Variational Multiscale Models for Charge Transport

Wei, Guo-Wei; Zheng, Qiong; Chen, Zhang; Xia, Kelin

doi:10.1137/110845690

Cited by 122 publications

(153 citation statements)

References 197 publications

(348 reference statements)

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“…[62][63][64] The essential idea is to use the differential geometry theory of surfaces and the geometric measure theory as a natural means to separate the solvent domain from the macromolecular domains. A number of physical phenomena, including polar and nonpolar solvation, molecular dynamics, quantum mechanics, fluid dynamics, electrokinetics, electrohydrodynamics, electrophoresis, and elastic dynamics are considered in our multiscale models via a total energy functional and a variational strategy.…”

Section: Introductionmentioning

confidence: 99%

“…11,12,[14][15][16][17]64 The first series of validations was done for multiscale solvation models. 14-17, 29, 57, 72 The Eulerian formulation, 14 Lagrangian formulation, 15 and quantum formulation are constructed 16 for the solvation analysis of hundreds of small and large molecules, including nonpolar ones.…”

Section: Introductionmentioning

confidence: 99%

“…17 Another series of validations was done on charge transport in realistic ion channels. 64,71 Continuum descriptions are applied to the solvent domain while channel proteins are treated in molecular detail. In our energy functional, nonpolar energy, polar (electrostatic) energy, chemical potential, and possibly fluid energy are considered on an equal footing.…”

Section: Introductionmentioning

confidence: 99%

“…Nonelectrostatic van der Waals (VDW) interactions among all the ions, and between ions and proteins, including size (steric) effects are accounted for in our treatment. 64 In this multiscale paradigm, the non-equilibrium multiscale transport theory reduces to the multiscale solvation model at equilibrium. Very good agreements between our model predictions and experimental measurements have been attained.…”

Section: Introductionmentioning

confidence: 99%

“…Very good agreements between our model predictions and experimental measurements have been attained. 64 The other series of validations of our multiscale models was on the proton transport through membrane proteins. 11,12 Proton transport plays an important role in the molecular mechanism of biological energy transduction, sensory systems, and reproduction of influenza A viruses.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Xia

Opron

Guo

2013

The Journal of Chemical Physics

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221

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The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the PoissonBoltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CE-WAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of O(N 2 ) at most, where N is the number of atoms or residues, in contrast to O(N 3 ) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Xia

Opron

Guo

2013

The Journal of Chemical Physics

Self Cite

221

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Molecular Dynamics Investigation of the Dielectric Decrement of Ion Solutions

Pache

Schmid

2018

ChemElectroChem

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Molecular dynamics simulations, using a classical force field model, have been used to determine the dependence of the static relative dielectric constant of ion solutions with respect to the nature and concentration of the ions and the field strength. The experimentally observed effect of a reduction of the dielectric permittivity due to solvated ions is known as dielectric decrement. We used both the polarization fluctuation at zero field and the constant dielectric displacement method for finite fields to determine the dielectric constant of the bulk solution. All the experimentally observed tendencies of the dielectric decrement could be qualitatively reproduced. The analysis of different solute solvent radial distribution functions indicate that the dielectric decrement arises from the competition between the macroscopic electric field and the local water‐ion interaction. The results suggest that the electric field eventually manages to overcome the local molecular interactions, breaking up the structure of the solvation shell and thus lowering the ion's effect on the dielectric constant. This effect seems to correlate with the solvation energy of the individual ions as well as the type of counter ion, indicating that also long range interactions might play a role. The results can be used to improve especially continuum electrolyte models, used to study electrochemical interfaces, where currently the dielectric decrement is generally not included.

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Geometric modeling of subcellular structures, organelles, and multiprotein complexes

Feng

Xia

Tong

et al. 2012

Numer Methods Biomed Eng

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SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes.

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Variational Multiscale Models for Charge Transport

Cited by 122 publications

References 197 publications

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Multiscale multiphysics and multidomain models—Flexibility and rigidity

Molecular Dynamics Investigation of the Dielectric Decrement of Ion Solutions

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

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