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Li HN, Zhang C, Xin JH, Liu YW, Yang HC, Zhu CY, Liu C, Xu ZK. Design of Photothermal "Ion Pumps" for Achieving Energy-Efficient, Augmented, and Durable Lithium Extraction from Seawater. ACS NANO 2024; 18:2434-2445. [PMID: 38206056 DOI: 10.1021/acsnano.3c10910] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Extracting lithium from seawater has emerged as a disruptive platform to resolve the issue of an ever-growing lithium shortage. However, achieving highly efficient and durable lithium extraction from seawater in an energy-efficient manner is challenging, as imposed by the low concentration of lithium ions (Li+) and high concentration of interfering ions in seawater. Here, we report a facile and universal strategy to develop photothermal "ion pumps" (PIPs) that allow achieving energy-efficient, augmented, and durable lithium extraction from seawater under sunlight. The key design of PIPs lies in the function fusion and spatial configuration manipulation of a hydrophilic Li+-trapping nanofibrous core and a hydrophobic photothermal shell for governing gravity-driven water flow and solar-driven water evaporation. Such a synergetic effect allows PIPs to achieve spontaneous, continuous, and augmented Li+ replenishment-diffusion-enrichment, as well as circumvent the impact of concentration polarization and scaling of interfering ions. We demonstrate that our PIPs exhibit dramatic enhancement in Li+ trapping rate and outstanding Li+ separation factor yet have ultralow energy consumption. Moreover, our PIPs deliver ultrastable Li+ trapping performance without scaling even under high-concentration interfering ions for 140 h operation, as opposed to the significant decrease of nearly 55.6% in conventional photothermal configuration. The design concept and material toolkit developed in this work can also find applications in extracting high-value-added resources from seawater and beyond.
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Affiliation(s)
- Hao-Nan Li
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Chao Zhang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Jia-Hui Xin
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Yu-Wei Liu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Hao-Cheng Yang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Cheng-Ye Zhu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Chang Liu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Zhi-Kang Xu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, MOE Engineering Research Center of Membrane and Water Treatment Technology, and Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China
- The "Belt and Road" Sino-Portugal Joint Lab on Advanced Materials, International Research Center for X Polymers, Zhejiang University, Hangzhou 310027, People's Republic of China
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Das D, Pradhan P, Chatterjee S. Optimum transport in systems with time-dependent drive and short-ranged interactions. Phys Rev E 2023; 108:034107. [PMID: 37849159 DOI: 10.1103/physreve.108.034107] [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: 08/14/2023] [Indexed: 10/19/2023]
Abstract
We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.
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Affiliation(s)
- Deepsikha Das
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Sakuntala Chatterjee
- Physics of Complex Systems, S.N. Bose National Centre for Basic Sciences Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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3
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Zhang Z, Lu Z. Nonequilibrium Theoretical Framework and Universal Design Principles of Oscillation-Driven Catalysis. J Phys Chem Lett 2023; 14:7541-7548. [PMID: 37586077 DOI: 10.1021/acs.jpclett.3c01677] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
At stationary environmental conditions, a catalyst's reaction kinetics may be restricted by its available designs and thermodynamic laws. Thus, its stationary performances may experience practical or theoretical restraints (e.g., catalysts cannot invert the spontaneous direction of a chemical reaction). However, many works have reported that if environments change rapidly, catalysts can be driven away from stationary states and exhibit anomalous performance. We present a general geometric nonequilibrium theory to explain anomalous catalytic behaviors driven by rapidly oscillating environments where stationary-environment restraints are broken. It leads to a universal design principle of novel catalysts with oscillation-pumped performances. Even though a single free energy landscape cannot describe catalytic kinetics at various environmental conditions, we propose a novel control-conjugate landscape to encode the reaction kinetics over a range of control parameters λ, inspired by the Arrhenius form. The control-conjugate landscape significantly simplifies the design principle applicable to large-amplitude environmental oscillations.
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Affiliation(s)
- Zhongmin Zhang
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
| | - Zhiyue Lu
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
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4
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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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5
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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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6
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Abstract
Ion pumps are important membrane-spanning transporters that pump ions against the electrochemical gradient across the cell membrane. In biological systems, ion pumping is essential to maintain intracellular osmotic pressure, to respond to external stimuli, and to regulate physiological activities by consuming adenosine triphosphate. In recent decades, artificial ion pumping systems with diverse geometric structures and functions have been developing rapidly with the progress of advanced materials and nanotechnology. In this Review, bioinspired artificial ion pumps, including four categories: asymmetric structure-driven ion pumps, pH gradient-driven ion pumps, light-driven ion pumps, and electron-driven ion pumps, are summarized. The working mechanisms, functions, and applications of those artificial ion pumping systems are discussed. Finally, a brief conclusion of underpinning challenges and outlook for future research are tentatively discussed.
