Compute Solvation Free Energies Research Articles

Effect of functionalization on the adsorption performance of carbon nanotube as a drug delivery system for imatinib: molecular simulation study

In this study, efficiency of functionalized carbon nanotube as a potential delivery system for imatinib anti-cancer drug was investigated. Accordingly, carboxyl and hydroxyl functionalized carbon nanotube were inspected as a notable candidate for the carriage of this drug in aqueous media. For this purpose, possible interactions of imatinib with pure and functionalized carbon nanotube were considered in aqueous media. The compounds were optimized in gas phase using density functional calculations. Solvation free energies and association free energies of the optimized structures were then studied by Monte Carlo simulation and perturbation method in water environment. Outcomes of quantum mechanical calculations presented that pure and functionalized carbon nanotubes can act as imatinib drug adsorbents in gas phase. However, results of association free energy calculations in aqueous solution indicated that only carboxyl and hydroxyl functionalized carbon nanotubes could interact with imatinib. Monte Carlo simulation results revealed that electrostatic interactions play a vital role in the intermolecular interaction energies after binding of drug and nanotube in aqueous solution. Computed solvation free energies in water showed that the interactions with functionalized carbon nanotubes significantly enhance the solubility of imatinib, which could improve its in vivo bioavailability.

Acceleration of Solvation Free Energy Calculation via Thermodynamic Integration Coupled with Gaussian Process Regression and Improved Gelman-Rubin Convergence Diagnostics.

The determination of the solvation free energy of ions and molecules holds profound importance across a spectrum of applications spanning chemistry, biology, energy storage, and the environment. Molecular dynamics simulations are powerful tools for computing this critical parameter. Nevertheless, the accurate and efficient calculation of the solvation free energy becomes a formidable endeavor when dealing with complex systems characterized by potent Coulombic interactions and sluggish ion dynamics and, consequently, slow transition across various metastable states. In the present study, we expose limitations stemming from the conventional calculation of the statistical inefficiency g in the thermodynamic integration method, a factor that can hinder the determination of convergence of the solvation free energy and its associated uncertainty. Instead, we propose a robust scheme based on Gelman-Rubin convergence diagnostics. We leverage this improved estimation of uncertainties to introduce an innovative accelerated thermodynamic integration method based on the Gaussian Process regression. This methodology is applied to the calculation of the solvation free energy of trivalent rare-earth elements immersed in ionic liquids, a scenario in which the aforementioned challenges render standard approaches ineffective. The proposed method proves to be effective in computing solvation free energy in situations where traditional thermodynamic integration methods fall short.

Interaction of sulfasalazine with outer surface of boron-nitride nanotube as a drug carrier in aqueous solution: insights from quantum mechanics and Monte Carlo simulation

The improvement of the solubility of sulfasalazine in physiological media was the major aim of this study. Accordingly, BNNT inspected as a notable candidate for the carriage of this drug in aqueous media. For this purpose, four possible interactions of two tautomer of sulfasalazine with (9,0) boron-nitride nanotube were considered in aqueous media. The compounds were optimized in gas phase using density functional calculations. Solvation free energies and association free energies of the optimized structures were then studied by Monte Carlo simulation and perturbation method in water environment. Outcomes of quantum mechanical calculations presented that interaction of keto form of sulfasalazine produce the most stable complexes with boron-nitride nanotube in gas phase. Simulation results revealed that electrostatic interactions play a vital role in the intermolecular interaction energies after binding of drug and nanotube in aqueous solution. Results of association free energy calculations indicated that complexes of both two sulfasalazine tautomers (keto and enol) and nanotube were stable in solution. Computed solvation free energies in water showed that the interaction with boron-nitride nanotube significantly improved the solubility of sulfasalazine, which could improve its in vivo bioavailability.

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.

Extended Conductor-like Polarizable Continuum Solvation Model (CPCM-X) for Semiempirical Methods.

We have developed a new method to accurately account for solvation effects in semiempirical quantum mechanics based on a polarizable continuum model (PCM). The extended conductor-like polarizable continuum model (CPCM-X) incorporates a computationally efficient domain decomposition conductor-like screening model (ddCOSMO) for extended tight binding (xTB) methods and uses a post-processing approach based on established solvation models, like the conductor-like screening model for real solvents (COSMO-RS) and the universal solvent model based on solute electron density (SMD). According to various benchmarks, the approach performs well across a broad range of systems and applications, including hydration free energies, non-aqueous solvation free energies, and large supramolecular association reactions of neutral and charged species. Our method for computing solvation free energies is much more accurate than the current methods in the xtb program package. It improves the accuracy of solvation free energies by up to 40% for larger supramolecular association reactions to match even the accuracy of higher-level DFT-based solvation models like COSMO-RS and SMD while being computationally more than 2 orders of magnitude faster. The proposed method and the underlying ddCOSMO model are readily available for a wide variety of solvents and are accessible in xtb for use in various computational applications.

