Fast summation boundary element method for calculating solvation free energies of macromolecules

We present a boundary element method (BEM) for calculating the reaction field energy of a macromolecule embedded in a high‐dielectric medium such as water. In a BEM calculation, the key computational task is the calculation of the induced surface charge distribution at the dielectric boundary. This is obtained by solving a system of linear equations whose dimension can run into the tens of thousands for a macromolecule. In this work, we use a fast summation hierarchical multipole method to solve for the induced surface charge densities. By careful analysis of the levels of approximation required for the various terms in the calculation, we avoid the unnecessary computation of terms that contribute negligibly to the final outcome and, consequently, achieve high computational efficiency. For a protein such as BPTI with 890 atoms, the calculation of the induced surface charge density distribution and the reaction field energy was completed in 7.9 s on an SGI workstation with an R10000 CPU. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1494–1504, 1998

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