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Affiliation(s)
- Tingting Mei
- Department of Biomedical Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, P.R. China
| | - Hongjie Zhang
- Department of Biomedical Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, P.R. China
| | - Kai Xiao
- Department of Biomedical Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, P.R. China
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Chen W, Wang L, Liang P, Mast J, Mathis C, Liu CY, Wei J, Zhang J, Fu L, Juncos LA, Buggs J, Liu R. Reducing ischemic kidney injury through application of a synchronization modulation electric field to maintain Na +/K +-ATPase functions. Sci Transl Med 2022; 14:eabj4906. [PMID: 35263146 PMCID: PMC9994383 DOI: 10.1126/scitranslmed.abj4906] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Renal ischemia-reperfusion injury is an important contributor to the development of delayed graft function after transplantation, which is associated with higher rejection rates and poorer long-term outcomes. One of the earliest impairments during ischemia is Na+/K+-ATPase (Na/K pump) dysfunction due to insufficient ATP supply, resulting in subsequent cellular damage. Therefore, strategies that preserve ATP or maintain Na/K pump function may limit the extent of renal injury during ischemia-reperfusion. Here, we applied a synchronization modulation electric field to activate Na/K pumps, thereby maintaining cellular functions under ATP-insufficient conditions. We tested the effectiveness of this technique in two models of ischemic renal injury: an in situ renal ischemia-reperfusion injury model (predominantly warm ischemia) and a kidney transplantation model (predominantly cold ischemia). Application of the synchronization modulation electric field to a renal ischemia-reperfusion injury mouse model preserved Na/K pump activity, thereby reducing kidney injury, as reflected by 40% lower plasma creatinine (1.17 ± 0.03 mg/dl) in the electric field-treated group as compared to the untreated control group (1.89 ± 0.06 mg/dl). In a mouse kidney transplantation model, renal graft function was improved by more than 50% with the application of the synchronization modulation electric field according to glomerular filtration rate measurements (85.40 ± 12.18 μl/min in the untreated group versus 142.80 ± 11.65 μl/min in the electric field-treated group). This technique for preserving Na/K pump function may have therapeutic potential not only for ischemic kidney injury but also for other diseases associated with Na/K pump dysfunction due to inadequate ATP supply.
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Affiliation(s)
- Wei Chen
- Department of Physics, College of Arts and Sciences, University of South Florida, Tampa, FL 33620, USA
| | - Lei Wang
- Department of Molecular Pharmacology and Physiology, College of Medicine, University of South Florida, Tampa, FL 33620, USA
| | - Pengfei Liang
- Department of Physics, College of Arts and Sciences, University of South Florida, Tampa, FL 33620, USA
| | - Jason Mast
- Department of Physics, College of Arts and Sciences, University of South Florida, Tampa, FL 33620, USA
| | - Clausell Mathis
- Department of Physics, College of Arts and Sciences, University of South Florida, Tampa, FL 33620, USA
| | - Catherine Y Liu
- Department of Molecular Pharmacology and Physiology, College of Medicine, University of South Florida, Tampa, FL 33620, USA
| | - Jin Wei
- Department of Molecular Pharmacology and Physiology, College of Medicine, University of South Florida, Tampa, FL 33620, USA
| | - Jie Zhang
- Department of Molecular Pharmacology and Physiology, College of Medicine, University of South Florida, Tampa, FL 33620, USA
| | - Liying Fu
- Department of Pathology, Scripps Green Hospital, La Jolla, CA 92037, USA
| | - Luis A Juncos
- Department of Internal Medicine, University of Arkansas for Medical Sciences, Little Rock, AR 72205, USA
| | | | - Ruisheng Liu
- Department of Molecular Pharmacology and Physiology, College of Medicine, University of South Florida, Tampa, FL 33620, USA
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9
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10
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Hino Y, Hayakawa H. Fluctuation relations for adiabatic pumping. Phys Rev E 2020; 102:012115. [PMID: 32795070 DOI: 10.1103/physreve.102.012115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 05/28/2020] [Indexed: 06/11/2023]
Abstract
We derive an extended fluctuation relation for an open system coupled with two reservoirs under adiabatic one-cycle modulation. We confirm that the geometrical phase caused by the Berry-Sinitsyn-Nemenman curvature in the parameter space generates non-Gaussian fluctuations. This non-Gaussianity is enhanced for the instantaneous fluctuation relation when the bias between the two reservoirs disappears.
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Affiliation(s)
- Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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11
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Takahashi K, Fujii K, Hino Y, Hayakawa H. Nonadiabatic Control of Geometric Pumping. PHYSICAL REVIEW LETTERS 2020; 124:150602. [PMID: 32357045 DOI: 10.1103/physrevlett.124.150602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 03/17/2020] [Indexed: 06/11/2023]
Abstract
We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the nontrivial part of the current is possible even in the nonadiabatic regime. The exact result allows us to find a smooth connection between the adiabatic Berry phase theory at low frequencies and the Floquet theory at high frequencies. We also study how to control the geometric current. Using the method of shortcuts to adiabaticity with the aid of an assisting field, we illustrate that it enhances the current.
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Affiliation(s)
- Kazutaka Takahashi
- Institute of Innovative Research, Tokyo Institute of Technology, Kanagawa 226-8503, Japan
| | - Keisuke Fujii
- Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan and iTHEMS Program, RIKEN, Saitama 351-0198, Japan
| | - Yuki Hino
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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Abstract
Recent developments in synthetic molecular motors and pumps have sprung from a remarkable confluence of experiment and theory. Synthetic accomplishments have facilitated the ability to design and create molecules, many of them featuring mechanically bonded components, to carry out specific functions in their environment-walking along a polymeric track, unidirectional circling of one ring about another, synthesizing stereoisomers according to an external protocol, or pumping rings onto a long rod-like molecule to form and maintain high-energy, complex, nonequilibrium structures from simpler antecedents. Progress in the theory of nanoscale stochastic thermodynamics, specifically the generalization and extension of the principle of microscopic reversibility to the single-molecule regime, has enhanced the understanding of the design requirements for achieving strong unidirectional motion and high efficiency of these synthetic molecular machines for harnessing energy from external fluctuations to carry out mechanical and/or chemical functions in their environment. A key insight is that the interaction between the fluctuations and the transition state energies plays a central role in determining the steady-state concentrations. Kinetic asymmetry, a requirement for stochastic adaptation, occurs when there is an imbalance in the effect of the fluctuations on the forward and reverse rate constants. Because of strong viscosity, the motions of the machine can be viewed as mechanical equilibrium processes where mechanical resonances are simply impossible but where the probability distributions for the state occupancies and trajectories are very different from those that would be expected at thermodynamic equilibrium.