Accurate modelling of pyrrolidinium ionic liquids with charge and vdW scaling

Molecular simulation as a complementing tool to experimental measurements has grown to be an instrument with predictive power for ionic liquids (ILs) derivatives. The combination of molecule-specific atomic charges generated with ab initio calculations and bonded and vdW parameters extracted from pre-fitted transferable force fields serves as the common practice in this field. Charge scaling is often applied to account for charge transfer and polarization effects and the scaling factor 0.8 has been concluded as a near-optimal solution in many scientific reports based on detailed analyses of various structural and thermodynamic observables. However, for ILs from the pyrrolidinium family investigated in the current work, we show that the charge scaling treatment cannot really minimize the experiment-simulation deviations to an acceptable level, which calls for further parameter adjustment. Following the modelling protocol summarized in our previous works, we tune the vdW radius of ILs-forming ions with a 298 K density scan and secure a parameter set that satisfactorily reproduces not only the room-temperature properties but also the mass densities in a large temperature range from 288 K to 348 K. The slopes of the vdW-scaling profiles are between −1.9 g/cm3 and −1.6 g/cm3, which are similar to quinuclidinium ILs investigated in our previous work. This phenomenon suggests the similarity of responding behaviors of the two ILs family during vdW scaling, and this range of response strengths could possibly be representative for ILs vdW scaling. Aside from bulk solvents, we further consider the interaction of ILs with a series of external organic agents. Following the previously accumulated experience, a slightly modified vdW scaling factor is picked as an option balancing different interactions within the heterogeneous solution. Nonequilibrium alchemical free energy calculations are conducted to compute solvation free energies in ILs and also the distribution (partition) behaviors of solutes between aqueous and ILs phases. The computed physiochemical properties involving pyrrolidinium ILs agree well with the experimental reference. Another feature of the selected pyrrolidinium ILs is the systematic variation of the length of the alkyl substituting chain, which enables a direct investigation of the chain-length dependence of the prediction accuracies for both bulk density and solvation/partition thermodynamics. Interestingly, with the chain-length variation, the error of bulk density exhibits a monotonic response, while a fluctuating (non-monotonic) behavior is observed for prediction errors of solvation and partition thermodynamics, which is related to the diverse features of solute-solvent interactions. Therefore, the observed behaviors of the properties of bulk solvents cannot be generalized to the solvation/partition behaviors of the same solvent, and accurate reproductions of bulk behaviors do not guarantee accurate calculations of solvation and partition thermodynamics.

Quantum Simulation of Molecules in Solution.

Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in the gas phase. Molecules in liquid solution are, however, most relevant for chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. In this work, we extend the variational quantum eigensolver to simulate solvated systems using the polarizable continuum model. To account for the state dependent solute-solvent interaction we generalize the variational quantum eigensolver algorithm to treat non-linear molecular Hamiltonians. We show that including solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to 12 spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated noisy quantum hardware (IBM Q, Mumbai) yield computed solvation free energies in fair agreement with the classical calculations.

Liquid-Phase Effects on Adsorption Processes in Heterogeneous Catalysis.

Aqueous solvation free energies of adsorption have recently been measured for phenol adsorption on Pt(111). Endergonic solvent effects of ∼1 eV suggest solvents dramatically influence a metal catalyst’s activity with significant implications for the catalyst design. However, measurements are indirect and involve adsorption isotherm models, which potentially reduces the reliability of the extracted energy values. Computational, implicit solvation models predict exergonic solvation effects for phenol adsorption, failing to agree with measurements even qualitatively. In this study, an explicit, hybrid quantum mechanical/molecular mechanical approach for computing solvation free energies of adsorption is developed, solvation free energies of phenol adsorption are computed, and experimental data for solvation free energies of phenol adsorption are reanalyzed using multiple adsorption isotherm models. Explicit solvation calculations predict an endergonic solvation free energy for phenol adsorption that agrees well with measurements to within the experimental and force field uncertainties. Computed adsorption free energies of solvation of carbon monoxide, ethylene glycol, benzene, and phenol over the (111) facet of Pt and Cu suggest that liquid water destabilizes all adsorbed species, with the largest impact on the largest adsorbates.

