Search

The recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains a challenging endeavour, mostly limited to small model cases. Here, we demonstrate accurate first principles based absolute binding free energy estimates for 128 pharmaceutically relevant targets. We use a novel rigorous method to generate protein-ligand ensembles for the ligand in its decoupled state. Not only do the calculations deliver accurate protein-ligand binding affinity estimates, but they also provide detailed physical insight into the structural determinants of binding. We identify subtle rotamer rearrangements between apo and holo states of a protein that are crucial for binding. When compared to relative binding free energy calculations, obtaining absolute binding free energies is considerably more challenging in large part due to the need to explicitly account for the protein in its apo state. In this work we present several approaches to obtain apo state ensembles for accurate absolute ΔG calculations, thus outlining protocols for prospective application of the methods for drug discovery.

Alchemical free energy calculations are becoming an increasingly prevalent tool in drug discovery efforts. Over the past decade, significant progress has been made in automating various aspects of this technique. However, one aspect hampering wider application is the construction of perturbation networks to connect ligands of interest. More specifically, ligand pairs with large dissimilarities should be avoided since they can lower convergence and decrease accuracy. Here, we propose a technique for automatic generation of intermediate molecules to break up problematic edges─calculations connecting two different ligands or molecules─into smaller perturbations. To this end, a modular tool was developed that generates intermediates for a molecule pair by enumerating R-group combinations called IMERGE-FEP (Intermediate MolEculaR GEnerator for Free Energy Perturbation). Intermediate enumeration of multiple, representative congeneric series showed that intermediates increase similarity regarding shared substructures, geometry, and LOMAP scores. Taken together, this tool eases integration of intermediate steps into free energy calculation protocols.

The rapid advancement in computational power available for research offers to bring not only quantitative improvements, but also qualitative changes in the field of biomolecular simulation. Here, we review the state of biomolecular dynamics simulations at the threshold to exascale resources becoming available. Both developments in parallel and distributed computing will be discussed, providing a perspective on the state of the art of both. A main focus will be on obtaining binding and conformational free energies, with an outlook to macromolecular complexes and (sub)cellular assemblies., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues., (© 2024 The Authors. Journal of Computational Chemistry published by Wiley Periodicals LLC.)

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. p K a is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although p K a values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of p K a prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 p K for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the p K a values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Binding free energy calculations predict the potency of compounds to protein binding sites in a physically rigorous manner and see broad application in prioritizing the synthesis of novel drug candidates. Relative binding free energy (RBFE) calculations have emerged as an industry-standard approach to achieve highly accurate rank-order predictions of the potency of related compounds; however, this approach requires that the ligands share a common scaffold and a common binding mode, restricting the methods' domain of applicability. This is a critical limitation since complex modifications to the ligands, especially core hopping, are very common in drug design. Absolute binding free energy (ABFE) calculations are an alternate method that can be used for ligands that are not congeneric. However, ABFE suffers from a known problem of long convergence times due to the need to sample additional degrees of freedom within each system, such as sampling rearrangements necessary to open and close the binding site. Here, we report on an alternative method for RBFE, called Separated Topologies (SepTop), which overcomes the issues in both of the aforementioned methods by enabling large scaffold changes between ligands with a convergence time comparable to traditional RBFE. Instead of only mutating atoms that vary between two ligands, this approach performs two absolute free energy calculations at the same time in opposite directions, one for each ligand. Defining the two ligands independently allows the comparison of the binding of diverse ligands without the artificial constraints of identical poses or a suitable atom-atom mapping. This approach also avoids the need to sample the unbound state of the protein, making it more efficient than absolute binding free energy calculations. Here, we introduce an implementation of SepTop. We developed a general and efficient protocol for running SepTop, and we demonstrated the method on four diverse, pharmaceutically relevant systems. We report the performance of the method, as well as our practical insights into the strengths, weaknesses, and challenges of applying this method in an industrial drug design setting. We find that the accuracy of the approach is sufficiently high to rank order ligands with an accuracy comparable to traditional RBFE calculations while maintaining the additional flexibility of SepTop.

We introduce the Open Force Field (OpenFF) 2.0.0 small molecule force field for drug-like molecules, code-named Sage, which builds upon our previous iteration, Parsley. OpenFF force fields are based on direct chemical perception, which generalizes easily to highly diverse sets of chemistries based on substructure queries. Like the previous OpenFF iterations, the Sage generation of OpenFF force fields was validated in protein-ligand simulations to be compatible with AMBER biopolymer force fields. In this work, we detail the methodology used to develop this force field, as well as the innovations and improvements introduced since the release of Parsley 1.0.0. One particularly significant feature of Sage is a set of improved Lennard-Jones (LJ) parameters retrained against condensed phase mixture data, the first refit of LJ parameters in the OpenFF small molecule force field line. Sage also includes valence parameters refit to a larger database of quantum chemical calculations than previous versions, as well as improvements in how this fitting is performed. Force field benchmarks show improvements in general metrics of performance against quantum chemistry reference data such as root-mean-square deviations (RMSD) of optimized conformer geometries, torsion fingerprint deviations (TFD), and improved relative conformer energetics (ΔΔ E ). We present a variety of benchmarks for these metrics against our previous force fields as well as in some cases other small molecule force fields. Sage also demonstrates improved performance in estimating physical properties, including comparison against experimental data from various thermodynamic databases for small molecule properties such as Δ H mix , ρ( x ), Δ G solv , and Δ G trans . Additionally, we benchmarked against protein-ligand binding free energies (Δ G bind ), where Sage yields results statistically similar to previous force fields. All the data is made publicly available along with complete details on how to reproduce the training results at https://github.com/openforcefield/openff-sage.

