Free energy transduction in membrane transport systems induced by externally imposed fluctuations in ligand...

The effect of externally induced fluctuations in ligand concentration on the transport of ligand across a membrane is studied theoretically. It is found that, when only one of the two baths is externally perturbed to fluctuate the concentration, a net transport of ligand from the unperturbed to the perturbed side of the membrane is always observed, even though the average concentrations of ligand of the two baths are equal. As a result, apparent up-hill transport against a gradient can be realized in this case. In the case of both baths being perturbed independently, apparent up-hill transport is also possible. However, the direction of net transport of ligand will depend on the amplitudes and the frequencies of the two fluctuations as well as the kinetic mechanism of the transport system. From these results, it is concluded that externally imposed fluctuations in ligand concentration act to reduce the chemical potential of the ligand so that the effective activity is always less than the mean concentration of the ligand. The conclusion is very general in that it applies to any transport model that involves one ligand per turnover. The same principle can be used to analyze the effect of fluctuations in equilibrium ligand binding and cyclic enzyme reactions in solution.