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Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

100%
Kreienkamp A. B., Liu L. Y., Minkara M. S., Knepley M. G., Bardhan J. P., Radhakrishnan M. L.
Molecular Based Mathematical Biology
|
2013
|
tom 1
124-150
EN
We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins¶a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundaryintegral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes.
2
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Efficient representations of Green’s functions for some elliptic equations with piecewise-constant coefficients

100%
Melnikov Y.
Open Mathematics
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2010
|
tom 8
|
nr 1
53-72
EN
Convenient for immediate computer implementation equivalents of Green’s functions are obtained for boundary-contact value problems posed for two-dimensional Laplace and Klein-Gordon equations on some regions filled in with piecewise homogeneous isotropic conductive materials. Dirichlet, Neumann and Robin conditions are allowed on the outer boundary of a simply-connected region, while conditions of ideal contact are assumed on interface lines. The objective in this study is to widen the range of effective applicability for the Green’s function version of the boundary integral equation method making the latter usable for equations with piecewise-constant coefficients.
3
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Progress in developing Poisson-Boltzmann equation solvers

81%
Li C., Li L., Petukh M., Alexov E.
Molecular Based Mathematical Biology
|
2013
|
tom 1
42-62
EN
This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nanoobjects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nanoobjects.
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