From Proteins to Ligands: Decoding Deep Learning Methods for Binding Affinity Prediction.

Accurate in silico prediction of protein-ligand binding affinity is important in the early stages of drug discovery. Deep learning-based methods exist but have yet to overtake more conventional methods such as giga-docking largely due to their lack of generalizability. To improve generalizability, we need to understand what these models learn from input protein and ligand data. We systematically investigated a sequence-based deep learning framework to assess the impact of protein and ligand encodings on predicting binding affinities for commonly used kinase data sets. The role of proteins is studied using convolutional neural network-based encodings obtained from sequences and graph neural network-based encodings enriched with structural information from contact maps. Ligand-based encodings are generated from graph-neural networks. We test different ligand perturbations by randomizing node and edge properties. For proteins, we make use of 3 different protein contact generation methods (AlphaFold2, Pconsc4, and ESM-1b) and compare these with a random control. Our investigation shows that protein encodings do not substantially impact the binding predictions, with no statistically significant difference in binding affinity for KIBA in the investigated metrics (concordance index, Pearson's R Spearman's Rank, and RMSE). Significant differences are seen for ligand encodings with random ligands and random ligand node properties, suggesting a much bigger reliance on ligand data for the learning tasks. Using different ways to combine protein and ligand encodings did not show a significant change in performance.

Benchmarking Active Learning Protocols for Ligand-Binding Affinity Prediction.

Active learning (AL) has become a powerful tool in computational drug discovery, enabling the identification of top binders from vast molecular libraries. To design a robust AL protocol, it is important to understand the influence of AL parameters, as well as the features of the data sets on the outcomes. We use four affinity data sets for different targets (TYK2, USP7, D2R, Mpro) to systematically evaluate the performance of machine learning models [Gaussian process (GP) model and Chemprop model], sample selection protocols, and the batch size based on metrics describing the overall predictive power of the model (R2, Spearman rank, root-mean-square error) as well as the accurate identification of top 2%/5% binders (Recall, F1 score). Both models have a comparable Recall of top binders on large data sets, but the GP model surpasses the Chemprop model when training data are sparse. A larger initial batch size, especially on diverse data sets, increased the Recall of both models as well as overall correlation metrics. However, for subsequent cycles, smaller batch sizes of 20 or 30 compounds proved to be desirable. Furthermore, adding artificial Gaussian noise to the data up to a certain threshold still allowed the model to identify clusters with top-scoring compounds. However, excessive noise (<1σ) did impact the model's predictive and exploitative capabilities.

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).

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.

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.

The Role of Surface Chemistry in the Orientational Behavior of Water at an Interface.

Molecular dynamics studies have demonstrated that molecular water at an interface, with either a gas or a solid, displays anisotropic orientational behavior in contrast to its bulk counterpart. This effect has been recently implicated in the like-charge attraction problem for colloidal particles in solution. Here, negatively charged particles in solution display a long-ranged attraction where continuum electrostatic theory predicts monotonically repulsive interactions, particularly in solutions with monovalent salt ions at low ionic strength. Anisotropic orientational behavior of solvent molecules at an interface gives rise to an excess interfacial electrical potential which we suggest generates an additional solvation contribution to the total free energy that is traditionally overlooked in continuum descriptions of interparticle interactions in solution. In the present investigation we perform molecular dynamics simulation based calculations of the interfacial potential using realistic surface models representing various chemistries as well as different solvents. Similar to previous work that focused on simple model surfaces constructed by using oxygen atoms, we find that solvents at more realistic model surfaces exhibit substantial anisotropic orientational behavior. We explore the dependence of the interfacial solvation potential on surface properties such as surface group chemistry and group density at silica and carboxylated polystyrene interfaces. For water, we note surprisingly good agreement between results obtained for a simple O-atom wall and more complex surface models, suggesting a general qualitative consistency of the interfacial solvation effect for surfaces in contact with water. In contrast, for an aprotic solvent such as DMSO, surface chemistry appears to exert a stronger influence on the sign and magnitude of the interfacial solvation potential. The study carries broad implications for molecular-scale interactions and may find relevance in explaining a range of phenomena in soft-matter physics and cell biology.