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

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      Kreienkamp, A. B.; Liu, L. Y.; Minkara,   M. S.; Knepley, M. G.; Bardhan, J. P.; Radhakrishnan, M.   L. “Analysis of fast boundary-integral approximations for   modeling electrostatic contributions of molecular binding”   Molecular Based Mathematical Biology,   2013, 1, 124-150.


        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   boundary-integral equations might reach unprecedented accuracy,   if the dipole and quadrupole modes can be captured quickly for   general shapes.

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