Can free energy be transduced from electric noise?

Abstract

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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Stochastic Resonance, Brownian Ratchets and the Fokker-Planck Equation

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Optimal modulation of a Brownian ratchet and enhanced sensitivity to a weak external force

“…Motivated by the desire to understand energy transduction in biological systems (1,2), recent attention has been devoted to the dynamics of particles moving in spatially anisotropic potentials that are fluctuating in time (for a recent review, see ref. 3).…”

“…Typically, the system is under the influence of an external potential V(x,t) and is in contact with an external bath that provides viscous damping of sufficient strength so that the inertia of the system is neglected. The system is described by a Langevin equation ␥ẋ͑t͒ ϭ ϪVЈ͑x,t͒ ϩ ͱ2͑t͒, [1] where ␥ is the coefficient of viscous friction, x is the coordinate of the center-of-mass of the particle, t is time, the prime denotes spatial differentiation, and the overdot denotes temporal differentiation. The noise strength is related to the temperature T and ␥ by the fluctuation dissipation relation: ϭ ␥k B T, where k B is Boltzmann's constant.…”