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Borsley S, Gallagher JM, Leigh DA, Roberts BMW. Ratcheting synthesis. Nat Rev Chem 2024; 8:8-29. [PMID: 38102412 DOI: 10.1038/s41570-023-00558-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/02/2023] [Indexed: 12/17/2023]
Abstract
Synthetic chemistry has traditionally relied on reactions between reactants of high chemical potential and transformations that proceed energetically downhill to either a global or local minimum (thermodynamic or kinetic control). Catalysts can be used to manipulate kinetic control, lowering activation energies to influence reaction outcomes. However, such chemistry is still constrained by the shape of one-dimensional reaction coordinates. Coupling synthesis to an orthogonal energy input can allow ratcheting of chemical reaction outcomes, reminiscent of the ways that molecular machines ratchet random thermal motion to bias conformational dynamics. This fundamentally distinct approach to synthesis allows multi-dimensional potential energy surfaces to be navigated, enabling reaction outcomes that cannot be achieved under conventional kinetic or thermodynamic control. In this Review, we discuss how ratcheted synthesis is ubiquitous throughout biology and consider how chemists might harness ratchet mechanisms to accelerate catalysis, drive chemical reactions uphill and programme complex reaction sequences.
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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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2
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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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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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4
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Rozenbaum VM, Shapochkina IV, Teranishi Y, Trakhtenberg LI. High-temperature ratchets driven by deterministic and stochastic fluctuations. Phys Rev E 2019; 99:012103. [PMID: 30780357 DOI: 10.1103/physreve.99.012103] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Indexed: 11/07/2022]
Abstract
We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.
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Affiliation(s)
- V M Rozenbaum
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan.,Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.,Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev 03164, Ukraine
| | - I V Shapochkina
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan.,Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.,Department of Physics, Belarusian State University, Prospekt Nezavisimosti 4, Minsk 220050, Belarus
| | - Y Teranishi
- Institute of Physics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu, Taiwan
| | - L I Trakhtenberg
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street 4, Moscow 119991, Russia; Moscow Institute of Physics and Technology, Institutsky Lane 9, Dolgoprudny 141700, Moscow Region, Russia; and Lomonosov Moscow State University, 1-3 Leninskie Gory, Moscow 119991, Russia
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5
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Goychuk I. Perfect anomalous transport of subdiffusive cargos by molecular motors in viscoelastic cytosol. Biosystems 2018; 177:56-65. [PMID: 30419266 DOI: 10.1016/j.biosystems.2018.11.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Revised: 11/06/2018] [Accepted: 11/07/2018] [Indexed: 11/17/2022]
Abstract
Multiple experiments show that various submicron particles such as magnetosomes, RNA messengers, viruses, and even much smaller nanoparticles such as globular proteins diffuse anomalously slow in viscoelastic cytosol of living cells. Hence, their sufficiently fast directional transport by molecular motors such as kinesins is crucial for the cell operation. It has been shown recently that the traditional flashing Brownian ratchet models of molecular motors are capable to describe both normal and anomalous transport of such subdiffusing cargos by molecular motors with a very high efficiency. This work elucidates further an important role of mechanochemical coupling in such an anomalous transport. It shows a natural emergence of a perfect subdiffusive ratchet regime due to allosteric effects, where the random rotations of a "catalytic wheel" at the heart of the motor operation become perfectly synchronized with the random stepping of a heavily loaded motor, so that only one ATP molecule is consumed on average at each motor step along microtubule. However, the number of rotations made by the catalytic engine and the traveling distance both scale sublinearly in time. Nevertheless, this anomalous transport can be very fast in absolute terms.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany.
