Relative Solvation Free Energies Research Articles

Calculations of Absolute Solvation Free Energies with Transformato─Application to the FreeSolv Database Using the CGenFF Force Field.

We recently introduced transformato, an open-source Python package for the automated setup of large-scale calculations of relative solvation and binding free energy differences. Here, we extend the capabilities of transformato to the calculation of absolute solvation free energy differences. After careful validation against the literature results and reference calculations with the PERT module of CHARMM, we used transformato to compute absolute solvation free energies for most molecules in the FreeSolv database (621 out of 642). The force field parameters were obtained with the program cgenff (v2.5.1), which derives missing parameters from the CHARMM general force field (CGenFF v4.6). A long-range correction for the Lennard-Jones interactions was added to all computed solvation free energies. The mean absolute error compared to the experimental data is 1.12 kcal/mol. Our results allow a detailed comparison between the AMBER and CHARMM general force fields and provide a more in-depth understanding of the capabilities and limitations of the CGenFF small molecule parameters.

Solv: An Alternative Continuum Model Implementation Based on Fixed Atomic Charges, Scaled Particle Theory, and the Atom-Atom Potential Method.

An alternative continuum model implementation is reported. The electrostatic contribution to the solvation Gibbs free energy utilizes the noniterative conductor-like screening model of Vyboishchikov and Voityuk (DOI: 10.1002/jcc.26531) based on the fixed partial atomic charges. The nonelectrostatic solute-solvent dispersion-repulsion energy is calculated through the Caillet-Claverie atom-atom potential method employing the grid-based approach. The nonelectrostatic cavitation energy is computed within the scaled particle theory (SPT) formalism with the solute hard-sphere radius obtained via the Pierotti-Claverie (PC) scheme, from the solute molecular surface (SPT-S) or volume (SPT-V). The solvent hard-sphere radius is derived through the fitting to the experimental total solvation free energies of 2530 neutral species in 92 solvents. Application of the model to reproduce both the absolute and relative (reaction net) solvation free energies indicates that the SPT-V approach based on the CM5 charges is the best performer. The method is suggested for the solvation free energy calculation in the nonaqueous solvents.

AMBER Drug Discovery Boost Tools: Automated Workflow for Production Free-Energy Simulation Setup and Analysis (ProFESSA).

We report an automated workflow for production free-energy simulation setup and analysis (ProFESSA) using the GPU-accelerated AMBER free-energy engine with enhanced sampling features and analysis tools, part of the AMBER Drug Discovery Boost package that has been integrated into the AMBER22 release. The workflow establishes a flexible, end-to-end pipeline for performing alchemical free-energy simulations that brings to bear technologies, including new enhanced sampling features and analysis tools, to practical drug discovery problems. ProFESSA provides the user with top-level control of large sets of free-energy calculations and offers access to the following key functionalities: (1) automated setup of file infrastructure; (2) enhanced conformational and alchemical sampling with the ACES method; and (3) network-wide free-energy analysis with the optional imposition of cycle closure and experimental constraints. The workflow is applied to perform absolute and relative solvation free-energy and relative ligand-protein binding free-energy calculations using different atom-mapping procedures. Results demonstrate that the workflow is internally consistent and highly robust. Further, the application of a new network-wide Lagrange multiplier constraint analysis that imposes key experimental constraints substantially improves binding free-energy predictions.

Probing Solvation Thermodynamics of Lithium Battery Electrolytes through Potentiometric Methods

The electrolyte is a principal component of a lithium battery that impacts almost every facet of the battery’s performance. Solvation of lithium ions in electrolyte solution is key to understanding the electrolyte, but our understanding of solvation lags behind its significance. Particularly, estimating solvation free energy has been largely limited to computational simulations. Despite their versatility, simulations can be computationally expensive, and experimental methods to complement simulations are desired.We have recently introduced a potentiometric technique to probe the relative solvation free energy of lithium ions in battery electrolytes. We devised an electrochemical cell composed of two half-cells, with symmetric electrodes but asymmetric electrolytes. Whereas the open circuit potential of a conventional lithium-ion battery measures the free energy differences of lithium ions in the two electrodes, our experimental setup measures the energy differences of the lithium ions in two different electrolytes. By measuring the cell potential with a reference electrolyte, we can quantitatively characterize lithium ion solvation energy of an electrolyte of interest. The effects of concentration, anion and solvent on solvation energy are explored and verified with simulations. Particularly, we establish a correlation between cell potential (Ecell) and cyclability of high-performance electrolytes for lithium metal anodes. We find that solvents with more negative cell potentials and positive solvation energies—those weakly binding to Li+—lead to improved cycling stability. Weaker solvents are conjectured to have more anion-rich solvation structures that lead to anion-derived solid-electrolyte interphases, a hypothesis supported by cryogenic electron microscopy. It reveals that weaker solvation is correlated to an inorganic anion-derived solid-electrolyte interphase that stabilizes cycling.

