Identifying low variance pathways for free energy calculations of molecular transformations in solution phase

Enhancing torsional sampling using fully adaptive simulated tempering

Enhanced sampling algorithms are indispensable when working with highly disconnected multimodal distributions. An important application of these is the conformational exploration of particular internal degrees of freedom of molecular systems. However, despite the existence of many commonly used enhanced sampling algorithms to explore these internal motions, they often rely on system-dependent parameters, which negatively impact efficiency and reproducibility. Here, we present fully adaptive simulated tempering (FAST), a variation of the irreversible simulated tempering algorithm, which continuously optimizes the number, parameters, and weights of intermediate distributions to achieve maximally fast traversal over a space defined by the change in a predefined thermodynamic control variable such as temperature or an alchemical smoothing parameter. This work builds on a number of previously published methods, such as sequential Monte Carlo, and introduces a novel parameter optimization procedure that can, in principle, be used in any expanded ensemble algorithms. This method is validated by being applied on a number of different molecular systems with high torsional kinetic barriers. We also consider two different soft-core potentials during the interpolation procedure and compare their performance. We conclude that FAST is a highly efficient algorithm, which improves simulation reproducibility and can be successfully used in a variety of settings with the same initial hyperparameters.

Kartograf: A Geometrically Accurate Atom Mapper for Hybrid-Topology Relative Free Energy Calculations

Relative binding free energy (RBFE) calculations have emerged as a powerful tool that supports ligand optimization in drug discovery. Despite many successes, the use of RBFEs can often be limited by automation problems, in particular, the setup of such calculations. Atom mapping algorithms are an essential component in setting up automatic large-scale hybrid-topology RBFE calculation campaigns. Traditional algorithms typically employ a 2D subgraph isomorphism solver (SIS) in order to estimate the maximum common substructure. SIS-based approaches can be limited by time-intensive operations and issues with capturing geometry-linked chemical properties, potentially leading to suboptimal solutions. To overcome these limitations, we have developed Kartograf, a geometric-graph-based algorithm that uses primarily the 3D coordinates of atoms to find a mapping between two ligands. In free energy approaches, the ligand conformations are usually derived from docking or other previous modeling approaches, giving the coordinates a certain importance. By considering the spatial relationships between atoms related to the molecule coordinates, our algorithm bypasses the computationally complex subgraph matching of SIS-based approaches and reduces the problem to a much simpler bipartite graph matching problem. Moreover, Kartograf effectively circumvents typical mapping issues induced by molecule symmetry and stereoisomerism, making it a more robust approach for atom mapping from a geometric perspective. To validate our method, we calculated mappings with our novel approach using a diverse set of small molecules and used the mappings in relative hydration and binding free energy calculations. The comparison with two SIS-based algorithms showed that Kartograf offers a fast alternative approach. The code for Kartograf is freely available on GitHub (https://github.com/OpenFreeEnergy/kartograf). While developed for the OpenFE ecosystem, Kartograf can also be utilized as a standalone Python package.

Tuning Potential Functions to Host-Guest Binding Data

Software to more rapidly and accurately predict protein-ligand binding affinities is of high interest for early-stage drug discovery, and physics-based methods are among the most widely used technologies for this purpose. The accuracy of these methods depends critically on the accuracy of the potential functions that they use. Potential functions are typically trained against a combination of quantum chemical and experimental data. However, although binding affinities are among the most important quantities to predict, experimental binding affinities have not to date been integrated into the experimental data set used to train potential functions. In recent years, the use of host-guest complexes as simple and tractable models of binding thermodynamics has gained popularity due to their small size and simplicity, relative to protein-ligand systems. Host-guest complexes can also avoid ambiguities that arise in protein-ligand systems such as uncertain protonation states. Thus, experimental host-guest binding data are an appealing additional data type to integrate into the experimental data set used to optimize potential functions. Here, we report the extension of the Open Force Field Evaluator framework to enable the systematic calculation of host-guest binding free energies and their gradients with respect to force field parameters, coupled with the curation of 126 host-guest complexes with available experimental binding free energies. As an initial application of this novel infrastructure, we optimized generalized Born (GB) cavity radii for the OBC2 GB implicit solvent model against experimental data for 36 host-guest systems. This refitting led to a dramatic improvement in accuracy for both the training set and a separate test set with 90 additional host-guest systems. The optimized radii also showed encouraging transferability from host-guest systems to 59 protein-ligand systems. However, the new radii are significantly smaller than the baseline radii and lead to excessively favorable hydration free energies (HFEs). Thus, users of the OBC2 GB model currently may choose between GB cavity radii that yield more accurate binding affinities and GB cavity radii that yield more accurate HFEs. We suspect that achieving good accuracy on both will require more far-reaching adjustments to the GB model. We note that binding free-energy calculations using the OBC2 model in OpenMM gain about a 10× speedup relative to corresponding explicit solvent calculations, suggesting a future role for implicit solvent absolute binding free-energy (ABFE) calculations in virtual compound screening. This study proves the principle of using host-guest systems to train potential functions that are transferrable to protein-ligand systems and provides an infrastructure that enables a range of applications.

