Computational Analysis of Statics and Dynamics of Macromolecules



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Macromolecules, such as proteins, play a salient part in biological processes. Conducting analysis on the statics and dynamics of such structures is a key to understanding naturally occurring phenomena and designing drugs for the prevention and cure of diseases. This thesis presents research that applies tools from math and computer science to study two problems in computational biology: 1) the flexibility of proteins, and 2) the motion of macromolecular structures in general. The first part of the thesis focuses on a phenomenon called the allosteric effect, which has been observed in nature, but is not well-understood. Proteins generally perform their functions by binding other molecules at designated locations called active sites. In some proteins, it has been found that small molecules can bind at a different allosteric location, thus causing a conformational (structural) change that affects the functionality of the protein. Gaining insight into how these conformational changes occur could lead to great advances in drug design. We take a computational approach by applying concepts from theoretical computer science, geometry and linear algebra to study the structural properties of macromolecules. We model proteins as discrete structures whose movements are restricted by specific geometric constraints. Then we apply techniques from rigidity theory to perform analysis on these constrained structures and display the results via an interactive web application. Conformational changes are essential to macromolecular function, but actual motions cannot be observed experimentally. Standard simulation approaches, such as molecular dynamics, are too computationally expensive to perform on the timescale in which "interesting" motions occur, due to the complexity of the macromolecules. As a result, novel techniques are being developed to improve simulation efficiency. However, the implementation of such techniques is not standardized, so there is no effective method for comparing the performance of various approaches. The second part of this thesis applies standard software engineering principles to the design of an infrastructure that provides for a robust development and comparison of motion simulation techniques.



protein, statics, rigidity, allosteric effect, design, infrastructure, molecule, structure, dynamics, Lie theory, infinitesimal velocity