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6
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Rozenbaum VM, Dekhtyar ML, Lin SH, Trakhtenberg LI. Photoinduced diffusion molecular transport. J Chem Phys 2016. [DOI: 10.1063/1.4960622] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Affiliation(s)
- Viktor M. Rozenbaum
- Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova St. 17, Kiev 03164, Ukraine
| | - Marina L. Dekhtyar
- Institute of Organic Chemistry, National Academy of Sciences of Ukraine, Murmanskaya St. 5, Kiev 02094, Ukraine
| | - Sheng Hsien Lin
- Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsuen Road, Hsinchu 300, Taiwan
| | - Leonid I. Trakhtenberg
- Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street 4, Moscow 119991, Russia and Moscow Institute of Physics and Technology (State University), Institutskii Per. 9, Dolgoprudnyi, Moscow Region 141700, Russia
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7
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Dekhtyar’ ML, Rozenbaum VM, Trakhtenberg LI. Near-surface transport of semiconductor nanoclusters upon cyclic photoexcitation. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A 2016. [DOI: 10.1134/s0036024416070062] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Goychuk I. Molecular machines operating on the nanoscale: from classical to quantum. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2016; 7:328-50. [PMID: 27335728 PMCID: PMC4901870 DOI: 10.3762/bjnano.7.31] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2015] [Accepted: 01/29/2016] [Indexed: 05/18/2023]
Abstract
The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation-dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
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9
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Goychuk I. Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechano-chemical coupling and anharmonicity of tether. Phys Biol 2015; 12:016013. [PMID: 25635368 DOI: 10.1088/1478-3975/12/1/016013] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Here we generalize our previous model of molecular motors trafficking subdiffusing cargos in viscoelastic cytosol by (i) including mechano-chemical coupling between cyclic conformational fluctuations of the motor protein driven by the reaction of ATP hydrolysis and its translational motion within the simplest two-state model of hand-over-hand motion of kinesin, and also (ii) by taking into account the anharmonicity of the tether between the motor and the cargo (its maximally possible extension length). It is shown that the major earlier results such as occurrence of normal versus anomalous transport depending on the amplitude of binding potential, cargo size and the motor turnover frequency not only survive in this more realistic model, but the results also look very similar for the correspondingly adjusted parameters. However, this more realistic model displays a substantially larger thermodynamic efficiency due to a bidirectional mechano-chemical coupling. For realistic parameters, the maximal thermodynamic efficiency can transiently be about 50% as observed for kinesins, and even larger, surprisingly also in a novel strongly anomalous (sub)transport regime, where the motor enzymatic turnovers become also anomalously slow and cannot be characterized by a turnover rate. Here anomalously slow dynamics of the cargo enforces anomalously slow cyclic kinetics of the motor protein.
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Affiliation(s)
- Igor Goychuk
- Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
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10
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Rozenbaum VM, Makhnovskii YA, Shapochkina IV, Sheu SY, Yang DY, Lin SH. Adiabatically driven Brownian pumps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012104. [PMID: 23944411 DOI: 10.1103/physreve.88.012104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2012] [Indexed: 06/02/2023]
Abstract
We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.
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Affiliation(s)
- Viktor M Rozenbaum
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
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11
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Rozenbaum VM, Shapochkina IV. Quasiequilibrium directed hopping in a time-dependent two-well periodic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051101. [PMID: 22181363 DOI: 10.1103/physreve.84.051101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2011] [Revised: 09/20/2011] [Indexed: 05/31/2023]
Abstract
We consider the directed motion of a Brownian particle in a two-well periodic potential with time-varying barriers and wells described by arbitrary periodic functions of time, v(t) and u(t), alternating with the period τ. In the framework of the low-temperature kinetic approach, we obtain explicit formulas for the probabilities of finding the particle in potential wells, average velocity of directed motion, input energy P(in) and useful work P(out) against additionally introduced stationary load force f. These formulas are considerably simplified by the assumption of the quasiequilibrium regime of motion corresponding to small values of u(t) and f. It is shown that depending on the same or opposite parity of the functions v(t) and u(t) with respect to time reversal, the motion direction of a Brownian particle is retained or reversed under the reversal of the direction of movement along the (v-u) loop in the phase space of the functions v(t) and u(t), and the nondiagonal kinetic coefficients are mutually symmetric or antisymmetric. In the adiabatic limit τ→∞, the average velocity is proportional to τ(-1) in two cases: (i) the above loop has a nonzero area, (ii) the functions v(t) and u(t) are proportional to each other (zero loop area) and include intervals of fast changes with small durations τ(0) on the period τ of their variations. In both of these cases, the efficiency of energy conversion, η=P(out)/P(in), tends to unity at large variations of the barriers v(t). In the second case, the deviation of η from unity can be split into two contributions: The former decreases exponentially with increasing amplitude v(0) of v(t), while the latter is a small nonadiabatic correction proportional to v(0)(-3/2). It is the nonadiabatic correction that limits high efficiencies at large variations of barriers.
