and Thermodynamic Bounds for Collective Motor-Driven Transport. PHYSICAL REVIEW LETTERS 2022; 129:118102. [PMID: 36154431 DOI: 10.1103/physrevlett.129.118102] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Accepted: 08/17/2022] [Indexed: 06/16/2023]
Abstract
Molecular motors work collectively to transport cargo within cells, with anywhere from one to several hundred motors towing a single cargo. For a broad class of collective-transport systems, we use tools from stochastic thermodynamics to derive a new lower bound for the entropy production rate which is tighter than the second law. This implies new bounds on the velocity, efficiency, and precision of general transport systems and a set of analytic Pareto frontiers for identical motors. In a specific model, we identify conditions for saturation of these Pareto frontiers.
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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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29
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Borsley S, Leigh DA, Roberts BMW, Vitorica-Yrezabal IJ. Tuning the Force, Speed, and Efficiency of an Autonomous Chemically Fueled Information Ratchet. J Am Chem Soc 2022; 144:17241-17248. [PMID: 36074864 PMCID: PMC9501901 DOI: 10.1021/jacs.2c07633] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Autonomous chemically fueled molecular machines that
function through
information ratchet mechanisms underpin the nonequilibrium processes
that sustain life. These biomolecular motors have evolved to be well-suited
to the tasks they perform. Synthetic systems that function through
similar mechanisms have recently been developed, and their minimalist
structures enable the influence of structural changes on machine performance
to be assessed. Here, we probe the effect of changes in the fuel and
barrier-forming species on the nonequilibrium operation of a carbodiimide-fueled
rotaxane-based information ratchet. We examine the machine’s
ability to catalyze the fuel-to-waste reaction and harness energy
from it to drive directional displacement of the macrocycle. These
characteristics are intrinsically linked to the speed, force, power,
and efficiency of the ratchet output. We find that, just as for biomolecular
motors and macroscopic machinery, optimization of one feature (such
as speed) can compromise other features (such as the force that can
be generated by the ratchet). Balancing speed, power, efficiency,
and directionality will likely prove important when developing artificial
molecular motors for particular applications.
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Affiliation(s)
- Stefan Borsley
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, U.K
| | - David A Leigh
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.,School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Benjamin M W Roberts
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, U.K
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30
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Arceo XG, Koslover EF, Zid BM, Brown AI. Mitochondrial mRNA localization is governed by translation kinetics and spatial transport. PLoS Comput Biol 2022; 18:e1010413. [PMID: 35984860 PMCID: PMC9432724 DOI: 10.1371/journal.pcbi.1010413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Revised: 08/31/2022] [Accepted: 07/19/2022] [Indexed: 11/24/2022] Open
Abstract
For many nuclear-encoded mitochondrial genes, mRNA localizes to the mitochondrial surface co-translationally, aided by the association of a mitochondrial targeting sequence (MTS) on the nascent peptide with the mitochondrial import complex. For a subset of these co-translationally localized mRNAs, their localization is dependent on the metabolic state of the cell, while others are constitutively localized. To explore the differences between these two mRNA types we developed a stochastic, quantitative model for MTS-mediated mRNA localization to mitochondria in yeast cells. This model includes translation, applying gene-specific kinetics derived from experimental data; and diffusion in the cytosol. Even though both mRNA types are co-translationally localized we found that the steady state number, or density, of ribosomes along an mRNA was insufficient to differentiate the two mRNA types. Instead, conditionally-localized mRNAs have faster translation kinetics which modulate localization in combination with changes to diffusive search kinetics across metabolic states. Our model also suggests that the MTS requires a maturation time to become competent to bind mitochondria. Our work indicates that yeast cells can regulate mRNA localization to mitochondria by controlling mitochondrial volume fraction (influencing diffusive search times) and gene translation kinetics (adjusting mRNA binding competence) without the need for mRNA-specific binding proteins. These results shed light on both global and gene-specific mechanisms that enable cells to alter mRNA localization in response to changing metabolic conditions.
