This article presents a reoptimization of the GROMOS 53A6 force field for hexopyranose-based carbohydrates (nearly equivalent to 45A4 for pure carbohydrate systems) into a new version 56A(CARBO) (nearly equivalent to 53A6 for non-carbohydrate systems). This reoptimization was found necessary to repair a number of shortcomings of the 53A6 (45A4) parameter set and to extend the scope of the force field to properties that had not been included previously into the parameterization procedure. The new 56A(CARBO) force field is characterized by: (i) the formulation of systematic build-up rules for the automatic generation of force-field topologies over a large class of compounds including (but not restricted to) unfunctionalized polyhexopyranoses with arbritrary connectivities; (ii) the systematic use of enhanced sampling methods for inclusion of experimental thermodynamic data concerning slow or unphysical processes into the parameterization procedure; and (iii) an extensive validation against available experimental data in solution and, to a limited extent, theoretical (quantum-mechanical) data in the gas phase. At present, the 56A(CARBO) force field is restricted to compounds of the elements C, O, and H presenting single bonds only, no oxygen functions other than alcohol, ether, hemiacetal, or acetal, and no cyclic segments other than six-membered rings (separated by at least one intermediate atom). After calibration, this force field is shown to reproduce well the relative free energies of ring conformers, anomers, epimers, hydroxymethyl rotamers, and glycosidic linkage conformers. As a result, the 56A(CARBO) force field should be suitable for: (i) the characterization of the dynamics of pyranose ring conformational transitions (in simulations on the microsecond timescale); (ii) the investigation of systems where alternative ring conformations become significantly populated; (iii) the investigation of anomerization or epimerization in terms of free-energy differences; and (iv) the design of simulation approaches accelerating the anomerization process along an unphysical pathway.

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The mechanism of solvent effects on the stereoselectivity of glycosylation reactions is investigated using quantum-mechanical (QM) calculations and molecular dynamics (MD) simulations, considering a methyl-protected glucopyranoside triflate as a glycosyl donor equivalent and the solvents acetonitrile, ether, dioxane, or toluene, as well as gas-phase conditions (vacuum). The QM calculations on oxacarbenium-solvent complexes do not provide support to the usual solvent-coordination hypothesis, suggesting that an experimentally observed β-selectivity (α-selectivity) is caused by the preferential coordination of a solvent molecule to the reactive cation on the α-side (β-side) of the anomeric carbon. Instead, explicit-solvent MD simulations of the oxacarbenium-counterion (triflate ion) complex (along with corresponding QM calculations) are compatible with an alternative mechanism, termed here the conformer and counterion distribution hypothesis. This new hypothesis suggests that the stereoselectivity is dictated by two interrelated conformational properties of the reactive complex, namely, (1) the conformational preferences of the oxacarbenium pyranose ring, modulating the steric crowding and exposure of the anomeric carbon toward the α or β face, and (2) the preferential coordination of the counterion to the oxacarbenium cation on one side of the anomeric carbon, hindering a nucleophilic attack from this side. For example, in acetonitrile, the calculations suggest a dominant B2,5 ring conformation of the cation with preferential coordination of the counterion on the α side, both factors leading to the experimentally observed β selectivity. Conversely, in dioxane, they suggest a dominant (4)H3 ring conformation with preferential counterion coordination on the β side, both factors leading to the experimentally observed α selectivity.