In drug discovery, computational methods are a key part of making informed design decisions and prioritising experiments. In particular, optimizing compound affinity is a central concern during the early stages of development. In the last 10 years, alchemical free energy (FE) calculations have transformed our ability to incorporate accurate in silico potency predictions in design decisions, and represent the 'gold standard' for augmenting experiment-driven drug discovery. However, relative FE calculations are complex to set up, require significant expert intervention to prepare the calculation and analyse the results or are provided only as closed-source software, not allowing for fine-grained control over the underlying settings. In this work, we introduce an end-to-end relative FE workflow based on the non-equilibrium switching approach that facilitates calculation of binding free energies starting from SMILES strings. The workflow is implemented using fully modular steps, allowing various components to be exchanged depending on licence availability. We further investigate the dependence of the calculated free energy accuracy on the initial ligand pose generated by various docking algorithms. We show that both commercial and open-source docking engines can be used to generate poses that lead to good correlation of free energies with experimental reference data., (© 2023. The Author(s).)

Drug discovery can be thought of as a search for a needle in a haystack: searching through a large chemical space for the most active compounds. Computational techniques can narrow the search space for experimental follow up, but even they become unaffordable when evaluating large numbers of molecules. Therefore, machine learning (ML) strategies are being developed as computationally cheaper complementary techniques for navigating and triaging large chemical libraries. Here, we explore how an active learning protocol can be combined with first-principles based alchemical free energy calculations to identify high affinity phosphodiesterase 2 (PDE2) inhibitors. We first calibrate the procedure using a set of experimentally characterized PDE2 binders. The optimized protocol is then used prospectively on a large chemical library to navigate toward potent inhibitors. In the active learning cycle, at every iteration a small fraction of compounds is probed by alchemical calculations and the obtained affinities are used to train ML models. With successive rounds, high affinity binders are identified by explicitly evaluating only a small subset of compounds in a large chemical library, thus providing an efficient protocol that robustly identifies a large fraction of true positives.

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin's paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks., (© 2022. The Author(s).)

Exascale computing has been a dream for ages and is close to becoming a reality that will impact how molecular simulations are being performed, as well as the quantity and quality of the information derived for them. We review how the biomolecular simulations field is anticipating these new architectures, making emphasis on recent work from groups in the BioExcel Center of Excellence for High Performance Computing. We exemplified the power of these simulation strategies with the work done by the HPC simulation community to fight Covid-19 pandemics. This article is categorized under:Data Science > Computer Algorithms and ProgrammingData Science > Databases and Expert SystemsMolecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods., (© 2022 Wiley Periodicals LLC.)

We assess costs and efficiency of state-of-the-art high-performance cloud computing and compare the results to traditional on-premises compute clusters. Our use case is atomistic simulations carried out with the GROMACS molecular dynamics (MD) toolkit with a particular focus on alchemical protein-ligand binding free energy calculations. We set up a compute cluster in the Amazon Web Services (AWS) cloud that incorporates various different instances with Intel, AMD, and ARM CPUs, some with GPU acceleration. Using representative biomolecular simulation systems, we benchmark how GROMACS performs on individual instances and across multiple instances. Thereby we assess which instances deliver the highest performance and which are the most cost-efficient ones for our use case. We find that, in terms of total costs, including hardware, personnel, room, energy, and cooling, producing MD trajectories in the cloud can be about as cost-efficient as an on-premises cluster given that optimal cloud instances are chosen. Further, we find that high-throughput ligand-screening can be accelerated dramatically by using global cloud resources. For a ligand screening study consisting of 19 872 independent simulations or ∼200 μs of combined simulation trajectory, we made use of diverse hardware available in the cloud at the time of the study. The computations scaled-up to reach peak performance using more than 4 000 instances, 140 000 cores, and 3 000 GPUs simultaneously. Our simulation ensemble finished in about 2 days in the cloud, while weeks would be required to complete the task on a typical on-premises cluster consisting of several hundred nodes.

