"New-version-fast-multipole-method" accelerated electrostatic calculations in biomolecular systems

  • Authors:

  • Benzhuo Lu;Xiaolin Cheng;J. Andrew McCammon

  • Affiliations:

  • Howard Hughes Medical Institute, Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0365, United States;Howard Hughes Medical Institute, Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0365, United States;Department of Chemistry and Biochemistry, Center for Theoretical Biological Physics, Department of Pharmacology, Howard Hughes Medical Institute, University of California at San Diego, La Jolla, C ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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Abstract

In this paper, we present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems. In our scheme, a boundary integral equation (BIE) approach is applied to discretize the linearized Poisson-Boltzmann (PB) equation. The resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule, and are solved efficiently using Krylov subspace based iterative methods such as generalized minimal residual (GMRES) or biconjugate gradient stabilized (BiCGStab) methods. In each iteration, the convolution type matrix-vector multiplications are accelerated by a new version of the fast multipole method (FMM). The implemented algorithm is asymptotically optimal O(N) both in CPU time and memory usage with optimized prefactors. Our approach enhances the present computational ability to treat electrostatics of large scale systems in protein-protein interactions and nano particle assembly processes. Applications including calculating the electrostatics of the nicotinic acetylcholine receptor (nAChR) and interactions between protein Sso7d and DNA are presented.