A substantial part of molecular functions involves motions in a wide range of length scales, e.g., from the vibrations of chemical bonds to global conformational changes of supermolecular complexes to macroscopic muscle contractions. The goal of this research is to introduce several new computational methods for describing the motions at any desired length scale without losing the details of atomic calculations, which is an unprecedented simulation capacity. The central method is substructure synthesis method that regards a given structure as an assemblage of substructures acting together in some ways. The choice of substructures is arbitrary, and sometimes quite natural, such as domains or subunits in supermolecular complexes. First, the vibrational modes for each substructure are determined by solving an eigenvalue problem. Next, various substructures are joined together by a set of constraints to enforce geometric compatibility at the inter-substructure interfaces. The modes for the assembled structure can then be computed by the Rayleigh-Ritz principle using a set of low-frequency substructure modes. Computationally, this represents a much more desirable problem than solving the full eigenvalue problem for the assembled structure. This new methods will be applied to F-actin, a typical filamentous system of several microns, to study its mechanical and dynamic properties at any length. This will also help interpret the experiments that measure molecular elastic properties.
The new methods for simulating motions in a wide range of length scales will not only have an impact on the study of molecular dynamics, but also will significantly contribute to the fields of bioengineering and chemistry. Moreover, since some concepts in the proposed methods are related to those in the mechanical engineering field, their implementation as methods for describing motions of complex molecules requires knowledge of multiple disciplines including biology, physics, and engineering. The success of this project will therefore be an excellent example of creative thinking and problem solving benefited from interdisciplinary communication. The beneficiaries will not only be the trainees who are directly involved in the project, but also a larger audience with diverse background who are commonly interested in problems in life sciences and engineering, but from very different perspectives. Particularly, it will expose undergraduate students to concepts of interdisciplinary research. Finally, a broader community will be reached via public distribution of the computer software developed in this work.