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Pezzato C, Cheng C, Stoddart JF, Astumian RD. Mastering the non-equilibrium assembly and operation of molecular machines. Chem Soc Rev 2018; 46:5491-5507. [PMID: 28338143 DOI: 10.1039/c7cs00068e] [Citation(s) in RCA: 203] [Impact Index Per Article: 33.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
In mechanically interlocked compounds, such as rotaxanes and catenanes, the molecules are held together by mechanical rather than chemical bonds. These compounds can be engineered to have several well-defined mechanical states by incorporating recognition sites between the different components. The rates of the transitions between the recognition sites can be controlled by introducing steric "speed bumps" or electrostatically switchable gates. A mechanism for the absorption of energy can also be included by adding photoactive, catalytically active, or redox-active recognition sites, or even charges and dipoles. At equilibrium, these Mechanically Interlocked Molecules (MIMs) undergo thermally activated transitions continuously between their different mechanical states where every transition is as likely as its microscopic reverse. External energy, for example, light, external modulation of the chemical and/or physical environment or catalysis of an exergonic reaction, drives the system away from equilibrium. The absorption of energy from these processes can be used to favour some, and suppress other, transitions so that completion of a mechanical cycle in a direction in which work is done on the environment - the requisite of a molecular machine - is more likely than completion in a direction in which work is absorbed from the environment. In this Tutorial Review, we discuss the different design principles by which molecular machines can be engineered to use different sources of energy to carry out self-organization and the performance of work in their environments.
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Affiliation(s)
- Cristian Pezzato
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, USA.
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14
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Watanabe KL, Hayakawa H. Geometric fluctuation theorem for a spin-boson system. Phys Rev E 2017; 96:022118. [PMID: 28950528 DOI: 10.1103/physreve.96.022118] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.
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Affiliation(s)
- Kota L Watanabe
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Hisao Hayakawa
- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa-oiwake cho, Sakyo-ku, Kyoto 606-8502, Japan
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15
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Rahav S. Validity of the no-pumping theorem in systems with finite-range interactions between particles. Phys Rev E 2017; 95:012159. [PMID: 28208507 DOI: 10.1103/physreve.95.012159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 06/06/2023]
Abstract
The no-pumping theorem states that seemingly natural driving cycles of stochastic machines fail to generate directed motion. Initially derived for single particle systems, the no-pumping theorem was recently extended to many-particle systems with zero-range interactions. Interestingly, it is known that the theorem is violated by systems with exclusion interactions. These two paradigmatic interactions differ by two qualitative aspects: the range of interactions and the dependence of branching fractions on the state of the system. In this work two different models are studied in order to identify the qualitative property of the interaction that leads to breakdown of no pumping. A model with finite-range interaction is shown analytically to satisfy no pumping. In contrast, a model in which the interaction affects the probabilities of reaching different sites, given that a particle is making a transition, is shown numerically to violate the no-pumping theorem. The results suggest that systems with interactions that lead to state-dependent branching fractions do not satisfy the no-pumping theorem.
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Affiliation(s)
- Saar Rahav
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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16
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Chatterjee R, Chatterjee S, Pradhan P. Symmetric exclusion processes on a ring with moving defects. Phys Rev E 2016; 93:062124. [PMID: 27415225 DOI: 10.1103/physreve.93.062124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Indexed: 11/07/2022]
Abstract
We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders-a generalization of the model we proposed earlier [Phys. Rev. E 89, 022138 (2014)PLEEE81539-375510.1103/PhysRevE.89.022138]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.
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Affiliation(s)
- Rakesh Chatterjee
- The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India.,Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Cuernavaca 62210, México
| | - Sakuntala Chatterjee
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Punyabrata Pradhan
- Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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Astumian RD, Mukherjee S, Warshel A. The Physics and Physical Chemistry of Molecular Machines. Chemphyschem 2016; 17:1719-41. [PMID: 27149926 PMCID: PMC5518708 DOI: 10.1002/cphc.201600184] [Citation(s) in RCA: 93] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2016] [Indexed: 12/25/2022]
Abstract
The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.
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Affiliation(s)
- R Dean Astumian
- Department of Physics, University of Maine, Orono, ME, 04469, USA.
| | - Shayantani Mukherjee
- Department of Chemistry, University of Southern California, Los Angeles, California, USA.
| | - Arieh Warshel
- Department of Chemistry, University of Southern California, Los Angeles, California, USA.
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18
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Esposito M, Parrondo JMR. Stochastic thermodynamics of hidden pumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052114. [PMID: 26066126 DOI: 10.1103/physreve.91.052114] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2014] [Indexed: 06/04/2023]
Abstract
We show that a reversible pumping mechanism operating between two states of a kinetic network can give rise to Poisson transitions between these two states. An external observer, for whom the pumping mechanism is not accessible, will observe a Markov chain satisfying local detailed balance with an emerging effective force induced by the hidden pump. Due to the reversibility of the pump, the actual entropy production turns out to be lower than the coarse-grained entropy production estimated from the flows and affinities of the resulting Markov chain. Moreover, in presence of a large time scale separation between the fast-pumping dynamics and the slow-network dynamics, a finite current with zero dissipation may be produced. We make use of these general results to build a synthetase-like kinetic scheme able to reversibly produce high free-energy molecules at a finite rate and a rotatory motor achieving 100% efficiency at finite speed.