O-Methylation in Carbohydrates: An NMR and MD Simulation Study with Application to Methylcellulose.

Methylated carbohydrates are important from both biological and technical perspectives. Specifically, methylcellulose is an interesting cellulose derivative that has applications in foods, materials, cosmetics, and many other fields. While the molecular dynamics simulation technique has the potential for both advancing the fundamental understanding of this polymer and aiding in the development of specific applications, a general drawback is the lack of experimentally validated interaction potentials for the methylated moieties. In the present study, simulations using the GROMOS 56 carbohydrate force field are compared to NMR spin–spin coupling constants related to the conformation of the exocyclic torsion angle ω in d-glucopyranose and derivatives containing a 6-O-methyl substituent and a 13C-isotopologue thereof. A 3JCC Karplus-type relationship is proposed for the C5–C6–O6–CMe torsion angle. Moreover, solvation free energies are compared to experimental data for small model compounds. Alkylation in the form of 6-O-methylation affects exocyclic torsion only marginally. Computed solvation free energies between nonmethylated and methylated molecules were internally consistent, which validates the application of these interaction potentials for more specialized purposes.

Solvation Thermodynamics from the Perspective of Endpoints DFT.

Solvation thermodynamics is concerned with the evaluation and physical interpretation of solvation free energies. Endpoints DFT provides a framework for computing solvation free energies by combining molecular simulations with a version of the classical density-functional theory of solutions which focuses on ω, the indirect (solvent-mediated) part of the solute-solvent potential of mean force (indirect PMF). The simulations are performed at the endpoints of a hypothetical charging process which transforms the solvent density from the pure liquid state to that of the solution state. The endpoints DFT expression for solvation free energy can be shown to be equivalent to the standard expression for which the key quantity is the direct correlation function, but it has the advantage that the indirect term ω is more focused on the change in solvent-solvent correlations with respect to the pure liquid as the solute is inserted into the solution. In this Perspective, we review recent developments of endpoints DFT, highlighting a series of papers we have written together beginning in 2017. We emphasize the importance of dimensionality reduction as the key to the evaluation of endpoints DFT expressions and present a recently developed, spatially resolved version of the theory. The role of interfacial water at certain positions which stabilize or destabilize a solute in solution can be analyzed with the spatially resolved version, and it is of considerable interest to investigate how changes in solvation affect protein-ligand binding and conformational landscapes from an endpoints DFT perspective. Endpoints DFT can also be employed in materials science; an example involving the rational design strategy for polymer membrane separation is described. The endpoints DFT method is a scheme to evaluate the solvation free energy by introducing approximations to integrate the classical density functional over a charging parameter. We have further proposed a new functional which captures the correct dependence of the indirect PMF ω at both endpoints of the charging process, and we review how it might be employed in future work.

Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K

The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations.

Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points.

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc.

Adapting the semi-explicit assembly solvation model for estimating water-cyclohexane partitioning with the SAMPL5 molecules.

We describe here some tests we made in the SAMPL5 communal event of 'Semi-Explicit Assembly' (SEA), a recent method for computing solvation free energies. We combined the prospective tests of SAMPL5 with followup retrospective calculations, to improve two technical aspects of the field variant of SEA. First, SEA uses an approximate analytical surface around the solute on which a water potential is computed. We have improved and simplified the mathematical model of that surface. Second, some of the solutes in SAMPL5 were large enough to need a way to treat solvating waters interacting with 'buried atoms', i.e. interior atoms of the solute. We improved SEA with a buried-atom correction. We also compare SEA to Thermodynamic Integration molecular dynamics simulations, so that we can sort out force field errors.

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here, we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g. replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g. hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyse two different approaches: the QM/MM–MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analysed here, both approaches seem productive although care needs to be exercised when analysing the perturbative corrections.

Understanding the Solubility of Acetaminophen in 1-n-Alkyl-3-methylimidazolium-Based Ionic Liquids Using Molecular Simulation.