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Affiliation(s)
- V M Rozenbaum
- Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Kiev, Ukraine.
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12
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Rozenbaum VM, Makhnovskii YA, Yang DY, Sheu SY, Lin SH. Reciprocating and Directed Motion on the Nanoscale: A Simple Kinetic Model. J Phys Chem B 2010; 114:1959-66. [DOI: 10.1021/jp910508t] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- V. M. Rozenbaum
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan; Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev, 03164, Ukraine; Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia; Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, and Structural Biology Program, National Yang-Ming University, Taipei 112,
| | - Yu. A. Makhnovskii
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan; Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev, 03164, Ukraine; Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia; Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, and Structural Biology Program, National Yang-Ming University, Taipei 112,
| | - D.-Y. Yang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan; Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev, 03164, Ukraine; Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia; Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, and Structural Biology Program, National Yang-Ming University, Taipei 112,
| | - S.-Y. Sheu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan; Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev, 03164, Ukraine; Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia; Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, and Structural Biology Program, National Yang-Ming University, Taipei 112,
| | - S. H. Lin
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan; Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev, 03164, Ukraine; Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Leninsky Prospect 29, 119991 Moscow, Russia; Department of Life Sciences and Institute of Genome Sciences, Institute of Biomedical Informatics, and Structural Biology Program, National Yang-Ming University, Taipei 112,
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Rozenbaum VM, Vovchenko OY, Korochkova TY. Brownian dipole rotator in alternating electric field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061111. [PMID: 18643221 DOI: 10.1103/physreve.77.061111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2008] [Indexed: 05/26/2023]
Abstract
The study addresses the azimuthal jumping motion of an adsorbed polar molecule in a periodic n -well potential under the action of an external alternating electric field. Starting from the perturbation theory of the Pauli equation with respect to the weak field intensity, explicit analytical expressions have been derived for the time dependence of the average dipole moment as well as the frequency dependences of polarizability and the average angular velocity, the three quantities exhibiting conspicuous stochastic resonance. As shown, unidirectional rotation can arise only provided simultaneous modulation of the minima and maxima of the potential by an external alternating field. For a symmetric potential of hindered rotation, the average angular velocity, if calculated by the second-order perturbation theory with respect to the field intensity, has a nonzero value only at n=2 , i.e., when two azimuthal wells specify a selected axis in the system. Particular consideration is given to the effect caused by the asymmetry of the two-well potential on the dielectric loss spectrum and other Brownian motion parameters. When the asymmetric potential in a system of dipole rotators arises from the average local fields induced by an orientational phase transition, the characteristics concerned show certain peculiarities which enable detection of the phase transition and determination of its parameters.
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Affiliation(s)
- V M Rozenbaum
- Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova Street 17, Kiev, Ukraine.
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14
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Dekhtyar ML, Ishchenko AA, Rozenbaum VM. Photoinduced molecular transport in biological environments based on dipole moment fluctuations. J Phys Chem B 2007; 110:20111-4. [PMID: 17034183 DOI: 10.1021/jp063795q] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Consideration is given to the possibility of a molecule moving unidirectionally in an electric field of a polar periodic substrate as a result of the fluctuations of molecular dipole moment occurring on the photoexcitation of the molecule. As estimated for such motion, molecules with sufficiently long fluorescence and strongly differing dipole moments in the ground and excited states can move with an average velocity of the same order as that typical of protein motors such as kinesin. This effect results from the mutual compensation of two opposite factors acting in dipole photomotors, namely, a lower energy of interaction with the substrate relative to that for protein motors and a shorter excited-state lifetime as compared with the duration of the hydrolytic splitting of adenosinetriphosphate in protein motors.
