Simulation of aqueous solutes using the adaptive solvent-scaling (AdSoS) scheme.

The Adaptive Solvent-Scaling (AdSoS) scheme [J. Chem. Phys. 155 (2021) 094107] is an adaptive-resolution approach for performing simulations of a solute embedded in a fine-grained (FG) solvent region surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, AdSoS is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by the s-dependent modulation of its mass and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. As a result, the AdSoS scheme minimizes the thermodynamic mismatch between different regions of the adaptive-resolution system. The present article generalizes the scheme initially introduced for a pure atomic liquid in slab geometry to more practically relevant situations involving (i) a molecular dipolar solvent (e.g., water); (ii) a radial geometry (i.e., spherical rather than planar layers); and (iii) the inclusion of a solute (e.g., water molecule, dipeptide, ion, or ion pair).

Simultaneous parametrization of torsional and third-neighbor interaction terms in force-field development: The LLS-SC algorithm.

The calibration of torsional interaction terms by fitting relative gas-phase conformational energies against their quantum-mechanical values is a common procedure in force-field development. However, much less attention has been paid to the optimization of third-neighbor nonbonded interaction parameters, despite their strong coupling with the torsions. This article introduces an algorithm termed LLS-SC, aimed at simultaneously parametrizing torsional and third-neighbor interaction terms based on relative conformational energies. It relies on a self-consistent (SC) procedure where each iteration involves a linear least-squares (LLS) regression followed by a geometry optimization of the reference structures. As a proof-of-principle, this method is applied to obtain torsional and third-neighbor interaction parameters for aliphatic chains in the context of the GROMOS 53A6 united-atom force field. The optimized parameter set is compared to the original one, which has been fitted manually against thermodynamic properties for small linear alkanes. The LLS-SC implementation is freely available under http://github.com/mssm-labmmol/profiler.

Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules.

Free-energy differences between pairs of end-states can be estimated based on molecular dynamics (MD) simulations using standard pathway-dependent methods such as thermodynamic integration (TI), free-energy perturbation, or Bennett's acceptance ratio. Replica-exchange enveloping distribution sampling (RE-EDS), on the other hand, allows for the sampling of multiple end-states in a single simulation without the specification of any pathways. In this work, we use the RE-EDS method as implemented in GROMOS together with generalized AMBER force-field (GAFF) topologies, converted to a GROMOS-compatible format with a newly developed GROMOS++ program amber2gromos, to compute relative hydration free energies for a series of benzene derivatives. The results obtained with RE-EDS are compared to the experimental data as well as calculated values from the literature. In addition, the estimated free-energy differences in water and in vacuum are compared to values from TI calculations carried out with GROMACS. The hydration free energies obtained using RE-EDS for multiple molecules are found to be in good agreement with both the experimental data and the results calculated using other free-energy methods. While all considered free-energy methods delivered accurate results, the RE-EDS calculations required the least amount of total simulation time. This work serves as a validation for the use of GAFF topologies with the GROMOS simulation package and the RE-EDS approach. Furthermore, the performance of RE-EDS for a large set of 28 end-states is assessed with promising results.

RestraintMaker: a graph-based approach to select distance restraints in free-energy calculations with dual topology.

The calculation of relative binding free energies (RBFE) involves the choice of the end-state/system representation, of a sampling approach, and of a free-energy estimator. System representations are usually termed "single topology" or "dual topology". As the terminology is often used ambiguously in the literature, a systematic categorization of the system representations is proposed here. In the dual-topology approach, the molecules are simulated as separate molecules. Such an approach is relatively easy to automate for high-throughput RBFE calculations compared to the single-topology approach. Distance restraints are commonly applied to prevent the molecules from drifting apart, thereby improving the sampling efficiency. In this study, we introduce the program RestraintMaker, which relies on a greedy algorithm to find (locally) optimal distance restraints between pairs of atoms based on geometric measures. The algorithm is further extended for multi-state methods such as enveloping distribution sampling (EDS) or multi-site [Formula: see text]-dynamics. The performance of RestraintMaker is demonstrated for toy models and for the calculation of relative hydration free energies. The Python program can be used in script form or through an interactive GUI within PyMol. The selected distance restraints can be written out in GROMOS or GROMACS file formats. Additionally, the program provides a human-readable JSON format that can easily be parsed and processed further. The code of RestraintMaker is freely available on GitHub https://github.com/rinikerlab/restraintmaker.

