6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

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.

/pdf/the-amber-biomolecular-simulation-programs-e2nyq1ef44.pdf

The Amber biomolecular simulation programs

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 A after 6 ns of simulation time. The structure of Barnase/Barstar complex is regenerated, starting from an unbound state, to within 1.9 A relative to the crystal structure of the complex. Proteins 2004;55:000–000. © 2004 Wiley-Liss, Inc.

/pdf/exploring-protein-native-states-and-large-scale-9vmx9euhl6.pdf

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

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.

https://dasher.wustl.edu/ponder/papers/advprotchem-66-27-03.pdf

Force fields for protein simulations

We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.

/pdf/routine-microsecond-molecular-dynamics-simulations-with-41c2fb6wpv.pdf

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born

The analytic generalized Born approximation is an efficient electrostatic model that describes molecules in solution. Here it is modified to permit a more accurate description of large macromolecul...

/pdf/modification-of-the-generalized-born-model-suitable-for-r7y74akg5g.pdf

Modification of the Generalized Born Model Suitable for Macromolecules

Density functional and continuum dielectric theories have been combined to calculate molecular properties such as hydration enthalpies, redox potentials, and absolute pKa values of transition metal cations in solution. The discrete cluster model, which is treated explicitly by density functional theory, includes six waters in the first hydration shell and another twelve waters in the second shell. The solvent reaction field is obtained from a finite-difference solution to the Poisson−Boltzmann equation and is coupled to the nonlocal density functional calculation in a self-consistent way. The calculated hydration enthalpies are 409, 1073, 431, and 1046 kcal/mol for Mn2+, Mn3+, Fe2+, and Fe3+, respectively, comparing fairly well to the experimental measurements of 440, 1087, 465, and 1060 kcal/mol. The calculated redox potentials for the Mn2+/Mn3+ and Fe2+/Fe3+ pairs are 1.59 and 1.06 V, respectively, in good agreement with the experimental values of 1.56 and 0.77 V. The computed absolute pKa values, 14.0,...

Calculation of Redox Potentials and pKa Values of Hydrated Transition Metal Cations by a Combined Density Functional and Continuum Dielectric Theory

The structures, energetics, and orbital- and charge-dependent properties of copper zinc superoxide dismutase (CuZnSOD) have been studied using density functional and electrostatic methods. The CuZnSOD was represented with a model consisting of copper and zinc sites connected by a bridging histidine ligand. In addition to the bridge, three histidine ligands and one water molecule were bonded to the Cu ion in the copper site as first-shell ligands. Two histidine ligands and an aspartate were coordinated to the zinc ion in the zinc site. Full optimization of the model was performed using different functionals, both local and nonlocal. Geometrical parameters calculated with the nonlocal functionals agree well with the experimental X-ray data. In our calculated results, the His61 Ne−Cu bond in the active site breaks during the reduction and protonation, consistent with a number of X-ray structures and with EXAFS and NMR evidence. The reduction potential and pKa of the coupled electron/proton reaction catalyzed...

and Donald Bashford

Papers

Modification of the Generalized Born Model Suitable for Macromolecules

Calculation of Redox Potentials and pKa Values of Hydrated Transition Metal Cations by a Combined Density Functional and Continuum Dielectric Theory

CuZn Superoxide Dismutase Geometry Optimization, Energetics, and Redox Potential Calculations by Density Functional and Electrostatic Methods.