Enzyme as catalytic wheel powered by a Markovian engine: conformational coupling and barrier surfing models

We examine a typical Michaelis-Menten Enzyme (MME) and redress it to form a transducer of free energy, and electric, acoustic, or other types of energy. This amendment and extension is necessary in lieu of recent experiments in which enzymes are shown to perform pump, motor, and locomotion functions resembling their macroscopic counterparts. Classical textbook depicts enzyme, or an MME, as biocatalyst which can enhance the rate of a chemical reaction by lowering the activation barrier but cannot shift the thermodynamic equilibrium of the biochemical reaction. An energy transducer, on the other hand, must also be able to harvest, store, or divert energy and in doing so alter the chemical equilibrium, change the energy form, fuel an energy consuming process, or perform all these functions stepwise in one catalytic turnover. The catalytic wheel presented in this communication is both a catalyst and an energy transducer and can perform all these tasks with ease. A Conformational Coupling Model for the rotary motors and a Barrier Surfing Model for the track-guided stepping motors and transporters, are presented and compared. It is shown that the core engine of the catalytic wheel, or a Brownian motor, is a Markovian engine. It remains to be seen if this core engine is the basic mechanism for a wide variety of bio-molecular energy transducers, as well as certain other dynamic systems, for example, the Parrondo's Games.