An extension 53A6 OXY+D to the GROMOS 53A6 OXY force field is reported that includes an accurate description of the vicinal diether function. The calibration is based on the model compound 1,2-dimethoxyethane (DXE) and involves a fitting of the relevant torsional-energy parameters against quantum-mechanical (QM) rotational energy profiles for the OCCO and CCOC dihedral angles in vacuum, followed by a validation against experimental conformer populations in the pure liquid and in aqueous mixtures. A systematic comparison between the 53A6, 56A6 CARBO , 53A6 OXY , and 53A6 OXY+D parameter sets is also performed in terms of these properties, as well as in terms of the thermodynamic properties of dimethylether (DME), diethylether (DEE), 1-methoxypropane (MPH), and DXE. Finally, the new parameter set is further validated in the context of polyethers, namely polyethyleneoxide (PEO) and polyethylenegycol (PEG). The 53A6 OXY+D set reproduces well the QM rotational profiles of DXE in vacuum (by calibration), the conformational populations of DXE in the pure liquid and in aqueous mixtures, and the experimental thermodynamic pure-liquid and (polar and nonpolar) solvation properties of DME, DEE, MPH, and DXE. In particular, it accounts appropriately for the gauche-effect, both in its solvent-independent stereoelectronic component and in its solvent-dependent dielectric-screening component. In contrast to 53A6 OXY , it also suggests a higher affinity of DXE for water compared to octanol, in agreement with the experimental partition coefficient. In the context of aqueous polyethers, the calculated size (Flory) exponent (ν g = 0.61) for the molecular-weight dependence of the radius of gyration and persistence length (L p = 0.39 ± 0.04 nm) agree well with estimates based on experiment or previous simulations with other force fields. The simulations also suggest a picture of aqueous polyethers as "water sponges", in which the diether function "adsorbs" an essentially constant number of water molecules corresponding to first-shell hydrogen-bonded saturation of its oxygen atoms, with a tendency to include other ether oxygen atoms along the chain in the second shell, resulting in "water bridging".

The calculation of the relative free energies of ligand-protein binding, of solvation for different compounds, and of different conformational states of a polypeptide is of considerable interest in the design or selection of potential enzyme inhibitors. Since such processes in aqueous solution generally comprise energetic and entropic contributions from many molecular configurations, adequate sampling of the relevant parts of configurational space is required and can be achieved through molecular dynamics simulations. Various techniques to obtain converged ensemble averages and their implementation in the GROMOS software for biomolecular simulation are discussed, and examples of their application to biomolecules in aqueous solution are given.

A method is proposed to combine the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single local elevation umbrella sampling (LEUS) scheme for (explicit-solvent) molecular dynamics (MD) simulations. In this approach, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized biasing potential within a subspace of conformationally relevant degrees of freedom, that is then used in a (comparatively longer) US sampling phase. This scheme dramatically enhances (in comparison with plain MD) the sampling power of MD simulations, taking advantage of the fact that the preoptimized biasing potential represents a reasonable approximation to the negative of the free energy surface in the considered conformational subspace. The method is applied to the calculation of the relative free energies of beta-D-glucopyranose ring conformers in water (within the GROMOS 45A4 force field). Different schemes to assign sampled conformational regions to distinct states are also compared. This approach, which bears some analogies with adaptive umbrella sampling and metadynamics (but within a very distinct implementation), is shown to be: (i) efficient (nearly all the computational effort is invested in the actual sampling phase rather than in searching and equilibration); (ii) robust (the method is only weakly sensitive to the details of the build-up protocol, even for relatively short build-up times); (iii) versatile (a LEUS biasing potential database could easily be preoptimized for small molecules and assembled on a fragment basis for larger ones).