Biliverdin IXβ reductase B (BLVRB) has recently been proposed as a novel therapeutic target for thrombocytopenia through its reactive oxygen species (ROS)-associated mechanism. Thus, we aim at repurposing drugs as new inhibitors of BLVRB. Based on IC 50 (<5 μM), we have identified 20 compounds out of 1496 compounds from the Food and Drug Administration (FDA)-approved library and have clearly mapped their binding sites to the active site. Furthermore, we show the detailed BLVRB-binding modes and thermodynamic properties (Δ H , Δ S , and K D ) with nuclear magnetic resonance (NMR) and isothermal titration calorimetry together with complex structures of eight water-soluble compounds. We anticipate that the results will serve as a novel platform for further in-depth studies on BLVRB effects for related functions such as ROS accumulation and megakaryocyte differentiation, and ultimately treatments of platelet disorders.

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity., (© 2021. The Author(s).)

Binding free energy calculations have become increasingly valuable to drive decision making in drug discovery projects. However, among other issues, inadequate sampling can reduce accuracy, limiting the value of the technique. In this paper, we apply absolute binding free energy calculations to ligands binding to T4 lysozyme L99A and HSP90 using equilibrium and nonequilibrium approaches. We highlight sampling problems encountered in these systems, such as slow side chain rearrangements and slow changes of water placement upon ligand binding. These same types of challenges are also likely to show up in other protein-ligand systems, and we propose some strategies to diagnose and test for such problems in alchemical free energy calculations. We also explore similarities and differences in how the equilibrium and the nonequilibrium approaches handle these problems. Our results show the large amount of work still to be done to make free energy calculations robust and reliable and provide insight for future research in this area.

Correlated mutations have played a pivotal role in the recent success in protein fold prediction. Understanding nonadditive effects of mutations is crucial for altering protein structure, as mutations of multiple residues may change protein stability or binding affinity in a manner unforeseen by the investigation of single mutants. While the couplings between amino acids can be inferred from homologous protein sequences, the physical mechanisms underlying these correlations remain elusive. In this work we demonstrate that calculations based on the first-principles of statistical mechanics are capable of capturing the effects of nonadditivities in protein mutations. The identified thermodynamic couplings cover the short-range as well as previously unknown long-range correlations. We further explore a set of mutations in staphyloccocal nuclease to unravel an intricate interaction pathway underlying the correlations between amino acid mutations.

In the current work we report on our participation in the SAMPL7 challenge calculating absolute free energies of the host-guest systems, where 2 guest molecules were probed against 9 hosts-cyclodextrin and its derivatives. Our submission was based on the non-equilibrium free energy calculation protocol utilizing an averaged consensus result from two force fields (GAFF and CGenFF). The submitted prediction achieved accuracy of [Formula: see text] in terms of the unsigned error averaged over the whole dataset. Subsequently, we further report on the underlying reasons for discrepancies between our calculations and another submission to the SAMPL7 challenge which employed a similar methodology, but disparate ligand and water force fields. As a result we have uncovered a number of issues in the dihedral parameter definition of the GAFF 2 force field. In addition, we identified particular cases in the molecular topologies where different software packages had a different interpretation of the same force field. This latter observation might be of particular relevance for systematic comparisons of molecular simulation software packages. The aforementioned factors have an influence on the final free energy estimates and need to be considered when performing alchemical calculations.

Natural or synthetic polycations are used as biocides or as drug/gene carriers. Understanding the interactions between these macromolecules and cell membranes at the molecular level is therefore of great importance for the design of effective polymer biocides or biocompatible polycation-based delivery systems. Until now, details of the processes at the interface between polycations and biological systems have not been fully recognized. In this study, we consider the effect of strong polycations with quaternary ammonium groups on the properties of anionic lipid membranes that we use as a model system for protein-free cell membranes. For this purpose, we employed experimental measurements and atomic-scale molecular dynamics (MD) simulations. MD simulations reveal that the polycations are strongly hydrated in the aqueous phase and do not lose the water shell after adsorption at the bilayer surface. As a result of strong hydration, the polymer chains reside at the phospholipid headgroup and do not penetrate to the acyl chain region. The polycation adsorption involves the formation of anionic lipid-rich domains, and the density of anionic lipids in these domains depends on the length of the polycation chain. We observed the accumulation of anionic lipids only in the leaflet interacting with the polymer, which leads to the formation of compositionally asymmetric domains. Asymmetric adsorption of the polycation on only one leaflet of the anionic membrane strongly affects the membrane properties in the polycation-membrane contact areas: (i) anionic lipid accumulates in the region near the adsorbed polymer, (ii) acyl chain ordering and lipid packing are reduced, which results in a decrease in the thickness of the bilayer, and (iii) polycation-anionic membrane interactions are strongly influenced by the presence and concentration of salt. Our results provide an atomic-scale description of the interactions of polycations with anionic lipid bilayers and are fully supported by the experimental data. The outcomes are important for understanding the correlation of the structure of polycations with their activity on biomembranes.

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work., Competing Interests: VG, Bd No competing interests declared, (© 2020, Gapsys and de Groot.)