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Affiliation(s)
- Ximena G. Arceo
- Department of Chemistry & Biochemistry, University of California, San Diego, La Jolla, California, United States of America
| | - Elena F. Koslover
- Department of Physics, University of California, San Diego, La Jolla, California, United States of America
| | - Brian M. Zid
- Department of Chemistry & Biochemistry, University of California, San Diego, La Jolla, California, United States of America
| | - Aidan I. Brown
- Department of Physics, Ryerson University, Toronto, Canada
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31
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Blaber S, Sivak DA. Optimal control with a strong harmonic trap. Phys Rev E 2022; 106:L022103. [PMID: 36110009 DOI: 10.1103/physreve.106.l022103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2022] [Accepted: 07/21/2022] [Indexed: 06/15/2023]
Abstract
Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.
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Affiliation(s)
- Steven Blaber
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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32
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Penocchio E, Avanzini F, Esposito M. Information thermodynamics for deterministic chemical reaction networks. J Chem Phys 2022; 157:034110. [DOI: 10.1063/5.0094849] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved.
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Affiliation(s)
- Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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33
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Borsley S, Leigh DA, Roberts BMW. Chemical fuels for molecular machinery. Nat Chem 2022; 14:728-738. [PMID: 35778564 DOI: 10.1038/s41557-022-00970-9] [Citation(s) in RCA: 40] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 05/10/2022] [Indexed: 12/11/2022]
Abstract
Chemical reaction networks that transform out-of-equilibrium 'fuel' to 'waste' are the engines that power the biomolecular machinery of the cell. Inspired by such systems, autonomous artificial molecular machinery is being developed that functions by catalysing the decomposition of chemical fuels, exploiting kinetic asymmetry to harness energy released from the fuel-to-waste reaction to drive non-equilibrium structures and dynamics. Different aspects of chemical fuels profoundly influence their ability to power molecular machines. Here we consider the structure and properties of the fuels that biology has evolved and compare their features with those of the rudimentary synthetic chemical fuels that have so far been used to drive autonomous non-equilibrium molecular-level dynamics. We identify desirable, but context-specific, traits for chemical fuels together with challenges and opportunities for the design and invention of new chemical fuels to power synthetic molecular machinery and other dissipative nanoscale processes.
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Affiliation(s)
- Stefan Borsley
- Department of Chemistry, University of Manchester, Manchester, UK
| | - David A Leigh
- Department of Chemistry, University of Manchester, Manchester, UK.
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34
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Wachtel A, Rao R, Esposito M. Free-Energy Transduction in Chemical Reaction Networks: from Enzymes to Metabolism. J Chem Phys 2022; 157:024109. [DOI: 10.1063/5.0091035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary---linear or nonlinear---open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the stoichiometric matrix and of the chemostatted species (i.e. the species maintained at constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force) thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they are able to transduce free energy.
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Affiliation(s)
- Artur Wachtel
- Yale University Department of Molecular Cellular and Developmental Biology, United States of America
| | - Riccardo Rao
- Institute for Advanced Study, United States of America
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35
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Ishimoto K, Moreau C, Yasuda K. Self-organized swimming with odd elasticity. Phys Rev E 2022; 105:064603. [PMID: 35854482 DOI: 10.1103/physreve.105.064603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 03/23/2022] [Indexed: 06/15/2023]
Abstract
We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a nonsymmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.
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Affiliation(s)
- Kenta Ishimoto
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Clément Moreau
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
| | - Kento Yasuda
- Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
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36
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Louwerse MD, Sivak D. Multidimensional minimum-work control of a 2D Ising model. J Chem Phys 2022; 156:194108. [DOI: 10.1063/5.0086079] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and thus decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations, and significantly reducing resistance and hence work.
