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Recently, we presented a method to assign atomic partial charges based on the DASH (dynamic attention-based substructure hierarchy) tree with high efficiency and quantum mechanical (QM)-like accuracy. In addition, the approach can be considered "rule based"—where the rules are derived from the attention values of a graph neural network—and thus, each assignment is fully explainable by visualizing the underlying molecular substructures. In this work, we demonstrate that these hierarchically sorted substructures capture the key features of the local environment of an atom and allow us to predict different atomic properties with high accuracy without building a new DASH tree for each property. The fast prediction of atomic properties in molecules with the DASH tree can, for example, be used as an efficient way to generate feature vectors for machine learning without the need for expensive QM calculations. The final DASH tree with the different atomic properties as well as the complete dataset with wave functions is made freely available. [ABSTRACT FROM AUTHOR]

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

Clustering has become an indispensable tool in the presence of increasingly large and complex datasets. Most clustering algorithms depend, either explicitly or implicitly, on the sampled density. However, estimated densities are fragile due to the curse of dimensionality and finite sampling effects, for instance, in molecular dynamics simulations. To avoid the dependence on estimated densities, an energy-based clustering (EBC) algorithm based on the Metropolis acceptance criterion is developed in this work. In the proposed formulation, EBC can be considered a generalization of spectral clustering in the limit of large temperatures. Taking the potential energy of a sample explicitly into account alleviates requirements regarding the distribution of the data. In addition, it permits the subsampling of densely sampled regions, which can result in significant speed-ups and sublinear scaling. The algorithm is validated on a range of test systems including molecular dynamics trajectories of alanine dipeptide and the Trp-cage miniprotein. Our results show that including information about the potential-energy surface can largely decouple clustering from the sampled density. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations enable the study of the motion of small and large (bio)molecules and the estimation of their conformational ensembles. The description of the environment (solvent) has, therefore, a large impact. Implicit solvent representations are efficient but, in many cases, not accurate enough (especially for polar solvents, such as water). More accurate but also computationally more expensive is the explicit treatment of the solvent molecules. Recently, machine learning has been proposed to bridge the gap and simulate, in an implicit manner, explicit solvation effects. However, the current approaches rely on prior knowledge of the entire conformational space, limiting their application in practice. Here, we introduce a graph neural network based implicit solvent that is capable of describing explicit solvent effects for peptides with different compositions than those contained in the training set. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The combination of Markov state modeling (MSM) and molecular dynamics (MD) simulations has been shown in recent years to be a valuable approach to unravel the slow processes of molecular systems with increasing complexity. While the algorithms for intermediate steps in the MSM workflow such as featurization and dimensionality reduction have been specifically adapted to MD datasets, conventional clustering methods are generally applied to the discretization step. This work adds to recent efforts to develop specialized density-based clustering algorithms for the Boltzmann-weighted data from MD simulations. We introduce the volume-scaled common nearest neighbor (vs-CNN) clustering that is an adapted version of the common nearest neighbor (CNN) algorithm. A major advantage of the proposed algorithm is that the introduced density-based criterion directly links to a free-energy notion via Boltzmann inversion. Such a free-energy perspective allows a straightforward hierarchical scheme to identify conformational clusters at different levels of a generally rugged free-energy landscape of complex molecular systems. [ABSTRACT FROM AUTHOR]

Thermally driven processes of molecular systems include transitions of energy barriers on the microsecond timescales and higher. Sufficient sampling of such processes with molecular dynamics simulations is challenging and often requires accelerating slow transitions using external biasing potentials. Different dynamic reweighting algorithms have been proposed in the past few years to recover the unbiased kinetics from biased systems. However, it remains an open question if and how these dynamic reweighting approaches are connected. In this work, we establish the link between the two main reweighting types, i.e., path-based and energy-based reweighting. We derive a path-based correction factor for the energy-based dynamic histogram analysis method, thus connecting the previously separate reweighting types. We show that the correction factor can be used to combine the advantages of path-based and energy-based reweighting algorithms: it is integrator independent, more robust, and at the same time able to reweight time-dependent biases. We can furthermore demonstrate the relationship between two independently derived path-based reweighting algorithms. Our theoretical findings are verified on a one-dimensional four-well system. By connecting different dynamic reweighting algorithms, this work helps to clarify the strengths and limitations of the different methods and enables a more robust usage of the combined types. [ABSTRACT FROM AUTHOR]

