Energy Flow Perspective on the Mechanism of the Conformational Dynamics in Biomolecules

Most functional processes of proteins involve significant conformational changes. In those activated processes, the system needs to cross an energy barrier. A comprehensive understanding of activated dynamics is necessary for understanding protein functions. We developed a rigorous method for computing the potential and kinetic energy flows of individual coordinates, which define the energy cost of their movements. Moreover, by introducing the generalized work functional, a fundamental mechanical operator that can characterize the effects of mechanical coupling, we can identify the reaction coordinates that determine the progress of a reaction process. Applying these methods to the isomerization reaction of an alanine dipeptide, we found that a large amount of kinetic energy accumulates in the reaction coordinates before the system starts to cross the activation barrier, which is then used to cover the potential energy cost during barrier crossing. Additionally, we studied the flap opening process of HIV-1 protease, which is essential for substrate binding. Through the energy flow analysis of individual coordinates, we found the extent of energy accumulations strongly correlates with the scale of movements of residues. The coordinates precisely cooperate to form collective modes with high-energy flows and control the reaction dynamics. Our method provides a rigorous scheme to systematically study the contributions of different coordinates to the reactive process and extract the coordinate collectivity from the energy flow perspective, which is fundamentally different from the intuition-guided approaches.