Potential energy functions for atomic-level simulations of water and organic and biomolecular systems

Abstract

An overview is provided on the development and status of potential energy functions that are used in atomic-level statistical mechanics and molecular dynamics simulations of water and of organic and biomolecular systems. Some topics that are considered are the form of force fields, their parameterization and performance, simulations of organic liquids, computation of free energies of hydration, universal extension for organic molecules, and choice of atomic charges. The discussion of water models covers some history, performance issues, and special topics such as nuclear quantum effects.T he last 30 years have witnessed remarkable progress in condensed-phase theory. Before that time, atomic-level computer simulations of fluids were largely restricted to atomic and diatomic systems. The first simulation of liquid water was not reported until 1969 and was a Monte Carlo (MC) effort (1), which was followed by the molecular dynamics (MD) studies of Rahman and Stillinger (2, 3) in the early 1970s. The state-of-the-art simulations of water in 1974 were performed for 216 molecules for Ͻ10 ps (3). Even by 1990, there had been almost no MD simulations for a protein in aqueous solution covering 100 ps (4), whereas today MD simulations for a protein with Ϸ10,000 water molecules for many nanoseconds or mixed quantum and molecular mechanics (QM͞ MM) simulations for an enzymatic reaction are not problematic. Of course, performing longer simulations for larger systems does not guarantee the production of useful results. Key underlying issues for accuracy are adequate configurational sampling and the quality of the description of the intramolecular and intermolecular energetics. Progress on the former issue has been aided greatly by massive increases in computing power, although the substantial technical developments in the latter area are the focus of this overview. The topic also has received attention in comprehensive, recent reviews for the treatment of water (5) and biomolecular systems (6-10) that go far beyond the present page limitations. So, the presentation here will be more condensed with a focus on force-field development, water, and aqueous solutions and with some emphasis on our personal experiences and viewpoint. Force FieldsA force field consists of classical potential energy expressions and the associated adjustable parameters. The large majority of condensed-phase simulations have invoked pairwise additivity such that the total potential energy for a collection of molecules and͞or ions (components) with coordinates X ជ is given by the sum of the intermolecular interaction energies between all components plus the sum of the intramolecular energies of the components (Eq. 1).The intramolecular potential energy is typically represented by harmonic terms for bond stretching and angle bending, a Fourier series for each torsional angle, and Coulomb and Lennard-Jones interactions between atoms separated by three or more bonds (Eqs. 2-5). The latter ''nonbonded'' interactions also are evaluated between intermolecular at...

Comparison of multiple Amber force fields and development of improved protein backbone parameters

“…Therefore the function we optimized was calculated as an average of QM and MM energy differences with each conformer's energy set as a reference in turn. This gives an average absolute error (aae) defined as follows: (4) where is the QM energy of conformer j with conformer i as a reference, and is the MM energy of conformer j with conformer i as a reference, N is number of conformers, which is 28 for Gly 3 . Another possibility to define a function for optimization is to concentrate on what the maximum absolute error (mae) might be when we consider all individual QM and MM differences and, again, take into account that any conformer may serve as a reference "zero energy".…”

“…For a more in-depth overview of current force fields and trends in force field development, the reader is referred to recent review articles [2][3][4] . In this report, we focus on the existing AMBER fixed charge additive force fields.…”

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

“…Recently, Caleman et al evaluated the performance of GAFF32 and OPLS/AA33 in organic solvents 34. They benchmarked the force fields by computing liquid properties such as density, enthalpy of vaporization, heat capacity, surface tension, isothermal compressibility, volumetric expansion coefficient, and dielectric constant of ∼150 organic liquids.…”

Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry

“…16,17,46 As was the case with early classical force fields, we proceed by introducing a number of heuristic but physically motivated propositions that allow us to tackle complex reaction networks with hundreds or thousands of distinct chemical species and transformations. The heuristics-aided quantum chemistry (HAQC) approach is based on the following assumptions.…”

“…2,11,12 Encouragingly, heuristic approaches have proven useful for solving complex and large-scale problems across diverse fields such as graph search, 13 sequence alignment, 14 and cheminformatics. 15 One does not have to look far to find heuristic methods: The classical force fields of molecular mechanics 16,17 may well be viewed as heuristic rules of classical chemical structure theory enforced by penalty functions and thus made amenable to computation. In the field of chemical reactivity of organic compounds, a similarly successful set of heuristic rules exists that regards chemical transformations as flows of electrons and is known under the moniker "arrow pushing" to students of organic chemistry.…”