During the manufacturing of pharmaceutical compounds, solvent mixtures are commonly used, where the addition of a cosolvent allows for the tuning of the intermolecular interactions present in the system. Here we demonstrate how a similar effect can be accomplished using a room temperature ionic liquid. The pharmaceutical compound acetaminophen is studied in 21 common ionic liquids composed of a 1-n-alkyl-3-methylimidazolium cation with 1 of 7 anions. Using the acetate anion, we predict a large enhancement in solubility of acetaminophen relative to water. We show how this is caused by a synergistic effect of favorable interactions between the ionic liquid and the phenyl, hydroxyl and amide groups of acetaminophen, demonstrating how the ionic liquid cation and anion may be chosen to preferentially solvate different functional groups of complex pharmaceutical compounds. Additionally, while the use of charge scaling in ionic liquid force fields has previously been found to have a minute effect on ionic liquid structural properties, we find it appreciably affects the computed solvation free energy of acetaminophen, which in turn affects the predicted solubility.

Incorporating excluded solvent volume and physical dipoles for computing solvation free energy.

The solvation free energy described using the Born equation depends on the solute charge, solute radius, and solvent dielectric constant. However, the dielectric polarization derived from Gauss's law used in the Born equation differs from that obtained from molecular dynamics simulations. Therefore, the adjustment of Born radii is insufficient for fitting the solvation free energy to various solute conformations. In order to mimic the dielectric polarization surrounding a solute in molecular dynamics simulations, the water molecule in the first coordination shell is modeled as a physical dipole in a van der Waals sphere, and the intermediate water is treated as a bulk solvent. The electric dipole of the first-shell water is modeled as positive and negative surface charge layers with fixed charge magnitudes, but with variable separation distance as derived from the distributions of hydrogen and oxygen atoms of water dictated by their orientational distribution functions. An equation that describes the solvation free energy of ions using this solvent scheme with a TIP3P water model is derived, and the values of the solvation free energies of ions estimated from this derived equation are found to be similar to those obtained from the experimental data.

Solvation of alanine and histidine functionalized carbon nanotubes in aqueous media: A Monte Carlo simulation study

In this research, the effect of adsorption of two amino acids on the solvation of carbon nanotubes is investigated. The complexes of β-Alanine and Histidine with armchair single wall carbon nanotube are studied by density functional theory. Then, the outcomes of Monte Carlo simulations of these nanotubes immersed in water to look at the effects of nanotube type on the solvation in water are reported. It is found that the binding energy of the interaction of β-Alanine with nanotube is larger than Histidine. The results of computer simulation in aqueous solution indicate that amino acid functionalization increases the intermolecular interactions of carbon nanotube and water. Computed solvation free energies are in this order: CNTAlanine>CNTHistidine>pure CNT.

ChemInform Abstract: Using Dispersion‐Corrected Density Functional Theory to Understand Supramolecular Binding Thermodynamics

AbstractReview: 121 refs.

ILOGP: a simple, robust, and efficient description of n-octanol/water partition coefficient for drug design using the GB/SA approach.

The n-octanol/water partition coefficient (logPo/w) is a key physicochemical parameter for drug discovery, design, and development. Here, we present a physics-based approach that shows a strong linear correlation between the computed solvation free energy in implicit solvents and the experimental log Po/w on a cleansed data set of more than 17,500 molecules. After internal validation by five-fold cross-validation and data randomization, the predictive power of the most interesting multiple linear model, based on two GB/SA parameters solely, was tested on two different external sets of molecules. On the Martel druglike test set, the predictive power of the best model (N = 706, r = 0.64, MAE = 1.18, and RMSE = 1.40) is similar to six well-established empirical methods. On the 17-drug test set, our model outperformed all compared empirical methodologies (N = 17, r = 0.94, MAE = 0.38, and RMSE = 0.52). The physical basis of our original GB/SA approach together with its predictive capacity, computational efficiency (1 to 2 s per molecule), and tridimensional molecular graphics capability lay the foundations for a promising predictor, the implicit log P method (iLOGP), to complement the portfolio of drug design tools developed and provided by the SIB Swiss Institute of Bioinformatics.

Incorporation of the TIP4P water model into a continuum solvent for computing solvation free energy

The continuum solvent model is one of the commonly used strategies to compute solvation free energy especially for large-scale conformational transitions such as protein folding or to calculate the binding affinity of protein–protein/ligand interactions. However, the dielectric polarization for computing solvation free energy from the continuum solvent is different than that obtained from molecular dynamic simulations. To mimic the dielectric polarization surrounding a solute in molecular dynamic simulations, the first-shell water molecules was modeled using a charge distribution of TIP4P in a hard sphere; the time-averaged charge distribution from the first-shell water molecules were estimated based on the coordination number of the solute, and the orientation distribution of the first-shell waters and the intermediate water molecules were treated as that of a bulk solvent. Based on this strategy, an equation describing the solvation free energy of ions was derived.