An N ·log(N) method for evaluating electrostatic energies and forces of large periodic systems is presented. The method is based on interpolation of the reciprocal space Ewald sums and evaluation of the resulting convolutions using fast Fourier transforms. Timings and accuracies are presented for three large crystalline ionic systems.

The previously developed particle mesh Ewald method is reformulated in terms of efficient B-spline interpolation of the structure factors. This reformulation allows a natural extension of the method to potentials of the form 1/r p with pу1. Furthermore, efficient calculation of the virial tensor follows. Use of B-splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy. We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N). For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 Å or less.

We describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a number of powerful tools of modern computational chemistry, focused on molecular dynamics and free energy calculations of proteins, nucleic acids, and carbohydrates.

Today's energy functions are not able yet to distinguish reliably between correct and almost correct protein models. Improving these near-native models is currently a major bottle-neck in homology modeling or experimental structure determination at low resolution. Increasingly accurate energy functions are required to complete the "last mile of the protein folding problem," for example during a molecular dynamics simulation. We present a new approach to reach this goal. For 50 high resolution X-ray structures, the complete unit cell was reconstructed, including disordered water molecules, counter ions, and hydrogen atoms. Simulations were then run at the pH at which the crystal was solved, while force-field parameters were iteratively adjusted so that the damage done to the structures was minimal. Starting with initial parameters from the AMBER force field, the optimization procedure converged at a new force field called YAMBER (Yet Another Model Building and Energy Refinement force field), which is shown to do significantly less damage to X-ray structures, often move homology models in the right direction, and occasionally make them look like experimental structures. Application of YAMBER during the CASP5 structure prediction experiment yielded a model for target 176 that was ranked first among 150 submissions. Due to its compatibility with the well-established AMBER format, YAMBER can be used by almost any molecular dynamics program. The parameters are freely available from www.yasara.org/yamber.