Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I. Algorithms and examples

Holst, Michael; Baker, Nathan A.; Wang, Feng

doi:10.1002/1096-987x(20001130)21:15<1319::aid-jcc1>3.0.co;2-8

Cited by 281 publications

(272 citation statements)

References 76 publications

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“…The most common numerical techniques for solving the PB equation are based on discretization of the domain of interest into small regions. Those methods include finite difference (Davis and McCammon, 1989;Nicholls and Honig, 1991;Holst and Saied, 1993;Holst and Saied, 1995;Baker et al, 2001), finite element Friesner, 1997a, 1997b;Baker et al, 2000;Holst et al, 2000;Baker et al, 2001;Dyshlovenko, 2002), and boundary element methods (Zauhar and Morgan, 1988;Juffer et al, 1991;Allison and Huber, 1995;Bordner and Huber, 2003;Boschitsch and Fenley, 2004), all of which continue to be developed to further improve the accuracy and efficiency of electrostatics calculations in the numerous biomolecular applications described below. The major software packages that can be used to solve the PB equation are listed in Table 1.…”

Section: Iiic Poisson-boltzmann Methodsmentioning

confidence: 99%

Computational Methods for Biomolecular Electrostatics

Dong

Olsen

Baker

2008

Methods in Cell Biology

116

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An understanding of intermolecular interactions is essential for insight into how cells develop, operate, communicate and control their activities. Such interactions include several components: contributions from linear, angular, and torsional forces in covalent bonds, van der Waals forces, as well as electrostatics. Among the various components of molecular interactions, electrostatics are of special importance because of their long range and their influence on polar or charged molecules, including water, aqueous ions, and amino or nucleic acids, which are some of the primary components of living systems. Electrostatics, therefore, play important roles in determining the structure, motion and function of a wide range of biological molecules. This chapter presents a brief overview of electrostatic interactions in cellular systems with a particular focus on how computational tools can be used to investigate these types of interactions.

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Section: Iiic Poisson-boltzmann Methodsmentioning

confidence: 99%

Computational Methods for Biomolecular Electrostatics

Dong

Olsen

Baker

2008

Methods in Cell Biology

116

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“…Our results establish a clear framework for future investigations aimed at defining the structure-function mechanisms that mediate the regulation of CLH-3b and other CLC proteins. (48). PQR files were generated using the PDB2PQR program (49).…”

Section: Function Of Clc Cbs and Bateman Domainsmentioning

confidence: 99%

Role of CBS and Bateman Domains in Phosphorylation-Dependent Regulation of a CLC Anion Channel

Yamada

Krzeminski

Bozóky

et al. 2016

Biophysical Journal

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Eukaryotic CLC anion channels and transporters are homodimeric proteins composed of multiple a-helical membrane domains and large cytoplasmic C-termini containing two cystathionine-b-synthase domains (CBS1 and CBS2) that dimerize to form a Bateman domain. The Bateman domains of adjacent CLC subunits interact to form a Bateman domain dimer. The functions of CLC CBS and Bateman domains are poorly understood. We utilized the Caenorhabditis elegans CLC-1/2/Ka/ Kb anion channel homolog CLH-3b to characterize the regulatory roles of CLC cytoplasmic domains. CLH-3b activity is reduced by phosphorylation or deletion of a 14-amino-acid activation domain (AD) located on the linker connecting CBS1 and CBS2. We demonstrate here that phosphorylation-dependent reductions in channel activity require an intact Bateman domain dimer and concomitant phosphorylation or deletion of both ADs. Regulation of a CLH-3b AD deletion mutant is reconstituted by intracellular perfusion with recombinant 14-amino-acid AD peptides. The sulfhydryl reactive reagent 2-(trimethylammonium)ethyl methanethiosulfonate bromide (MTSET) alters in a phosphorylation-dependent manner the activity of channels containing single cysteine residues that are engineered into the short intracellular loop connecting membrane a-helices H and I (H-I loop), the AD, CBS1, and CBS2. In contrast, MTSET has no effect on channels in which cysteine residues are engineered into intracellular regions that are dispensable for regulation. These studies together with our previous work suggest that binding and unbinding of the AD to the Bateman domain dimer induces conformational changes that are transduced to channel membrane domains via the H-I loop. Our findings provide new, to our knowledge, insights into the roles of CLC Bateman domains and the structurefunction relationships that govern the regulation of CLC protein activity by diverse ligands and signaling pathways.

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“…al [9] maintained an approximating triangulation of a deforming skin surface. Simplex subdivision schemes are used to generate tetrahedral meshes for molecular structures in solving the Poisson-Boltzmann equation [22]. Gaussian functions have been used to construct density maps [5] [21] [33] [1] [31], from which implicit solvation models are approximated as an isocontour [21] [27] [18].…”

Section: Molecular Surface Approximationmentioning

confidence: 99%

“…As used for Poisson-Boltzmann electrostatics calculations in [22], a characteristic function f (x) is selected to represent an 'inflated' van der Waals-based accessibility (1) where (x i , r i ) are the centers and radii of the N atoms in the biomolecule, and σ is the radius of the diffusing species, here we choose σ = 2 [43]. When σ = 0, the VWS is constructed.…”

Section: Gaussian Density Mapmentioning

confidence: 99%

Quality meshing of implicit solvation models of biomolecular structures

Zhang

Bajaj

2006

Computer Aided Geometric Design

104

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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 two-level clustering technique. This enables the selection of a smooth implicit solvation surface approximation to the Lee-Richards 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 binding rate constants.

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Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I. Algorithms and examples

Abstract: On page 1332 of the above article the statement "For example, in DelPhi, one may only employ cubical meshes with 63 mesh lines in each direction" is no longer accurate; more recent versions of DelPhi have been extended to allow for the use of larger cubical meshes.

Cited by 281 publications

References 76 publications

Computational Methods for Biomolecular Electrostatics

Computational Methods for Biomolecular Electrostatics

Role of CBS and Bateman Domains in Phosphorylation-Dependent Regulation of a CLC Anion Channel

Quality meshing of implicit solvation models of biomolecular structures

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