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12
Adaptive Grid Based Methods for Computing Molecular Surfaces and Properties
, 2006
"... 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 surf ..."
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Cited by 9 (2 self)
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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 concept
An algebraic spline model of molecular surfaces
 ACM Symp. Sol. Phys. Model
"... Figure 1: Molecular models of a protein(1HIA). (a) The van der Waals surface model (693 atoms); (b) An initial triangulated solvent excluded surface (SES) model (27480 triangles); (c) The decimated triangulated SES model(7770 triangles); (d) Our algebraic spline molecular surface model (7770 patches ..."
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Cited by 5 (3 self)
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Figure 1: Molecular models of a protein(1HIA). (a) The van der Waals surface model (693 atoms); (b) An initial triangulated solvent excluded surface (SES) model (27480 triangles); (c) The decimated triangulated SES model(7770 triangles); (d) Our algebraic spline molecular surface model (7770 patches) generated from (c). 1
Smooth surface constructions via a higher order level set method
, 2007
"... We present a general framework for a higherorder spline levelset (HLS) method and apply this to smooth surface constructions. Starting from a first order energy functional, we derive the general level set formulation, and provide an efficient solution of a second order geometric partial differenti ..."
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Cited by 4 (1 self)
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We present a general framework for a higherorder spline levelset (HLS) method and apply this to smooth surface constructions. Starting from a first order energy functional, we derive the general level set formulation, and provide an efficient solution of a second order geometric partial differential equation using a C² spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Ztransform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. We provide two demonstrative smooth surface construction examples of our HLS method. The first is the construction of a smooth surface model (an implicit solvation interface) of biomolecules in solvent, given their individual atomic coordinates and solvated radii. The second is the smooth surface reconstruction from a cloud of points generated from a 3D surface scanner.
3d image registration using fast fourier transform, with potential applications to geoinformatics and bioinformatics
 In Proceedings of the International Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems IPMU’06
, 2006
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An ALgebraic Spline Modle of Molecular . . .
 TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
, 2009
"... In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constru ..."
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In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the BernsteinBezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation.
F 2 Dock: A Fast and Fourier Based ErrorBounded Approach to
, 2006
"... The functions of proteins is often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determinatio ..."
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The functions of proteins is often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination and understanding function and structure relationships. We provide a model for rigid docking and errorbounded approximation algorithms to solve the model and predict docking sites. Translational search is sped up using the Fourier domain. Shape based interactions is shown to give good results for a large range of pairs of proteins. 1
An Algebraic Spline Model of Molecular Surfaces
"... In this paper, we describe a new method to generate a smooth algebraic spline (AS) model approximation of the molecular surface (MS), based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first ..."
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In this paper, we describe a new method to generate a smooth algebraic spline (AS) model approximation of the molecular surface (MS), based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold Ps covering the PDB structure, and then generates piecewise polynomial BernsteinBezier (BB) spline function approximation F within Ps, which are nearly C 1 everywhere. Approximation error and point sampling convergence bounds are also computed. An implicit AS model of the MS which is free of singularity, is extracted as the zero contours of F. Furthermore, we generate a polynomial parametrization of the implicit MS, which allows for an efficient point sampling on the MS, and thereby simplifies the accurate estimation of integrals needed for electrostatic solvation energy calculations. 1
and Force Computations
"... Many thanks go to Shan Yang for teaching me how to use Maple and sharing with me her knowledge on optimization, Andrea Hawkins, Omar al Hinai, and Henry Chang for helping me with the proofreading of this thesis. I am grateful to the other CAM students. Thank them for their friendship, enthusiasm, a ..."
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Many thanks go to Shan Yang for teaching me how to use Maple and sharing with me her knowledge on optimization, Andrea Hawkins, Omar al Hinai, and Henry Chang for helping me with the proofreading of this thesis. I am grateful to the other CAM students. Thank them for their friendship, enthusiasm, and numerous suggestions, especially to Paul Bauman, David Fuentes, Nikolay Shestopalov, Shweta Bansal, Wenhao Wang, Jun Li, Kent Van Vels, Michael Harmon, and Ju Liu. I appreciate all the help that the ICES staff has provided to me, especially to Suzanne Bailey and Stephanie Rodriguez. I owe too much to my parents for their years of efforts of bringing me up and to my sister for giving me all her love and support. Words are not enough to express my gratitude towards them. I thank my parentsinlaw for their encouragement whenever I was depressed. Finally and especially, I want to thank my husband Liangfeng for his love, trust, and encouragement.