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Affiliation(s)
- Massimiliano Esposito
- Complex Systems and Statistical Mechanics, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Juan M R Parrondo
- Departamento de Fisica Atómica, Molecular y Nuclear and GISC, Universidad Complutense Madrid, 28040 Madrid, Spain
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Nakagawa N. Universal expression for adiabatic pumping in terms of nonequilibrium steady states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022108. [PMID: 25215690 DOI: 10.1103/physreve.90.022108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2014] [Indexed: 06/03/2023]
Abstract
We develop a unified treatment of pumping and nonequilibrium thermodynamics. We show that the pumping current generated through an adiabatic mechanical operation in equilibrium can be expressed in terms of the stationary distribution of the corresponding driven nonequilibrium system. We also show that the total transfer in pumping can be evaluated from the work imported to the driven counterpart. These findings lead us to a unified viewpoint for pumping and nonequilibrium thermodynamics.
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Affiliation(s)
- Naoko Nakagawa
- College of Science, Ibaraki University, Mito, Ibaraki 310-8512, Japan
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20
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Asban S, Rahav S. No-pumping theorem for many particle stochastic pumps. PHYSICAL REVIEW LETTERS 2014; 112:050601. [PMID: 24580580 DOI: 10.1103/physrevlett.112.050601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2013] [Indexed: 06/03/2023]
Abstract
Stochastic pumps are models of artificial molecular machines which are driven by periodic time variation of parameters, such as site and barrier energies. The no-pumping theorem states that no directed motion is generated by variation of only site or barrier energies [S. Rahav, J. Horowitz, and C. Jarzynski, Phys. Rev. Lett. 101, 140602 (2008)]. We study stochastic pumps of several interacting particles and demonstrate that the net current of particles satisfies an additional no-pumping theorem.
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Affiliation(s)
- Shahaf Asban
- Faculty of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Saar Rahav
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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21
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Abstract
FO-ATP synthase (FO) is a rotary motor that converts potential energy from ions, usually protons, moving from high- to low-potential sides of a membrane into torque and rotary motion. Here we propose a mechanism whereby electric fields emanating from the proton entry and exit channels act on asymmetric charge distributions in the c-ring, due to protonated and deprotonated sites, and drive it to rotate. The model predicts a scaling between time-averaged torque and proton motive force, which can be hindered by mutations that adversely affect the channels. The torque created by the c-ring of FO drives the γ-subunit to rotate within the ATP-producing complex (F1) overcoming, with the aid of thermal fluctuations, an opposing torque that rises and falls with angular position. Using the analogy with thermal Brownian motion of a particle in a tilted washboard potential, we compute ATP production rates vs. proton motive force. The latter shows a minimum, needed to drive ATP production, which scales inversely with the number of proton binding sites on the c-ring.
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Ai BQ, He YF, Li FG, Zhong WR. Hydrodynamically enforced entropic Brownian pump. J Chem Phys 2013; 138:154107. [DOI: 10.1063/1.4801661] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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23
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Mandal D, Jarzynski C. Hybrid models of molecular machines and the no-pumping theorem. J Chem Phys 2012; 137:234104. [PMID: 23267468 DOI: 10.1063/1.4771657] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Synthetic nanoscale complexes capable of mechanical movement are often studied theoretically using discrete-state models that involve instantaneous transitions between metastable states. A number of general results have been derived within this framework, including a "no-pumping theorem" that restricts the possibility of generating directed motion by the periodic variation of external parameters. Motivated by recent experiments using time-resolved vibrational spectroscopy [Panman et al., Science 328, 1255 (2010)], we introduce a more detailed and realistic class of models in which transitions between metastable states occur by finite-time, diffusive processes rather than sudden jumps. We show that the no-pumping theorem remains valid within this framework.
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Affiliation(s)
- Dibyendu Mandal
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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24
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Zhang L, Fang Z, Chen W. Quick and effective hyperpolarization of the membrane potential in intact smooth muscle cells of blood vessels by synchronization modulation electric field. J Bioenerg Biomembr 2012; 44:385-95. [PMID: 22454211 DOI: 10.1007/s10863-012-9432-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2011] [Accepted: 02/29/2012] [Indexed: 11/26/2022]
Abstract
Blood vessel dilation starts from activation of the Na/K pumps and inward rectifier K channels in the vessel smooth muscle cells, which hyperpolarizes the cell membrane potential and closes the Ca channels. As a result, the intracellular Ca concentration reduces, and the smooth muscle cells relax and the blood vessel dilates. Activation of the Na/K pumps and the membrane potential hyperpolarization plays a critical role in blood vessel functions. Previously, we developed a new technique, synchronization modulation, to control the pump functions by electrically entraining the pump molecules. We have applied the synchronization modulation electric field noninvasively to various intact cells and demonstrated the field-induced membrane potential hyperpolarization. We further applied the electric field to blood vessels and investigated the field induced functional changes of the vessels. In this paper, we report the results in a study of the membrane potential change in the smooth muscle cells of mesenteric blood vessels in response to the oscillating electric field. We found that the synchronization modulation electric field can effectively hyperpolarize the muscle membrane potential quickly in seconds under physiological conditions.