Background: HIV-1 can develop resistance to antiretroviral drugs, mainly through mutations within the target regions of the drugs. In HIV-1 protease, a majority of resistance-associated mutations that develop in response to therapy with protease inhibitors are found in the protease's active site that serves also as a binding pocket for the protease inhibitors, thus directly impacting the protease-inhibitor interactions. Some resistance-associated mutations, however, are found in more distant regions, and the exact mechanisms how these mutations affect protease-inhibitor interactions are unclear. Furthermore, some of these mutations, e.g. N88S and L76V, do not only induce resistance to the currently administered drugs, but contrarily induce sensitivity towards other drugs. In this study, mutations N88S and L76V, along with three other resistance-associated mutations, M46I, I50L, and I84V, are analysed by means of molecular dynamics simulations to investigate their role in complexes of the protease with different inhibitors and in different background sequence contexts., Results: Using these simulations for alchemical calculations to estimate the effects of mutations M46I, I50L, I84V, N88S, and L76V on binding free energies shows they are in general in line with the mutations' effect on [Formula: see text] values. For the primary mutation L76V, however, the presence of a background mutation M46I in our analysis influences whether the unfavourable effect of L76V on inhibitor binding is sufficient to outweigh the accompanying reduction in catalytic activity of the protease. Finally, we show that L76V and N88S changes the hydrogen bond stability of these residues with residues D30/K45 and D30/T31/T74, respectively., Conclusions: We demonstrate that estimating the effect of both binding pocket and distant mutations on inhibitor binding free energy using alchemical calculations can reproduce their effect on the experimentally measured [Formula: see text] values. We show that distant site mutations L76V and N88S affect the hydrogen bond network in the protease's active site, which offers an explanation for the indirect effect of these mutations on inhibitor binding. This work thus provides valuable insights on interplay between primary and background mutations and mechanisms how they affect inhibitor binding.

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein-ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol -1 , equivalent to Schrödinger's FEP+ AUE of 3.66 ± 0.14 kJ mol -1 . For the first time, a setup is presented for overall high precision and high accuracy relative protein-ligand alchemical free energy calculations based on open-source software., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Using the D3R Grand Challenge 4 dataset containing Beta-secretase 1 (BACE) and Cathepsin S (CatS) inhibitors, we have evaluated the performance of our in-house docking workflow that involves in the first step the selection of the most suitable docking software for the system of interest based on structural and functional information available in public databases, followed by the docking of the dataset to predict the binding modes and ranking of ligands. The macrocyclic nature of the BACE ligands brought additional challenges, which were dealt with by a careful preparation of the three-dimensional input structures for ligands. This provided top-performing predictions for BACE, in contrast with CatS, where the predictions in the absence of guiding constraints provided poor results. These results highlight the importance of previous structural knowledge that is needed for correct predictions on some challenging targets. After the end of the challenge, we also carried out free energy calculations (i.e. in a non-blinded manner) for CatS using the pmx software and several force fields (AMBER, Charmm). Using knowledge-based starting pose construction allowed reaching remarkable accuracy for the CatS free energy estimates. Interestingly, we show that the use of a consensus result, by averaging the results from different force fields, increases the prediction accuracy.

Resistance to small molecule drugs often emerges in cancer cells, viruses, and bacteria as a result of the evolutionary pressure exerted by the therapy. Protein mutations that directly impair drug binding are frequently involved in resistance, and the ability to anticipate these mutations would be beneficial in drug development and clinical practice. Here, we evaluate the ability of three distinct computational methods to predict ligand binding affinity changes upon protein mutation for the cancer target Abl kinase. These structure-based approaches rely on first-principle statistical mechanics, mixed physics- and knowledge-based potentials, and machine learning, and were able to estimate binding affinity changes and identify resistant mutations with remarkable accuracy. We expect that these complementary approaches will enable the routine prediction of resistance-causing mutations in a variety of other target proteins., Competing Interests: The authors declare no competing financial interest.

A recent molecular dynamics investigation into the stability of hemoglobin concluded that the unliganded protein is only stable in the T state when a solvent box is used in the simulations that is ten times larger than what is usually employed (El Hage et al., 2018). Here, we express three main concerns about that study. In addition, we find that with an order of magnitude more statistics, the reported box size dependence is not reproducible. Overall, no significant effects on the kinetics or thermodynamics of conformational transitions were observed., Competing Interests: VG, Bd No competing interests declared, (© 2019, Gapsys and de Groot.)

Pyruvate carboxylase deficiency (PCD) is caused by biallelic mutations of the PC gene. The reported clinical spectrum includes a neonatal form with early death (type B), an infantile fatal form (type A), and a late-onset form with isolated mild intellectual delay (type C). Apart from homozygous stop-codon mutations leading to type B PCD, a genotype-phenotype correlation has not otherwise been discernible. Indeed, patients harboring biallelic heterozygous variants leading to PC activity near zero can present either with a fatal infantile type A or with a benign late onset type C form. In this study, we analyzed six novel patients with type A (three) and type C (three) PCD, and compared them with previously reported cases. First, we observed that type C PCD is not associated to homozygous variants in PC. In silico modeling was used to map former and novel variants associated to type A and C PCD, and to predict their potential effects on the enzyme structure and function. We found that variants lead to type A or type C phenotype based on the destabilization between the two major enzyme conformers. In general, our study on novel and previously reported patients improves the overall understanding on type A and C PCD., (© 2019 Wiley Periodicals, Inc.)

Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally, we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well as large-scale mutational scans.

The design of proteins with novel ligand-binding functions holds great potential for application in biomedicine and biotechnology. However, our ability to engineer ligand-binding proteins is still limited, and current approaches rely primarily on experimentation. Computation could reduce the cost of the development process and would allow rigorous testing of our understanding of the principles governing molecular recognition. While computational methods have proven successful in the early stages of the discovery process, optimization approaches that can quantitatively predict ligand affinity changes upon protein mutation are still lacking. Here, we assess the ability of free energy calculations based on first-principles statistical mechanics, as well as the latest Rosetta protocols, to quantitatively predict such affinity changes on a challenging set of 134 mutations. After evaluating different protocols with computational efficiency in mind, we investigate the performance of different force fields. We show that both the free energy calculations and Rosetta are able to quantitatively predict changes in ligand binding affinity upon protein mutations, yet the best predictions are the result of combining the estimates of both methods. These closely match the experimentally determined ΔΔ G values, with a root-mean-square error of 1.2 kcal/mol for the full benchmark set and of 0.8 kcal/mol for a subset of protein systems providing the most reproducible results. The currently achievable accuracy offers the prospect of being able to employ computation for the optimization of ligand-binding proteins as well as the prediction of drug resistance., Competing Interests: The authors declare no competing financial interest.

Despite a large number of antiretroviral drugs targeting HIV-1 protease for inhibition, mutations in this protein during the course of patient treatment can render them inefficient. This emerging resistance inspired numerous computational studies of the HIV-1 protease aimed at predicting the effect of mutations on drug binding in terms of free binding energy Δ G, as well as in mechanistic terms. In this study, we analyze ten different protease-inhibitor complexes carrying major resistance-associated mutations (RAMs) G48V, I50V, and L90M using molecular dynamics simulations. We demonstrate that alchemical free energy calculations can consistently predict the effect of mutations on drug binding. By explicitly probing different protonation states of the catalytic aspartic dyad, we reveal the importance of the correct choice of protonation state for the accuracy of the result. We also provide insight into how different mutations affect drug binding in their specific ways, with the unifying theme of how all of them affect the crucial drug binding regions of the protease.

Dipole-dipole cross-correlated relaxation (CCR) between two spin pairs is rich with macromolecular structural and dynamic information on inter-nuclear bond vectors. Measurement of short range dipolar CCR rates has been demonstrated for a variety of inter-nuclear vector spin pairs in proteins and nucleic acids, where the multiple quantum coherence necessary for observing the CCR rate is created by through-bond scalar coupling. In principle, CCR rates can be measured for any pair of inter-nuclear vectors where coherence can be generated between one spin of each spin pair, regardless of both the distance between the two spin pairs and the distance of the two spins forming the multiple quantum coherence. In practice, however, long range CCR (lrCCR) rates are challenging to measure due to difficulties in linking spatially distant spin pairs. By utilizing through-space relaxation allowed coherence transfer (RACT), we have developed a new method for the measurement of lrCCR rates involving CαHα bonds on opposing anti-parallel β-strands. The resulting lrCCR rates are straightforward to interpret since only the angle between the two vectors modulates the strength of the interference effect. We applied our lrCCR measurement to the third immunoglobulin-binding domain of the streptococcal protein G (GB3) and utilize published NMR ensembles and static NMR/X-ray structures to highlight the relationship between the lrCCR rates and the CαHα-CαHα inter-bond angle and bond mobility. Furthermore, we employ the lrCCR rates to guide the selection of sub-ensembles from the published NMR ensembles for enhancing the structural and dynamic interpretation of the data. We foresee this methodology for measuring lrCCR rates as improving the generation of structural ensembles by providing highly accurate details concerning the orientation of CαHα bonds on opposing anti-parallel β-strands., (Copyright © 2018 Elsevier Inc. All rights reserved.)

The diphenyl-pyrazole compound anle138b is a known inhibitor of oligomeric aggregate formation in vitro and in vivo. Therefore, anle138b is considered a promising drug candidate to beneficially interfere with neurodegenerative processes causing devastating pathologies in humans. The atomistic details of the aggregation inhibition mechanism, however, are to date unknown since the ensemble of small nonfibrillar aggregates is structurally heterogeneous and inaccessible to direct structural characterization. Here, we set out to elucidate anle138b's mode of action using all-atom molecular dynamics simulations on the multi-microsecond time scale. By comparing simulations of dimeric to tetrameric aggregates from fragments of four amyloidogenic proteins (Aβ, hTau40, hIAPP, and Sup35N) in the presence and absence of anle138b, we show that the compound reduces the overall number of intermolecular hydrogen bonds, disfavors the sampling of the aggregated state, and remodels the conformational distributions within the small oligomeric peptide aggregates. Most notably, anle138b preferentially interacts with the disordered structure ensemble via its pyrazole moiety, thereby effectively blocking interpeptide main chain interactions and impeding the spontaneous formation of ordered β-sheet structures, in particular those with out-of-register antiparallel β-strands. The structurally very similar compound anle234b was previously identified as inactive by in vitro experiments. Here, we show that anle234b has no significant effect on the aggregation process in terms of reducing the β-structure content. Moreover, we demonstrate that the hydrogen bonding capabilities are autoinhibited due to steric effects imposed by the molecular geometry of anle234b and thereby indirectly confirm the proposed inhibitory mechanism of anle138b. We anticipate that the prominent binding of anle138b to partially disordered and dynamical aggregate structures is a generic basis for anle138b's ability to suppress toxic oligomer formation in a wide range of amyloidogenic peptides and proteins.

