How enzymes can capture and transmit free energy from an oscillating electric field.

Westerhoff, Hans V.; Tsong, Tian Yow; Chock, P. Boon; Chen, Yi-Der; Astumian, R. Dean

doi:10.1073/pnas.83.13.4734

Cited by 153 publications

(79 citation statements)

References 17 publications

(16 reference statements)

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“…Eq. 5 is a necessary but not sufficient condition for detailed balance (19). Periodic modulation of the energies E i , i ϭ 1, 2, 3, even at modulation carried out so slowly that Eq.…”

mentioning

confidence: 99%

Adiabatic operation of a molecular machine

Astumian

2007

Proc. Natl. Acad. Sci. U.S.A.

111

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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 T here has been great recent progress in constructing molecular machines from complexes held together by mechanical rather than chemical bonds (1-3). Structures with fascinating topologies have been created (4) and combined to assemble intricate devices, including molecular ''elevators'' (5) and nanoscale switchable valves (6). Perhaps the greatest interest in these mechanically linked molecules lies in the fact that they can be engineered to have large-scale motions controllable through external changes in the environment. This feature facilitates the design of molecular motors (7,8) and rotors (9), devices that can be caused to undergo directional motion by an external source of chemical (10), optical (11), or electrical (12) energy. Control is achieved by incorporating two or more recognition stations (sites where the components of the complex interact strongly) to define several intracomplex binding sites (13,14) and, hence, several configurational states of the molecule. The relative thermodynamic stability of the different sites (and hence states) is controlled by, e.g., protonation/deprotonation, reduction/ oxidation, or absorption of light. By changing the pH, redox potential, or light intensity, the molecule can be switched from one state to another externally.Recently catenanes-structures with two or more interlocked rings-have been designed that allow external control not only of the relative stabilities of the binding sites but also of the relative labilities of the pathways linking the sites (10). By carrying out a sequence of external cyclical changes to the labilities and stabilities of the sites, the rings could be squeezed to undergo directional rotation by a mechanism similar to peristalsis (15), except that the transitions occur by thermal noise so the system operates as a Brownian motor (16).Here I will describe how a molecular machine can be operated arbitrarily close to chemical equilibrium at every instant and still do significant work at an appreciable rate. Consider the threering catenane shown in Fig. 1. The larger gray ring has three distinct recognition stations, labeled 1, 2, and 3, for the two identical yellow rings. The yellow rings cannot pass one another, nor can they occupy the same station, because they make thermally activated transitions from one station to another. Thus, there are a total of three states, labeled A, B, and C. The interaction between a yellow ring with a station is characterized by an interacti...

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“…Eq. 5 is a necessary but not sufficient condition for detailed balance (19). Periodic modulation of the energies E i , i ϭ 1, 2, 3, even at modulation carried out so slowly that Eq.…”

mentioning

confidence: 99%

Adiabatic operation of a molecular machine

Astumian

2007

Proc. Natl. Acad. Sci. U.S.A.

111

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“…The apparent paradox points out that if one combines two dynamics in which a given variable decreases the same variable can increase in the resulting dynamics. Examples of related phenomena include enzyme transport analyzed by a four-state rate model [8], finance models where capital grows by investing in an asset with negative typical growth rate [9], stability produced by combining unstable systems [10], counterintuitive drift in the physics of granular flow [11], the combination of declining branching processes producing an increase [12], and counterintuitive drift in switched diffusion processes in random media [13].…”

mentioning

confidence: 99%

New Paradoxical Games Based on Brownian Ratchets

2000

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Two losing games, when alternated in a periodic or random fashion, can produce a winning game. This paradox occurs in a family of stochastic processes: if one combines two or more dynamics where a given quantity decreases, the result can be a dynamic system where this quantity increases. The paradox could be applied to a number of stochastic systems and has drawn the attention of researchers from different areas. In this paper we show how the phenomenon can be used to design Brownian or molecular motors, i.e., thermal engines that operate by rectifying fluctuations. We briefly review the literature on Brownian motors, pointing out that a new thermodynamics of Brownian motors will be fundamental to the understanding of most processes of energy transduction in molecular biology.

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“…Recently, it was demonstrated (1,2) that an oscillating electric field is competent to do chemical work when coupled through an enzyme with differences in macroscopic polarization and basic free energy between its conformational states. These results might well account for the observation that the Na+/K+-ATPase mediates active transport when subjected to an oscillating electric field (1,3,4).…”

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confidence: 99%

Can free energy be transduced from electric noise?

Astumian¹,

Chock²,

Tsong³

et al. 1987

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

121

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Recently, it was shown that free energy can be transduced from a regularly oscillating electric field to do chemical or transport work when coupled through an enzyme with appropriate electrical characteristics. Here we report that randomly pulsed electric fields can also lead to work being done, giving rise to speculation as to whether appropriately designed enzymes can extract and convert free energy from the inherent fluctuations in their environment. The paradox is resolved by showing that equilibrium electrical noise resulting from the environment around an enzyme cannot be completely random but is correlated to the state that the enzyme is in. If the noise has the appropriate reciprocal interaction with the enzyme, its potential to serve as a free-energy source disappears. This is shown by Monte Carlo and other numerical calculations and is proven analytically by use of the diagram method. This method also is used to provide an explicit equation showing that, under a range of conditions, our model enzyme will be induced by uncorrelated ("autonomous") noise to undergo net cyclic flux. That work can be transduced from the "random" noise is demonstrated by using numerical methods.Recently, it was demonstrated (1, 2) that an oscillating electric field is competent to do chemical work when coupled through an enzyme with differences in macroscopic polarization and basic free energy between its conformational states. These results might well account for the observation that the Na+/K+-ATPase mediates active transport when subjected to an oscillating electric field (1, 3, 4).In vivo, fluctuating electric fields have been observed around cells (reviewed in ref. 5), and, certainly, large potential fluctuations must occur in the vicinity of ion channels upon opening or closing. This has been used (1, 6) as the basis for a model ofATP synthesis via the FO/Fl-ATPase, in which coupling factor Fo serves as a field-modulating channel, the opening and closing of which is linked to the binding and release of ligands in F1. Also, it was suggested that the electric field around HW-transporting ATPase in free energytransducing membranes might oscillate because of turnover of neighboring electron-transfer chains, and that these oscillations might contain the free energy often missing in free energy balances (2).In preliminary calculations, we found that totally random noise, when applied to the system described previously (1, 2), led to work being done. This result suggests that many (indeed most) forms offield fluctuations can do work. Yet we must realize that, in keeping with the laws of thermodynamics, internal noise arising in a system at equilibrium certainly cannot do work.Although the effects of field fluctuations have been studied before for both noncyclic (7) and cyclic (8) systems, our results demonstrate that energy can be transduced from a randomly fluctuating field, allowing an enzyme to do work.In a subsequent paper (9), the general asymmetry requirements for a four-state enzyme to work will be studied i...

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How enzymes can capture and transmit free energy from an oscillating electric field.

Cited by 153 publications

References 17 publications

Adiabatic operation of a molecular machine

Adiabatic operation of a molecular machine

New Paradoxical Games Based on Brownian Ratchets

Can free energy be transduced from electric noise?

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