Stochastic energy transition of peptide bond under the action of hydrolytic enzyme

Stochastic energy transition of peptide bond (PB) in enzyme–substrate complex (ESC) is investigated. By introducing the Pippard model and thermal fluctuation as the noise, the two important mechanisms of enhancing PB breaking rate, i.e., the Fermi resonance and the reduction of potential barrier height due to oxygen ion O− are studied. The necessary frequency ratio 1:2 for Fermi resonance is verified by using the deterministic averaging method. With the noise terms present, the average energy transition rate of PB is predicted by using the stochastic averaging method combined with solving the Pontryagin equation or assuming the PB breaking as a Poisson process. Comparison of the numerical results with those from Monte Carlo simulations shows that the theoretical analysis is effective. To include the influence of the oxygen ion on the PB breaking, a proposal is presented to describe the vibration of the oxygen ion and to couple it with PB vibration. In terms of the coupled system, the two mechanisms may be investigated in a unified framework.