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Abstract
Molecular switches and motors are essential components of artificial molecular machines. In this perspective, we discuss progress in our design, synthesis, and functioning of photochemical and electrochemical switches and chemical and light-driven molecular motors. Special emphasis is given to the control of a range of functions and properties, including luminescence, self-assembly, motion, color, conductance, transport, and chirality. We will also discuss our efforts to control mechanical movement at the molecular level, a feature that is at the heart of molecular motors and machines. The anchoring of molecular motors on surfaces and molecular motors at work are discussed.
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Affiliation(s)
- Ben L Feringa
- Laboratory of Organic Chemistry, Stratingh Institute for Chemistry & Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands.
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16
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Rozenbaum VM, Korochkova TY, Liang KK. Conventional and generalized efficiencies of flashing and rocking ratchets: analytical comparison of high-efficiency limits. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061115. [PMID: 17677228 DOI: 10.1103/physreve.75.061115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2007] [Indexed: 05/16/2023]
Abstract
We consider two basic types of Brownian motors which generate directed motion in a periodic asymmetric piecewise-linear potential as a result of random half-period shifts of the potential relief (flashing ratchets) or due to a temporally asymmetric unbiased force applied to the system (rocking ratchets). Analytical relationships have been derived which enable the comparison of the upper limits for the conventional and generalized energy conversion efficiencies in these motors. As found, the increasing amplitude of a sawtooth potential (or the decreasing temperature) makes the conventional efficiency tend to the unity limit faster for a rocking ratchet (in the absence of temporal asymmetry) than for a flashing ratchet. The inverse is true for the generalized efficiency. The potential amplitude being the same, the generalized efficiency is always less than the conventional efficiency. A decreased asymmetry of the potential always results in the reduction of both efficiencies. The temporal asymmetry of an unbiased force has an opposite effect on the conventional and generalized efficiencies: the former rises and the latter drops as the positive signal component becomes shorter in time and larger in amplitude.
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Affiliation(s)
- V M Rozenbaum
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan.
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17
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Tsong TY, Chang CH. A Markovian engine for a biological energy transducer: the catalytic wheel. Biosystems 2006; 88:323-33. [PMID: 17188806 DOI: 10.1016/j.biosystems.2006.08.014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2006] [Accepted: 08/01/2006] [Indexed: 10/23/2022]
Abstract
The molecular machines in biological cells are made of proteins, DNAs and other classes of molecules. The structures of these molecules are characteristically "soft", highly flexible, and yet their interactions with other molecules or ions are specific and selective. This chapter discusses a prevalent form, the catalytic wheel, or the energy transducer of cells, examines its mechanism of action, and extracts from it a set of simple but general rules for understanding the energetics of the biomolecular devices. These rules should also benefit design of manmade nanometer scale machines such as rotary motors or track-guided linear transporters. We will focus on an electric work that, by matching system dynamics and then enhancing the conformational fluctuation of one or several driver proteins, converts stochastic input of energy into rotation or locomotion of a receptor protein. The spatial (or barrier) and temporal symmetry breakings required for selected driver/receptor combinations are examined. This electric ratchet consists of a core engine that follows the Markovian dynamic, alleviates difficulties encountered in rigid mechanical model, and tailors to the soft-matter characteristics of the biomolecules.
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Affiliation(s)
- Tian Yow Tsong
- Institute of Physics, Academy of Sciences, Taipei 115, Taiwan.