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Affiliation(s)
- Liping Zhang
- Cellular and Molecular Biophysics Lab, Department of Physics, University of South Florida, Tampa, FL 33620, USA
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25
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Hyperpolarization of the membrane potential in cardiomyocyte tissue slices by the synchronization modulation electric field. J Membr Biol 2012; 245:97-105. [PMID: 22359065 DOI: 10.1007/s00232-012-9418-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2011] [Accepted: 01/31/2012] [Indexed: 10/28/2022]
Abstract
Our previous studies have shown that a specially designed, so-called synchronization modulation electric field can entrain active transporter Na/K pumps in the cell membrane. This approach was previously developed in a study of single cells using a voltage clamp to monitor the pump currents. We are now expanding our study from isolated single cells to aggregated cells in a 3-dimensional cell matrix, through the use of a tissue slice from the rat heart. The slice is about 150 μm in thickness, meaning the slices contain many cell layers, resulting in a simplified 3-dimensional system. A fluorescent probe was used to identify the membrane potential and the ionic concentration gradients across the cell membrane. In spite of intrinsic cell-to-cell interactions and the difficulty in stimulating cell aggregation in the tissue slice, the oscillating electric field increased the intracellular fluorescent intensity, indicating elevation of the cell ionic concentration and hyperpolarization of the cell membrane. Blockage of these changes by ouabain confirmed that the results are directly related to Na/K pumps. These results along with the backward modulation indicate that the synchronization modulation electric field can influence the Na/K pumps in tissue cells of a 3-dimensional matrix and therefore hyperpolarize the cell membrane.
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Astumian RD. Stochastic Conformational Pumping: A Mechanism for Free-Energy Transduction by Molecules. Annu Rev Biophys 2011; 40:289-313. [DOI: 10.1146/annurev-biophys-042910-155355] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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27
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Basu U, Chaudhuri D, Mohanty PK. Bimodal response in periodically driven diffusive systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031115. [PMID: 21517462 DOI: 10.1103/physreve.83.031115] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2010] [Indexed: 05/23/2023]
Abstract
We study the response of one-dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system can be characterized in terms of the structure factor. We find an interesting frequency-dependent response; the current-carrying majority excitons cyclically crosses over from a short wavelength mode to a long wavelength mode with an intermediate regime of coexistence. This effect being boundary driven decays inversely with system size. Analytic calculations show that this behavior is common to diffusive systems, both in the absence and presence of correlations.
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Affiliation(s)
- Urna Basu
- TCMP Division, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India.
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28
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Thermodynamics and kinetics of molecular motors. Biophys J 2010; 98:2401-9. [PMID: 20513383 DOI: 10.1016/j.bpj.2010.02.040] [Citation(s) in RCA: 92] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2009] [Revised: 02/03/2010] [Accepted: 02/16/2010] [Indexed: 11/20/2022] Open
Abstract
Molecular motors are first and foremost molecules, governed by the laws of chemistry rather than of mechanics. The dynamical behavior of motors based on chemical principles can be described as a random walk on a network of states. A key insight is that any molecular motor in solution explores all possible motions and configurations at thermodynamic equilibrium. By using input energy and chemical design to prevent motion that is not wanted, what is left behind is the motion that is desired. This review is focused on two-headed motors such as kinesin and Myosin V that move on a polymeric track. By use of microscopic reversibility, it is shown that the ratio between the number of forward steps and the number of backward steps in any sufficiently long time period does not directly depend on the mechanical properties of the linker between the two heads. Instead, this ratio is governed by the relative chemical specificity of the heads in the front-versus-rear position for the fuel, adenosine triphosphate and its products, adenosine diphosphate and inorganic phosphate. These insights have been key factors in the design of biologically inspired synthetic molecular walkers constructed out of DNA or out of small organic molecules.
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29
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Maes C, Netočný K, Thomas SR. General no-go condition for stochastic pumping. J Chem Phys 2010; 132:234116. [DOI: 10.1063/1.3446811] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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30
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Muneyuki E, Sekimoto K. Allosteric model of an ion pump. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011137. [PMID: 20365353 DOI: 10.1103/physreve.81.011137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2008] [Revised: 11/25/2009] [Indexed: 05/29/2023]
Abstract
We present a simple model of a free-energy transducer made of allosterically coupled two ratchet subsystems. Each of the subsystems transports particles from one particle reservoir to another. The coupling of the subsystems imposes correlated transitions of the potential profiles of the two subsystems. As a result, a downhill flux in one subsystem with higher chemical-potential difference drives an uphill flux in the other subsystem with lower chemical-potential difference. The direction of the driven flux inverts depending on the direction of the driving flux. The ratio between the fluxes conveyed by the two subsystems is variable and nonstoichiometric. By selecting appropriate parameters, the maximum ratio of the driven flux to driving flux and maximum free-energy transducing efficiency reaches some 90 and 40%, respectively. At a stalled state, the driven flux vanishes while the driving flux remains finite. The allosteric model enables explicit analysis of the timing between binding-unbinding of particles and transitions of potential profile. The behavior of the model is similar to but different from that of the alternate access model, which is a biochemical model for active transport proteins. Our model works also as a regulatory system. We suggest that the correlated transitions of the subsystems (subunits or domains) through allosteric interaction are the origin of the diverse functions of the protein machineries.
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Affiliation(s)
- Eiro Muneyuki
- Faculty of Science and Engineering, Department of Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan.
