Alkali (Li+, Na+, K+, Rb+, and Cs+) and halide (F−, Cl−, Br−, and I−) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Åqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4PEW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.

The dynamic and energetic properties of the alkali and halide ions were calculated using molecular dynamics (MD) and free energy simulations with various different water and ion force fields including our recently developed water-model-specific ion parameters. The properties calculated were activity coefficients, diffusion coefficients, residence times of atomic pairs, association constants, and solubility. Through calculation of these properties, we can assess the validity and range of applicability of the simple pair potential models and better understand their limitations. Due to extreme computational demands, the activity coefficients were only calculated for a subset of the models. The results qualitatively agree with experiment. Calculated diffusion coefficients and residence times between cation−anion, water−cation, and water−anion showed differences depending on the choice of water and ion force field used. The calculated solubilities of the alkali−halide salts were generally lower than the true solubility of the salts. However, for both the TIP4PEW and SPC/E water-model-specific ion parameters, solubility was reasonably well-reproduced. Finally, the correlations among the various properties led to the following conclusions: (1) The reliability of the ion force fields is significantly affected by the specific choice of water model. (2) Ion−ion interactions are very important to accurately simulate the properties, especially solubility. (3) The SPC/E and TIP4PEW water-model-specific ion force fields are preferred for simulation in high salt environments compared to the other ion force fields.

Molecular dynamics based free energy calculations allow the determination of a variety of thermodynamic quantities from computer simulations of small molecules. Thermodynamic integration (TI) calculations can suffer from instabilities during the creation or annihilation of particles. This ‘singularity’ problem can be addressed with soft-core potential functions which keep pairwise interaction energies finite for all configurations and provide smooth free energy curves. “One-step” transformations, in which electrostatic and van der Waals forces are simultaneously modified, can be simpler and less expensive than “two-step” transformations in which these properties are changed in separate calculations. Here we study solvation free energies for molecules of different hydrophobicity using both models. We provide recommended values for the two parameters αLJ and βC controlling the behaviour of the soft-core Lennard-Jones and Coulomb potentials and compare one-step and two-step transformations with regard to their suitability for numerical integration. For many types of transformations, the one-step procedure offers a convenient and accurate approach to free energy estimates.

Characterizing glycans and glycoconjugates in the context of three-dimensional structures is important in understanding their biological roles and developing efficient therapeutic agents. Computational modeling and molecular simulation have become an essential tool complementary to experimental methods. Here, we present a computational tool, Glycan Modeler for in silico N-/O-glycosylation of the target protein and generation of carbohydrate-only systems. In our previous study, we developed Glycan Reader, a web-based tool for detecting carbohydrate molecules from a PDB structure and generation of simulation system and input files. As integrated into Glycan Reader in CHARMM-GUI, Glycan Modeler (Glycan Reader & Modeler) enables to generate the structures of glycans and glycoconjugates for given glycan sequences and glycosylation sites using PDB glycan template structures from Glycan Fragment Database (http://glycanstructure.org/ fragment-db). Our benchmark tests demonstrate the universal applicability of Glycan Reader & Modeler to various glycan sequences and target proteins. We also investigated the structural properties of modeled glycan structures by running 2-μs molecular dynamics simulations of HIV envelope protein. The simulations show that the modeled glycan structures built by Glycan Reader & Modeler have the similar structural features compared to the ones solved by X-ray crystallography. We also describe the representative examples of glycoconjugate modeling with video demos to illustrate the practical applications of Glycan Reader & Modeler. Glycan Reader & Modeler is freely available at http://charmm-gui.org/input/glycan.

The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures.

Using the dielectrically consistent reference interaction site model (DRISM) of molecular solvation, we have calculated structural and thermodynamic information of alkali-halide salts in aqueous solution, as a function of salt concentration. The impact of varying the closure relation used with DRISM is investigated using the partial series expansion of order-n (PSE-n) family of closures, which includes the commonly used hypernetted-chain equation (HNC) and Kovalenko-Hirata closures. Results are compared to explicit molecular dynamics (MD) simulations, using the same force fields, and to experiment. The mean activity coefficients of ions predicted by DRISM agree well with experimental values at concentrations below 0.5 m, especially when using the HNC closure. As individual ion activities (and the corresponding solvation free energies) are not known from experiment, only DRISM and MD results are directly compared and found to have reasonably good agreement. The activity of water directly estimated from DRISM is nearly consistent with values derived from the DRISM ion activities and the Gibbs-Duhem equation, but the changes in the computed pressure as a function of salt concentration dominate these comparisons. Good agreement with experiment is obtained if these pressure changes are ignored. Radial distribution functions of NaCl solution at three concentrations were compared between DRISM and MD simulations. DRISM shows comparable water distribution around the cation, but water structures around the anion deviate from the MD results; this may also be related to the high pressure of the system. Despite some problems, DRISM-PSE-n is an effective tool for investigating thermodynamic properties of simple electrolytes.

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ABSTRACT:Angiogenesis is the formation of new capillary blood vessels from preexisting vessels. It is involved in many normal and diseased conditions, as well as in the application of tissue-engineered products. Th ere has been extensive eff ort made to develop strategies for controlling pathological angiogenesis and for promoting vascularization in biomedical engineering applications. Central to advancing these strategies is a mechanistic understanding of the angiogenic process. Angiogenesis is tightly regulated by local tissue environmental factors, including soluble molecules, extracellular matrices, cell-cell interactions, and diverse mechanical forces. Great advances have been made in identifying the biochemical factors and intracellular signaling pathways that mediate the control of angiogenesis. Th is review focuses on work that explores the biophysical aspect of angiogenesis regulation. Specifi cally, we discuss the role of cell-generated forces, counterforces from the extracellular matrix, and mechanical forces associated with blood fl ow and extravascular tissue activity in the regulation of angiogenesis. Because angiogenesis occurs in a mechanically dynamic environment, future investigations should aim at understanding how cells integrate chemical and mechanical signals so that a rational approach to controlling angiogenesis will become possible. In this regard, computational models that incorporate multiple epigenetic factors to predict capillary patterning will be useful.