Molecular dynamics studies of the solubility behavior of carbon dioxide (CO2 ), difluoromethane (R-32), 1-chloro-3,3,3-trifluoropropene (R-1233zd(E)) and 2,3,3,3-tetrafluoro-1-propene (R-1234yf) in pentaerythritol tetra(2-ethylhexanoate) (PEB8), pentaerythritol tetrabutyrate (PEC4) and pentaerythritol tetraoctanoate (PEC8)

To reduce the climate impact of thermal engines such as heat pumps or refrigeration machines, refrigerants with a low global warming potential need to be paired with fitting lubricants. As the contamination of those liquid components influences the efficiency and lifetime of these machines, knowledge about their solubility behavior is of great interest. Molecular simulations offer mighty tools to investigate these solubilities while giving structural insight into the systems. Here the solubility behavior of CO2 , R-32, R-1233zd(E), and R-1234yf in PEB8, PEC4, and PEC8 is compared through the solvation free energy ∆GSolv obtained by molecular dynamics simulations. To derive ∆GSolv at low computational cost, an iterative method is used to find an optimal number and distribution of intermediate states. The resulting distributions are investigated with regard to different parameters of the employed softcore-potential. ∆GSolv values for the different refrigerant-lubricant pairings at different temperatures are provided, followed by a structural analysis.

Development and Benchmarking of Open Force Field 2.0.0: The Sage Small Molecule Force Field

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 (ΔΔE). 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 ΔHmix, ρ(x), ΔGsolv, and ΔGtrans. Additionally, we benchmarked against protein-ligand binding free energies (ΔGbind), 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.

Understanding the sources of error in MBAR through asymptotic analysis

Many sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple states. The Multistate Bennett Acceptance Ratio (MBAR) formalism is a widely used way of recombining the resulting data. However, the error of the MBAR estimator is not well-understood: previous error analyses of MBAR assumed independent samples. In this work, we derive a central limit theorem for MBAR estimates in the presence of correlated data, further justifying the use of MBAR in practical applications. Moreover, our central limit theorem yields an estimate of the error that can be decomposed into contributions from the individual Markov chains used to sample the states. This gives additional insight into how sampling in each state affects the overall error. We demonstrate our error estimator on an umbrella sampling calculation of the free energy of isomerization of the alanine dipeptide and an alchemical calculation of the hydration free energy of methane. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual states can contribute considerably to the total MBAR error, highlighting the importance of accurately addressing the effect of sample correlation.

Predicting antibiotic resistance in complex protein targets using alchemical free energy methods

Drug resistant Mycobacterium tuberculosis, which mostly results from single nucleotide polymorphisms in antibiotic target genes, poses a major threat to tuberculosis treatment outcomes. Relative binding free energy (RBFE) calculations can rapidly predict the effects of mutations, but this approach has not been tested on large, complex proteins. We use RBFE calculations to predict the effects of M. tuberculosis RNA polymerase and DNA gyrase mutations on rifampicin and moxifloxacin susceptibility respectively. These mutations encompass a range of amino acid substitutions with known effects and include large steric perturbations and charged moieties. We find that moderate numbers (n = 3-15) of short RBFE calculations can predict resistance in cases where the mutation results in a large change in the binding free energy. We show that the method lacks discrimination in cases with either a small change in energy or that involve charged amino acids, and we investigate how these calculation errors may be decreased.

A New Formulation for the Concerted Alchemical Calculation of van der Waals and Coulomb Components of Solvation Free Energies

Alchemical free energy calculations via molecular dynamics have been widely used to obtain thermodynamic properties related to protein-ligand binding and solute-solvent interactions. Although soft-core modeling is the most common approach, the linear basis function (LBF) methodology [Naden, L. N.; et al. J. Chem. Theory Comput.2014, 10 (3), 1128; 2015, 11 (6), 2536] has emerged as a suitable alternative. It overcomes the end-point singularity of the scaling method while maintaining essential advantages such as ease of implementation and high flexibility for postprocessing analysis. In the present work, we propose a simple LBF variant and formulate an efficient protocol for evaluating van der Waals and Coulomb components of an alchemical transformation in tandem, in contrast to the prevalent sequential evaluation mode. To validate our proposal, which results from a careful optimization study, we performed solvation free energy calculations and obtained octanol-water partition coefficients of small organic molecules. Comparisons with results obtained via the sequential mode using either another LBF approach or the soft-core model attest to the effectiveness and correctness of our method. In addition, we show that a reaction field model with an infinite dielectric constant can provide very accurate hydration free energies when used instead of a lattice-sum method to model solute-solvent electrostatics.

