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476
PDB2PQR: an automated pipeline for the setup of Poisson–Boltzmann electrostatics calculations
 Nucleic Acids Res
, 2004
"... Continuum solvation models, such as Poisson– Boltzmann and Generalized Born methods, have become increasingly popular tools for investigating the influence of electrostatics on biomolecular structure, energetics and dynamics. However, the use of such methods requires accurate and complete structural ..."
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Cited by 95 (3 self)
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Continuum solvation models, such as Poisson– Boltzmann and Generalized Born methods, have become increasingly popular tools for investigating the influence of electrostatics on biomolecular structure, energetics and dynamics. However, the use of such methods requires accurate and complete structural data as well as force field parameters such as atomic charges and radii. Unfortunately, the limiting step in continuum electrostatics calculations is often the addition of missing atomic coordinates to molecular structures from the Protein Data Bank and the assignment of parameters to biomolecular structures. To address this problem, we have developed the PDB2PQR web service
A New Paradigm for Parallel Adaptive Meshing Algorithms
 SIAM J. Sci. Comput
, 2003
"... We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to ru ..."
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Cited by 46 (9 self)
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We present a new approach to the use of parallel computers with adaptive finite element methods. This approach addresses the load balancing problem in a new way, requiring far less communication than current approaches. It also allows existing sequential adaptive PDE codes such as PLTMG and MC to run in a parallel environment without a large investment in recoding. In this new approach, the load balancing problem is reduced to the numerical solution of a small elliptic problem on a single processor, using a sequential adaptive solver, without requiring any modifications to the sequential solver. The small elliptic problem is used to produce a posteriori error estimates to predict future element densities in the mesh, which are then used in a weighted recursive spectral bisection of the initial mesh. The bulk of the calculation then takes place independently on each processor, with no communication, using possibly the same sequential adaptive solver. Each processor adapts its region of the mesh independently, and a nearly loadbalanced mesh distribution is usually obtained as a result of the initial weighted spectral bisection. Only the initial fanout of the mesh decomposition to the processors requires communication. Two additional steps requiring boundary exchange communication may be employed after the individual processors reach an adapted solution, namely, the construction of a global conforming mesh from the independent subproblems, followed by a final smoothing phase using the subdomain solutions as an initial guess. We present a series of convincing numerical experiments that illustrate the e#ectiveness of this approach. The justification of the initial refinement prediction step, as well as the justification of skipping the two communicationintensive steps, ...
Texmol: Interactive visual exploration of large flexible multicomponent molecular complexes
 In VIS ’04: Proceedings of the conference on Visualization ’04
, 2004
"... While molecular visualization software has advanced over the years, today, most tools still operate on individual molecular structures with limited facility to manipulate large multicomponent complexes. We approach this problem by extending 3D imagebased rendering via programmable graphics units, r ..."
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Cited by 44 (10 self)
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While molecular visualization software has advanced over the years, today, most tools still operate on individual molecular structures with limited facility to manipulate large multicomponent complexes. We approach this problem by extending 3D imagebased rendering via programmable graphics units, resulting in an order of magnitude speedup over traditional trianglebased rendering. By incorporating a biochemically sensitive levelofdetail hierarchy into our molecular representation, we communicate appropriate volume occupancy and shape while dramatically reducing the visual clutter that normally inhibits higherlevel spatial comprehension. Our hierarchical, image based rendering also allows dynamically computed physical properties data (e.g. electrostatics potential) to be mapped onto the molecular surface, tying molecular structure to molecular function. Finally, we present another approach to interactive molecular exploration using volumetric and structural rendering in tandem to discover molecular properties that neither rendering mode alone could reveal. These visualization techniques are realized in a highperformance, interactive molecular exploration tool we call TexMol, short for Texture Molecular viewer.
Quality meshing of implicit solvation models of biomolecular structures
 COMPUT. AIDED GEOM. DES
, 2006
"... This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gauss ..."
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Cited by 32 (9 self)
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This paper describes a comprehensive approach to construct quality meshes for implicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric electron density map is constructed from atomic data using weighted Gaussian isotropic kernel functions and a twolevel clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the LeeRichards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flow techniques are used to improve the surface and volume mesh quality. Several examples are presented, including generated meshes for biomolecules that have been successfully used in finite element simulations involving solvation energetics and rate binding constants.
Free energy simulations come of age: protein–ligand recognition
 Acc. Chem. Res. (in press
, 2002
"... In recent years, molecular dynamics simulations of biomolecular free energy differences have benefited from significant methodological advances and increased computer power. Applications to molecular recognition provide an understanding of the interactions involved that goes beyond, and is an import ..."
