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Derivatives of molecular surface area and volume: Simple and exact analytical formulas

Authors

  • Konstantin V. Klenin,

    1. Steinbuch Center for Computing, Karlsruhe Institute of Technology, P.O. Box 3640, D-76021 Karlsruhe, Germany
    2. Center for Functional Nanostructures, Karlsruhe Institute of Technology, P.O. Box 6980, D-76049 Karlsruhe, Germany
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  • Frank Tristram,

    1. Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, D-76021 Karlsruhe, Germany
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  • Timo Strunk,

    1. Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, D-76021 Karlsruhe, Germany
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  • Wolfgang Wenzel

    Corresponding author
    1. Center for Functional Nanostructures, Karlsruhe Institute of Technology, P.O. Box 6980, D-76049 Karlsruhe, Germany
    2. Institute of Nanotechnology, Karlsruhe Institute of Technology, P.O. Box 3640, D-76021 Karlsruhe, Germany
    • Center for Functional Nanostructures, Karlsruhe Institute of Technology, P.O. Box 6980, D-76049 Karlsruhe, Germany
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Abstract

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

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