Assessing the effect of forcefield parameter sets on the accuracy of relative binding free energy calculations

Software for accurate prediction of protein-ligand binding affinity can be a key enabling tool for small molecule drug discovery. Free energy perturbation (FEP) is a computational technique that can be used to compute binding affinity differences between molecules in a congeneric series. It has shown promise in reliably generating accurate predictions and is now widely used in the pharmaceutical industry. However, the high computational cost and use of commercial software, together with the technical challenges to setup, run, and analyze the simulations, limits the usage of FEP. Here, we use an automated FEP workflow which uses the open-source OpenMM package. To enable effective application of FEP, we compared the performance of different water models, partial charge assignments, and AMBER protein forcefields in eight benchmark test cases previously assembled for FEP validation studies.

Optimal control with a strong harmonic trap

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.

Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman's, Pearson's and Kendall's tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

Enhancing Ligand and Protein Sampling Using Sequential Monte Carlo

The sampling problem is one of the most widely studied topics in computational chemistry. While various methods exist for sampling along a set of reaction coordinates, many require system-dependent hyperparameters to achieve maximum efficiency. In this work, we present an alchemical variation of adaptive sequential Monte Carlo (SMC), an irreversible importance resampling method that is part of a well-studied class of methods that have been used in various applications but have been underexplored in computational biophysics. Afterward, we apply alchemical SMC on a variety of test cases, including torsional rotations of solvated ligands (butene and a terphenyl derivative), translational and rotational movements of protein-bound ligands, and protein side chain rotation coupled to the ligand degrees of freedom (T4-lysozyme, protein tyrosine phosphatase 1B, and transforming growth factor β). We find that alchemical SMC is an efficient way to explore targeted degrees of freedom and can be applied to a variety of systems using the same hyperparameters to achieve a similar performance. Alchemical SMC is a promising tool for preparatory exploration of systems where long-timescale sampling of the entire system can be traded off against short-timescale sampling of a particular set of degrees of freedom over a population of conformers.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

Comparing the Performance of Different AMBER Protein Forcefields, Partial Charge Assignments, and Water Models for Absolute Binding Free Energy Calculations

Identifying chemical starting points is a vital first step in small molecule drug discovery and can take significant time and money. For this reason, computational approaches to virtual screening are of great interest as they can lower the cost and shorten timeframes. However, simple approaches such as molecular docking and pharmacophore screening are of limited accuracy and provide a low probability of success. Alchemical binding free energies represent a promising approach for virtual screening as they naturally incorporate the key effects of water molecules, protein flexibility, and binding entropy. However, the calculations are technically very challenging, with performance depending on the specific forcefield used. For this reason, it is important that the community has access to benchmark test sets to assess prediction accuracy. In this paper, we present an approach to alchemical binding free energies using OpenMM. We identify effective simulation parameters using an existing BRD4(1) test set and present two new benchmark sets (cMET and PDE2A) that can be used in the community for validation purposes. Our findings also highlight the effectiveness of some AMBER forcefields, in particular, AMBER ff15ipq.

Small-to-large length scale transition of TMAO interaction with hydrophobic solutes

We report the effect of trimethylamine N-oxide (TMAO) on the solvation of nonpolar solutes in water studied with molecular dynamics (MD) simulations and free-energy calculations. The simulation data indicate the occurrence of a length scale crossover in the TMAO interaction with repulsive Weeks-Chandler-Andersen (WCA) solutes: while TMAO is depleted from the hydration shell of a small WCA solute (methane) and increases the free-energy cost of solute-cavity formation, it preferentially binds to a large WCA solute (α-helical polyalanine), reducing the free-energy cost of solute-cavity formation via a surfactant-like mechanism. Significantly, we show that this surfactant-like behaviour of TMAO reinforces the solvent-mediated attraction between large WCA solutes by means of an entropic force linked to the interfacial accumulation of TMAO. Specifically, this entropic force arises from the natural tendency of adsorbed TMAO molecules to mix back into the bulk. It therefore favours solute-solute contact states that minimise the surface area exposed to the solvent and have a small overall number of TMAO molecules adsorbed. In contrast to the well-known depletion force, its effect is compensated by enthalpic solute-solvent interactions. Correspondingly, the hydrophobic association free energy of the large α-helical solutes passes through a minimum at low TMAO concentration when cohesive solute-solvent van der Waals interactions are considered. The observations reported herein are reminiscent to cosolvent effects on hydrophobic polymer coil-globule collapse free energies (Bharadwaj et al., Commun. Chem. 2020, 3, 165) and may be of general significance in systems whose properties are determined by hydrophobic self-assembly.

Small-sample limit of the Bennett acceptance ratio method and the variationally derived intermediates

Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the two states for which the free energy difference is calculated. The Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods are optimal estimator and intermediate states in that the mean-squared error of free energy calculations based on independent sampling is minimized. However, BAR and VI have been derived based on several approximations that do not hold for very few sample points. Analyzing one-dimensional test systems, we show that in such cases BAR and VI are suboptimal and that established uncertainty estimates are inaccurate. Whereas for VI to become optimal, less than seven samples per state suffice in all cases; for BAR the required number increases unboundedly with decreasing configuration space densities overlap of the end states. We show that for BAR, the required number of samples is related to the overlap through an inverse power law. Because this relation seems to hold universally and almost independent of other system properties, these findings can guide the proper choice of estimators for free energy calculations.

