Efficient table lookup without inverse square roots for calculation of pair wise atomic interactions in classical...

Area of Science:

• Computational Chemistry
• Biophysics
• Molecular Dynamics

Background:

• Calculating pairwise nonbonded interactions (Coulomb, van der Waals) is a major bottleneck in atomistic simulations of biomolecular systems.
• Existing methods reduce complexity from O(N^2) to O(N log N) or O(N), but computational cost remains significant.

Purpose of the Study:

• To develop and evaluate a novel lookup table method for accelerating the calculation of nonbonded interactions in molecular dynamics simulations.
• To assess the speedup and accuracy of the lookup table approach compared to traditional methods.

Main Methods:

• Implementation of a lookup table code in FORTRAN 95 within the CHARMM program.
• Utilizing linear interpolation with varying table densities (e.g., 100 points/Ų and 10 points/Ų) for interaction calculations.
• Comparison of the lookup table method against standard, highly optimized FORTRAN code and hand-coded assembler routines.

Main Results:

• Achieved a 1.5- to 2-fold speedup in molecular dynamics simulations across various system sizes.
• Demonstrated that linear interpolation with a modest table density (100 points/Ų) maintains accuracy comparable to standard double precision calculations.
• Showed that a less dense table (10 points/Ų) for proteins in explicit water offers a 10-20% speed increase with only slight accuracy reduction.
• The lookup table method proved faster than hand-coded assembler routines in most cases due to reduced inner loop operation counts.

Conclusions:

• The developed lookup table method provides a significant acceleration for calculating nonbonded interactions in biomolecular simulations.
• This approach offers a practical solution to a major computational bottleneck, enabling larger and longer simulations.
• The method achieves high accuracy with efficient computational performance, outperforming existing optimized routines.