Can free energy be transduced from electric noise?

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.