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31
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Tomruk A, Guler G, Dincel AS. The Influence of 1800 MHz GSM-like Signals on Hepatic Oxidative DNA and Lipid Damage in Nonpregnant, Pregnant, and Newly born Rabbits. Cell Biochem Biophys 2009; 56:39-47. [DOI: 10.1007/s12013-009-9068-1] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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32
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Ohkubo J. Variational principle of counting statistics in master equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:012101. [PMID: 19658749 DOI: 10.1103/physreve.80.012101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2009] [Indexed: 05/28/2023]
Abstract
We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not an approximation, but a valid procedure in the present derivation. Hence, a variational principle in the counting statistics is naturally derived. In order to obtain the variational principle, we employ many independent replicas of the same system. In addition, the Euler-Maclaurin formula is used in order to connect the discrete and continuous properties of the system.
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Affiliation(s)
- Jun Ohkubo
- Institute for Solid State Physics, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa-shi, Chiba 277-8581, Japan.
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33
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Mousavy SJ, Riazi GH, Kamarei M, Aliakbarian H, Sattarahmady N, Sharifizadeh A, Safarian S, Ahmad F, Moosavi–Movahedi AA. Effects of mobile phone radiofrequency on the structure and function of the normal human hemoglobin. Int J Biol Macromol 2009; 44:278-85. [DOI: 10.1016/j.ijbiomac.2009.01.001] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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34
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Ohkubo J. Current and fluctuation in a two-state stochastic system under nonadiabatic periodic perturbation. J Chem Phys 2008; 129:205102. [DOI: 10.1063/1.3026510] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Rahav S, Horowitz J, Jarzynski C. Directed flow in nonadiabatic stochastic pumps. PHYSICAL REVIEW LETTERS 2008; 101:140602. [PMID: 18851514 DOI: 10.1103/physrevlett.101.140602] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Indexed: 05/26/2023]
Abstract
We analyze the operation of a molecular machine driven by the nonadiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a "no-pumping theorem" for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression.
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Affiliation(s)
- Saar Rahav
- Department of Chemistry, University of Maryland, College Park, Maryland 20742, USA
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37
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Abstract
A Brownian pump in nonlinear diffusive media is investigated in the presence of an unbiased external force. The pumping system is embedded in a finite region and bounded by two particle reservoirs. In the adiabatic limit, we obtain the analytical expressions of the current and the pumping capacity as a function of temperature for normal diffusion, subdiffusion, and superdiffusion. It is found that important anomalies are detected in comparison with the normal diffusion case. The superdiffusive regime, compared with the normal one, exhibits an opposite current for low temperatures. In the subdiffusive regime, the current may become forbidden for low temperatures and negative for high temperatures.
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Affiliation(s)
- Bao-quan Ai
- Institute for Condensed Matter Physics, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, China.
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38
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Chen W. Synchronization of Ion Exchangers by an Oscillating Electric Field: Theory. J Phys Chem B 2008; 112:10064-70. [DOI: 10.1021/jp0754637] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Wei Chen
- Cellular and Molecular Biophysics, Department of Physics, University of South Florida, 4202 East Fowler Avenue, Tampa, Florida 33620
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39
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Gomez-Marin A, Sancho JM. Brownian pump powered by a white-noise flashing ratchet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:031108. [PMID: 18517330 DOI: 10.1103/physreve.77.031108] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2007] [Indexed: 05/26/2023]
Abstract
A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. We propose a simulation framework for the consistent evaluation of such observable quantities.
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Affiliation(s)
- A Gomez-Marin
- Facultat de Fisica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain
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40
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Chen W, Dando R. Membrane potential hyperpolarization in Mammalian cardiac cells by synchronization modulation of Na/K pumps. J Membr Biol 2008; 221:165-73. [PMID: 18288434 DOI: 10.1007/s00232-008-9094-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2007] [Accepted: 01/18/2008] [Indexed: 11/25/2022]
Abstract
In previously reported work, we developed a new technique, synchronization modulation, to electrically activate Na/K pump molecules. The fundamental mechanism involved in this technique is a dynamic entrainment procedure of the pump molecules, carried out in a stepwise pattern. The entrainment procedure consists of two steps: synchronization and modulation. We theoretically predicted that the pump functions can be activated exponentially as a function of the membrane potential. We have experimentally demonstrated synchronization of the Na/K pump molecules and acceleration of their pumping rates by many fold through use of voltage-clamp techniques, directly monitoring the pump currents. We further applied this technique to intact skeletal muscle fibers from amphibians and found significant effects on the membrane resting potential. Here, we extend our study to intact mammalian cardiomyocytes. We employed a noninvasive confocal microscopic fluorescent imaging technique to monitor electric field-induced changes in ionic concentration gradient and membrane resting potential. Our results further confirm that the well-designed synchronization modulation electric field can effectively accelerate the Na/K pumping rate, increasing the ionic concentration gradient across the cell membrane and hyperpolarizing the membrane resting potential.
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Affiliation(s)
- Wei Chen
- Cellular and Molecular Biophysics, University of South Florida, Tampa, FL 33620, USA.
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41
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Treo EF, Felice CJ. Importance of intermediary transitions and waveform in the enzyme-electric field interaction. Bioelectrochemistry 2008; 72:127-34. [PMID: 18262855 DOI: 10.1016/j.bioelechem.2008.01.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2007] [Accepted: 01/02/2008] [Indexed: 10/22/2022]
Abstract
The current theory of enzymes and electric field interaction does not account for all the observed data since we could not observe non-linear behavior of cell suspensions as anticipated by other authors. In our case, we used a pure sinusoidal source, however the experiments that do account for responses used a sum of a central sinusoidal and its harmonics frequencies. As a result, we suggest that the enzyme and electric interaction are favored when the field has a non-strictly sinusoidal waveform, and this behavior is related to the true intermediate transitions of the enzyme during its catalytic cycle. Therefore, we developed an iterative model of the interaction process based on previous models and actual trends. The model well verified all the previous simulations and showed that, for a non-symmetrical enzyme, the energy can harvest its maximal for non sinusoidal fields.