Direct Calculation of Entropic Components in Cohesive Interaction Free Energies

Cohesive interaction free energies entail an entropic component related to fluctuations of the energy associated with the attractive portion of the solute-solvent potential. The corresponding "fluctuation entropy" is fundamental in the solvation thermodynamics of macromolecular solutes and is linked to interfacial solvent density fluctuations and hydrophobic effects. Since the direct calculation of fluctuation entropy in molecular simulations is hampered by the poor sampling of high-energy tails in the solute-solvent energy distribution, indirect, and often approximate, routes for the calculation of fluctuation entropy are usually required, involving the modeling of geometrically frozen repulsive solute cavities in thermodynamic integration approaches. Herein, we propose a method to directly compute the fluctuation entropy by employing indirect umbrella sampling (INDUS). To validate the method, we consider model systems consisting of subnanometer oil droplets in water for which the fluctuation entropy can be computed exactly using indirect methods. The fluctuation entropy calculated with the newly proposed direct method agrees with the indirect reference calculations. We also observe that the solvation free energy and the contribution of the fluctuation entropy to it are of comparable magnitudes, particularly for larger oil droplets (∼1 nm). The proposed method can readily be employed for flexible macromolecular solutes and systems with extended hydrophobic surfaces or in the vicinity of a dewetting transition.

New Features of the Open Source Monte Carlo Software Brick-CFCMC: Thermodynamic Integration and Hybrid Trial Moves

We present several new major features added to the Monte Carlo (MC) simulation code Brick-CFCMC for phase- and reaction equilibria calculations (https://gitlab.com/ETh_TU_Delft/Brick-CFCMC). The first one is thermodynamic integration for the computation of excess chemical potentials (μ^ex). For this purpose, we implemented the computation of the ensemble average of the derivative of the potential energy with respect to the scaling factor for intermolecular interactions (). Efficient bookkeeping is implemented so that the quantity is updated after every MC trial move with negligible computational cost. We demonstrate the accuracy and reliability of the calculation of μ^ex for sodium chloride in water. Second, we implemented hybrid MC/MD translation and rotation trial moves to increase the efficiency of sampling of the configuration space. In these trial moves, short Molecular Dynamics (MD) trajectories are performed to collectively displace or rotate all molecules in the system. These trajectories are accepted or rejected based on the total energy drift. The efficiency of these trial moves can be tuned by changing the time step and the trajectory length. The new trial moves are demonstrated using MC simulations of a viscous fluid (deep eutectic solvent).

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

Artificial intelligence in drug design: algorithms, applications, challenges and ethics

The discovery paradigm of drugs is rapidly growing due to advances in machine learning (ML) and artificial intelligence (AI). This review covers myriad faces of AI and ML in drug design. There is a plethora of AI algorithms, the most common of which are summarized in this review. In addition, AI is fraught with challenges that are highlighted along with plausible solutions to them. Examples are provided to illustrate the use of AI and ML in drug discovery and in predicting drug properties such as binding affinities and interactions, solubility, toxicology, blood–brain barrier permeability and chemical properties. The review also includes examples depicting the implementation of AI and ML in tackling intractable diseases such as COVID-19, cancer and Alzheimer’s disease. Ethical considerations and future perspectives of AI are also covered in this review.

An interplay of excluded-volume and polymer-(co)solvent attractive interactions regulates polymer collapse in mixed solvents

Cosolvent effects on the coil-globule transitions in aqueous polymer solutions are not well understood, especially in the case of amphiphilic cosolvents that preferentially adsorb on the polymer and lead to both polymer swelling and collapse. Although a predominant focus in the literature has been placed on the role of polymer-cosolvent attractive interactions, our recent work has shown that excluded-volume interactions (repulsive interactions) can drive both preferential adsorption of the cosolvent and polymer collapse via a surfactant-like mechanism. Here, we further study the role of polymer-(co)solvent attractive interactions in two kinds of polymer solutions, namely, good solvent (water)-good cosolvent (alcohol) (GSGC) and poor solvent-good cosolvent (PSGC) solutions, both of which exhibit preferential adsorption of the cosolvent and a non-monotonic change in the polymer radius of gyration with the addition of the cosolvent. Interestingly, at low concentrations, the polymer-(co)solvent energetic interactions oppose polymer collapse in the GSGC solutions and contrarily support polymer collapse in the PSGC solutions, indicating the importance of the underlying polymer chemistry. Even though the alcohol molecules are preferentially adsorbed on the polymer, the trends of the energetic interactions at low cosolvent concentrations are dominated by the polymer-water energetic interactions in both the cases. Therefore, polymer-(co)solvent energetic interactions can either reinforce or compensate the surfactant-like mechanism, and it is this interplay that drives coil-to-globule transitions in polymer solutions. These results have implications for rationalizing the cononsolvency transitions in real systems such as polyacrylamides in aqueous alcohol solutions where the understanding of microscopic driving forces is still debatable.