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

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

Chemical potential and surface free energy of a hard spherical particle in hard-sphere fluid over the full range of particle diameters

The excess chemical potential μex(σ, η) of a test hard spherical particle of diameter σ in a fluid of hard spheres of diameter σ0 and packing fraction η can be computed with high precision using Widom’s particle insertion method [B. Widom, J. Chem. Phys. 39, 2808 (1963)] for σ between 0 and just larger than 1 and/or small η. Heyes and Santos [J. Chem. Phys. 145, 214504 (2016)] analytically showed that the only polynomial representation of μex consistent with the limits of σ at zero and infinity has a cubic form. On the other hand, through the solvation free energy relationship between μex and the surface free energy γ of hard-sphere fluids at a hard spherical wall, we can obtain precise measurements of μex for large σ, extending up to infinity (flat wall) [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 149, 174706 (2018)]. Within this approach, the cubic polynomial representation is consistent with the assumptions of morphometric thermodynamics. In this work, we present the measurements of μex that combine the two methods to obtain high-precision results for the full range of σ values from zero to infinity, which show statistically significant deviations from the cubic polynomial form. We propose an empirical functional form for the μex dependence on σ and η, which better fits the measurement data while remaining consistent with the analytical limiting behavior at zero and infinite σ.

Alchemical free energy simulations without speed limits. A generic framework to calculate free energy differences independent of the underlying molecular dynamics program.

We describe the theory of the so‐called common‐core/serial‐atom‐insertion (CC/SAI) approach to compute alchemical free energy differences and its practical implementation in a Python package called Transformato. CC/SAI is not tied to a specific biomolecular simulation program and does not rely on special purpose code for alchemical transformations. To calculate the alchemical free energy difference between several small molecules, the physical end‐states are mutated into a suitable common core. Since this only requires turning off interactions, the setup of intermediate states is straightforward to automate. Transformato currently supports CHARMM and OpenMM as back ends to carry out the necessary molecular dynamics simulations, as well as post‐processing calculations. We validate the method by computing a series of relative solvation free energy differences.

Dummy Atoms in Alchemical Free Energy Calculations.

In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same. This necessitates the introduction of dummy atoms. These placeholders interact with the physical system only by bonded energy terms. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to kBT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.

Computing Relative Binding Affinity of Ligands to Receptor: An Effective Hybrid Single-Dual-Topology Free-Energy Perturbation Approach in NAMD.

An effective hybrid single-dual-topology protocol is designed for the calculation of relative binding affinities of small ligands to a receptor. The protocol was developed as an extension of the NAMD molecular dynamics program, which exclusively supports a dual-topology framework for relative alchemical free-energy perturbation (FEP) calculations. In this protocol, the alchemical end states are represented as two separate molecules sharing a common substructure identified through maximum structural mapping. Within the substructure, an atom-to-atom correspondence is established, and each pair of corresponding atoms is holonomically constrained to share identical coordinates at all time throughout the simulation. The forces are projected and combined at each step for propagation. Following this formulation, a set of illustrative calculations of reliable experiment/simulation data, including relative solvation free energies of small molecules and relative binding affinities of drug compounds to proteins, are presented. To enhance sampling of the dual-topology region, the FEP calculations were carried out within a replica-exchange MD scheme supported by the multiple-copy algorithm module of NAMD, with periodically attempted swapping of the thermodynamic coupling parameter λ between neighboring states. The results are consistent with experiments and benchmarks reported in the literature, lending support to the validity of the current protocol. In summary, this hybrid single-dual-topology approach combines the conceptual simplicity of the dual-topology paradigm with the advantageous sampling efficiency of the single-topology approach, making it an ideal strategy for high-throughput in silico drug design.