Leveraging the sampling efficiency of RE-EDS in OpenMM using a shifted reaction-field with an atom-based cutoff.

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions but not when using lattice-sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group-based cutoff, which is not supported by most small-molecule force fields as well as other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

Replica-Exchange Enveloping Distribution Sampling: Calculation of Relative Free Energies in GROMOS.

Molecular dynamics (MD) simulations have become an important tool to investigate biological systems. Free-energy calculations based on MD are playing an increasingly important role for computer-aided drug design and material discovery in recent years. Free-energy differences between pairs of end-states can be estimated using well-established methods such as thermodynamic integration (TI) or Bennett's acceptance ratio (BAR). An attractive alternative is the recently developed replica-exchange enveloping distribution sampling (RE-EDS) method, which enables estimating relative free-energy differences between multiple molecules from a single simulation. Here, we provide an introduction to the principles underlying RE-EDS and give an overview of the RE-EDS pipeline. In addition, we provide a description of the two complementary tools RestraintMaker and amber2gromos. We briefly discuss the findings of three recent applications of RE-EDS to calculate relative binding or hydration free energies. In all three studies, good agreement was found between the results obtained using RE-EDS and experimental values as well as values obtained using other free-energy methods.

On the Effect of the Various Assumptions and Approximations used in Molecular Simulations on the Properties of Bio-Molecular Systems: Overview and Perspective on Issues.

Computer simulations of molecular systems enable structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic or supra-molecular level and plays an increasingly important role in chemistry, biology and physics. To interpret the results of such simulations appropriately, the degree of uncertainty and potential errors affecting the calculated properties must be considered. Uncertainty and errors arise from (1) assumptions underlying the molecular model, force field and simulation algorithms, (2) approximations implicit in the interatomic interaction function (force field), or when integrating the equations of motion, (3) the chosen values of the parameters that determine the accuracy of the approximations used, and (4) the nature of the system and the property of interest. In this overview, advantages and shortcomings of assumptions and approximations commonly used when simulating bio-molecular systems are considered. What the developers of bio-molecular force fields and simulation software can do to facilitate and broaden research involving bio-molecular simulations is also discussed.

Systematic optimization of a fragment-based force field against experimental pure-liquid properties considering large compound families: application to oxygen and nitrogen compounds.

The CombiFF approach is a workflow for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. One peculiarity of this approach is that it relies on an electronegativity-equalization scheme to account for induction effects within molecules, with values of the atomic hardness and electronegativity as electrostatic parameters, rather than the partial charges themselves. In a previous article [M. P. Oliveira, M. Andrey, S. R. Rieder, L. Kern, D. F. Hahn, S. Riniker, B. A. C. Horta and P. H. Hünenberger, J. Chem. Theory. Comput. 2020, 16, 7525], CombiFF was introduced and applied to calibrate a GROMOS-compatible united-atom force field for the saturated acyclic (halo-)alkane family. Here, this scheme is employed for the construction of a corresponding force field for saturated acyclic compounds encompassing eight common chemical functional groups involving oxygen and/or nitrogen atoms, namely: ether, aldehyde, ketone, ester, alcohol, carboxylic acid, amine, and amide. Monofunctional as well as homo-polyfunctional compounds are considered. A total of 1712 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 1175 molecules are used for the calibration (339 molecules) and validation (836 molecules) of the 102 non-bonded interaction parameters of the force field. Using initial parameter values based on the GROMOS 2016H66 parameter set, convergence is reached after five iterations. Given access to one processor per simulated system, this operation only requires a few days of wall-clock computing time. After optimization, the root-mean-square deviations from experiment are 29.9 (22.4) kg m-3 for ρliq and 4.1 (5.5) kJ mol-1 for ΔHvap for the calibration (validation) set. Thus, a very good level of agreement with experiment is achieved in terms of these two properties, although the errors are inhomogeneously distributed across the different chemical functional groups.

Evaluation of nine condensed-phase force fields of the GROMOS, CHARMM, OPLS, AMBER, and OpenFF families against experimental cross-solvation free energies.

