Asymmetric synthesis and σ receptor affinity of enantiomerically pure 1,4-disubstituted tetrahydro-1H-3-benzazepines

A very short (three steps) asymmetric synthesis of enantiomerically pure 1,4-disubstituted tetrahydro-1H-3-benzazepines 14 has been elaborated upon, starting from the trans- and cis-configured 11a-substituted 3-phenyl-2,3,11,11a-tetrahydro[1,3]oxazolo[2,3-b]-[3]-benzazepin-5(6H)-ones 6 and 7. The stereoisomerically pure lactams 6 and 7 were benzylated to give 6-benzyl-substituted products 8 and 9. NOE experiments showed a trans-configuration of the benzyl residue and the residue in the 11a-position indicated that the stereochemistry of the benzylation reaction was controlled by the stereocenter at the 11a-position. Reduction of the benzylated tricyclic benzolactams 8 and 9 with AlCl₃/LiAlH₄ (1/3) yielded the 1,3,4-trisubstituted 3-benzazepines 12 and 13, which were formed stereoselectively with the retention of configuration. Finally, removal of the N-(2-hydroxy-1-phenylethyl) residue by hydrogenolytic cleavage resulted in the formation of enantiomerically pure 1,4-disubstituted 3-benzazepines 14. The σ₁, σ₂, and NMDA receptor affinities of the enantiomerically pure 3-benzazepines 14 and ent-14 were investigated in competitive receptor binding studies. The butyl derivative ent-14c showed a high affinity towards σ₁ and σ₂ receptors, with K_i-values of 26 nM and 41 nM, respectively.     

Comparison of free energy methods for molecular systems

We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation DeltaF estimates as compared to other methods used in this report, while also offering rapid estimation of DeltaF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, "fast-growth" nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.     

Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

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.     

Rapid prediction of solvation free energy. 3. Application to the SAMPL2 challenge

The SAMPL2 hydration free energy blind prediction challenge consisted of a data set of 41 molecules divided into three subsets: explanatory, obscure and investigatory, where experimental hydration free energies were given for the explanatory, withheld for the obscure, and not known for the investigatory molecules. We employed two solvation models for this challenge, a linear interaction energy (LIE) model based on explicit-water molecular dynamics simulations, and the first-shell hydration (FiSH) continuum model previously calibrated to mimic LIE data. On the 23 compounds from the obscure (blind) dataset, the prospectively submitted LIE and FiSH models provided predictions highly correlated with experimental hydration free energy data, with mean-unsigned-errors of 1.69 and 1.71 kcal/mol, respectively. We investigated several parameters that may affect the performance of these models, namely, the solute flexibility for the LIE explicit-solvent model, the solute partial charging method, and the incorporation of the difference in intramolecular energy between gas and solution phases for both models. We extended this analysis to the various chemical classes that can be formed within the SAMPL2 dataset. Our results strengthen previous findings on the excellent accuracy and transferability of the LIE explicit-solvent approach to predict transfer free energies across a wide spectrum of functional classes. Further, the current results on the SAMPL2 test dataset provide additional support for the FiSH continuum model as a fast yet accurate alternative to the LIE explicit-solvent model. Overall, both the LIE explicit-solvent model and the FiSH continuum solvation model show considerable improvement on the SAMPL2 data set over our previous continuum electrostatics-dispersion solvation model used in the SAMPL1 blind challenge.     

Shared solvation of sodium ions in alcohol-water solutions explains the non-ideality of free energy of solvation

In order to explain the discrepancies between theories and experiments regarding the non-ideality in the free energy of solvation, here we present a microscopic picture of sodium ions dissolved in water-alcohol mixed solvents. We used X-ray absorption spectroscopy to probe the K-edge of sodium ions in mixed solvents of water and alcohols (methanol, ethanol) and in the respective pure solvents. In the mixed solvents a shared solvation of the sodium ions is observed. We find that specifically the water component plays a key role in stabilizing the solvation shell in mixed solvents, which was revealed by a selective photochemical process occurring only in the pure alcohol solvents.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Application of the frozen atom approximation to the GB/SA continuum model for solvation free energy

