Biological functions of macromolecules and their assemblages play critical roles in a living cell. Comprehending such a biological mechanism helps us understand better the biological phenomena of the human body, in part, the mysteries of its functions. More importantly, it enables us to propose many viable suggestions for improving human life in a variety of ways (e.g. medical innovation). Computational approaches such as molecular dynamics (MD) and various coarse-grained elastic network models (ENMs) have emerged as powerful tools to comprehend and analyze biological functions and malfunctions otherwise inaccessible, thereby contributing to understanding functional disorders which may eventually cause diseases in the human body. Despite their technical and theoretical contributions, some drawbacks such as a limitation of computational efficiency in MD or the loss of local dynamics information in coarse-grained ENMs have also been observed in utilizing those computational tools. In the study of molecular dynamics, functional conformational changes can be largely resolved into hinge and shear motions (Gerstein 1998) and they are associated with the collective behavior of rigid domains involved (i.e. secondary structures). Therefore, we hypothesize that the global dynamics of large macromolecules can be described by using only several DOFs strongly related to collective motions of the systems rather than bringing their full DOFs into play, which is computationally so expensive. From this hypothesis, we develop a reduced DOF model called hybrid ENM in which rigid domains are represented as rigid clusters while all of the flexible regions (i.e. hinge, loop, and etc) are modeled in atomic detail to present the local dynamics. Hybrid ENM enables us to not only handle very large macromolecules in a PC but also represent global and local dynamics efficiently without loss of generality. A variety of applications addressed in this study show its potential and effectiveness as an innovative tool for the study of macromolecular structure and dynamics. In this dissertation, the mathematical description for hybrid ENM is fully derived from conventional coarse-grained ENM and applied to 70S ribosome, a very large macromolecule containing over ten thousands residues, in order to understand the global ratchet like motions and the complete cycle of tRNA translocation. Hybrid ENM is also utilized to predict folding pathways of antithrombin (1E05). A nascent polypeptide chain of antithrombin which includes at least the first four Cysteine residues is modeled using hybrid ENM to investigate the topological role of disulfide bonds (SS) and the effect of Carbohydrate (CHO) structure in the co-translational folding of antithrombin. Hybrid ENM is also applicable to fracture mechanics. The interaction between polymer matrix and nano/micro size particles is modeled at atomic level in order to understand the physics of the deformation and the fracture processes at crack tips of polymer composites. Even a 2-D simple lattice model explains well the phenomena observed in many previous experiments. A 3-D ENM is also investigated to obtain more realistic simulation results. Another contribution of this dissertation is the development of UMass Morph Server (UMMS) which provides both harmonic and anharmonic analysis tools online for anyone who are not mathematically oriented to directly adopt these methodologies to his/her studies. UMMS cannot only cross-validate the NMA and/or pathway generated by other morph servers, but also provide several unique features such as symmetry-constrained, rigid-cluster, and hybrid ENMs. Consequently, hybrid ENM can play an important role in the study of macromolecular dynamics and fracture mechanics of polymer composites by achieving both computational efficiency and physical realism of the simulation