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37
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Albaugh A, Gingrich TR. Simulating a chemically fueled molecular motor with nonequilibrium molecular dynamics. Nat Commun 2022; 13:2204. [PMID: 35459863 PMCID: PMC9033874 DOI: 10.1038/s41467-022-29393-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 02/23/2022] [Indexed: 01/26/2023] Open
Abstract
Most computer simulations of molecular dynamics take place under equilibrium conditions-in a closed, isolated system, or perhaps one held at constant temperature or pressure. Sometimes, extra tensions, shears, or temperature gradients are introduced to those simulations to probe one type of nonequilibrium response to external forces. Catalysts and molecular motors, however, function based on the nonequilibrium dynamics induced by a chemical reaction's thermodynamic driving force. In this scenario, simulations require chemostats capable of preserving the chemical concentrations of the nonequilibrium steady state. We develop such a dynamic scheme and use it to observe cycles of a particle-based classical model of a catenane-like molecular motor. Molecular motors are frequently modeled with detailed-balance-breaking Markov models, and we explicitly construct such a picture by coarse graining the microscopic dynamics of our simulations in order to extract rates. This work identifies inter-particle interactions that tune those rates to create a functional motor, thereby yielding a computational playground to investigate the interplay between directional bias, current generation, and coupling strength in molecular information ratchets.
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Affiliation(s)
- Alex Albaugh
- grid.16753.360000 0001 2299 3507Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 USA
| | - Todd R. Gingrich
- grid.16753.360000 0001 2299 3507Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 USA
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38
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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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39
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Manzano G, Roldán É. Survival and extreme statistics of work, heat, and entropy production in steady-state heat engines. Phys Rev E 2022; 105:024112. [PMID: 35291142 DOI: 10.1103/physreve.105.024112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities do not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in nonequilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.
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Affiliation(s)
- Gonzalo Manzano
- Institute for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain
- Institute for Quantum Optics and Quantum Information IQOQI, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Édgar Roldán
- ICTP-Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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40
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Lathouwers E, Sivak DA. Internal energy and information flows mediate input and output power in bipartite molecular machines. Phys Rev E 2022; 105:024136. [PMID: 35291132 DOI: 10.1103/physreve.105.024136] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
Microscopic biological systems operate far from equilibrium, are subject to strong fluctuations, and are composed of many coupled components with interactions varying in nature and strength. Researchers are actively investigating the general design principles governing how biomolecular machines achieve effective free-energy transduction in light of these challenges. We use a model of two strongly coupled stochastic rotary motors to explore the effect of coupling strength between components of a molecular machine. We observe prominent thermodynamic characteristics at intermediate coupling strength, near that which maximizes output power: a maximum in power and information transduced from the upstream to the downstream system, and equal subsystem entropy production rates. These observations are unified through a bound on the machine's input and output power, which accounts for both the energy and information transduced between subsystems.
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Affiliation(s)
- Emma Lathouwers
- Department of Physics, Simon Fraser University, Burnaby, BC, Canada, V5A1S6
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, BC, Canada, V5A1S6
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41
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Valiyev I, Ghosh A, Paul I, Schmittel M. Concurrent base and silver(I) catalysis pulsed by fuel acid. Chem Commun (Camb) 2022; 58:1728-1731. [PMID: 35024705 DOI: 10.1039/d1cc06398g] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Treatment of a crown-ether receptor and a silver(I)-loaded cyclam derivative (NetState-I) with a fuel acid reversibly afforded the protonated cyclam and the silver(I)-loaded crown ether (NetState-II). While NetState-I was catalytically OFF, a base-catalysed Michael addition and a silver(I)-catalysed oxime cyclisation reaction was pulsed under dissipative conditions in NetState-II.
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Affiliation(s)
- Isa Valiyev
- Center of Micro and Nanochemistry and (Bio)Technology, Organische Chemie I, Universität Siegen, Adolf-Reichwein-Str. 2, Siegen D-57068, Germany.
| | - Amit Ghosh
- Center of Micro and Nanochemistry and (Bio)Technology, Organische Chemie I, Universität Siegen, Adolf-Reichwein-Str. 2, Siegen D-57068, Germany.
| | - Indrajit Paul
- Center of Micro and Nanochemistry and (Bio)Technology, Organische Chemie I, Universität Siegen, Adolf-Reichwein-Str. 2, Siegen D-57068, Germany.
| | - Michael Schmittel
- Center of Micro and Nanochemistry and (Bio)Technology, Organische Chemie I, Universität Siegen, Adolf-Reichwein-Str. 2, Siegen D-57068, Germany.
