New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

Correlation of the gibbs free energy of transfer of fluoride ion from water to other solvents with solvent actidity and polarity parameters

Linear free energy relationships between the free energy of transfer of fluoride ion from water to other solvents or solvent mixtures and each of several parameters describing the acidity of the solvent were found. The correlation is about of the same quality for the A parameter of Swain or the acceptor number, AN, and almost as good for the parameter of Taft. The correlation was somewhat poorer with the E _T (30) parameter.     

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.     

Ermod: Fast and versatile computation software for solvation free energy with approximate theory of solutions

ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed‐phase systems of the solution of interest and the reference solvent with test‐particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free‐energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano‐inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod . © 2014 Wiley Periodicals, Inc.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

The performance of ANI-ML potentials for ligand-n(H2O) interaction energies and estimation of hydration free energies from end-point MD simulations

Here, we investigate the performance of “Accurate NeurAl networK engINe for Molecular Energies” (ANI), trained on small organic compounds, on bulk systems including non-covalent interactions and applicability to estimate solvation (hydration) free energies using the interaction between the ligand and explicit solvent (water) from single-step MD simulations. The method is adopted from ANI using the Atomic Simulation Environment (ASE) and predicts the non-covalent interaction energies at the accuracy of wb97x/6-31G(d) level by a simple linear scaling for the conformations sampled by molecular dynamics (MD) simulations of ligand-n(H₂O) systems. For the first time, we test ANI potentials' abilities to reproduce solvation free energies using linear interaction energy (LIE) formulism by modifying the original LIE equation. Our results on ~250 different complexes show that the method can be accurate and have a correlation of R² = 0.88–0.89 (MAE <1.0 kcal/mol) to the experimental solvation free energies, outperforming current end-state methods. Moreover, it is competitive to other conventional free energy methods such as FEP and BAR with 15-20 × fold reduced computational cost.     

A novel approach to the calculation of the free energy due to molecular flexibility

The contribution of the molecular flexibility to the solvation excess free energy is expressed in terms of probabilities of reaching hard limits on intramolecular coordinates in a series of calculations successively relaxing those limits. Numerical tests on the harmonic oscillator are also presented and used to make suggestion about computational issues.     

The application of three approximate free energy calculations methods to structure based ligand design: Trypsin and its complex with inhibitors

Three approximate free energy calculation methods are examined and applied to an example ligand design problem. The first of the methods uses a single simulation to estimate the relative binding free energies for related ligands that are not simulated. The second method is similar, except that it uses only first derivatives of free energy with respect to atomic parameters (most often charge, van der Waals equilibrium distance, and van der Waals well depth) to calculate free energy differences. The last method PROFEC (Pictorial Representation of Free Energy Components), generates contour maps that show how binding free energy changes when additional particles are added near the ligand. These three methods are applied to a benzamidine/trypsin complex. They each reproduce the general trends in the binding free energies, indicating that they might be useful for suggesting how ligands could be modified to improve binding and, consequently, useful in structure-based drug design.     

Improvement of anti-inflammatory and anticancer activities of poly(lactic-co-glycolic acid)-sulfasalazine microparticle via density functional theory,molecular docking and ADMET analysis

In the present study, we assessed improvement of anti-inflammatory activity and drug delivery of sulfasalazine (SSZ) by the poly(lactic-co-glycolic acid), (PLGA), in H₂O and dichloromethane (DCM) environments via density functional theory (DFT), ADMET, and molecular docking. Our calculated results based on binding energy and thermodynamic parameter represents that the interaction between SSZ and PLGA in Complex A via double hydrogen bonds is stronger in comparison with Complex B. The analysis of Ultraviolet–visible (UV–VIS) spectra proved the interaction of SSZ with PLGA by time-dependent density functional theory (TDDFT). Infrared (IR) spectra demonstrated that the structure of PLGA was shifted in the presence of the SSZ. The interaction of SSZ with PLGA leads to an increase in dipole moment and higher solubility with more negative Gibbs free solvation energy (ΔG_solv) values and lowering of the energy gap (E_g). The obtained results by Molecular docking demonstrates that the interaction of SSZ via its carboxylate group with PLGA (complex A) had a strong interaction towards the binding pocket of the target and as a potential inhibitor of the COX-2, TNF-α, and IL-1 receptors at the binding site as compared with the complex B.     

Semiglobal simplex optimization and its application to determining the preferred solvation sites of proteins

The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underestimator (CGU) method, the search is carried out on a surface spanned by local minima. The SGS and CGU methods are compared by minimizing a set of test functions of increasing complexity, each with a known global minimum and many local minima. Although CGU delivers substantially better success rates in simple problems, the two methods become comparable as the complexity of the problems increases. Because SGS is generally faster than CGU, it is the method of choice for solving optimization problems in which function evaluation is computationally inexpensive and the search region is large. The extreme simplicity of the method is also a factor. The SGS method is applied here to the problem of finding the most preferred (i.e., minimum free energy) solvation sites on a streptavidin monomer. It is shown that the SGS method locates the same lowest free energy positions as an exhaustive multistart Simplex search of the protein surface, with less than one-tenth the number of minizations. The combination of the two methods, i.e.. multistart simplex and SGS, provides a reliable procedure for predicting all potential solvation sites of a protein.     