Solvent, structural, quantum chemical study and antioxidative activity of symmetrical 1-methyl-2,6-bis[2-(substituted phenyl)ethenyl]pyridinium iodides

15 symmetric 1-methyl-2,6-bis[2-(substituted phenyl)ethenyl]pyridinium iodides were synthesized in this work. Their structures were characterized using IR, 1H and 13C NMR, and UV–Vis spectroscopy. DFT calculations indicated that s-trans/s-trans conformation prevail in all compounds. The effects of specific and non-specific solvent–solute interactions on the UV–Vis absorption maxima shifts were evaluated using linear solvation-free energy relationships (LSER), i.e., Kamlet–Taft and Catalan models. A linear free energy relationship (LFER) in the form of single substituent parameter equations (SSP) was used to postulate quantitative structure–property relations of substituent effect on NMR data. TD-DFT results showed dependence of electronic transition on the substituent effects. The push–pull character of these compounds was analyzed by differences in 13C chemical shift of the ethylenic double bond in 2- and 6-positions of cross-conjugated with pyridinum central ring. Also, the quotient of the occupations for the bonding π and anti-bonding π* orbitals of this bond was considered. Good correlations of the selected parameter between double bond lengths with π*/π and 13C chemical shift differences of the bridging group proved them to be adequate descriptor of push–pull character. Synthesized compounds were screened for the antioxidant activity, using 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) radical methods, and results demonstrated moderate antioxidant potential.

(Invited) Quantification of DNA/SWCNT Solvation Differences By Aqueous Two Phase Separation

Single wall carbon nanotubes (SWCNTs) coated with single-stranded DNA can be effectively separated into various chiralities using an aqueous two phase (ATP) system. Partitioning is driven by small differences in the dissolution characteristics of the hybrid between the two phases. Thus, in addition to being a separation technique, the ATP system potentially also offers a way to quantify and rank the dissolution properties of the solute (here the DNA/SWCNT hybrids), such as the solvation free energy or solubility. In this study, we propose two different approaches to analyze quantitatively the ATP partitioning of DNA/SWCNT hybrids. First, we present a model that extracts relative solvation free energy of various DNA/SWCNT hybrids by using an expansion relative to a standard state. Second, we extract a solubility parameter by analyzing the partitioning of hybrids in the ATP system. The two approaches are found to be consistent, providing some confidence in each as a method of quantifying differences in solubility of various DNA/SWCNT hybrids.

Quantification of DNA/SWCNT Solvation Differences by Aqueous Two-Phase Separation.

Single-walled carbon nanotubes (SWCNTs) coated with single-stranded DNA can be effectively separated into various chiralities using an aqueous two-phase (ATP) system. Partitioning is driven by small differences in the dissolution characteristics of the hybrid between the two phases. Thus, in addition to being a separation technique, the ATP system potentially also offers a way to quantify and rank the dissolution properties of the solute (here the DNA/SWCNT hybrids), such as the solvation free energy and solubility. In this study, we propose two different approaches to quantitatively analyze the ATP partitioning of DNA/SWCNT hybrids. First, we present a model that extracts the relative solvation free energy of various DNA/SWCNT hybrids by using an expansion relative to a standard state. Second, we extract a solubility parameter by analyzing the partitioning of hybrids in the ATP system. The two approaches are found to be consistent, providing some confidence in each as a method of quantifying differences in the solubility of various DNA/SWCNT hybrids.

Gibbs Sampler-Based λ-Dynamics and Rao–Blackwell Estimator for Alchemical Free Energy Calculation

λ-dynamics is a generalized ensemble method for alchemical free energy calculations. In traditional λ-dynamics, the alchemical switch variable λ is treated as a continuous variable ranging from 0 to 1 and an empirical estimator is utilized to approximate the free energy. In the present article, we describe an alternative formulation of λ-dynamics that utilizes the Gibbs sampler framework, which we call Gibbs sampler-based λ-dynamics (GSLD). GSLD, like traditional λ-dynamics, can be readily extended to calculate free energy differences between multiple ligands in one simulation. We also introduce a new free energy estimator, the Rao-Blackwell estimator (RBE), for use in conjunction with GSLD. Compared with the current empirical estimator, the advantage of RBE is that RBE is an unbiased estimator and its variance is usually smaller than the current empirical estimator. We also show that the multistate Bennett acceptance ratio equation or the unbinned weighted histogram analysis method equation can be derived using the RBE. We illustrate the use and performance of this new free energy computational framework by application to a simple harmonic system as well as relevant calculations of small molecule relative free energies of solvation and binding to a protein receptor. Our findings demonstrate consistent and improved performance compared with conventional alchemical free energy methods.