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Cited by 24 (4 self)
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In recent years, molecular dynamics simulations of biomolecular free energy differences have benefited from significant methodological advances and increased computer power. Applications to molecular recognition provide an understanding of the interactions involved that goes beyond, and is an important complement to, experimental studies. PoissonBoltzmann electrostatic models provide a faster and simpler free energy method in cases where electrostatic interactions are important. We illustrate both molecular dynamics and PoissonBoltzmann methods with a detailed study of amino acid recognition by aspartyltRNA synthetase, whose specificity is important for maintaining the integrity of the genetic code. 1.
Evaluation of ion binding to DNA duplexes using a sizemodified Poisson–Boltzmann theory
 Biophys. J
, 2007
"... ABSTRACT PoissonBoltzmann (PB) theory is among the most widely applied electrostatic theories in biological and chemical science. Despite its reasonable success in explaining a wide variety of phenomena, it fails to incorporate two basic physical effects, ion size and ionion correlations, into its ..."
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Cited by 22 (0 self)
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ABSTRACT PoissonBoltzmann (PB) theory is among the most widely applied electrostatic theories in biological and chemical science. Despite its reasonable success in explaining a wide variety of phenomena, it fails to incorporate two basic physical effects, ion size and ionion correlations, into its theoretical treatment. Recent experimental work has shown significant deviations from PB theory in competitive monovalent and divalent ion binding to a DNA duplex. The experimental data for monovalent binding are consistent with a hypothesis that attributes these deviations to counterion size. To model the observed differences, we have generalized an existing sizemodified PoissonBoltzmann (SMPB) theory and developed a new numerical implementation that solves the generalized theory around complex, atomistic representations of biological molecules. The results of our analysis show that good agreement to data at monovalent ion concentrations up to;150 mM can be attained by adjusting the ionsize parameters in the new sizemodified theory. SMPB calculations employing calibrated ionsize parameters predict experimental observations for other nucleic acid structures and salt conditions, demonstrating that the theory is predictive. We are, however, unable to model the observed deviations in the divalent competition data with a theory that only accounts for size but neglects ionion correlations, highlighting the need for theoretical descriptions that further incorporate ionion correlations. The accompanying numerical solver has been released publicly, providing the general scientific community the ability to compute SMPB solutions around a variety of different biological structures with only modest computational resources.
FeaturePreserving Adaptive Mesh Generation for Molecular Shape Modeling and Simulation
, 2007
"... We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a n ..."
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Cited by 18 (7 self)
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We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: featurepreservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvment of meshes in a broad range of applications.
PoissonNernstPlanck Equations for Simulating Biomolecular DiffusionReaction Processes I: Finite Element Solutions
, 2010
"... In this paper we developed accurate finite element methods for solving 3D PoissonNernstPlanck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Ner ..."
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Cited by 16 (2 self)
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In this paper we developed accurate finite element methods for solving 3D PoissonNernstPlanck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the NernstPlanck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, wellposed PNP equations. An inexactNewton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an AdamsBashforthCrankNicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the NernstPlanck equation, and theoretically proved that the transformed formulation is always associated with an illconditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molec
PCE: web tools to compute protein continuum electrostatics
 Nucleic Acids Res
, 2005
"... PCE (protein continuum electrostatics) is an online service for protein electrostatic computations presently based on the MEAD (macroscopic electrostatics with atomic detail) package initially developed by D. Bashford [(2004) Front Biosci., 9, 1082–1099]. This computer method uses a macroscopic ele ..."
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Cited by 16 (1 self)
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PCE (protein continuum electrostatics) is an online service for protein electrostatic computations presently based on the MEAD (macroscopic electrostatics with atomic detail) package initially developed by D. Bashford [(2004) Front Biosci., 9, 1082–1099]. This computer method uses a macroscopic electrostatic model for the calculation of protein electrostatic properties, such as pKa values of titratable groups and electrostatic potentials. The MEAD package generates electrostatic energies via finite difference solution to the Poisson–Boltzmann equation. Users submit a PDB file and PCE returns potentials and pKa values as well as color (static or animated) figures displaying electrostatic potentials mapped on the molecular surface. This service is intended to facilitate electrostatics analyses of proteins and thereby broaden the accessibility to continuum electrostatics to the biological community. PCE can be accessed at
PBEQSolver for online visualization of electrostatic potential of biomolecules
 Nucleic Acids Research
"... of biomolecules ..."
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