Experimental solvation free energies are nowadays commonly included as target properties in the validation of condensed-phase force fields, sometimes even in their calibration. In a previous article [Kashefolgheta et al., J. Chem. Theory. Comput., 2020, 16, 7556-7580], we showed how the involved comparison between experimental and simulation results could be made more systematic by considering a full matrix of cross-solvation free energies . For a set of N molecules that are all in the liquid state under ambient conditions, such a matrix encompasses N×N entries for considering each of the N molecules either as solute (A) or as solvent (B). In the quoted study, a cross-solvation matrix of 25 × 25 experimental value was introduced, considering 25 small molecules representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This experimental data was used to compare the relative accuracies of four popular condensed-phase force fields, namely GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In the present work, the comparison is extended to five additional force fields, namely GROMOS-54A7, GROMOS-ATB, OPLS-LBCC, AMBER-GAFF2, and OpenFF. Considering these nine force fields, the correlation coefficients between experimental values and simulation results range from 0.76 to 0.88, the root-mean-square errors (RMSEs) from 2.9 to 4.8 kJ mol-1, and average errors (AVEEs) from -1.5 to +1.0 kJ mol-1. In terms of RMSEs, GROMOS-2016H66 and OPLS-AA present the best accuracy (2.9 kJ mol-1), followed by OPLS-LBCC, AMBER-GAFF2, AMBER-GAFF, and OpenFF (3.3 to 3.6 kJ mol-1), and then by GROMOS-54A7, CHARM-CGenFF, and GROMOS-ATB (4.0 to 4.8 kJ mol-1). These differences are statistically significant but not very pronounced, and are distributed rather heterogeneously over the set of compounds within the different force fields.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme.

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level NG (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, NG = s3 is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s3ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling.

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff.

In molecular dynamics (MD) simulations of condensed-phase systems, straight-cutoff truncation of the non-bonded interactions is well known to cause cutoff noise and serious artifacts in many simulated properties. These effects can be drastically reduced by applying the truncation based on distances between neutral charge groups (CG) rather than between individual atoms (AT). In addition, the mean effect of the omitted electrostatic interactions beyond the cutoff distance can be reintroduced using the reaction-field (RF) method, where the medium outside the cutoff sphere is approximated as a dielectric continuum of permittivity equal to that of the solvent. The RF scheme is generally applied with CG truncation. This is justified for low solvent permittivities, where the RF correction is small and an AT truncation would lead to severe issues, just as in the straight-cutoff case. However, it is less appropriate for solvents with high permittivities, where the RF correction acts as a physically motivated shifting function, and a CG truncation may in turn lead to artifacts and poorer energy conservation. In this study, we assess the impact of truncation artifacts considering the 57 organic liquids which were used in the calibration of the GROMOS-compatible 2016H66 force field. Combinations of shifting or switching schemes with RF-based electrostatic interactions as well as van der Waals (Lennard-Jones) interactions are then introduced to resolve the issues with AT truncation. These shifting and switching schemes have the following properties: (i) they bring the force but not the potential energy to zero at the cutoff; (ii) as a result, they lead to a modification of the interaction that is comparatively small; (iii) they permit to conduct rigorously conservative simulations; (iv) the energies can easily be corrected back to the unmodified form, either on the fly or in a post-processing step. The mathematical formalism of these schemes is presented in detail, and their validation is performed using the 57 organic liquids.

Interfacial solvation can explain attraction between like-charged objects in aqueous solution.

Over the past few decades, the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in aqueous solution. Examples include nucleic acids and colloidal particles in the bulk solution and under confinement, and biological liquid-liquid phase separation. This observation is at odds with the intuitive expectation of an interparticle repulsion that decays monotonically with distance. Although attraction between like-charged particles can be rationalized theoretically in the strong-coupling regime, e.g., in the presence of multivalent counterions, recurring accounts of long-range attraction in aqueous solution containing monovalent ions at low ionic strength have posed an open conundrum. Here, we show that the behavior of molecular water at an interface-traditionally disregarded in the continuum electrostatics picture-provides a mechanism to explain the attraction between like-charged objects in a broad spectrum of experiments. This basic principle will have important ramifications in the ongoing quest to better understand intermolecular interactions in solution.

