Using harmonic analysis and optimization to study macromolecular dynamics

Mechanical system dynamics plays an important role in the area of computational structural biology. Elastic network models (ENMs) for macromolecules (e.g., polymers, proteins, and nucleic acids such as DNA and RNA) have been developed to understand the relationship between their structure and biological function. For example, a protein, which is basically a folded polypeptide chain, can be simply modeled as a mass-spring system from the mechanical viewpoint. Since the conformational flexibility of a protein is dominantly subject to its chemical bond interactions (e.g., covalent bonds, salt bridges, and hydrogen bonds), these constraints can be modeled as linear spring connections between spatially proximal representatives in a variety of coarse-grained ENMs. Coarse-graining approaches enable one to simulate harmonic and anharmonic motions of large macromolecules in a PC, while all-atom based molecular dynamics (MD) simulation has been conventionally performed with an aid of supercomputer. A harmonic analysis of a macroscopic mechanical system, called normal mode analysis, has been adopted to analyze thermal fluctuations of a microscopic biological system around its equilibrium state. Furthermore, a structure-based system optimization, called elastic network interpolation, has been developed to predict nonlinear transition (or folding) pathways between two different functional states of a same macromolecule. The good agreement of simulation and experiment allows the employment of coarse-grained ENMs as a versatile tool for the study of macromolecular dynamics.