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KEY WORDS: free energies, particle mesh Ewald, fast multipole, periodic boundary conditions, Ewald summation
ABSTRACT
Current computer simulations of biomolecules typically make use of classical molecular dynamics methods, as a very large number (tens to hundreds of thousands) of atoms are involved over timescales of many nanoseconds. The methodology for treating short-range bonded and van der Waals interactions has matured. However. long-range electrostatic interactions still represent a bottleneck in simulations. In this article, we introduce the basic issues for an accurate representation of the relevant electrostatic interactions. In spite of the huge computational time demanded by most biomolecular systems, it is no longer necessary to resort to uncontrolled approximations such as the use of cutoffs. In particular, we discuss the Ewald summation methods, the fast particle mesh methods, and the fast multipole methods. We also review recent efforts to understand the role of boundary conditions in systems with long-range interactions, and conclude with a short perspective on future trends.
INTRODUCTION
The explosive growth of computer power over the past two decades has led to the development of large-scale simulation techniques whose aim is to directly reproduce or simulate processes on a molecular level. Molecular dynamics (MD) simulations, of both a classical and quantum nature, have proven to be invaluable in elucidating the structural, mechanical, electrical, and chemical properties of diverse sets of materials. For example, MD simulations have been used to study the liquid state, the bulk solid, diffusion, wetting phenomena, phase transformations, polymers, and protein dynamics, to name several examples. Indeed, it may be argued that MD simulations [and variants ( 1 )] represent the future of theoretical endeavors in the fields of physics, chemistry, and molecular biology.
The simulation of biologically active molecules poses its own unique set of problems to the computational scientist. When contemplating an MD simulation of biomolecules, one would ideally like to carry out a quantum mechanical calculation, based for example on the density functional theory approach (DFT). Schemes such as the Fast-Fourier transform based Car-Parrinello technique (2) or other real-space multigrid methods (3) have reached maturity. These methods are known to be reliable, with truly predictive powers. Indeed, they have provided us with some of the most accurate theoretical descriptions of materials to date....