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Affiliation(s)
- Ernesto Federico Treo
- Departamento de Bioingeniería, FACET, Universidad Nacional de Tucumán, Tucumán, Argentina.
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42
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Ai BQ, Liu LG. A channel Brownian pump powered by an unbiased external force. J Chem Phys 2008; 128:024706. [DOI: 10.1063/1.2813420] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Astumian RD. Adiabatic operation of a molecular machine. Proc Natl Acad Sci U S A 2007; 104:19715-19718. [PMCID: PMC2148363 DOI: 10.1073/pnas.0708040104] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2007] [Indexed: 08/18/2023] Open
Abstract
Operation of a molecular machine is often thought of as a “far from equilibrium” process in which energy released by some high free energy fuel molecule or by light is used to drive a nonequilibrium “power stroke” to do work on the environment. Here we discuss how a molecular machine can be operated arbitrarily close to chemical equilibrium and still perform significant work at an appreciable rate: micrometer per second velocities against piconewton loads. As a specific example, we focus on a motor based on a three-ring catenane similar to that discussed by Leigh [Leigh DA, Wong JKY, Dehez F, Zerbetto F (2003) Nature 424:174–179]. The machine moves through its working cycle under the influence of external modulation of the energies of the states, where the modulation is carried out slowly enough that the state probabilities obey a Boltzmann equilibrium distribution at every instant. The mechanism can be understood in terms of the geometric phase [Berry MV (1990) Phys Today 43(12):34–40] in which the system moves adiabatically around a closed loop in parameter space, completing, on average, nearly one-half mechanical cycle each time it does so. Because the system is very close to equilibrium at every instant, the efficiency can approach 100%.
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Affiliation(s)
- R. Dean Astumian
- Department of Physics and Astronomy, University of Maine, Orono, ME 04469-5709
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44
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Jain K, Marathe R, Chaudhuri A, Dhar A. Driving particle current through narrow channels using a classical pump. PHYSICAL REVIEW LETTERS 2007; 99:190601. [PMID: 18233057 DOI: 10.1103/physrevlett.99.190601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2007] [Indexed: 05/25/2023]
Abstract
We study a symmetric exclusion process in which the hopping rates at two chosen adjacent sites vary periodically in time and have a relative phase difference. This mimics a colloidal suspension subjected to external time-dependent modulation of the local chemical potential. The two special sites act as a classical pump by generating an oscillatory current with a nonzero dc value whose direction depends on the applied phase difference. We analyze various features in this model through simulations and obtain an expression for the dc current via a novel perturbative treatment.
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Affiliation(s)
- Kavita Jain
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
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45
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Berthoumieux H, Jullien L, Lemarchand A. Response to a temperature modulation as a signature of chemical mechanisms. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:056112. [PMID: 18233723 DOI: 10.1103/physreve.76.056112] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2007] [Indexed: 05/25/2023]
Abstract
We consider n reactive species involved in unimolecular reactions and submitted to a temperature modulation of small amplitude. We determine the conditions on the rate constants for which the deviations from the equilibrium concentrations of each species can be optimized and find the analytical expression of the frequency associated with an extremum of concentration shift in the case n=3. We prove that the frequency dependence of the displacement of equilibrium gives access to the number n of species involved in the mechanism. We apply the results to the case of the transformation of a reactant into a product through a possible reactive intermediate and find the order relation obeyed by the activation energies of the different barriers. The results typically apply to enzymatic catalysis with kinetics of Michaelis-Menten type.
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Affiliation(s)
- H Berthoumieux
- Ecole Normale Supérieure, CNRS-UMR 8640, Département de Chimie, Université Pierre et Marie Curie-Paris 6, 24, rue Lhomond, 75231 Paris Cedex 05, France
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46
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Chen W, Zhang Z, Huang F. Entrainment of Na/K pumps by a synchronization modulation electric field. J Bioenerg Biomembr 2007; 39:331-9. [PMID: 17899338 DOI: 10.1007/s10863-007-9096-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
We studied entrainment of the catalytic cycle of the Na/K pumps by an imposed external AC electric field. Our results show that a well designed dichotomous oscillating electric field with a frequency close to the pumps' natural turnover rate can synchronize the pump molecules. Characteristics of the synchronized pumps include: (1) outward pump currents responding to Na-extrusion and inward pump currents responding to K-pumping in are separated; (2) magnitude of the outward pump currents can be up to three times higher than that of the randomly paced pump currents; (3) magnitude ratio of the outward over inward pump currents reveals the 3:2 stoichiometry of the pumps. We, further, gradually increased the field oscillating frequency in a stepwise pattern and kept pump synchronization in each step. We found that the pumps' turnover rate could be modulated up as the field frequency increased. Consequently, the pump currents significantly increased by many fold. In summary, these results show that the catalytic cycle of Na/K pumps can be synchronized and modulated by a well designed oscillating electric field resulting in activation of the pump functions.