Reaction-field (RF) methods have been extensively used in molecular dynamics simulations to efficiently compute long-range electrostatic interactions. They assume a continuous dielectric medium outside a certain cutoff, which has shown to be a reasonable approximation in many cases. However, lattice sum or fast multipole methods are nowadays often used instead, which treat long-range interactions explicitly but may introduce different artefacts. In the following work, the major issue of RFs is addressed, i.e., their inability to account for inhomogeneity even in heterogenous environments (e.g., membranes or protein binding pockets). By using a first-order Laplace series expansion of the dielectric permittivity on the cutoff sphere, local anisotropic effects can be described in a simple form. It is shown that the resulting boundary-value problem cannot be solved analytically, but instead a well-behaved approximative anisotropic reaction field (ARF) is introduced, which preserves coordinate invariance and approaches the standard RF solution for homogeneous systems. The comparison of RF to the state-of-the-art particle-particle particle-mesh (P3M) method shows a difference in the orientation of molecules close to the interface between two different dielectrics (water/chloroform). It was found that the ARF leads to a correction of the orientational distribution toward the P3M reference for planar and spherical interfaces. [ABSTRACT FROM AUTHOR]

In molecular dynamics (MD) simulations, free-energy differences are often calculated using free energy perturbation or thermodynamic integration (TI) methods. However, both techniques are only suited to calculate free-energy differences between two end states. Enveloping distribution sampling (EDS) presents an attractive alternative that allows to calculate multiple free-energy differences in a single simulation. In EDS, a reference state is simulated which "envelopes" the end states. The challenge of this methodology is the determination of optimal reference-state parameters to ensure equal sampling of all end states. Currently, the automatic determination of the reference-state parameters for multiple end states is an unsolved issue that limits the application of the methodology. To resolve this, we have generalised the replica-exchange EDS (RE-EDS) approach, introduced by Lee et al. [J. Chem. Theory Comput. 10, 2738 (2014)] for constant-pH MD simulations. By exchanging configurations between replicas with different reference-state parameters, the complexity of the parameter-choice problem can be substantially reduced. A new robust scheme to estimate the reference-state parameters from a short initial RE-EDS simulation with default parameters was developed, which allowed the calculation of 36 free-energy differences between nine small-molecule inhibitors of phenylethanolamine N-methyltransferase from a single simulation. The resulting freeenergy differences were in excellent agreement with values obtained previously by TI and two-state EDS simulations. [ABSTRACT FROM AUTHOR]

The time- and length-scale accessible to molecular dynamics simulations of biomolecular systems using atomic-level (AL) models is most limited by the calculation of the solvent-solvent interactions, which comprise the majority of the interactions and yet are seldom of specific interest. Coarse-graining (CG), in which multiple solvent molecules are subsumed into a single bead, provides a means of overcoming this limitation without resorting to implicit solvation models, which basically misrepresent the hydrophobic effect. Most existing CG models, however, do not explicitly include electrostatic interactions, and thus fail to reproduce important properties of the solvent such as dielectric screening. Moreover, CG models for one type of solvent molecule are seldom compatible with those for other solvents. Here, we develop polarizable CG models for the solvents dimethyl sulfoxide, chloroform, and methanol that are compatible with an existing CG model for water. The inclusion of polarizability greatly improves the reproduction of thermodynamic data measured experimentally and calculated from AL simulations for both the pure liquids and binary mixtures. [ABSTRACT FROM AUTHOR]