Binding thermodynamics and interaction patterns of human purine nucleoside phosphorylase-inhibitor complexes from extensive free energy calculations

Human purine nucleoside phosphorylase (hPNP) plays a significant role in the catabolism of deoxyguanosine. The trimeric protein is an important target in the treatment of T-cell cancers and autoimmune disorders. Experimental studies on the inhibition of the hPNP observe that the first ligand bound to one of three subunits effectively inhibits the protein, while the binding of more ligands to the subsequent sites shows negative cooperativities. In this work, we performed extensive end-point and alchemical free energy calculations to determine the binding thermodynamics of the trimeric protein-ligand system. 13 Immucillin inhibitors with experimental results are under calculation. Two widely accepted charge schemes for small molecules including AM1-BCC and RESP are adopted for ligands. The results of RESP are in better agreement with the experimental reference. Further investigations of the interaction networks in the protein-ligand complexes reveal that several residues play significant roles in stabilizing the complex structure. The most commonly observed ones include PHE200, GLU201, MET219, and ASN243. The conformations of the protein in different protein-ligand complexes are observed to be similar. We expect these insights to aid the development of potent drugs targeting hPNP.

Per|Mut: Spatially Resolved Hydration Entropies from Atomistic Simulations

The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol.

Solubility of Carbon Dioxide, Hydrogen Sulfide, Methane, and Nitrogen in Monoethylene Glycol; Experiments and Molecular Simulation

Knowledge on the solubility of gases, especially carbon dioxide (CO₂), in monoethylene glycol (MEG) is relevant for a number of industrial applications such as separation processes and gas hydrate prevention. In this study, the solubility of CO₂ in MEG was measured experimentally at temperatures of 333.15, 353.15, and 373.15 K. Experimental data were used to validate Monte Carlo (MC) simulations. Continuous fractional component MC simulations in the osmotic ensemble were performed to compute the solubility of CO₂ in MEG at the same temperatures and at pressures up to 10 bar. MC simulations were also used to study the solubility of methane (CH₄), hydrogen sulfide (H₂S), and nitrogen (N₂) in MEG at 373.15 K. Solubilities from experiments and simulations are in good agreement at low pressures, but deviations were observed at high pressures. Henry coefficients were also computed using MC simulations and compared to experimental values. The order of solubilities of the gases in MEG at 373.15 K was computed as H₂S > CO₂ > CH₄ > N₂. Force field modifications may be required to improve the prediction of solubilities of gases in MEG at high pressures and low temperatures.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself in a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called molecular darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves. We apply this technique to a simple dipeptide system, a ligand binding to T4 lysozyme L99A, and ligand binding to HIV integrase to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal and rotational/translational degrees of freedom in these systems.

Optimization of Alchemical Pathways Using Extended Thermodynamic Integration

Thermodynamic integration (TI) is a commonly used method to determine free-energy differences. One of its disadvantages is that many intermediate λ-states need to be sampled in order to be able to integrate accurately over ⟨∂H/∂λ⟩. Here, we use the recently introduced extended TI to study alternative parameterizations of H(λ) and its influence on the smoothness of the ⟨∂H/∂λ⟩ curves as well as the efficiency of the simulations. We find that the extended TI approach can be used to select curves of low curvature. An optimal parameterization is suggested for the calculation of hydration free energies. For calculations of relative binding free energies, we show that optimized parameterizations of the Hamiltonian in the unbound state also effectively lower the curvature in the bound state of the ligand.

Excess chemical potential of thiophene in [C4MIM] [BF4, Cl, Br, CH3COO] ionic liquids, determined by molecular simulations

The excess chemical potential of thiophene in imidazolium-based ionic liquids [C₄mim][BF₄], [C₄mim][Cl], [C₄mim][Br], and [C₄mim][CH₃COO] were determined by means of molecular dynamics in conjunction with free energy perturbation techniques employing non-polarizable force fields at 300 K and 343.15 K. In addition, energetic and structural analysis were performed such as: interaction energies, averaged noncovalent interactions, radial, and combined distribution functions. The results from this work revealed that the ionic liquids (ILs) presenting the most favorable excess chemical potentials ([C₄mim][BF₄], [C₄mim][CH₃COO]) are associated with the strongest energetic interaction between the thiophene molecule and the ionic liquid anion, and with the weakest energetic interaction between the thiophene molecule and the ionic liquid cation.

Excess chemical potential of thiophene in imidazolium-based ionic liquids [C₄mim][BF₄], [C₄mim][Cl], [C₄mim][Br], and [C₄mim][CH₃COO] determined by molecular simulations.

