Minimal molecular surfaces and their applications

Bates, Peter W.; Wei, Guo-Wei; Zhao, Shan

doi:10.1002/jcc.20796

Cited by 124 publications

(250 citation statements)

References 69 publications

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“…When q = 0 and P = 0, Eq. (5) recovers the mean curvature flow used in our earlier construction of minimal molecular surfaces [6]. It reproduces the surface diffusion flow [4] when q = 1 and P = 0.…”

Section: Introductionsupporting

confidence: 68%

“…Since variational approaches have found their success in a variety of scientific and engineering fields [6, 16, 18–20, 45, 60, 62], a variational derivation of the PDE transform has also been presented [55, 76]. Here we briefly review the variational derivation of the PDE transform.…”

Section: Theory and Algorithmmentioning

confidence: 99%

“…Piecewise-constant initial values are commonly used in our earlier work for molecular surface generation [5, 6, 18]. In this work, we set the piecewise-constant initial value as

u false(boldr, 0 false) = true{\begin{matrix} left 0, & left r \in \cup_{i} O ({boldr}_{i}, r_{i}); \\ left 1, & left otherwise, \end{matrix}

where r i and r i are the atomic coordinate and radius of atom i , respectively.…”

Section: Numerical Test and Validationmentioning

confidence: 99%

See 2 more Smart Citations

High-order fractional partial differential equation transform for molecular surface construction

Chen

Wei

2012

Computational and Mathematical Biophysics

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Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

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Section: Introductionsupporting

confidence: 68%

Section: Theory and Algorithmmentioning

confidence: 99%

“…Piecewise-constant initial values are commonly used in our earlier work for molecular surface generation [5, 6, 18]. In this work, we set the piecewise-constant initial value as

u false(boldr, 0 false) = true{\begin{matrix} left 0, & left r \in \cup_{i} O ({boldr}_{i}, r_{i}); \\ left 1, & left otherwise, \end{matrix}

where r i and r i are the atomic coordinate and radius of atom i , respectively.…”

Section: Numerical Test and Validationmentioning

confidence: 99%

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High-order fractional partial differential equation transform for molecular surface construction

Chen

Wei

2012

Computational and Mathematical Biophysics

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“…The triangulated surface mesh can be better represented by NURBS [5] or algebraic spline models [54]. Another more recent approach to molecular surface generation, based on a "soft" model, was described in [9], where the molecular surface was given by minimizing the surface free energy.…”

Section: Introductionmentioning

confidence: 99%

“…The mesh quality should be guaranteed in molecular modeling and simulation due to the fact that "skinny" triangles often cause poor approximation quality in finite/boundary element methods [27]. The molecular mesh generation approaches mentioned above can usually capture the features of a molecule (although the definition of a feature may vary), but they have either no mesh adaptation (e.g., [16]) or very low mesh quality (e.g., [9,37]). …”

Section: Introductionmentioning

confidence: 99%

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

Holst

McCammon

2008

Journal of Molecular Graphics and Modelling

106

122

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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: feature-preservation, 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.

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Pseudo‐time‐coupled nonlinear models for biomolecular surface representation and solvation analysis

Zhao

2011

Numer Methods Biomed Eng

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SUMMARYThis paper presents an improved mathematical model for biomolecular surface representation and solvation analysis. Based on the Eulerian formulation, the polar and nonpolar contributions to the solvation process can be equally accounted for via a unified free energy functional. Using the variational analysis, two nonlinear partial differential equations, that is, one Poisson-Boltzmann (PB) type equation for electrostatic potential and one geometric flow type equation defining the solute-solvent interface, can be derived. To achieve a more efficient and stable coupling, we propose a time-dependent PB equation by introducing a pseudo-time. The system of nonlinear partial differential equations can then be coupled via the standard time integration. Furthermore, the numerical treatment of nonlinear terms becomes easier in the present model. Based on a hypersurface function, the biomolecular surface is represented as a smooth interface. However, for the nonlinear PB equation, such a smooth interface may cause unphysical blowup because of the existence of nonvanishing values within the solute domain. A filtering process is proposed to circumvent this problem. Example solvation analysis of various compounds and proteins was carried out to validate the proposed model. The contributions of electrostatic interactions to the protein-protein binding affinity are studied for selected protein complexes.

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Minimal molecular surfaces and their applications

Cited by 124 publications

References 69 publications

High-order fractional partial differential equation transform for molecular surface construction

High-order fractional partial differential equation transform for molecular surface construction

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

Pseudo‐time‐coupled nonlinear models for biomolecular surface representation and solvation analysis

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