A fast algorithm for particle simulations
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Dynamic maintenance and visualization of molecular surfaces
Discrete Applied Mathematics - Special issue: Computational molecular biology series issue IV
Multilevel summation for the fast evaluation of forces for the simulation of biomolecules
Multilevel summation for the fast evaluation of forces for the simulation of biomolecules
Fast Molecular Solvation Energetics and Forces Computation
SIAM Journal on Scientific Computing
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Bio-molecules reach their stable configuration in solvent which is primarily water with a small concentration of salt ions. One approximation of the total free energy of a bio-molecule includes the classical molecular mechanical energy EMM (which is understood as the self intra-molecular energy in vacuum) and the solvation energy Gsol which is caused by the change of the environment of the molecule from vacuum to solvent (and hence also known as the molecule-solvent interaction energy). This total free energy is used to model and study the stability of bio-molecules in isolation or in their interactions with drugs. In this paper we present fast O (N log N) multi-level grid based approximation algorithms (where N is the number of atoms) for efficiently estimating the compute-intensive terms of EMM and Gsol. The fast octree-based algorithm for Gsol is additionally dependent on an O (N) size computation of the biomolecular surface and its spatial derivatives (normals). We also provide several examples with timing results, and speed/accuracy tradeoffs, demonstrating the efficiency and scalability of our fast free energy estimation of bio-molecules, potentially with millions of atoms.