Quantitative Analysis of Aqueous Two Phase Separation of DNA-SWCNT Hybrids

Carbon nanotubes have attracted considerable interest due to their outstanding physical, electronical and optical properties. Since those properties depends on the chirality, sorting single walled carbon nanotubes (SWCNT) by chirality is essential. Hybrids of DNA and SWCNTs have been used successfully to solve tje long-standing recalcitrant problem of structure-based sorting of complex mixtures of SWCNTs. Recently, it is shown that single stranded DNA coated SWCNTs could be separated effectively into various chiralities using an aqueous two phase system. SWCNT partition in the ATP system is determined by the SWCNT solvation energy difference between the two phases. In this way, we suggest that the ATP process is both a technique for separation and a method by which to evaluate and rank hydration or solvation free energy. In this study, we performed a systematic study of various DNA sequences on different species of SWCNT in ATP systems of two different polymer composition. We observe strong sequence-dependent of partitioning. We developed a model that can phenomenologically describe the experimental observation well and be used to extract a quantitative measure of relative solvation free energy of various DNA/SWCNT hybrids. Furthermore, to investigate a structural basis for experimental findings, we have employed molecular dynamics to examine a few of the ssDNA/CNT combinations.

Reparametrisation of united-atom amine solvation in the GROMOS force field

ABSTRACTNew parameters for ammonia, mono-, di- and trimethylated amine compatible with GROMOS force fields are presented. A directed search in parameter space by steepest descent minimisation led to an optimised charge set with good agreement to experimental data on absolute and relative free energies of solvation in water, chloroform and carbon tetrachloride. The final model is characterised in terms of structural and dynamic properties.

Replacement of Oxygen by Sulfur in Small Organic Molecules. 2. Theoretical Studies on the Tautomeric Equilibria of the 5-OH Substituted Oxazole, Thiazole, Isoxazole, and Isothiazole in the Isolated State and in Solution

Heterocycles are frequently appearing structure-building elements in drug candidates. The present paper investigates the consequences of the replacement of the oxygen atom by a sulfur atom in the isomeric rings of 5OH-oxazole and 5OH-isoxazole. Theoretical calculations at the B97D/aug-cc-pvqz level (with five additional “d” functions on the S atom) and considering the CCSD(T) level at the complete basis set limit followed the structural and concomitant free energy changes for the four title molecules in the isolated state, and in dichloromethane and water solvents. The selected species are subject to both conformational and tautomeric transformations. The polarizable continuum method (PCM) was applied for in-solution geometry optimization and estimation of the free energy components. In addition, explicit solvent Monte Carlo simulations were performed to calculate the relative solvation free energies of selected tautomers. This latter method allows for presenting solute atom - solvent atom radial distribution functions and the estimation of the number solute-solvent hydrogen bonds. The tautomeric preferences for the oxygen and sulfur containing species, which are sometimes different, were discussed and the calculated results were compared with experimental measurements for the structure composition available for 5OH-isoxazole and its methyl derivatives of in water. Potential of mean force curves were calculated for the 5-one tautomers of 5OH-isothiazole in dichloromethane and the possible tautomeric pathways for this solute in a non-protic solvent was discussed. Keywords: Conformational/tautomeric equilibria, Monte Carlo, PCM, potential of mean force, solution structure, tautomerization mechanism.

Replacement of Oxygen by Sulfur in Small Organic Molecules. 3. Theoretical Studies on the Tautomeric Equilibria of the 2OH and 4OH-Substituted Oxazole and Thiazole and the 3OH and 4OH-Substituted Isoxazole and Isothiazole in the Isolated State and in Solution.

