Modeling and visualization of flexible protein-protein interactions
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Protein-protein interactions form the basis of macromolecular formation and function. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as protein-protein docking. Computational approaches to proteinprotein docking are therefore a necessary pathway to virtual drug screening, plausible macro-molecular structures, and elucidating the function of proteins in assemblages. Protein conformational changes play a crucial role in such interactions, leading to a very high dimensional search space. The computational challenge is further increased as we obtain imaging data for larger and larger proteins, bridging the gap between proteins and cells. Traditional algorithms for the construction and visualization of protein structure and function have not scaled to handle large proteins, macromolecular assemblies and viruses. In this thesis, we provide: data structures and algorithms to represent flexible protein structures, scalable error bounded techniques to compute soft protein-protein docking, a hierarchical flexible docking scheme and novel methods to visualize large interacting molecular complexes and assemblies. Accurate and robust molecular surface computation is vital for parameterizing affinity functions and modeling interactions. We provide a adaptive grid based function definition, whose contours yield a family of relevant surfaces. We show that these are free of self intersections and provide methods to compute regions of C0 continuity. The structure and functions of molecules are represented in a radial basis format, with smooth particle data representing electron density kernels, charges and solvent modulated dielectric coefficients. A fast summation algorithm, based on non-equispaced fast Fourier transforms, is presented to accurately, efficiently and adaptively compute these functions. Based on the previous surfaces and fast summation algorithms, we provide a model for soft docking and error-bounded approximation algorithms to solve the model and predict docking sites. The flexibility space is adaptively sampled using a domain decomposition of the protein into a Flexible Chain Complex. We then provide a flexible docking algorithm based on a multiresolution representation of the proteins, adaptive sampling of conformation, orientation spaces and greedy fit of residues at interfaces. Scientific visualization of protein interfaces and active sites is employed for both data analysis and discovery. We provide algorithms to interactively render both the traditional ball and stick model of molecules and contours of the sum of Gaussians based electron density. To visualize schematic models of large and flexible proteins at interactive rates and high quality, we introduce a novel hardware accelerated, imposter-based scheme to render curved surfaces like spherical patches, cylinders and helices, with correct per pixel shading, using limited geometric primitives. A telescoping rover is used together with our fast summation algorithm and adaptive isocontouring to efficiently visualize density contours of proteins in a multiresolution fashion. All the above algorithms are implemented in a public domain software package called TexMol.