The relative binding free energy between two ligands to a specific protein can be obtained using various computational methods. The more accurate and also computationally more demanding techniques are the so-called free energy methods which use conformational sampling from molecular dynamics or Monte Carlo simulations to generate thermodynamic averages. Two such widely applied methods are the thermodynamic integration (TI) and the recently introduced enveloping distribution sampling (EDS) methods. In both cases relative binding free energies are obtained through the alchemical perturbations of one ligand into another in water and inside the binding pocket of the protein. TI requires many separate simulations and the specification of a pathway along which the system is perturbed from one ligand to another. Using the EDS approach, only a single automatically derived reference state enveloping both end states needs to be sampled. In addition, the choice of an optimal pathway in TI calculations is not trivial and a poor choice may lead to poor convergence along the pathway. Given this, EDS is expected to be a valuable and computationally efficient alternative to TI. In this study, the performances of these two methods are compared using the binding of ten tetrahydroisoquinoline derivatives to phenylethanolamine N-transferase as an example. The ligands involve a diverse set of functional groups leading to a wide range of free energy differences. In addition, two different schemes to determine automatically the EDS reference state parameters and two different topology approaches are compared. [ABSTRACT FROM AUTHOR]

The development of coarse-grained (CG) models that correctly represent the important features of compounds is essential to overcome the limitations in time scale and system size currently encountered in atomistic molecular dynamics simulations. Most approaches reported in the literature model one or several molecules into a single uncharged CG bead. For water, this implicit treatment of the electrostatic interactions, however, fails to mimic important properties, e.g., the dielectric screening. Therefore, a coarse-grained model for water is proposed which treats the electrostatic interactions between clusters of water molecules explicitly. Five water molecules are embedded in a spherical CG bead consisting of two oppositely charged particles which represent a dipole. The bond connecting the two particles in a bead is unconstrained, which makes the model polarizable. Experimental and all-atom simulated data of liquid water at room temperature are used for parametrization of the model. The experimental density and the relative static dielectric permittivity were chosen as primary target properties. The model properties are compared with those obtained from experiment, from clusters of simple-point-charge water molecules of appropriate size in the liquid phase, and for other CG water models if available. The comparison shows that not all atomistic properties can be reproduced by a CG model, so properties of key importance have to be selected when coarse graining is applied. Yet, the CG model reproduces the key characteristics of liquid water while being computationally 1-2 orders of magnitude more efficient than standard fine-grained atomistic water models. [ABSTRACT FROM AUTHOR]

The use of a supra-molecular coarse-grained (CG) model for liquid water as solvent in molecular dynamics simulations of biomolecules represented at the fine-grained (FG) atomic level of modelling may reduce the computational effort by one or two orders of magnitude. However, even if the pure FG model and the pure CG model represent the properties of the particular substance of interest rather well, their application in a hybrid FG/CG system containing varying ratios of FG versus CG particles is highly non-trivial, because it requires an appropriate balance between FG-FG, FG-CG, and CG-CG energies, and FG and CG entropies. Here, the properties of liquid water are used to calibrate the FG-CG interactions for the simple-point-charge water model at the FG level and a recently proposed supra-molecular water model at the CG level that represents five water molecules by one CG bead containing two interaction sites. Only two parameters are needed to reproduce different thermodynamic and dielectric properties of liquid water at physiological temperature and pressure for various mole fractions of CG water in FG water. The parametrisation strategy for the FG-CG interactions is simple and can be easily transferred to interactions between atomistic biomolecules and CG water. [ABSTRACT FROM AUTHOR]

Reducing the number of degrees of freedom in molecular models-so-called coarse-graining-is a popular approach to increase the accessible time scales and system sizes in molecular dynamics simulations. It involves, however, per se a loss of information. In order to retain a high accuracy in the region of interest, hybrid methods that combine two levels of resolution in a single system are an attractive trade-off. Hybrid atomistic (AT)/coarse-grained (CG) simulations have previously been shown to preserve the secondary structure elements of AT proteins in CG water but to cause an artificial increase in intramolecular hydrogen bonds, resulting in a reduced flexibility of the proteins. Recently, it was found that the AT-CG interactions employed in these simulations were too favourable for apolar solutes and not favourable enough for polar solutes. Here, the AT-CG interactions are reparametrised to reproduce the solvation free energy of a series of AT alkanes and side-chain analogues in CG water, while retaining the good mixing behaviour of AT water with CG water. The new AT-CG parameters are tested in hybrid simulations of four proteins in CG water. Structural and dynamic properties are compared to those obtained in fully AT simulations and, if applicable, to experimental data. The results show that the artificial increase of intramolecular hydrogen bonds is drastically reduced, leading to a better reproduction of the structural properties and flexibility of the proteins in atomistic water, without the need for an atomistic solvent layer.