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration.

The absolute intrinsic hydration free energy GH+,wat◦ of the proton, the surface electric potential jump χwat◦ upon entering bulk water, and the absolute redox potential VH+,wat◦ of the reference hydrogen electrode are cornerstone quantities for formulating single-ion thermodynamics on absolute scales. They can be easily calculated from each other but remain fundamentally elusive, i.e., they cannot be determined experimentally without invoking some extra-thermodynamic assumption (ETA). The Born model provides a natural framework to formulate such an assumption (Born ETA), as it automatically factors out the contribution of crossing the water surface from the hydration free energy. However, this model describes the short-range solvation inaccurately and relies on the choice of arbitrary ion-size parameters. In the present study, both shortcomings are alleviated by performing first-principle calculations of the hydration free energies of the sodium (Na+) and potassium (K+) ions. The calculations rely on thermodynamic integration based on quantum-mechanical molecular-mechanical (QM/MM) molecular dynamics (MD) simulations involving the ion and 2000 water molecules. The ion and its first hydration shell are described using a correlated ab initio method, namely resolution-of-identity second-order Møller-Plesset perturbation (RIMP2). The next hydration shells are described using the extended simple point charge water model (SPC/E). The hydration free energy is first calculated at the MM level and subsequently increased by a quantization term accounting for the transformation to a QM/MM description. It is also corrected for finite-size, approximate-electrostatics, and potential-summation errors, as well as standard-state definition. These computationally intensive simulations provide accurate first-principle estimates for GH+,wat◦, χwat◦, and VH+,wat◦, reported with statistical errors based on a confidence interval of 99%. The values obtained from the independent Na+ and K+ simulations are in excellent agreement. In particular, the difference between the two hydration free energies, which is not an elusive quantity, is 73.9 ± 5.4 kJ mol-1 (K+ minus Na+), to be compared with the experimental value of 71.7 ± 2.8 kJ mol-1. The calculated values of GH+,wat◦, χwat◦, and VH+,wat◦ (-1096.7 ± 6.1 kJ mol-1, 0.10 ± 0.10 V, and 4.32 ± 0.06 V, respectively, averaging over the two ions) are also in remarkable agreement with the values recommended by Reif and Hünenberger based on a thorough analysis of the experimental literature (-1100 ± 5 kJ mol-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V, respectively). The QM/MM MD simulations are also shown to provide an accurate description of the hydration structure, dynamics, and energetics.

Simulating Bilayers of Nonionic Surfactants with the GROMOS-Compatible 2016H66 Force Field.

Polyoxyethylene glycol alkyl ether amphiphiles (CiEj) are important nonionic surfactants, often used for biophysical and membrane protein studies. In this work, we extensively test the GROMOS-compatible 2016H66 force field in molecular dynamics simulations involving the lamellar phase of a series of CiEj surfactants, namely C12E2, C12E3, C12E4, C12E5, and C14E4. The simulations reproduce qualitatively well the monitored structural properties and their experimental trends along the surfactant series, although some discrepancies remain, in particular in terms of the area per surfactant, the equilibrium phase of C12E5, and the order parameters of C12E3, C12E4, and C12E5. The polar head of the CiEj surfactants is highly hydrated, almost like a single polyethyleneoxide (PEO) molecule at full hydration, resulting in very compact conformations. Within the bilayer, all CiEj surfactants flip-flop spontaneously within tens of nanoseconds. Water-permeation is facilitated, and the bending rigidity is 4 to 5 times lower than that of typical phospholipid bilayers. In line with another recent theoretical study, the simulations show that the lamellar phase of CiEj contains large hydrophilic pores. These pores should be abundant in order to reproduce the comparatively low NMR order parameters. We show that their contour length is directly correlated to the order parameters, and we estimate that they should occupy approximately 7-10% of the total membrane area. Due to their highly dynamic nature (rapid flip-flops, high water permeability, observed pore formation), CiEj surfactant bilayers are found to represent surprisingly challenging systems in terms of modeling. Given this difficulty, the results presented here show that the 2016H66 parameters, optimized independently considering pure-liquid as well as polar and nonpolar solvation properties of small organic molecules, represent a good starting point for simulating these systems.