The generalized Born/surface area (GB/SA) continuum model for solvation free energy is a fast and accurate alternative to using discrete water molecules in molecular simulations of solvated systems. However, computational studies of large solvated molecular systems such as enzyme-ligand complexes can still be computationally expensive even with continuum solvation methods simply because of the large number of atoms in the solute molecules. Because in such systems often only a relatively small portion of the system such as the ligand binding site is under study, it becomes less attractive to calculate energies and derivatives for all atoms in the system. To curtail computation while still maintaining high energetic accuracy, atoms distant from the site of interest are often frozen; that is, their coordinates are made invariant. Such frozen atoms do not require energetic and derivative updates during the course of a simulation. Herein we describe methodology and results for applying the frozen atom approach to both the generalized Born (GB) and the solvent accessible surface area (SASA) parts of the GB/SA continuum model for solvation free energy. For strictly pairwise energetic terms, such as the Coulombic and van-der-Waals energies, contributions from pairs of frozen atoms can be ignored. This leaves energetic differences unaffected for conformations that vary only in the positions of nonfrozen atoms. Due to the nonlocal nature of the GB analytical form, however, excluding such pairs from a GB calculation leads to unacceptable inaccuracies. To apply a frozen-atom scheme to GB calculations, a buffer region within the frozen-atom zone is generated based on a user-definable cutoff distance from the nonfrozen atoms. Certain pairwise interactions between frozen atoms in the buffer region are retained in the GB computation. This allows high accuracy in conformational GB comparisons to be maintained while achieving significant savings in computational time compared to the full (nonfrozen) calculation. A similar approach for using a buffer region of frozen atoms is taken for the SASA calculation. The SASA calculation is local in nature, and thus exact SASA energies are maintained. With a buffer region of 8 A for the frozen-atom cases, excellent agreement in differences in energies for three different conformations of cytochrome P450 with a bound camphor ligand are obtained with respect to the nonfrozen cases. For various minimization protocols, simulations run 2 to 10.5 times faster and memory usage is reduced by a factor of 1.5 to 5. Application of the frozen atom method for GB/SA calculations thus can render computationally tractable biologically and medically important simulations such as those used to study ligand-receptor binding conformations and energies in a solvated environment.     

Calculation of solvation free energy using RISM theory for peptide in salt solution

We developed a robust, highly efficient algorithm for solving the full reference interaction site model (RISM) equations for salt solutions near a solute molecule with many atomic sites. It was obtained as an extension of our previously reported algorithm for pure water near the solute molecule. The algorithm is a judicious hybrid of the Newton–Raphson and Picard methods. The most striking advantage is that the Jacobian matrix is just part of the input data and need not be recalculated at all. To illustrate the algorithm, we solved the full RISM equations for a dipeptide (NH₂(SINGLE BOND)CHCH₃(SINGLE BOND)CONH(SINGLE BOND)CHCH₃(SINGLE BOND)COOH) in a 1 M NaCl solution. The extended simple point charge (SPC/E) model was employed for water molecules. Two different conformations of the dipeptide were considered. It was assumed for each conformation that the dipeptide was present either as an un-ionized form or as a zwitterion. The structure of the salt solution near the dipeptide and salt effects on the solvation free energy were also discussed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1724–1735, 1998     

Efficient use of nonequilibrium measurement to estimate free energy differences for molecular systems

A promising method for calculating free energy differences DeltaF is to generate nonequilibrium data via "fast-growth" simulations or by experiments--and then use Jarzynski's equality. However, a difficulty with using Jarzynski's equality is that DeltaF estimates converge very slowly and unreliably due to the nonlinear nature of the calculation--thus requiring large, costly data sets. The purpose of the work presented here is to determine the best estimate for DeltaF given a (finite) set of work values previously generated by simulation or experiment. Exploiting statistical properties of Jarzynski's equality, we present two fully automated analyses of nonequilibrium data from a toy model, and various simulated molecular systems. Both schemes remove at least several k(B)T of bias from DeltaF estimates, compared to direct application of Jarzynski's equality, for modest sized data sets (100 work values), in all tested systems. Results from one of the new methods suggest that good estimates of DeltaF can be obtained using 5-40-fold less data than was previously possible. Extending previous work, the new results exploit the systematic behavior of bias due to finite sample size. A key innovation is better use of the more statistically reliable information available from the raw data.     

