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.

Simulations of the HIV-l 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 aI., J. Chern. Phys. 98, 10 089 (1993)], and illustrates the importance of including long-range electrostatic forces in large macromolecular systems.

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The structure of estrogen sulphotransferase has been solved in the presence of inactive cofactor PAP and substrate 17 beta-estradiol. This structure reveals structural similarities between cytosolic sulphotransferases and nucleotide kinases.

LI3@niehs.nih.gov

The accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of "partial charges" is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald "direct sum" is evaluated through a McMurchie-Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The "reciprocal sum" has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigrid-based approach. We find that even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole-hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussian-based electrostatics in the future. It is hoped that this new formalism will facilitate the systematic implementation of higher order multipoles in classical biomolecular force fields.

Sulfotransferases (STs) catalyze the transfer reaction of the sulfate group from the ubiquitous donor 3 -phosphoadenosine 5 -phosphosulfate (PAPS) to an acceptor group of numerous substrates. This reaction, often referred to as sulfuryl transfer, sulfation, or sulfonation, is widely observed from bacteria to humans and plays a key role in various biological processes such as cell communication, growth and development, and defense. The cytosolic STs sulfate small molecules such as steroids, bioamines, and therapeutic drugs, while the Golgi-membrane counterparts sulfate large molecules including glucosaminylglycans and proteins. We have now solved the X-ray crystal structures of four cytosolic and one membrane ST. All five STs are globular proteins composed of a single ␣/␤ domain with the characteristic five-stranded ␤-sheet. The ␤-sheet constitutes the core of the Paps-binding and catalytic sites. Structural analysis of the PAPS-, PAP-, substrate-, and/or orthovanadate (VO 4 3؊ )-bound enzymes has also revealed the common molecular mechanism of the transfer reaction catalyzed by sulfotransferses. The X-ray crystal structures have opened a new era for the study of sulfotransferases.