Kinetic energy flows in activated dynamics of biomolecules

Protein conformational changes are activated processes essential for protein functions. Activation in a protein differs from activation in a small molecule in that it involves directed and systematic energy flows through preferred channels encoded in the protein structure. Understanding the nature of these energy flow channels and how energy flows through them during activation is critical for understanding protein conformational changes. We recently [W. Li and A. Ma, J. Chem. Phys. 144, 114103 (2016)] developed a rigorous statistical mechanical framework for understanding potential energy flows. Here, we complete this theoretical framework with a rigorous theory for kinetic energy flows: potential and kinetic energies interconvert when impressed forces oppose inertial forces, whereas kinetic energy transfers directly from one coordinate to another when inertial forces oppose each other. This theory is applied to analyzing a prototypic system for biomolecular conformational dynamics: the isomerization of an alanine dipeptide. Among the two essential energy flow channels for this process, dihedral ϕ confronts the activation barrier, whereas dihedral θ₁ receives energy from potential energy flows. Intriguingly, θ₁ helps ϕ to cross the activation barrier by transferring to ϕ via direct kinetic energy flow all the energy it received-an increase in θ̇₁ caused by potential energy flow converts into an increase in ϕ̇. As a compensation, θ₁ receives kinetic energy from bond angle α via a direct mechanism and bond angle β via an indirect mechanism.