Asymmetry and external noise-induced free energy transduction

The effect of fluctuations in rate constants on the kinetic behavior of cyclic reacting systems, caused by a fluctuating external parameter, is studied. It is shown (i) that the stochastic properties of the system can be analyzed analytically by using the usual master equation approach when the external parameter is fluctuating with discrete square pulses and (ii) that the system is equivalent to an expanded chemical kinetic system with no fluctuation in rate constants. When applied to a linear four-state cyclic enzyme system, the formalism can be used to prove analytically the finding that an enzyme can extract the free energy from an externally applied fluctuating membrane potential and perform active free energy transduction. The formalism also can be used to assess the asymmetry constraints imposed on the values of the rate constants in order for the model to work.