A new method, ball-and-stick local elevation umbrella sampling (B&S-LEUS), is proposed to enhance the sampling in computer simulations of (bio)molecular systems. It enables the calculation of conformational free-energy differences between states (or alchemical free-energy differences between molecules), even in situations where the definition of these states relies on a conformational subspace involving more than a few degrees of freedom. The B&S-LEUS method consists of the following steps: (A) choice of a reduced conformational subspace; (B) representation of the relevant states by means of spheres ("balls"), each associated with a biasing potential involving a one-dimensional radial memory-based term and a radial confinement term; (C) definition of a set of lines ("sticks") connecting these spheres, each associated with a biasing potential involving a one-dimensional longitudinal memory-based term and a transverse confinement term; (D) unification of the biasing potentials corresponding to the union of all of the spheres and lines (active subspace) into a single biasing potential according to the enveloping distribution sampling (EDS) scheme; (E) build-up of the memory using the local elevation (LE) procedure, leading to a biasing potential enabling a nearly uniform sampling (radially within the spheres, longitudinally within the lines) of the active subspace; (F) generation of a biased ensemble of configurations using this preoptimized biasing potential, following an umbrella sampling (US) approach; and (G) calculation of the relative free energies of the states via reweighting and state assignment. The main characteristics of this approach are: (i) a low internal dimensionality, that is, the memory only involves one-dimensional grids (acceptable memory requirements); (ii) a minimal irrelevant volume, that is, the conformational volume opened to sampling includes a minimal fraction of irrelevant regions in terms of the free energy of the physical system or of user-specified metastable states (acceptable build-up duration requirements, high statistical efficiency); and (iii) a problem-adapted geometry (a priori specification of the conformational regions considered as relevant or irrelevant). In particular, the use of lines to connect the spheres ensures both a minimal irrelevant volume and a sufficient number of transitions between the states. As an illustration, the B&S-LEUS method is applied here to three test systems: (i) a solvated (blocked) alanine monopeptide (two-dimensional conformational subspace), used as a toy system to illustrate the versatility of the method in promoting the sampling of arbritrary regions of the Ramachandran map; (ii) a solvated polyalanine decapeptide (nine-dimensional conformational subspace), to evaluate the relative free energies of three different types of helices (π, α, and 310) based on a single simulation; and (iii) a solvated artifical hexopyranose, termed the "mother" of all d-hexopyranoses and constructed as a hybrid of all d-hexopyranose stereoisomers, where the method...

A new method, fragment-based local elevation umbrella sampling (FB-LEUS), is proposed to enhance the conformational sampling in explicit-solvent molecular dynamics (MD) simulations of solvated polymers. The method is derived from the local elevation umbrella sampling (LEUS) method [ Hansen and Hünenberger , J. Comput. Chem. 2010 , 31 , 1 - 23 ], which combines the local elevation (LE) conformational searching and the umbrella sampling (US) conformational sampling approaches into a single scheme. In LEUS, an initial (relatively short) LE build-up (searching) phase is used to construct an optimized (grid-based) biasing potential within a subspace of conformationally relevant degrees of freedom, which is then frozen and used in a (comparatively longer) US sampling phase. This combination dramatically enhances the sampling power of MD simulations but, due to computational and memory costs, is only applicable to relevant subspaces of low dimensionalities. As an attempt to expand the scope of the LEUS approach to solvated polymers with more than a few relevant degrees of freedom, the FB-LEUS scheme involves an US sampling phase that relies on a superposition of low-dimensionality biasing potentials optimized using LEUS at the fragment level. The feasibility of this approach is tested using polyalanine (poly-Ala) and polyvaline (poly-Val) oligopeptides. Two-dimensional biasing potentials are preoptimized at the monopeptide level, and subsequently applied to all dihedral-angle pairs within oligopeptides of 4,  6,  8, or 10 residues. Two types of fragment-based biasing potentials are distinguished: (i) the basin-filling (BF) potentials act so as to "fill" free-energy basins up to a prescribed free-energy level above the global minimum; (ii) the valley-digging (VD) potentials act so as to "dig" valleys between the (four) free-energy minima of the two-dimensional maps, preserving barriers (relative to linearly interpolated free-energy changes) of a prescribed magnitude. The application of these biasing potentials may lead to an impressive enhancement of the searching power (volume of conformational space visited in a given amount of simulation time). However, this increase is largely offset by a deterioration of the statistical efficiency (representativeness of the biased ensemble in terms of the conformational distribution appropriate for the physical ensemble). As a result, it appears difficult to engineer FB-LEUS schemes representing a significant improvement over plain MD, at least for the systems considered here.