Revision of the GROMOS 56A6(CARBO) force field: Improving the description of ring-conformational equilibria in hexopyranose-based carbohydrates chains.

This article describes a revised version 56A6(CARBO_R) of the GROMOS 56A6(CARBO) force field for hexopyranose-based carbohydrates. The simulated properties of unfunctionalized hexopyranoses are unaltered with respect to 56A6CARBO . In the context of both O1 -alkylated hexopyranoses and oligosaccharides, the revision stabilizes the regular (4) C1 chair for α-anomers, with the opposite effect for ß-anomers. As a result, spurious ring inversions observed in α(1→4)-linked chains when using the original 56A6(CARBO) force field are alleviated. The (4) C1 chair is now the most stable conformation for all d-hexopyranose residues, irrespective of the linkage type and anomery, and of the position of the residue along the chain. The methylation of a d-hexopyranose leads to a systematic shift in the ring-inversion free energy ((4) C1 to (1) C4 ) by 7-8 kJ mol(-1), positive for the α-anomers and negative for the ß-anomers, which is qualitatively compatible with the expected enhancement of the anomeric effect upon methylation at O1. The ring-inversion free energies for residues within chains are typically smaller in magnitude compared to those of the monomers, and correlate rather poorly with the latter. This suggests that the crowding of ring substituents upon chain formation alters the ring flexibility in a nonsystematic fashion. In general, the description of carbohydrate chains afforded by 56A6(CARBO_R) suggests a significant extent of ring flexibility, i.e., small but often non-negligible equilibrium populations of inverted chairs, and challenges the "textbook" picture of conformationally locked carbohydrate rings.

Orthogonal sampling in free-energy calculations of residue mutations in a tripeptide: TI versus λ-LEUS.

In a recent article (Bieler et al., J. Chem. Theory Comput. 2014, 10, 3006), we introduced a combination of λ-dynamics and local-elevation umbrella-sampling termed λ-LEUS to calculate free-energy changes associated with alchemical processes using molecular dynamics simulations. This method was suggested to be more efficient than thermodynamic integration (TI), because the dynamical variation of the alchemical variable λ opens up pathways to circumvent barriers in the orthogonal space (defined by the N - 1 degrees of freedom that are not subjected to the sampling enhancement), a feature λ-LEUS shares with Hamiltonian replica-exchange (HR) approaches. However, the mutation considered, hydroquinone to benzene in water, was no real challenge in terms of orthogonal-space properties, which were restricted to solvent-relaxation processes. In the present article, we revisit the comparison between TI and λ-LEUS considering non-trivial mutations of the central residue X of a KXK tripeptide in water (with X = G, E, K, S, F, or Y). Side-chain interactions that may include salt bridges, hydrogen bonds or steric clashes lead to slow relaxation in the orthogonal space, mainly in the two-dimensional subspace spanned by the central φ and ψ dihedral angles of the peptide. The efficiency enhancement afforded by λ-LEUS is confirmed in this more complex test system and can be attributed explicitly to the improved sampling of the orthogonal space. The sensitivity of the results to the nontrivial choices of a mass parameter and of a thermostat coupling time for the alchemical variable is also investigated, resulting in recommended ranges of 50 to 100 u nm(2) and 0.2 to 0.5 ps, respectively.

On the ambiguity of conformational states: A B&S-LEUS simulation study of the helical conformations of decaalanine in water.