Skewed thermodynamic geometry and optimal free energy estimation

Free energy differences are a central quantity of interest in physics, chemistry, and biology. We develop design principles that improve the precision and accuracy of free energy estimators, which have potential applications to screening for targeted drug discovery. Specifically, by exploiting the connection between the work statistics of time-reversed protocol pairs, we develop near-equilibrium approximations for moments of the excess work and analyze the dominant contributions to the precision and accuracy of standard nonequilibrium free-energy estimators. Within linear response, minimum-dissipation protocols follow the geodesics of the Riemannian metric induced by the Stokes friction tensor. We find that the next-order contribution arises from the rank-3 supra-Stokes tensor that skews the geometric structure such that minimum-dissipation protocols follow the geodesics of a generalized cubic Finsler metric. Thus, near equilibrium, the supra-Stokes tensor determines the leading-order contribution to the bias of bidirectional free-energy estimators.

Binding Thermodynamics and Interaction Patterns of Inhibitor-Major Urinary Protein-I Binding from Extensive Free-Energy Calculations: Benchmarking AMBER Force Fields

Mouse major urinary protein (MUP) plays a key role in the pheromone communication system. The one-end-closed β-barrel of MUP-I forms a small, deep, and hydrophobic central cavity, which could accommodate structurally diverse ligands. Previous computational studies employed old protein force fields and short simulation times to determine the binding thermodynamics or investigated only a small number of structurally similar ligands, which resulted in sampled regions far from the experimental structure, nonconverged sampling outcomes, and limited understanding of the possible interaction patterns that the cavity could produce. In this work, extensive end-point and alchemical free-energy calculations with advanced protein force fields were performed to determine the binding thermodynamics of a series of MUP-inhibitor systems and investigate the inter- and intramolecular interaction patterns. Three series of inhibitors with a total of 14 ligands were simulated. We independently simulated the MUP-inhibitor complexes under two advanced AMBER force fields. Our benchmark test showed that the advanced AMBER force fields including AMBER19SB and AMBER14SB provided better descriptions of the system, and the backbone root-mean-square deviation (RMSD) was significantly lowered compared with previous computational studies with old protein force fields. Surprisingly, although the latest AMBER force field AMBER19SB provided better descriptions of various observables, it neither improved the binding thermodynamics nor lowered the backbone RMSD compared with the previously proposed and widely used AMBER14SB. The older but widely used AMBER14SB actually achieved better performance in the prediction of binding affinities from the alchemical and end-point free-energy calculations. We further analyzed the protein-ligand interaction networks to identify important residues stabilizing the bound structure. Six residues including PHE38, LEU40, PHE90, ALA103, LEU105, and TYR120 were found to contribute the most significant part of protein-ligand interactions, and 10 residues were found to provide favorable interactions stabilizing the bound state. The two AMBER force fields gave extremely similar interaction networks, and the secondary structures also showed similar behavior. Thus, the intra- and intermolecular interaction networks described with the two AMBER force fields are similar. Therefore, AMBER14SB could still be the default option in free-energy calculations to achieve highly accurate binding thermodynamics and interaction patterns.

Variationally derived intermediates for correlated free-energy estimates between intermediate states

Free-energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the stepwise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean-squared error that account for these correlations and assess its accuracy.

Protein Denaturation, Zero Entropy Temperature, and the Structure of Water around Hydrophobic and Amphiphilic Solutes

The hydrophobic effect plays a key role in many chemical and biological processes, including protein folding. Nonetheless, a comprehensive picture of the effect of temperature on hydrophobic hydration and protein denaturation remains elusive. Here, we study the effect of temperature on the hydration of model hydrophobic and amphiphilic solutes, through molecular dynamics, aiming at getting insight on the singular behavior of water, concerning the zero-entropy temperature, T_S, and entropy convergence, T_S^*, also observed for some proteins, upon denaturation. We show that, similar to hydrocarbons, polar amphiphilic solutes exhibit a T_S, although strongly dependent on solute-water interactions, opposite to hydrocarbons. Further, the temperature dependence of the hydration entropy, normalized by the solvent accessible surface area, is shown to be nearly solute size independent for hydrophobic but not for amphiphilic solutes, for similar reasons. These results are further discussed in the light of information theory (IT) and the structure of water around hydrophobic groups. The latter shows that the tetrahedral enhancement of some water molecules around hydrophobic groups, associated with the reduction of water defects, leads to the strengthening of the weakest hydrogen bonds, relative to bulk water. In addition, a larger tetrahedrality is found in low density water populations, demonstrating that pure water has encoded structural information, similar to that associated with hydrophobic hydration. The reversal of the hydration entropy dependence on the solute size, above T_S^*, is also analyzed and shown to be associated with a greater loss of water molecules exhibiting enhanced orientational order, in the coordination sphere of large solutes. Finally, the source of the differences between Kauzmann's "hydrocarbon model" on protein denaturation and hydrophobic hydration is discussed, with relatively large amphiphilic hydrocarbons seemingly displaying a more similar behavior to some globular proteins than aliphatic hydrocarbons.