Nucleotide-sequence-dependent interactions between proteins and DNA are responsible for a wide range of gene regulatory functions. Accurate and generalizable methods to evaluate the strength of protein-DNA binding have long been sought. While numerous computational approaches have been developed, most of them require fitting parameters to experimental data to a certain degree, e.g., machine learning algorithms or knowledge-based statistical potentials. Molecular-dynamics-based free energy calculations offer a robust, system-independent, first-principles-based method to calculate free energy differences upon nucleotide mutation. We present an automated procedure to set up alchemical MD-based calculations to evaluate free energy changes occurring as the result of a nucleotide mutation in DNA. We used these methods to perform a large-scale mutation scan comprising 397 nucleotide mutation cases in 16 protein-DNA complexes. The obtained prediction accuracy reaches 5.6 kJ/mol average unsigned deviation from experiment with a correlation coefficient of 0.57 with respect to the experimentally measured free energies. Overall, the first-principles-based approach performed on par with the molecular modeling approaches Rosetta and FoldX. Subsequently, we utilized the MD-based free energy calculations to construct protein-DNA binding profiles for the zinc finger protein Zif268. The calculation results compare remarkably well with the experimentally determined binding profiles. The software automating the structure and topology setup for alchemical calculations is a part of the pmx package; the utilities have also been made available online at http://pmx.mpibpc.mpg.de/dna&#95;webserver.html .

With the increase of available computational power and improvements in simulation algorithms, alchemical molecular dynamics based free energy calculations have developed into routine usage. To further facilitate the usability of alchemical methods for amino acid mutations, we have developed a web based infrastructure for obtaining hybrid protein structures and topologies. The presented webserver allows amino acid mutation selection in five contemporary molecular mechanics force fields. In addition, a complete mutation scan with a user defined amino acid is supported. The output generated by the webserver is directly compatible with the Gromacs molecular dynamics engine and can be used with any of the alchemical free energy calculation setup. Furthermore, we present a database of input files and precalculated free energy differences for tripeptides approximating a disordered state of a protein, of particular use for protein stability studies. Finally, the usage of the webserver and its output is exemplified by performing an alanine scan and investigating thermodynamic stability of the Trp cage mini protein. The webserver is accessible at http://pmx.mpibpc.mpg.de.

Pathogenic enterobacteria need to survive the extreme acidity of the stomach to successfully colonize the human gut. Enteric bacteria circumvent the gastric acid barrier by activating extreme acid-resistance responses, such as the arginine-dependent acid resistance system. In this response, l-arginine is decarboxylated to agmatine, thereby consuming one proton from the cytoplasm. In Escherichia coli, the l-arginine/agmatine antiporter AdiC facilitates the export of agmatine in exchange of l-arginine, thus providing substrates for further removal of protons from the cytoplasm and balancing the intracellular pH. We have solved the crystal structures of wild-type AdiC in the presence and absence of the substrate agmatine at 2.6-Å and 2.2-Å resolution, respectively. The high-resolution structures made possible the identification of crucial water molecules in the substrate-binding sites, unveiling their functional roles for agmatine release and structure stabilization, which was further corroborated by molecular dynamics simulations. Structural analysis combined with site-directed mutagenesis and the scintillation proximity radioligand binding assay improved our understanding of substrate binding and specificity of the wild-type l-arginine/agmatine antiporter AdiC. Finally, we present a potential mechanism for conformational changes of the AdiC transport cycle involved in the release of agmatine into the periplasmic space of E. coli., Competing Interests: The authors declare no conflict of interest.

The formation of well-defined filamentous amyloid structures involves a polydisperse collection of oligomeric states for which relatively little is known in terms of structural organization. Here we use extensive, unbiased explicit solvent molecular dynamics (MD) simulations to investigate the structural and dynamical features of oligomeric aggregates formed by a number of highly amyloidogenic peptides at atomistic resolution on the μs time scale. A consensus approach has been adopted to analyse the simulations in multiple force fields, yielding an in-depth characterization of pre-fibrillar oligomers and their global and local structure properties. A collision cross section analysis revealed structurally heterogeneous aggregate ensembles for the individual oligomeric states that lack a single defined quaternary structure during the pre-nucleation phase. To gain insight into the conformational space sampled in early aggregates, we probed their substructure and found emerging β-sheet subunit layers and a multitude of ordered intermolecular β-structure motifs with growing aggregate size. Among those, anti-parallel out-of-register β-strands compatible with toxic β-barrel oligomers were particularly prevalent already in smaller aggregates and formed prior to ordered fibrillar structure elements. Notably, also distinct fibril-like conformations emerged in the oligomeric state and underscore the notion that pre-nucleated oligomers serve as a critical intermediate step on-pathway to fibrils.