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42
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Razavi M, Saberi Fathi SM, Tuszynski JA. The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms. ENTROPY 2022; 24:e24010094. [PMID: 35052120 PMCID: PMC8775074 DOI: 10.3390/e24010094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Revised: 12/04/2021] [Accepted: 12/28/2021] [Indexed: 12/14/2022]
Abstract
The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.
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Affiliation(s)
- Mohammad Razavi
- Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran;
| | - Seyed Majid Saberi Fathi
- Department of Physics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran;
- Correspondence:
| | - Jack Adam Tuszynski
- Department of Oncology, University of Alberta, Edmonton, AB T6G 1Z2, Canada;
- Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
- Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Torino, Italy
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43
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Speck T. Modeling of biomolecular machines in non-equilibrium steady states. J Chem Phys 2021; 155:230901. [PMID: 34937348 DOI: 10.1063/5.0070922] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium, such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with tens of thousands or even millions of degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared toward the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.
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Affiliation(s)
- Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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44
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Blaber S, Louwerse MD, Sivak DA. Steps minimize dissipation in rapidly driven stochastic systems. Phys Rev E 2021; 104:L022101. [PMID: 34525515 DOI: 10.1103/physreve.104.l022101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 07/09/2021] [Indexed: 02/04/2023]
Abstract
Micro- and nanoscale systems driven by rapid changes in control parameters (control protocols) dissipate significant energy. In the fast-protocol limit, we find that protocols that minimize dissipation at fixed duration are universally given by a two-step process, jumping to and from a point that balances jump size with fast relaxation. Jump protocols could be exploited by molecular machines or thermodynamic computing to improve energetic efficiency, and implemented in nonequilibrium free-energy estimation to improve accuracy.
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Affiliation(s)
- Steven Blaber
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| | - Miranda D Louwerse
- Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
| | - David A Sivak
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
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45
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Valdiviezo J, Zhang P, Beratan DN. Electron ratcheting in self-assembled soft matter. J Chem Phys 2021; 155:055102. [PMID: 34364335 DOI: 10.1063/5.0044420] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Abstract
Ratcheted multi-step hopping electron transfer systems can plausibly produce directional charge transport over very large distances without requiring a source-drain voltage bias. We examine molecular strategies to realize ratcheted charge transport based on multi-step charge hopping, and we illustrate two ratcheting mechanisms with examples based on DNA structures. The charge transport times and currents that may be generated in these assemblies are also estimated using kinetic simulations. The first ratcheting mechanism described for nanoscale systems requires local electric fields on the 109 V/m scale to realize nearly 100% population transport. The second ratcheting mechanism for even larger systems, based on electrochemical gating, is estimated to generate currents as large as 0.1 pA for DNA structures that are a few μm in length with a gate voltage of about 5 V, a magnitude comparable to currents measured in DNA wires at the nanoscale when a source-drain voltage bias of similar magnitude is applied, suggesting an approach to considerably extend the distance range over which DNA charge transport devices may operate.
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Affiliation(s)
- Jesús Valdiviezo
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - David N Beratan
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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46
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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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47
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Abstract
We describe as 'reversible' a bidirectional catalyst that allows a reaction to proceed at a significant rate in response to even a small departure from equilibrium, resulting in fast and energy-efficient chemical transformation. Examining the relation between reaction rate and thermodynamic driving force is the basis of electrochemical investigations of redox reactions, which can be catalysed by metallic surfaces and biological or synthetic molecular catalysts. This relation has also been discussed in the context of biological energy transduction, regarding the function of biological molecular machines that harness chemical reactions to do mechanical work. This Perspective describes mean-field kinetic modelling of these three types of systems - surface catalysts, molecular catalysts of redox reactions and molecular machines - with the goal of unifying concepts in these different fields. We emphasize that reversibility should be distinguished from other figures of merit, such as rate or directionality, before its design principles can be identified and used to engineer synthetic catalysts.