Molecular Dynamics with Very Large Time Steps for the Calculation of Solvation Free Energies

In multiple time scale molecular dynamics, the use of isokinetic constraints along with massive thermostatting has enabled the adoption of very large integration steps, well beyond the limits imposed by resonance artifacts in standard algorithms. In this work, we present two new contributions to this topic. First, we investigate the velocity distribution and the temperature-kinetic energy relationship associated with the isokinetic Nosé-Hoover family of methods, showing how they depend on the number of thermostats attached to each atomic degree of freedom. Second, we investigate the performance of these methods in the calculation of solvation free energies, the determination of which is often key for understanding the partition of a chemical species among distinct environments. We show how one can extract this property from canonical (constant-NVT) simulations and compare the result to experimental data obtained at a specific pressure. Finally, we demonstrate that large time steps can, in fact, be used to improve the efficiency of these calculations and that attaching multiple thermostats per degree of freedom is beneficial for effectively exploring the configurational space of a molecular system.

A cosolvent surfactant mechanism affects polymer collapse in miscible good solvents

The coil-globule transition of aqueous polymers is of profound significance in understanding the structure and function of responsive soft matter. In particular, the remarkable effect of amphiphilic cosolvents (e.g., alcohols) that leads to both swelling and collapse of stimuli-responsive polymers has been hotly debated in the literature, often with contradictory mechanisms proposed. Using molecular dynamics simulations, we herein demonstrate that alcohols reduce the free energy cost of creating a repulsive polymer-solvent interface via a surfactant-like mechanism which surprisingly drives polymer collapse at low alcohol concentrations. This hitherto neglected role of interfacial solvation thermodynamics is common to all coil-globule transitions, and rationalizes the experimentally observed effects of higher alcohols and polymer molecular weight on the coil-to-globule transition of thermoresponsive polymers. Polymer-(co)solvent attractive interactions reinforce or compensate this mechanism and it is this interplay which drives polymer swelling or collapse.

SAMPL7 TrimerTrip host-guest binding affinities from extensive alchemical and end-point free energy calculations

The prediction of host-guest binding affinities with computational modelling is still a challenging task. In the 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge, a new host named TrimerTrip was synthesized and the thermodynamic parameters of 16 structurally diverse guests binding to the host were characterized. In the TrimerTrip-guest challenge, only structures of the host and the guests are provided, which indicates that the predictions of both the binding poses and the binding affinities are under assessment. In this work, starting from the binding poses obtained from our previous enhanced sampling simulations in the configurational space, we perform extensive alchemical and end-point free energy calculations to calculate the host-guest binding affinities retrospectively. The alchemical predictions with two widely accepted charge schemes (i.e. AM1-BCC and RESP) are in good agreement with the experimental reference, while the end-point estimates perform poorly in reproducing the experimental binding affinities. Aside from the absolute value of the binding affinity, the rank of binding free energies is also crucial in drug design. Surprisingly, the end-point MM/PBSA method seems very powerful in reproducing the experimental rank of binding affinities. Although the length of our simulations is long and the intermediate spacing is dense, the convergence behavior is not very good, which may arise from the flexibility of the host molecule. Enhanced sampling techniques in the configurational space may be required to obtain fully converged sampling. Further, as the length of sampling in alchemical free energy calculations already achieves several hundred ns, performing direct simulations of the binding/unbinding event in the physical space could be more useful and insightful. More details about the binding pathway and mechanism could be obtained in this way. The nonequilibrium method could also be a nice choice if one insists to use the alchemical method, as the intermediate sampling is avoided to some extent.

Free-Energy Calculation of Ribonucleic Inosines and Its Application to Nearest-Neighbor Parameters

Can current simulations quantitatively predict the stability of ribonucleic acids (RNAs)? In this research, we apply a free-energy perturbation simulation of RNAs containing inosine, a modified ribonucleic base, to the derivation of RNA nearest-neighbor parameters. A parameter set derived solely from 30 simulations was used to predict the free-energy difference of the RNA duplex with a mean unbiased error of 0.70 kcal/mol, which is a level of accuracy comparable to that obtained with parameters derived from 25 experiments. We further show that the error can be lowered to 0.60 kcal/mol by combining the simulation-derived free-energy differences with experimentally measured differences. This protocol can be used as a versatile method for deriving nearest-neighbor parameters of RNAs with various modified bases.

Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

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.

SAMPL7 TrimerTrip host-guest binding poses and binding affinities from spherical-coordinates-biased simulations

Host-guest binding remains a major challenge in modern computational modelling. The newest 7th statistical assessment of the modeling of proteins and ligands (SAMPL) challenge contains a new series of host-guest systems. The TrimerTrip host binds to 16 structurally diverse guests. Previously, we have successfully employed the spherical coordinates as the collective variables coupled with the enhanced sampling technique metadynamics to enhance the sampling of the binding/unbinding event, search for possible binding poses and calculate the binding affinities in all three host-guest binding cases of the 6th SAMPL challenge. In this work, we report a retrospective study on the TrimerTrip host-guest systems by employing the same protocol to investigate the TrimerTrip host in the SAMPL7 challenge. As no binding pose is provided by the SAMPL7 host, our simulations initiate from randomly selected configurations and are proceeded long enough to obtain converged free energy estimates and search for possible binding poses. The calculated binding affinities are in good agreement with the experimental reference, and the obtained binding poses serve as a nice starting point for end-point or alchemical free energy calculations. Note that as the work is performed after the close of the SAMPL7 challenge, we do not participate in the challenge and the results are not formally submitted to the SAMPL7 challenge.