The prediction of mutation-induced free-energy changes in protein thermostability or protein-protein binding is of particular interest in the fields of protein design, biotechnology, and bioengineering. Herein, we achieve remarkable accuracy in a scan of 762 mutations estimating changes in protein thermostability based on the first principles of statistical mechanics. The remaining error in the free-energy estimates appears to be due to three sources in approximately equal parts, namely sampling, force-field inaccuracies, and experimental uncertainty. We propose a consensus force-field approach, which, together with an increased sampling time, leads to a free-energy prediction accuracy that matches those reached in experiments. This versatile approach enables accurate free-energy estimates for diverse proteins, including the prediction of changes in the melting temperature of the membrane protein neurotensin receptor 1., (© 2016 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.)

Intrinsically disordered proteins (IDPs) are notoriously challenging to study both experimentally and computationally. The structure of IDPs cannot be described by a single conformation but must instead be described as an ensemble of interconverting conformations. Atomistic simulations are increasingly used to obtain such IDP conformational ensembles. Here, we have compared the IDP ensembles generated by eight all-atom empirical force fields against primary small-angle X-ray scattering (SAXS) and NMR data. Ensembles obtained with different force fields exhibit marked differences in chain dimensions, hydrogen bonding, and secondary structure content. These differences are unexpectedly large: changing the force field is found to have a stronger effect on secondary structure content than changing the entire peptide sequence. The CHARMM 22* ensemble performs best in this force field comparison: it has the lowest error in chemical shifts and J-couplings and agrees well with the SAXS data. A high population of left-handed α-helix is present in the CHARMM 36 ensemble, which is inconsistent with measured scalar couplings. To eliminate inadequate sampling as a reason for differences between force fields, extensive simulations were carried out (0.964 ms in total); the remaining small sampling uncertainty is shown to be much smaller than the observed differences. Our findings highlight how IDPs, with their rugged energy landscapes, are highly sensitive test systems that are capable of revealing force field deficiencies and, therefore, contributing to force field development.

Intrinsically disordered proteins (IDPs) are best described by ensembles of conformations and a variety of approaches have been developed to determine IDP ensembles. Because of the large number of conformations, however, cross-validation of the determined ensembles by independent experimental data is crucial. The (1)JCαHα coupling constant is particularly suited for cross-validation, because it has a large magnitude and mostly depends on the often less accessible dihedral angle ψ. Here, we reinvestigated the connection between (1)JCαHα values and protein backbone dihedral angles. We show that accurate amino-acid specific random coil values of the (1)JCαHα coupling constant, in combination with a reparameterized empirical Karplus-type equation, allow for reliable cross-validation of molecular ensembles of IDPs.

Computational protein design requires methods to accurately estimate free energy changes in protein stability or binding upon an amino acid mutation. From the different approaches available, molecular dynamics-based alchemical free energy calculations are unique in their accuracy and solid theoretical basis. The challenge in using these methods lies in the need to generate hybrid structures and topologies representing two physical states of a system. A custom made hybrid topology may prove useful for a particular mutation of interest, however, a high throughput mutation analysis calls for a more general approach. In this work, we present an automated procedure to generate hybrid structures and topologies for the amino acid mutations in all commonly used force fields. The described software is compatible with the Gromacs simulation package. The mutation libraries are readily supported for five force fields, namely Amber99SB, Amber99SB*-ILDN, OPLS-AA/L, Charmm22*, and Charmm36., (© 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.)

Molecular dynamics simulations enable access to free energy differences governing the driving force underlying all biological processes. In the current chapter we describe alchemical methods allowing the calculation of relative free energy differences. We concentrate on the binding free energies that can be obtained using non-equilibrium approaches based on the Crooks Fluctuation Theorem. Together with the theoretical background, the chapter covers practical aspects of hybrid topology generation, simulation setup, and free energy estimation. An important aspect of the validation of a simulation setup is illustrated by means of calculating free energy differences along a full thermodynamic cycle. We provide a number of examples, including protein-ligand and protein-protein binding as well as ligand solvation free energy calculations.