Predicting the energy of the water exchange reaction and free energy of solvation for the uranyl ion in aqueous solution

The structures and vibrational frequencies of UO2(H2O)4(2+) and UO2(H2O)5(2+) have been calculated using density functional theory and are in reasonable agreement with experiment. The energies of various reactions were calculated at the density functional theory (DFT) and MP2 levels; the latter provides the best results. Self-consistent reaction field calculations in the PCM and SCIPCM approximations predicted the free energy of the water exchange reaction, UO2(H2O)4(2+) + H2O <--> UO2(H2O)5(2+). The calculated free energies of reaction are very sensitive to the choice of radii (O and H) and isodensity values in the PCM and SCIPCM models, respectively. Results consistent with the experimental HEXS value of -1.19 +/- 0.42 kcal/mol (within 1-3 kcal/mol) are obtained with small cavities. The structures and vibrational frequencies of the clusters with second solvation shell waters: UO2(H2O)4(H2O)8(2+), UO2(H2O)4(H2O)10(2+), UO2(H2O)4(H2O)11(2+), UO2(H2O)5(H2O)7(2+), and UO2(H2O)5(H2O)10(2+), were calculated and are in better agreement with experiment as compared to reactions involving only UO2(H2O)4(2+) and UO2(H2O)5(2+). The MP2 reaction energies for water exchange gave gas-phase results that agreed with experiment in the range -5.5 to +3.3 kcal/mol. The results were improved by inclusion of a standard PCM model with differences of -1.2 to +2.7 kcal/mol. Rearrangement reactions based on an intramolecular isomerization leading to a redistribution of water in the two shells provide good values in comparison to experiment with values of Delta G(exchange) from -2.2 to -0.5 kcal/mol so the inclusion of a second hydration sphere accounts for most solvation effects. Calculation of the free energy of solvation of the uranyl cation yielded an upper bound to the solvation energy of -410 +/- 5 kcal/mol, consistent with the best experimental value of -421 +/- 15 kcal/mol.     

Atomic decomposition of the protein solvation free energy and its application to amyloid-beta protein in water

We report the development of an atomic decomposition method of the protein solvation free energy in water, which ascribes global change in the solvation free energy to local changes in protein conformation as well as in hydration structure. So far, empirical decomposition analyses based on simple continuum solvation models have prevailed in the study of protein-protein interactions, protein-ligand interactions, as well as in developing scoring functions for computer-aided drug design. However, the use of continuum solvation model suffers serious drawbacks since it yields the protein free energy landscape which is quite different from that of the explicit solvent model and since it does not properly account for the non-polar hydrophobic effects which play a crucial role in biological processes in water. Herein, we develop an exact and general decomposition method of the solvation free energy that overcomes these hindrances. We then apply this method to elucidate the molecular origin for the solvation free energy change upon the conformational transitions of 42-residue amyloid-beta protein (Aβ42) in water, whose aggregation has been implicated as a primary cause of Alzheimer's disease. We address why Aβ42 protein exhibits a great propensity to aggregate when transferred from organic phase to aqueous phase.     

Calculation of the free energy of solvation for neutral analogs of amino acid side chains

The ability of the GROMOS96 force field to reproduce partition constants between water and two less polar solvents (cyclohexane and chloroform) for analogs of 18 of the 20 naturally occurring amino acids has been investigated. The estimations of the solvation free energies in water, in cyclohexane solution, and chloroform solution are based on thermodynamic integration free energy calculations using molecular dynamics simulations. The calculations show that while the force field reproduces the experimental solvation free energies of nonpolar analogs with reasonable accuracy the solvation free energies of polar analogs in water are systematically overestimated (too positive). The dependence of the calculated free energies on the atomic partial charges was also studied.     

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.     

