Proteins are fundamental functional units in cells. Proteins form stable and yet somewhat flexible 3D structures and often function by interacting with other molecules. Their functional behaviors are determined by their 3-D structures as well as their flexibilities. In this thesis, I focus my study on protein dynamics and its role in protein function.

One of the most powerful computational methods for studying protein dynamics is normal mode analysis (NMA). Especially its low frequency modes having the intrinsic dynamics of proteins are of interest for most of protein dynamics studies. Although NMA provides analytical solutions to a protein's collective motions, it is inconvenient to use because of its requirement of energy minimization, and it is prohibitive due to the large memory consumption and the long computation time especially when the system is too large. Additionally, it is unclear what meanings the frequencies of normal modes have, and if those meanings can be validated by comparison with the experimental results.

The majority of this thesis resolves the above issues. I have addressed following sequence of questions and developed several simplified NMAs as answers: (1) what is the role of inter residue forces; (2) how to remove the energy minimization requirement in NMA yet to keep most of accuracy; (3) how to efficiently build the coarse-grained model from the all-atomic model with keeping atomic accuracy. Additionally, using newly developed models and traditional NMA, I have examined the meaning of normal modes in all frequency range, and have found the connection with experimental results.

The last part of this thesis addresses, as an application of normal modes, how the normal modes can depict the sequence of breathing motion of myoglobin to find the transition pathway that dynamically opens ligand migration channels. The results have an excellent agreement with molecular dynamics simulation results and experimentally determined reaction rate constants.