Serine/arginine-rich (SR) proteins are important players in RNA metabolism and are extensively phosphorylated at serine residues in RS repeats. Here, we show that phosphorylation switches the RS domain of the serine/arginine-rich splicing factor 1 from a fully disordered state to a partially rigidified arch-like structure. Nuclear magnetic resonance spectroscopy in combination with molecular dynamics simulations revealed that the conformational switch is restricted to RS repeats, critically depends on the phosphate charge state and strongly decreases the conformational entropy of RS domains. The dynamic switch also occurs in the 100 kDa SR-related protein hPrp28, for which phosphorylation at the RS repeat is required for spliceosome assembly. Thus, a phosphorylation-induced dynamic switch is common to the class of serine/arginine-rich proteins and provides a molecular basis for the functional redundancy of serine/arginine-rich proteins and the profound influence of RS domain phosphorylation on protein-protein and protein-RNA interactions., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

In the field of biomolecular simulations, dynamics of phospholipid membranes is of special interest. A number of proteins, including channels, transporters, receptors and short peptides are embedded in lipid bilayers and tightly interact with phospholipids. While the experimental measurements report on the spatial and/or temporal average membrane properties, simulation results are not restricted to the average properties. In the current study, we present a collection of methods for an efficient local membrane property calculation, comprising bilayer thickness, area per lipid, deuterium order parameters, Gaussian and mean curvature. The local membrane property calculation allows for a direct mapping of the membrane features, which subsequently can be used for further analysis and visualization of the processes of interest. The main features of the described methods are highlighted in a number of membrane systems, namely: a pure dimyristoyl-phosphatidyl-choline (DMPC) bilayer, a fusion peptide interacting with a membrane, voltage-dependent anion channel protein embedded in a DMPC bilayer, cholesterol enriched bilayer and a coarse grained simulation of a curved palmitoyl-oleoyl-phosphatidyl-choline lipid membrane. The local membrane property analysis proves to provide an intuitive and detailed view on the observables that are otherwise interpreted as averaged bilayer properties.

Analysis of the internal dynamics of a biological molecule requires the successful removal of overall translation and rotation. Particularly for flexible or intrinsically disordered peptides, this is a challenging task due to the absence of a well-defined reference structure that could be used for superpositioning. In this work, we started the analysis with a widely known formulation of an objective for the problem of superimposing a set of multiple molecules as variance minimization over an ensemble. A negative effect of this superpositioning method is the introduction of ambiguous rotations, where different rotation matrices may be applied to structurally similar molecules. We developed two algorithms to resolve the suboptimal rotations. The first approach minimizes the variance together with the distance of a structure to a preceding molecule in the ensemble. The second algorithm seeks for minimal variance together with the distance to the nearest neighbors of each structure. The newly developed methods were applied to molecular-dynamics trajectories and normal-mode ensembles of the Aβ peptide, RS peptide, and lysozyme. These new (to our knowledge) superpositioning methods combine the benefits of variance and distance between nearest-neighbor(s) minimization, providing a solution for the analysis of intrinsic motions of flexible molecules and resolving ambiguous rotations., (Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Understanding the structural and energetic requirements of non-fibrillar oligomer formation harbors the potential to decipher an important yet still elusive part of amyloidogenic peptide and protein aggregation. Low-molecular-weight oligomers are described to be transient and polymorphic intermediates in the nucleated self-assembly process to highly ordered amyloid fibers and were additionally found to exhibit a profound cytotoxicity. However, detailed structural information on the oligomeric species involved in the nucleation cannot be readily inferred from experiments. Here, we study the spontaneous assembly of steric zipper peptides from the tau protein, insulin and α-synuclein with atomistic molecular dynamics simulations on the microsecond timescale. Detailed analysis of the forces driving the oligomerization reveals a common two-step process akin to a general condensation-ordering mechanism and thus provides a rational understanding of the molecular basis of peptide self-assembly. Our results suggest that the initial formation of partially ordered peptide oligomers is governed by the solvation free energy, whereas the dynamical ordering and emergence of β-sheets are mainly driven by optimized inter-peptide interactions in the collapsed state. A novel mapping technique based on collective coordinates is employed to highlight similarities and differences in the conformational ensemble of small oligomer structures. Elucidating the dynamical and polymorphic β-sheet oligomer conformations at atomistic detail furthermore suggests complementary sheet packing characteristics similar to steric zipper structures, but with a larger heterogeneity in the strand alignment pattern and sheet-to-sheet arrangements compared to the cross-β motif found in the fibrillar or crystalline states., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

The fields of rational drug design and protein engineering benefit from accurate free energy calculations based on molecular dynamics simulations. A thermodynamic integration scheme is often used to calculate changes in the free energy of a system by integrating the change of the system's Hamiltonian with respect to a coupling parameter. These methods exploit nonphysical pathways over thermodynamic cycles involving particle introduction and annihilation. Such alchemical transitions require the modification of the classical nonbonded potential energy terms by applying soft-core potential functions to avoid singularity points. In this work, we propose a novel formulation for a soft-core potential to be applied in nonequilibrium free energy calculations that alleviates singularities, numerical instabilities, and additional minima in the potential energy for all combinations of nonbonded interactions at all intermediate alchemical states. The method was validated by application to (a) the free energy calculations of a closed thermodynamic cycle, (b) the mutation influence on protein thermostability, (c) calculations of small ligand solvation free energies, and (d) the estimation of binding free energies of trypsin inhibitors. The results show that the novel soft-core function provides a robust and accurate general purpose solution to alchemical free energy calculations.