Atomistic and coarse-grained simulations of membrane proteins: A practical guide

Membrane proteins are amphipathic macromolecules whose exposed hydrophobic surfaces promote interactions with lipid membranes. Membrane proteins are remarkably diverse in terms of chemical composition and correspondingly, their biological functions and general biophysical behavior. Conventional experimental techniques provide an approach to study specific properties of membrane proteins e.g. their surface features, the nature and abundance of stabilizing intramolecular forces, preferred bilayer orientation, and the characteristics of their annular lipid shells. Molecular modeling software-and in particular, the suite of molecular dynamics algorithms-enables a more comprehensive exploration of dynamic membrane protein behavior. Molecular dynamics methods enable users to produce stepwise trajectories of proteins on arbitrary spatiotemporal scales that enable the easy identification of dynamic interactions that are beyond the scope of conventional analytical techniques. This article explains the molecular dynamics theoretical framework and popular step-by-step approaches for simulating membrane proteins in planar, and to a lesser extent, nonplanar lipid geometries. We detail popular procedures and computational tools that produce well-packed configurations of lipids and proteins and additionally, the efficient molecular dynamics simulation algorithms that reproduce their dynamic interactions.

SAMPL6 host-guest binding affinities and binding poses from spherical-coordinates-biased simulations

Host-guest binding is a challenging problem in computer simulation. The prediction of binding affinities between hosts and guests is an important part of the statistical assessment of the modeling of proteins and ligands (SAMPL) challenges. In this work, the volume-based variant of well-tempered metadynamics is employed to calculate the binding affinities of the host-guest systems in the SAMPL6 challenge. By biasing the spherical coordinates describing the relative position of the host and the guest, the initial-configuration-induced bias vanishes and all possible binding poses are explored. The agreement between the predictions and the experimental results and the observation of new binding poses indicate that the volume-based technique serves as a nice candidate for the calculation of binding free energies and the search of the binding poses.

On the transferability of ion parameters to the TIP4P/2005 water model using molecular dynamics simulations

Countless molecular dynamics studies have relied on available ion and water force field parameters to model aqueous electrolyte solutions. The TIP4P/2005 model has proven itself to be among the best rigid water force fields, whereas many of the most successful ion parameters were optimized in combination with SPC/E, TIP3P, or TIP4P/Ew water. Many researchers have combined these ions with TIP4P/2005, hoping to leverage the strengths of both parameter sets. To assess if this widely used approach is justified and to provide a guide in selecting ion parameters, we investigated the transferability of various commonly used monovalent and multivalent ion parameters to the TIP4P/2005 water model. The transferability is evaluated in terms of ion hydration free energy, hydration radius, coordination number, and self-diffusion coefficient at infinite dilution. For selected ion parameters, we also investigated density, ion pairing, chemical potential, and mean ionic activity coefficients at finite concentrations. We found that not all ions are equally transferable to TIP4P/2005 without compromising their performance. In particular, ions optimized for TIP3P water were found to be poorly transferable to TIP4P/2005, whereas ions optimized for TIP4P/Ew water provided nearly perfect transferability. The latter ions also showed good overall agreement with experimental values. The one exception is that no combination of ion parameters and water model considered here was found to accurately reproduce experimental self-diffusion coefficients. Additionally, we found that cations optimized for SPC/E and TIP3P water displayed consistent underpredictions in the hydration free energy, whereas anions consistently overpredicted the hydration free energy.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Applicability of a thermodynamic cycle approach for a force field parametrization targeting non-aqueous solvation free energies

Accurate solvation free energy ΔG_solv predictions require well parametrized force fields. In order to refit Lennard-Jones (LJ) parameters for improved ΔG_solv predictions for a variety of compound classes and chemical environments, a large number of ΔG_solv calculations is required. As the calculation of ΔG_solv is computational expensive, there is need for efficient but precise calculation methods. In this work, we focus on the computation of non-aqueous solvation free energies. We compare ΔG_solv results from highly precise reference simulations for transferring a solute from the vacuum into a condensed phase and results obtained from a thermodynamic cycle implementation. As test systems, we alter LJ parameters ε and σ of widely used GAFF atom types ca, cl, n1, oh and os in various solute/solvent combinations. We examine the degree of configurational space overlap and find an impact by hydrogen bonds and the solvent accessible surface area. We conclude that the application of a thermodynamic cycle for the parametrization of force fields targeting ΔG_solv is useful if the adaptation of LJ parameters is limited to atom types in the solute or if only ε is changed.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.