Relation between Protein Intrinsic Normal Mode Weights and Pre-Existing Conformer Populations

Intrinsic fluctuations of a protein enable it to sample a large repertoire of conformers including the open and closed forms. These distinct forms of the protein called conformational substates pre-exist together in equilibrium as an ensemble independent from its ligands. The role of ligand might be simply to alter the equilibrium toward the most appropriate form for binding. Normal mode analysis is proved to be useful in identifying the directions of conformational changes between substates. In this study, we demonstrate that the ratios of normalized weights of a few normal modes driving the protein between its substates can give insights about the ratios of kinetic conversion rates of the substates, although a direct relation between the eigenvalues and kinetic conversion rates or populations of each substate could not be observed. The correlation between the normalized mode weight ratios and the kinetic rate ratios is around 83% on a set of 11 non-enzyme proteins and around 59% on a set of 17 enzymes. The results are suggestive that mode motions carry intrinsic relations with thermodynamics and kinetics of the proteins.