This follow-up paper completes the author’s investigations to explore the in-solution structural preferences and relative free energies of all OH-substituted oxazole, thiazole, isoxazole, and isothiazole systems. The polarizable continuum dielectric solvent method calculations in the integral-equation formalism (IEF-PCM) were performed at the DFT/B97D/aug-cc-pv(q+(d))z level for the stable neutral tautomers with geometries optimized in dichloromethane and aqueous solution. With the exception of the predictions for the predominant tautomers of the 3OH isoxazole and isothiazole, the results of the IEF-PCM calculations for identifying the most stable tautomer of the given species in the two selected solvents agreed with those from experimental investigations. The calculations predict that the hydroxy proton, with the exception for the 4OH isoxazole and 4OH isothiazole, moves preferentially to the ring nitrogen or to a ring carbon atom in parallel with the development of a C=O group. The remaining, low-fraction OH tautomers will not be observable in the equilibrium compositions. Relative solvation free energies obtained by the free energy perturbation method implemented in Monte Carlo simulations are in moderate accord with the IEF-PCM results, but consideration of the ΔGsolv/MC values in calculating ΔGstot maintains the tautomeric preferences. It was revealed from the Monte Carlo solution structure analyses that the S atom is not a hydrogen-bond acceptor in any OH-substituted thiazole or isothiazole, and the OH-substituted isoxazole and oxazole ring oxygens may act as a weak hydrogen-bond acceptor at most. The molecules form 1.0−3.4 solute−water hydrogen bonds in generally unexplored numbers at some specific solute sites. Nonetheless, hydrogen-bond formation is favorable with the NH, C=O and OH groups.

A Python tool to set up relative free energy calculations in GROMACS.

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper (LOMAP;Liu et al. in J Comput Aided Mol Des 27(9):755-770, 2013), recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge (Mobley et al. in J Comput Aided Mol Des 28(4):135-150, 2014). Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations.

Quantum Chemical Studies on Detail Mechanism of Nitrosylation of NAMI-A-HSA Adduct.

Hydrolysis of NAMI-A in NAMI-A-HSA (HSA = human serum albumin) and nitrosylation of hydrolyzed NAMI-A-HSA adduct have been studied in detail using density functional theory method. It has been observed that the chloride exchange reaction with water in the NAMI-A-HSA adduct follows an interchange dissociative mechanism passing through an unstable heptacoordinated activated complex. The computed free energy of activation (ΔG) and rate constant (k) for the hydrolysis process in aqueous medium are observed to be 24.85 kcal mol(-1) and 3.81 × 10(-6) s(-1), respectively. Nitrosylation of hydrolyzed NAMI-A-HSA adduct with nitric oxide is found to be thermodynamically more favorable with the incorporation of solvent effect and provides a detailed understanding related to the antimetastatic activity of the NAMI-A drug. This investigation shows that nitric oxide coordinates linearly to NAMI-A-HSA adduct leading to the reduction of ruthenium(III) to more active ruthenium(II), with the reduction potential of -2.32 V. Negative relative solvation and relative binding free energies suggest that the hydrolysis and nitrosylation reactions are found to be thermodynamically favorable and faster. Our computed results provide a detailed thermodynamics and kinetics which may be highly beneficial for understanding antimetastatic activity as well as the nitric oxide scavenging ability of NAMI-A.

Theoretical in-Solution Conformational/Tautomeric Analyses for Chain Systems with Conjugated Double Bonds Involving Nitrogen(s).

Conformational/tautomeric transformations for X=CH–CH=Y structures (X = CH2, O, NH and Y = NH) have been studied in the gas phase, in dichloromethane and in aqueous solutions. The paper is a continuation of a former study where s-cis/s-trans conformational equilibria were predicted for analogues. The s-trans conformation is preferred for the present molecules in the gas phase on the basis of its lowest internal free energy as calculated at the B97D/aug-cc-pvqz and CCSD(T)CBS (coupled-cluster singles and doubles with non-iterative triples extrapolated to the complete basis set) levels. Transition state barriers are of 29–36 kJ/mol for rotations about the central C–C bonds. In solution, an s-trans form is still favored on the basis of its considerably lower internal free energy compared with the s-cis forms as calculated by IEF-PCM (integral-equation formalism of the polarizable continuum dielectric solvent model) at the theoretical levels indicated. A tetrahydrate model in the supermolecule/continuum approach helped explore the 2solute-solvent hydrogen bond pattern. The calculated transition state barrier for rotation about the C–C bond decreased to 27 kJ/mol for the tetrahydrate. Considering explicit solvent models, relative solvation free energies were calculated by means of the free energy perturbation method through Monte Carlo simulations. These calculated values differ remarkably from those by the PCM approach in aqueous solution, nonetheless the same prevalent conformation was predicted by the two methods. Aqueous solution structure-characteristics were determined by Monte Carlo. Equilibration of conformers/tautomers through water-assisted double proton-relay is discussed. This mechanism is not viable, however, in non-protic solvents where the calculated potential of mean force curve does not predict remarkable solute dimerization and subsequent favorable orientation.