Tom Darden

Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems

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.

A smooth particle mesh Ewald method

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/rp with p≥1. 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 Nu2009log(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 A or less.

The Amber biomolecular simulation programs.

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.

Making Optimal Use of Empirical Energy Functions: Force-Field Parameterization in Crystal Space

Todays 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. Proteins 2004.

New tricks for modelers from the crystallography toolkit: the particle mesh Ewald algorithm and its use in nucleic acid simulations

We thank the North Carolina Supercomputing Center, the Pittsburgh Supercomputing Center and the National Cancer Institute Supercomputing Center for access to resources. LGP thanks the National Institutes of Health for HL-06350 and the National Institute of Environmental Health Sciences (NIEHS) for access to their facilities.

The effect of long‐range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods

Simulations of the HIV‐1 protease unit cell using a 9 A cutoff, 9/18 A ‘‘twin‐range’’ cutoff, and full Ewald sums have been carried out to 300 ps. The results indicate that long‐range electrostatic interactions are essential for proper representation of the HIV‐1 protease crystal structure. The 9 A simulation did not converge in 300 ps. Inclusion of a 9/18 A ‘‘twin‐range’’ cutoff showed significant improvement. Simulation using the Ewald summation convention gave the best overall agreement with x‐ray crystallographic data, and showed the least internal differences in the time average structures of the asymmetric units. The Ewald simulation represents an efficient implementation of the Particle Mesh Ewald method [Darden et al., J. Chem. Phys. 98, 10u2009089 (1993)], and illustrates the importance of including long‐range electrostatic forces in large macromolecular systems.

Efficient particle-mesh Ewald based approach to fixed and induced dipolar interactions

We have implemented classical Ewald and particle-mesh Ewald (PME) based treatments of fixed and induced point dipoles into the sander molecular dynamics (MD) module of AMBER 6. During MD the induced dipoles can be propagated along with the atomic positions either by iteration to self-consistency at each time step, or by a Car–Parrinello (CP) technique using an extended Lagrangian formalism. In this paper we present the derivation of the new algorithms and compare the various options with respect to accuracy, efficiency, and effect on calculated properties of a polarizable water model. The use of PME for electrostatics of fixed charges and induced dipoles together with a CP treatment of dipole propagation in MD simulations leads to a cost overhead of only 33% above that of MD simulations using standard PME with fixed charges, allowing the study of polarizability in large macromolecular systems.

ORAC: A Molecular dynamics program to simulate complex molecular systems with realistic electrostatic interactions

In this study, we present a new molecular dynamics program for simulation of complex molecular systems. The program, named ORAC, combines state‐of‐the‐art molecular dynamics (MD) algorithms with flexibility in handling different types and sizes of molecules. ORAC is intended for simulations of molecular systems and is specifically designed to treat biomolecules efficiently and effectively in solution or in a crystalline environment. Among its unique features are: (i) implementation of reversible and symplectic multiple time step algorithms (or r‐RESPA, reversible reference system propagation algorithm) specifically designed and tuned for biological systems with periodic boundary conditions; (ii) availability for simulations with multiple or single time steps of standard Ewald or smooth particle mesh Ewald (SPME) for computation of electrostatic interactions; and (iii) possibility of simulating molecular systems in a variety of thermodynamic ensembles. We believe that the combination of these algorithms makes ORAC more advanced than other MD programs using standard simulation algorithms.u2003© 1997 John Wiley & Sons, Inc.u2003J Comput Chem 18: 1848–1862, 1997

IONIC CHARGING FREE ENERGIES : SPHERICAL VERSUS PERIODIC BOUNDARY CONDITIONS

Ionic charging free energies calculated by Ewald summation differ substantially from those calculated in spherical cluster calculations, with or without the inclusion of a Born correction in the latter. Using Gauss’ law, we derive an electrostatic potential for ions in spherical clusters that involves contributions only from the interior solvent. This “interior” potential agrees with the “P-summation” approach proposed by Hummer et al. [J. Phys. Chem. B 101, 3017 (1997)], and leads to charging free energies which agree, within simulation error, with those given by Ewald summation with finite-size corrections. The difference in charging free energies between this approach and the conventional cluster free energies including the Born correction is traced to the surface potential of water.

Gaussian induced dipole polarization model.

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole‐induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.