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48
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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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49
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Shukla S, Baumgart T. Enzymatic trans-bilayer lipid transport: Mechanisms, efficiencies, slippage, and membrane curvature. BIOCHIMICA ET BIOPHYSICA ACTA. BIOMEMBRANES 2021; 1863:183534. [PMID: 33340491 PMCID: PMC8351443 DOI: 10.1016/j.bbamem.2020.183534] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Revised: 12/03/2020] [Accepted: 12/07/2020] [Indexed: 12/12/2022]
Abstract
The eukaryotic plasma membrane's lipid composition is found to be ubiquitously asymmetric comparing inner and outer leaflets. This membrane lipid asymmetry plays a crucial role in diverse cellular processes critical for cell survival. A specialized set of transmembrane proteins called translocases, or flippases, have evolved to maintain this membrane lipid asymmetry in an energy-dependent manner. One potential consequence of local variations in membrane lipid asymmetry is membrane remodeling, which is essential for cellular processes such as intracellular trafficking. Recently, there has been a surge in the identification and characterization of flippases, which has significantly advanced the understanding of their functional mechanisms. Furthermore, there are intriguing possibilities for a coupling between membrane curvature and flippase activity. In this review we highlight studies that link membrane shape and remodeling to differential stresses generated by the activity of lipid flippases with an emphasis on data obtained through model membrane systems. We review the common mechanistic models of flippase-mediated lipid flipping and discuss common techniques used to test lipid flippase activity. We then compare the existing data on lipid translocation rates by flippases and conclude with potential future directions for this field.
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Affiliation(s)
- Sankalp Shukla
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, United States
| | - Tobias Baumgart
- Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104, United States.
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Brown AI, Koslover EF. Design principles for the glycoprotein quality control pathway. PLoS Comput Biol 2021; 17:e1008654. [PMID: 33524026 PMCID: PMC7877790 DOI: 10.1371/journal.pcbi.1008654] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 02/11/2021] [Accepted: 12/21/2020] [Indexed: 01/11/2023] Open
Abstract
Newly-translated glycoproteins in the endoplasmic reticulum (ER) often undergo cycles of chaperone binding and release in order to assist in folding. Quality control is required to distinguish between proteins that have completed native folding, those that have yet to fold, and those that have misfolded. Using quantitative modeling, we explore how the design of the quality-control pathway modulates its efficiency. Our results show that an energy-consuming cyclic quality-control process, similar to the observed physiological system, outperforms alternative designs. The kinetic parameters that optimize the performance of this system drastically change with protein production levels, while remaining relatively insensitive to the protein folding rate. Adjusting only the degradation rate, while fixing other parameters, allows the pathway to adapt across a range of protein production levels, aligning with in vivo measurements that implicate the release of degradation-associated enzymes as a rapid-response system for perturbations in protein homeostasis. The quantitative models developed here elucidate design principles for effective glycoprotein quality control in the ER, improving our mechanistic understanding of a system crucial to maintaining cellular health. We explore the architecture and limitations of the quality-control pathway responsible for efficient folding of secretory proteins. Newly-synthesized proteins are tagged by the attachment of a ‘glycan’ sugar chain which facilitates their binding to a chaperone that assists protein folding. Removal of a specific sugar group on the glycan ends the interaction with the chaperone, and not-yet-folded proteins can be re-tagged for another round of chaperone binding. A degradation pathway acts in parallel with the folding cycle, to remove those proteins that have remained unfolded for a sufficiently long time. We develop and solve a mathematical model of this quality-control system, showing that the cyclical design found in living cells is uniquely able to maximize folded protein throughput while avoiding accumulation of unfolded proteins. Although this physiological model provides the best performance, its parameters must be adjusted to perform optimally under different protein production loads, and any single fixed set of parameters leads to poor performance when production rate is altered. We find that a single adjustable parameter, the protein degradation rate, is sufficient to allow optimal performance across a range of conditions. Interestingly, observations of living cells suggest that the degradation speed is indeed rapidly adjusted.
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Affiliation(s)
- Aidan I. Brown
- Department of Physics, University of California, San Diego, San Diego, California, United States of America
| | - Elena F. Koslover
- Department of Physics, University of California, San Diego, San Diego, California, United States of America
- * E-mail:
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