Compressed Representations of Macromolecular Structures and Properties

SummaryWe introduce a new and unified, compressed volumetric representation for macromolecular structures at varying feature resolutions, as well as for many computed associated properties. Important caveats of this compressed representation are fast random data access and decompression operations. Many computational tasks for manipulating large structures, including those requiring interactivity such as real-time visualization, are greatly enhanced by utilizing this compact representation. The compression scheme is obtained by using a custom designed hierarchical wavelet basis construction. Due to the continuity offered by these wavelets, we retain very good accuracy of molecular surfaces, at very high compression ratios, for macromolecular structures at multiple resolutions

VIPERdb: a relational database for structural virology

VIPERdb () is a database for icosahedral virus capsid structures. Our aim is to provide a comprehensive resource specific to the needs of the structural virology community, with an emphasis on the description and comparison of derived data from structural and energetic analyses of capsids. A relational database implementation based on a schema for macromolecular structure makes the data highly accessible to the user, allowing detailed queries at the atomic level. Together with curation practices that maintain data uniformity, this will facilitate structural bioinformatics studies of virus capsids. User friendly search, visualization and educational tools on the website allow both structural and derived data to be examined easily and extensively. Links to relevant literature, sequence and taxonomy databases are provided for each entry

Modeling and visualization of flexible protein-protein interactions

textProtein-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.Computer Science

Fast error-bounded surfaces and derivatives computation for volumetric particle data

Volumetric smooth particle data arise as atomic coordinates with electron density kernels for molecular structures, as well as fluid particle coordinates with a smoothing kernel in hydrodynamic flow simulations. In each case there is the need for efficiently computing approximations of relevant surfaces (molecular surfaces, material interfaces, shock waves, etc), along with surface and volume derivatives (normals, curvatures, etc.), from the irregularly spaced smooth particles. Additionally, molecular properties (charge density, polar potentials), as well as field variables from numerical simulations are often evaluated on these computed surfaces. In this paper we show how all the above problems can be reduced to a fast summation of irregularly spaced smooth kernel functions. For a scattered smooth particle system of M smooth kernels in R 3, where the Fourier coefficients have a decay of the type 1/ω 3, we present an O(M + n 3 log n + N) time, Fourier based algorithm to compute N approximate, irregular samples of a level set surface and its derivatives within a relative L2 error norm ǫ, where n is O(M 1/3 ǫ 1/3). Specifically, a truncated Gaussian of the form e −bx2 has the above decay, and n grows as √ b. In the case when the N output points are samples on a uniform grid, the back transform can be done exactly using a Fast Fourier transform algorithm, giving us an algorithm with O(M + n 3 log n + N log N) time complexity, where n is now approximately half its previously estimated value

Adaptive Grid Based Methods for Computing Molecular Surfaces and Properties

We present an adaptive grid based algorithm to compute a family of relevant molecular surfaces. Molecular interfaces are important in simulations and visualization involving biomolecules. The Richards surface has traditionally been used as a good approximation to the surface, and defined as the surface formed by the inner facing part of a solvent probe atom rolling along the van der Waals surface of the molecule. Computing and representing this surface has traditionally involved complex geometrical data structures like alpha shapes. Adaptive and uniform trilinear grids are commonly used in various simulations involving interactions of molecules or computation of electrostatics and other energy terms. We make use of this grid directly to compute the Molecular Surface and properties like area, volume, curvatures, surface atoms and other surfaces. We compare geometrical and biochemical properties with other methods as a validation. 1 Molecular Surface Definitions Explicit surface definitions as the interface between the solvent and proteins have been given since 1970s. Since it is easier to handle implicitly defined models mathematically, different implicit approximations to these surfaces have been developed. 1.1 van der Waals and Lee Richards Surface Definitions The most common model for molecules is as a collection of atoms represented by spheres, with radii equal to their van der Waals radii. The surface of the set of spheres is known as the van der Waals surface. Lee and Richards introduced the concep

Volumetric Video Compression for Interactive Playback

We develop a volumetric video system which supports interactive browsing of compressed time-varying volumetric features ( significant isosurfaces and interval volumes ). Since the size of even one volumetric frame in a time-varying 3D data set is very large, transmission and on-line reconstruction are the main bottlenecks for interactive remote visualization of time-varying volume and surface data. We describe a compression scheme for encoding time-varying volumetric features in a unified way, which allows for on-line reconstruction and rendering. To increase the run-time decompression speed and compression ratio, we decompose the volume into small blocks and encode only the significant blocks that contribute to the isosurfaces and interval volumes. The results show that our compression scheme achieves high compression ratio with fast reconstruction, which is effective for interactive client-side rendering of time-varying volumetric features