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Affiliation(s)
- Wei Chen
- Cellular and Molecular Biophysics, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
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Chen W, Dando R. Electrical Activation of Na/K Pumps Can Increase Ionic Concentration Gradient and Membrane Resting Potential. J Membr Biol 2007; 214:147-55. [PMID: 17558530 DOI: 10.1007/s00232-006-0069-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2006] [Revised: 12/15/2006] [Indexed: 10/23/2022]
Abstract
It has been previously demonstrated by our group that our specifically designed synchronization modulation electric field can dynamically entrain the Na/K ATPase molecules, effectively accelerating the pumping action of these molecules. The ATPase molecules are first synchronized by the field, and subsequently their pumping rates are gradually modulated in a stepwise pattern to progressively higher and higher levels. Here, we present results obtained on application of the field to intact twitch skeletal muscle fibers. The ionic concentration gradient across the cell membrane was monitored, with the membrane potential extrapolated using a slow fluorescent probe with a confocal microimaging technique. The applied synchronization-modulation electric field is able to slowly but consistently increase the ionic concentration gradient across the membrane and, hence, hyperpolarize the membrane potential. All of these results were fully eliminated if ouabain was applied to the bathing solution, indicating a correlation with the action of the Na/K pump molecules. These results in combination with our previous results into the entrainment of the pump molecules show that the synchronization-modulation electric field-induced activation of the Na/K pump functions can effectively increase the ionic concentration gradient and the membrane potential.
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Affiliation(s)
- Wei Chen
- Department of Cellular and Molecular Biophysics, University of South Florida, Tampa, Florida 33620, USA.
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Chen W, Dando R. Synchronization modulation of Na/K pump molecules can hyperpolarize the membrane resting potential in intact fibers. J Bioenerg Biomembr 2007; 39:117-26. [PMID: 17318394 DOI: 10.1007/s10863-006-9068-4] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2006] [Accepted: 09/25/2006] [Indexed: 10/23/2022]
Abstract
Previously, we have theoretically studied the possibility of electrical rhythmic entrainment of carrier-mediated ion transporters, and experimentally realized synchronization and acceleration of the Na/K pumping rate in the cell membrane of skeletal muscle fibers by a specially designed synchronization modulation electric field. In these studies we either used cut fibers under a voltage clamp or intact fibers, but in the presence of ion channels blockers. A question remained as to whether the field-induced activation observed in the pump molecules could effectively increase the intracellular ionic concentration and the membrane potential at physiological conditions. In this paper, we studied the effects of the field on intact fibers without any channel blockers. We monitored the field-induced changes in the ionic concentration gradient across the cell membrane and the membrane potential non-invasively by using a fluorescent probe and confocal microscopic imaging techniques. The results clearly show that the entrainment of the pump molecules by the synchronization modulation electric field can effectively increase the ionic concentration gradient, and hence, hyperpolarize the membrane potential.
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Affiliation(s)
- Wei Chen
- Cellular and Molecular Biophysics, University of South Florida, Tampa, FL 33620, USA.
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Astumian RD. Design principles for Brownian molecular machines: how to swim in molasses and walk in a hurricane. Phys Chem Chem Phys 2007; 9:5067-83. [PMID: 17878982 DOI: 10.1039/b708995c] [Citation(s) in RCA: 171] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Protein molecular motors-perfected over the course of millions of years of evolution-play an essential role in moving and assembling biological structures. Recently chemists have been able to synthesize molecules that emulate in part the remarkable capabilities of these biomolecular motors (for extensive reviews see the recent papers: E. R. Kay, D. A. Leigh and F. Zerbetto, Angew. Chem., Int. Ed., 2006, 46, 72-191; W. R. Browne and B. L. Feringa, Nat. Nanotechnol., 2006, 1, 25-35; M. N. Chatterjee, E. R. Kay and D. A. Leigh, J. Am. Chem. Soc., 2006, 128, 4058-4073; G. S. Kottas, L. I. Clarke, D. Horinek and J. Michl, Chem. Rev., 2005, 105, 1281-1376; M. A. Garcia-Garibay, Proc. Natl. Acad. Sci., U. S. A., 2005, 102, 10771-10776)). Like their biological counterparts, many of these synthetic machines function in an environment where viscous forces dominate inertia-to move they must "swim in molasses". Further, the thermal noise power exchanged reversibly between the motor and its environment is many orders of magnitude greater than the power provided by the chemical fuel to drive directed motion. One might think that moving in a specific direction would be as difficult as walking in a hurricane. Yet biomolecular motors (and increasingly, synthetic motors) move and accomplish their function with almost deterministic precision. In this Perspective we will investigate the physical principles that govern nanoscale systems at the single molecule level and how these principles can be useful in designing synthetic molecular machines.
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Affiliation(s)
- R Dean Astumian
- Department of Physics, University of Maine, Orono, Maine 04469-5709, USA.
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Abstract
We experimentally studied the Na/K pump currents evoked by a train of squared pulses whose pulse-duration is about the time course of Na-extrusion at physiological conditions. The magnitude of the measured pump current can be as much as three-fold of that induced by the traditional single pulse measurement. The increase in the pump current is directly dependent on the number of pre-pulses. The larger the number of the pre-pulses is, the higher the current magnitude can be obtained. At a particular number of pre-pulses, the pump current becomes saturated. These results suggest that a large number of pre-pulses may synchronize the pump molecules to work at the same pace. As a result, the pump molecules may extrude Na ions at the same time corresponding to the stimulation pulses, and pump in K ions at the same time during the pulse intervals. Therefore, the measured pump current is three-fold of that measured by a single pulse where the outward and inward pump currents are canceled each other.
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Affiliation(s)
- Wei Chen
- Center for Cellular and Molecular Biophysics, Department of Physics, University of South Florida, 4020 E. Fowler Ave., Tampa, FL 33620, USA.
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