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18
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Qian H, Beard DA. Metabolic futile cycles and their functions: a systems analysis of energy and control. ACTA ACUST UNITED AC 2006; 153:192-200. [PMID: 16986621 DOI: 10.1049/ip-syb:20050086] [Citation(s) in RCA: 52] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Abstract
It has long been hypothesised that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, a quantitative theory was developed for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the stoichiometric sensitivity of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similar to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibility of different roles for the two major mechanisms within cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.
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Affiliation(s)
- H Qian
- Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.
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Abstract
In this review we chart recent advances in what is at once an old and very new field of endeavour--the achievement of control of motion at the molecular level including solid-state and surface-mounted rotors, and its natural progression to the development of synthetic molecular machines. Besides a discussion of design principles used to control linear and rotary motion in such molecular systems, this review will address the advances towards the construction of synthetic machines that can perform useful functions. Approaches taken by several research groups to construct wholly synthetic molecular machines and devices are compared. This will be illustrated with molecular rotors, elevators, valves, transporters, muscles and other motor functions used to develop smart materials. The demonstration of molecular machinery is highlighted through recent examples of systems capable of effecting macroscopic movement through concerted molecular motion. Several approaches to illustrate how molecular motor systems have been used to accomplish work are discussed. We will conclude with prospects for future developments in this exciting field of nanotechnology.
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Affiliation(s)
- Wesley R Browne
- Organic and Molecular Inorganic Chemistry, Stratingh Institute, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
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Dubkov AA, Spagnolo B. Acceleration of diffusion in randomly switching potential with supersymmetry. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:041104. [PMID: 16383359 DOI: 10.1103/physreve.72.041104] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2004] [Revised: 07/22/2005] [Indexed: 05/05/2023]
Abstract
We investigate the overdamped Brownian motion in a supersymmetric periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ from each other by a shift of one-half period. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential. For the sawtooth potential, we obtain the exact expression for the effective diffusion coefficient, which is valid for the arbitrary mean rate of potential switchings and arbitrary intensity of white Gaussian noise. We find the acceleration of diffusion in comparison with the free diffusion case and a finite net diffusion in the absence of thermal noise. Such a potential could be used to enhance the diffusion over its free value by an appropriate choice of parameters.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Nizhni Novgorod State University, 23 Gagarin Ave., 603950 Nizhni Novgorod, Russia.
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Rozenbaum VM, Korochkova TY, Yang DY, Lin SH, Tsong TY. Two approaches toward a high-efficiency flashing ratchet. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041102. [PMID: 15903652 DOI: 10.1103/physreve.71.041102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2004] [Indexed: 05/02/2023]
Abstract
For a flashing ratchet with periodic potentials fluctuating via random shifts of one-half period, a high efficiency is shown to result from two mechanisms. The previously reported one [Yu. A. Makhnovskii, Phys. Rev. E 69, 021102 (2004); V. M. Rozenbaum, JETP Lett. 79, 388 (2004)] is realized in the near-equilibrium region and implies, first, the presence of a high barrier V0 blocking the reverse movement of a Brownian particle and, second, identical, though energy-shifted, portions of the asymmetric flat potential profile on both half periods. We report another mechanism acting far from equilibrium, typical of strongly asymmetric potentials which are shaped identically on both half periods with a large energetic shift DeltaV . The two mechanisms exhibit radically different limiting behavior of the maximum possible efficiency: eta(m) approximately 1-exp (-beta V0 /2) for the former and eta(m) approximately 1-ln (2betaDeltaV) /betaDeltaV for the latter ( beta being the reciprocal temperature in energy units). The flux and the efficiency for a Brownian motor with a piecewise-linear potential are calculated using the transfer matrix method; an exact analytical solution can thus be obtained for an extremely asymmetric sawtooth potential, the simplest example of the second high-efficiency mechanism. As demonstrated, the mechanisms considered are also characteristic of a two-well periodic potential treated in terms of the kinetic approach.
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Affiliation(s)
- V M Rozenbaum
- Institute of Atomic and Molecular Sciences, Academia Sinica, P. O. Box 23-166, Taipei, Taiwan, Republic of China.
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