Estimating the relative stabilities of different conformational states of a (bio-)molecule using molecular dynamics simulations involves two challenging problems: the conceptual problem of how to define the states of interest and the technical problem of how to properly sample these states, along with achieving a sufficient number of interconversion transitions. In this study, the two issues are addressed in the context of a decaalanine peptide in water, by considering the 310-, α-, and π-helical states. The simulations rely on the ball-and-stick local-elevation umbrella-sampling (B&S-LEUS) method. In this scheme, the states are defined as hyperspheres (balls) in a (possibly high dimensional) collective-coordinate space and connected by hypercylinders (sticks) to ensure transitions. A new object, the pipe, is also introduced here to handle curvilinear pathways. Optimal sampling within the so-defined space is ensured by confinement and (one-dimensional) memory-based biasing potentials associated with the three different kinds of objects. The simulation results are then analysed in terms of free energies using reweighting, possibly relying on two distinct sets of collective coordinates for the state definition and analysis. The four possible choices considered for these sets are Cartesian coordinates, hydrogen-bond distances, backbone dihedral angles, or pairwise sums of successive backbone dihedral angles. The results concerning decaalanine underline that the concept of conformational state may be extremely ambiguous, and that its tentative absolute definition as a free-energy basin remains subordinated to the choice of a specific analysis space. For example, within the force-field employed and depending on the analysis coordinates selected, the 310-helical state may refer to weakly overlapping collections of conformations, differing by as much as 25 kJ mol(-1) in terms of free energy. As another example, the π-helical state appears to correspond to a free-energy basin for three choices of analysis coordinates, but to be unstable with the fourth one. The problem of conformational-state definition may become even more intricate when comparison with experiment is involved, where the state definition relies on spectroscopic or functional observables.

Effect of the cosolutes trehalose and methanol on the equilibrium and phase-transition properties of glycerol-monopalmitate lipid bilayers investigated using molecular dynamics simulations.

The influence of the cosolutes trehalose and methanol on the structural, dynamic and thermodynamic properties of a glycerol-1-monopalmitate (GMP) bilayer and on its main transition temperature [Formula: see text] is investigated using atomistic molecular dynamics simulations (600 ns) of a GMP bilayer patch (2 × 8 × 8 lipids) at different temperatures in the range of 302 to 338 K and considering three different cosolute concentrations. Depending on the environment and temperature, these simulations present no or a single GL[Formula: see text]LC, LC[Formula: see text]GL or LC[Formula: see text]ID transition, where LC, GL and ID are the liquid crystal, gel and interdigitated phases, respectively. The trehalose molecules form a coating layer at the bilayer surface, promote the hydrogen-bonded bridging of the lipid headgroups, preserve the interaction of the headgroups with trapped water and induce a slight lateral expansion of the bilayer in the LC phase, observations that may have implications for the phenomenon of anhydrobiosis. However, this cosolute does not affect [Formula: see text] and its dependence on hydration in the concentration range considered. On the other hand, methanol molecules intercalate between the lipid headgroups, promote a lateral expansion of the bilayer in the LC phase and induce a concentration dependent decrease of [Formula: see text], observations that may have implications for the phenomenon of anesthesia. The occurrence of an ID phase in the presence of this cosolute may be viewed as an extreme consequence of lateral expansion. The analysis of the simulations also suggests the existence of two basic conservation principles: (1) the hydrogen-bond saturation principle rests on the observation that for all species present in the different systems, the total numbers of hydrogen-bonds per molecule is essentially constant, the only factor of variability being their distribution among different partners; (2) the densest packing principle rests on the observation that the effective volume per methylene group in the interior of the bilayer is only weakly sensitive to the environment, with values comparable to those for liquid (LC) and solid (ID) alkanes, or intermediate (GL).

Communication: estimating the initial biasing potential for λ-local-elevation umbrella-sampling (λ-LEUS) simulations via slow growth.

In a recent article [Bieler et al., J. Chem. Theory Comput. 10, 3006-3022 (2014)], we introduced a combination of the λ-dynamics (λD) approach for calculating alchemical free-energy differences and of the local-elevation umbrella-sampling (LEUS) memory-based biasing method to enhance the sampling along the alchemical coordinate. The combined scheme, referred to as λ-LEUS, was applied to the perturbation of hydroquinone to benzene in water as a test system, and found to represent an improvement over thermodynamic integration (TI) in terms of sampling efficiency at equivalent accuracy. However, the preoptimization of the biasing potential required in the λ-LEUS method requires "filling up" all the basins in the potential of mean force. This introduces a non-productive pre-sampling time that is system-dependent, and generally exceeds the corresponding equilibration time in a TI calculation. In this letter, a remedy is proposed to this problem, termed the slow growth memory guessing (SGMG) approach. Instead of initializing the biasing potential to zero at the start of the preoptimization, an approximate potential of mean force is estimated from a short slow growth calculation, and its negative used to construct the initial memory. Considering the same test system as in the preceding article, it is shown that of the application of SGMG in λ-LEUS permits to reduce the preoptimization time by about a factor of four.