David A. Case

Development and testing of a general amber force field.

We describe here a general Amber force field (GAFF) for organic molecules. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most organic and pharmaceutical molecules that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited number of atom types, but incorporates both empirical and heuristic models to estimate force constants and partial atomic charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallographic structures were compared to GAFF minimized structures, with a root‐mean‐square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, respectively). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermolecular energies were compared to MP2/6‐31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, respectively. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, respectively), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to experiment) is about 0.5 kcal/mol. GAFF can be applied to wide range of molecules in an automatic fashion, making it suitable for rational drug design and database searching.

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.

An all atom force field for simulations of proteins and nucleic acids

We present an all atom potential energy function for the simulation of proteins and nucleic acids. This work is an extension of the CH united atom function recently presented by S.J. Weiner et al. J. Amer. Chem. Soc., 106, 765 (1984). The parameters of our function are based on calculations on ethane, propane, n−butane, dimethyl ether, methyl ethyl ether, tetrahydrofuran, imidazole, indole, deoxyadenosine, base paired dinucleoside phosphates, adenine, guanine, uracil, cytosine, thymine, insulin, and myoglobin. We have also used these parameters to carry out the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach.

AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules

We describe the development, current features, and some directions for future development of the AMBER package of computer programs. This package has evolved from a program that was constructed to do Assisted Model Building and Energy Refinement to a group of programs embodying a number of the powerful tools of modern computational chemistry-molecular dynamics and free energy calculations.

Exploring protein native states and large‐scale conformational changes with a modified generalized born model

Implicit solvation models provide, for many applications, a reasonably accurate and computationally effective way to describe the electrostatics of aqueous solvation. Here, a popular analytical Generalized Born (GB) solvation model is modified to improve its accuracy in calculating the solvent polarization part of free energy changes in large‐scale conformational transitions, such as protein folding. In contrast to an earlier GB model (implemented in the AMBER‐6 program), the improved version does not overstabilize the native structures relative to the finite‐difference Poisson–Boltzmann continuum treatment. In addition to improving the energy balance between folded and unfolded conformers, the algorithm (available in the AMBER‐7 and NAB molecular modeling packages) is shown to perform well in more than 50 ns of native‐state molecular dynamics (MD) simulations of thioredoxin, protein‐A, and ubiquitin, as well as in a simulation of Barnase/Barstar complex formation. For thioredoxin, various combinations of input parameters have been explored, such as the underlying gas‐phase force fields and the atomic radii. The best performance is achieved with a previously proposed modification to the torsional potential in the Amber ff99 force field, which yields stable native trajectories for all of the tested proteins, with backbone root‐mean‐square deviations from the native structures being ∼1.5 Å after 6 ns of simulation time. The structure of Barnase/Barstar complex is regenerated, starting from an unbound state, to within 1.9 Å relative to the crystal structure of the complex. Proteins 2004;55:000–000.

Force fields for protein simulations.

Publisher Summary The chapter focuses on a general description of the force fields that are most commonly used at present, and it gives an indication of the directions of current research that may yield better functions in the near future. After a brief survey of current models, mostly generated during the 1990s, the focus of the chapter is on the general directions the field is taking in developing new models. The most commonly used protein force fields incorporate a relatively simple potential energy function: The emphasis is on the use of continuum methods to model the electrostatic effects of hydration and the introduction of polarizability to model the electronic response to changes in the environment. Some of the history and performance of widely used protein force fields based on an equation on simplest potential energy function or closely related equations are reviewed. The chapter outlines some promising developments that go beyond this, primarily by altering the way electrostatic interactions are treated. The use of atomic multipoles and off-center charge distributions, as well as attempts to incorporate electronic polarizability, are also discussed in the chapter.

Theory and applications of the generalized born solvation model in macromolecular simulations

Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface‐area based “hydrophobic” term) to explicit solvent simulations for a 10 base‐pair DNA oligomer, and for the 108‐residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NHO and NHN internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.

An overview of the Amber biomolecular simulation package

Molecular dynamics (MD) allows the study of biological and chemical systems at the atomistic level on timescales from femtoseconds to milliseconds. It complements experiment while also offering a way to follow processes difficult to discern with experimental techniques. Numerous software packages exist for conducting MD simulations of which one of the widest used is termed Amber. Here, we outline the most recent developments, since version 9 was released in April 2006, of the Amber and AmberTools MD software packages, referred to here as simply the Amber package. The latest release represents six years of continued development, since version 9, by multiple research groups and the culmination of over 33 years of work beginning with the first version in 1979. The latest release of the Amber package, version 12 released in April 2012, includes a substantial number of important developments in both the scientific and computer science arenas. We present here a condensed vision of what Amber currently supports and where things are likely to head over the coming years. Figure 1 shows the performance in ns/day of the Amber package version 12 on a single‐core AMD FX‐8120 8‐Core 3.6GHz CPU, the Cray XT5 system, and a single GPU GTX680.

Orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters

Abstract The interconnections among orbital interactions, electron delocalization and spin coupling in iron-sulfur clusters are reviewed, with special attention to the complex nature of spin and orbital states in 4Fe4S complexes. We summarize the uses of broken symmetry density functional calculations and spin projection methods for extracting Heisenberg spin coupling and electron delocalization parameters, as well as for understanding charge distributions and orbital aspects of electronic structure. The value of spin projection coefficients for sorting out spin coupling patterns in complex systems is also emphasized. Among the systems examined are oxidized, high-potential, iron-sulfur proteins, 4Fe ferredoxin proteins and related synthetic complexes. By analysis of experimental hyperfine parameters, a detailed model of spin coupling for the “double cubane” P cluster of nitrogenase has been proposed in recent work based on Mossbauer, electron paramagnetic resonance (EPR) and X-ray structural data; there is one pairwise valence delocalized and one trapped valence cubane in the P (oxidized) state. In the area of electron transfer energetics, we have found that Heisenberg spin coupling and electron delocalization both contribute substantially to the redox potentials of 4Fe4S complexes, and Heisenberg coupling contributes to the difference in redox potential between 1Fe and 2Fe2S complexes, based on recent density functional calculations for model systems in solvents.

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf.

Estimating protein–protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H‐Ras/C‐Raf1 using the MM‐PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas‐phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit‐solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent‐accessible surface area‐dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute–solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson–Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal‐mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper “one‐trajectory‐alternative” to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras–Raf obtained in this study of −8.3 kcal mol−1 is in good agreement with the experimental result of −9.6 kcal mol−1, however, further probing the transferability of the applied protocol that led to this result is necessary.