Modeling of novel CDK7 inhibitors activity by molecular dynamics and free energy perturbation methods

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Heuristic molecular lipophilicity potential (HMLP): lipophilicity and hydrophilicity of amino acid side chains

Heuristic molecular lipophilicity potential (HMLP) is applied in the study of lipophilicity and hydrophilicity of 20 natural amino acids side chains. The HMLP parameters, surface area S(i), lipophilic indices L(i), and hydrophilic indices H(i) of amino acid side chains are derived from lipophilicity potential L(r). The parameters are correlated with the experimental data of phase-transferring free energies of vapor-to-water, vapor-to-cyclohexane, vapor-to-octanol, cyclohexane-to-water, octanol-to-water, and cyclohexane-to-octanol through a linear free energy equation DeltaG(0)(tr,i) = b(0) + b(1)S(i) (+) + b(2)S(i) (-) + b(3)L(i) + b(4)H(i). For all above six phase-transfer free energies, the HMLP parameters of 20 amino acid side chains give good calculation results using linear free energy equation. HMLP is an ab initio quantum chemical approach and a structure-based technique. Except for atomic van der Waals radii, there are no other empirical parameters used. The HMLP has clear physical and chemical meaning and provides useful lipophilic and hydrophilic parameters for the studies of proteins and peptides.     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

NMR study on solubility of benzyl alcohol and its transfer free energy from D_2O to cationic micelle

A new kind of surfactant, [CnH_(2n+1)OCH2CH(OH)CH2N(CH3)3]Cl (n=12, 14, 16) was synthesized. The solubility of benzyl alcohol in micellar solutions was determined by 1H NMR method. The results indicate that the length of alkyl chains of surfactant affects the solubility of ben-zyl alcohol in 2.5 × l0~(-2) mol/L micellar solutions. The solubility of benzyl alcohol per liter of micellar solution is 0.095 mole for n=12, 0.115 mole for n=14, 0.165 mole for n=16. The transfer free energy of benzyl alcohol from aqueous phase to micellar phase is -24.29 kJ/mol for n=12, -24.37 kJ/mol for n=14, -24.49 kJ/mol for n=16.     

Virtual screening of B-Raf kinase inhibitors: A combination of pharmacophore modelling,molecular docking, 3D-QSAR model and binding free energy calculation studies

B-Raf kinase has been identified as an important target in recent cancer treatment. In order to discover structurally diverse and novel B-Raf inhibitors (BRIs), a virtual screening of BRIs against ZINC database was performed by using a combination of pharmacophore modelling, molecular docking, 3D-QSAR model and binding free energy (ΔG_bind) calculation studies in this work. After the virtual screening, six promising hit compounds were obtained, which were then tested for inhibitory activities of A375 cell lines. In the result, five hit compounds show good biological activities (IC₅₀ < 50 μM). The present method of virtual screening can be applied to find structurally diverse inhibitors, and the obtained five structurally diverse compounds are expected to develop novel BRIs.     

Application of reference‐modified density functional theory: Temperature and pressure dependences of solvation free energy

Recently, we proposed a reference‐modified density functional theory (RMDFT) to calculate solvation free energy (SFE), in which a hard‐sphere fluid was introduced as the reference system instead of an ideal molecular gas. Through the RMDFT, using an optimal diameter for the hard‐sphere reference system, the values of the SFE calculated at room temperature and normal pressure were in good agreement with those for more than 500 small organic molecules in water as determined by experiments. In this study, we present an application of the RMDFT for calculating the temperature and pressure dependences of the SFE for solute molecules in water. We demonstrate that the RMDFT has high predictive ability for the temperature and pressure dependences of the SFE for small solute molecules in water when the optimal reference hard‐sphere diameter determined for each thermodynamic condition is used. We also apply the RMDFT to investigate the temperature and pressure dependences of the thermodynamic stability of an artificial small protein, chignolin, and discuss the mechanism of high‐temperature and high‐pressure unfolding of the protein. © 2017 Wiley Periodicals, Inc.     

The preparation of ribose-free ‘artificial dinucleotides’: A new approach to molecular recognition?

The synthesis of the cytosine-guanine linked dimer1, and its symmetric guanine-guanine analogue2 are described. Compound1 is the first homogeneous ribose-free system to be prepared and characterized in which molecular recognition by complementary guanine-cytosine base-pairing might be possible. It is thus prototypical of a new and potentially large class of artificial oligonucleotides.     

Electron-transfer reactions through the associated interaction between cytochrome c and self-assembled monolayers of optically active cobalt(III) complexes: molecular recognition ability induced by the chirality of the cobalt(III) units

Self-assembled monolayers (SAMs) of optically active Co(III) complexes ((S)-2/(R)-2) that contain (S)- or (R)-phenylalanine derivatives as a molecular recognition site were constructed on Au electrodes ((S)-2-Au/(R)-2-Au). Molecular recognition characteristics induced by the S and R configurations were investigated by measurements of electron-transfer reactions with horse heart cytochrome c (cyt c). The electrochemical studies indicate that the maximum current of cyt c reduction is obtained when the Au electrode is modified by 2 with a moderate coverage of approximately 4.0 x 10(-11) mol cm(-2). Since the Au electrode is not densely packed with the Co(III) units at this concentration, we conclude that the penetrative association process between cyt c and the Co(III) unit plays an important role in this electron-transfer system. The differences in the electron-transfer rates of (S)-2-Au and (R)-2-Au increase with increasing scan rates, a result indicating that the chiral ligand has an influence on the rate of association of the complexes with cyt c. 3-Au has a mixed monolayer composed of 2 and hexanethiol and exhibits electron-transfer behavior comparable to 2-Au. The difference in the association rates of (S)-3-Au and (R)-3-Au is larger than that between (S)-2-Au and (R)-2-Au, which indicates that the molecular recognition ability of 3-Au has been enhanced by filling the gap between molecules of 2 with hexanethiols. The differences in the oxidation rates of cyt c(II) between (S)-2-Au and (R)-2-Au and between (S)-3-Au and (R)-3-Au were larger than the differences in the rates of the reduction of cyt c(III); this suggests that the size of the heme crevice varies according to the oxidation state of cyt c.