Normal mode analysis and beyond

Normal mode analysis provides a powerful tool in biophysical computations. Particularly, we shed light on its application to protein properties because they directly lead to biological functions. As a result of normal mode analysis, the protein motion is represented as a linear combination of mutually independent normal mode vectors. It has been widely accepted that the large amplitude motions throughout the entire protein molecule can be well described with a few low-frequency normal modes. Furthermore, it is possible to represent the effect of external perturbations, e.g., ligand binding, hydrostatic pressure, as the shifts of normal mode variables. Making use of this advantage, we are able to explore mechanical properties of proteins such as Young’s modulus and compressibility. Within thermally fluctuating protein molecules under physiological conditions, tightly packed amino acid residues interact with each other through heat and energy exchanges. Since the structure and dynamics of protein molecules are highly anisotropic, the flow of energy and heat should also be anisotropic. Based on the harmonic approximation of the heat current operator, it is possible to analyze the communication map of a protein molecule. By using this method, the energy transfer pathways of photoactive yellow protein were calculated. It turned out that these pathways are similar to those obtained via the Green-Kubo formalism with equilibrium molecular dynamics simulations, indicating that normal mode analysis captures the intrinsic nature of the transport properties of proteins.