Calculation of the solvation free energy of neutral and ionic molecules in diverse solvents

The solvation free energy density (SFED) model was modified to extend its applicability and predictability. The parametrization process was performed with a large, diverse set of solvation free energies that included highly polar and ionic molecules. The mean absolute error for 1200 solvation free energies of the 379 neutral molecules in 9 organic solvents and water was 0.40 kcal/mol, and for 90 hydration free energies of ions was 1.7 kcal/mol. Overall, the calculated solvation free energies of a wide range of solute functional groups in diverse solvents were consistent with experimental data.     

Comparison of different methods to estimate the uncertainty in composition measurement by chromatography

Natural gas is a mixture that contains hydrocarbons and other compounds, such as CO₂ and N₂. Natural gas composition is commonly measured by gas chromatography, and this measurement is important for the calculation of some thermodynamic properties that determine its commercial value. The estimation of uncertainty in chromatographic measurement is essential for an adequate presentation of the results and a necessary tool for supporting decision making. Various approaches have been proposed for the uncertainty estimation in chromatographic measurement. The present work is an evaluation of three approaches of uncertainty estimation, where two of them (guide to the expression of uncertainty in measurement method and prediction method) were compared with the Monte Carlo method, which has a wider scope of application. The aforementioned methods for uncertainty estimation were applied to gas chromatography assays of three different samples of natural gas. The results indicated that the prediction method and the guide to the expression of uncertainty in measurement method (in the simple version used) are not adequate to calculate the uncertainty in chromatography measurement, because uncertainty estimations obtained by those approaches are in general lower than those given by the Monte Carlo method.     

Application of solvation excess concept to solutions of 3 : 1 and 1 : 3 electrolytes

Data on water activity in solutions of a series of 3 : 1 and 1 : 3 electrolytes [AlCl₃, Al(NO₃)₃, LaCl₃, La(NO₃)₃, H₃PO₄, NaH₂PO₄] have been generalized in the frame of solvation excesses concept. Solvation excess reflects the distribution of the selected structural elements (ions or solvent particles) in the solution. The computed values have demonstrated the opposite contributions of ion association and hydration of ions and ion associates. Solvation excess concept allows determination of water molecules fraction constituting the excess at ions and their associates. The comparison of results obtained with different choice of model structural units has shown the electrolyte concentration ranges of validity of the respective models.     

Variation of surface partition in GEPOL: effects on solvation free energy and free-energy profiles

The problem of defining efficient strategies for partitioning the cavity surface in QM solvation procedures based on boundary elements methods is considered here. The GEPOL procedure to get the cavity surface, and its partition into tesserae is adopted as a starting point: a version with variable tesselation is presented. The procedure to build the new sphere tesselations is described and several different options to select the surface partition have been implemented. The effects of the variation of the surface partition on the free energy of solvation of several solutes are also presented. Two free energy of solvation profiles evaluated with several different cavity partitions are analysed. We find that a radius-driven tesselation for every sphere reduces the number and extension of the cavity artefacts. Received: 6 August 1997 / Accepted: 23 October 1997     

A method to estimate the Gibbs free energy of non-equilibrium alloys by thermal analysis

A method has been developed to estimate the Gibbs free energy $ \left( {G_{\text{S}}^{\text{NE}} } \right) $ of the non-equilibrium solid alloys with multicomponents based on differential scanning calorimetry (DSC) analysis. In this method, the DSC curves of the non-equilibrium and equilibrium alloys during heating up to fully melting and those of the alloys during solidifying were measured. Then the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states and the equilibrium solidification could be calculated. By evolving the traditional equal-G curve principle to equal-G point, the Gibbs free energy of the equilibrium solid alloy with multicomponents could be obtained on condition that the free energy of the liquid alloy was known. Considering the thermal effects of the solid phase transformations from non-equilibrium to equilibrium states, the Gibbs free energy value of the non-equilibrium alloys with a given composition could be achieved although the phase constitution of the equilibrium solid alloys and the Gibbs free energy of each phase were not known, and the calculation errors could be reduced by dividing the alloys into many infinitesimal virtual pure metals. The Gibbs free energy of the non-equilibrium Al?CSi?CMn alloys was calculated by using this method, confirming the validity of this method.