Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.