Theoretical calculation of partition coefficients of dimethoxypyrimidinylsalicylic acids

Despite their importance as herbicides, dimethoxypyrimidinylsalicylic acids has been poorly characterized from a physical-chemical point of view. This lack of information has prevented the assessment of their impact in the environment once they are released. In this study, environmentally important properties (free energy of solvation, Henry’s law constant, octanol/air, and octanol/water partition coefficients) of 39 dimethoxypyrimidinylsalicylic derived compounds are calculated by density functional theory (DFT) methods at B3LYP/6-31G(d,p) level of theory using the Poisson-Boltzmann solvation model. These properties have not been reported previously for this family of compounds, neither experimentally or theoretically.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.     

Amino acid/water interactions study: a new amino acid scale

Partition ratios of 8 free l-amino acids (Gln, Glu, His, Lys, Met, Ser, Thr, and Tyr) were measured in 10 different polymer/polymer aqueous two-phase systems containing 0.15?M NaCl in 0.01?M phosphate buffer, pH 7.4. The solute-specific coefficients representing the solute dipole/dipole, hydrogen-bonding and electrostatic interactions with the aqueous environment of the amino acids were determined by multiple linear regression analysis using a modified linear solvation energy relationship. The solute-specific coefficients determined in this study together with the solute-specific coefficients reported previously for amino acids with non-polar side-chains where used in a Quantitative Structure/Property Relationship analysis. It is shown that linear combinations of these solute-specific coefficients are correlated well with various physicochemical, structural, and biological properties of amino acids.     

Prediction of the aqueous solvation free energy of organic compounds by using autocorrelation of molecular electrostatic potential surface properties combined with response surface analysis

Several quantitative structure-property relationship (QSPR) approaches have been explored for the prediction of aqueous solubility or aqueous solvation free energies, DeltaG(sol), as crucial parameter affecting the pharmacokinetic profile and toxicity of chemical compounds. It is mostly accepted that aqueous solvation free energies can be expressed quantitatively in terms of properties of the molecular surface electrostatic potentials of the solutes. In the present study we have introduced autocorrelation molecular electrostatic potential (autoMEP) vectors in combination with nonlinear response surface analysis (RSA) as alternative 3D-QSPR strategy to evaluate the aqueous solvation free energy of organic compounds. A robust QSPR model (r(cv)=0.93) has been obtained by using a collection of 248 organic chemicals. An external test set based on 23 molecules confirmed the good predictivity of the autoMEP/RSA model suggesting its further applicability in the in silico prediction of water solubility of large organic compound libraries.     

Partitioning of amino-acid analogues in a five-slab membrane model

The positional preferences of the twenty amino-acid residues in a phospholipid bilayer are investigated by calculating the solvation free energy of the corresponding side chain analogues using a five-slab continuum electrostatic model. The side-chain analogues of the aromatic residues tryptophan and tyrosine are found to partition in the head-group region, due to compensation between the increase of the non-polar component of the solvation free energy at the boundary with the aqueous region and the decrease in the electrostatic component. The side chain analogue of phenylalanine differs from the other aromatic molecules by being able to partition in both the head-group region and the membrane core. This finding is consistent with experimental findings of the position of phenylalanine in membrane helices. Interestingly, the charged side-chain analogues of arginine and lysine are shown to prefer the head-group region in an orientation that allows the charged moiety to interact with the aqueous layer. The orientation adopted is similar to the “snorkelling” effect seen in lysine and arginine residues in membrane helices. In contrast, the preference of the charged side-chain analogues of histidine (protonated) and aspartate (deprotonated) for the aqueous layer is shown to be due to a steep decrease in the electrostatic component of the solvation free energy at the boundary to the aqueous region. The calculations allow an understanding of the origins of side chain positioning in membranes and are thus useful in understanding membrane-protein:lipid thermodynamics.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

Application of a universal solvation model to nucleic acid bases: comparison of semiempirical molecular orbital theory, ab initio Hartree-Fock theory, and density functional theory

The free energies of solvation of six nucleic acid bases (adenine, cytosine, hypoxanthine, guanine, thymine, and uracil) in water and chloroform are calculated using CM2 class IV charges and SM5.42R atomic surface tensions. Using any of three approximations to the electronic wave function (AM1, Hartree-Fock, or DFT), we obtain good agreement with experiment for five cases where the experimental results are known for the partition coefficients between the two solvents. Decomposition of the solvation effects into bulk electrostatic contributions and first-solvation-shell effects shows that the partitioning is dominated by the former, and this illustrates the importance of using accurate partial atomic charges for modeling these molecules in aqueous solution.     

Electrostatic effects and calcium ion concentration as modulators of acid phosphatase bound to plant cell walls

At 'low' ionic strength, acid phosphatase bound to plant cell walls exhibits an apparent negative co-operativity, whereas it displays classic Michaelis-Menten kinetics in free solution. Conversely, at 'high' ionic strength, the bound enzyme and the soluble enzyme behave identically. This apparent negative co-operativity is explained by the existence of an electrostatic partition of the charged substrate by the fixed negative charges of the cell wall. Raising the ionic strength suppresses these electrostatic repulsion effects. Calcium may be removed from the cell walls by acid treatment and the acid phosphatase is apparently strongly inhibited. This inhibition occurs together with an increased apparent negative co-operativity of the enzyme. Incubating cell wall fragments previously depleted of calcium with CaCl2 restores the initial behaviour of the enzyme. Calcium, which tightly binds to cell wall pectic compounds, has by itself no effect on the enzyme in free solution. It affects the net charge of the cell wall and therefore the amplitude of electrostatic repulsion effects. Non-linear least-square fitting methods make it possible to estimate the density of fixed negative charges as well as the electrostatic partition coefficient, for both the 'native' and 'calcium-deprived' cell wall fragments. It may be shown directly that calcium loading and unloading in the cell wall controls the electrostatic effects, by monitoring proton extrusion from cell wall fragments upon raising the ionic strength. Proton outflux in the bulk phase is considerably enhanced upon removal of calcium from the cell walls. The main conclusion is that loading and unloading of calcium during cell elongation and division may regulate the activity of cell wall enzymes.     

Optimized atomic radii for protein continuum electrostatics solvation forces

Recently, we presented a Green's function approach for the calculation of analytic continuum electrostatic solvation forces based on numerical solutions of the finite-difference Poisson-Botzmann (FDPB) equation [Im et al., Comp. Phys. Comm. 111 (1998) 59]. In this treatment the analytic forces were explicitly defined as the first derivative of the FDPB continuum electrostatic free energy with respect to the coordinates of the solute atoms. A smooth intermediate region for the solute-solvent dielectric boundary needed to be introduced to avoid abrupt discontinuous variations in the solvation free energy and forces as a function of the atomic positions. In the present paper we extend the set of optimized radii, which was previously parametrized from molecular dynamics free energy simulations of the 20 standard amino acids with explicit solvent molecules [Nina et al., J. Phys. Chem. 101 (1997) 5239], to yield accurate solvation free energy by taking the influence of the smoothed dielectric region into account.     

蛋白质-蛋白质对接中打分函数的研究

通过分析蛋白质－蛋白质间的静电、疏水作用和熵效应与相对于晶体结构的蛋白质主链原子的均方根偏差（RMSD）的相关性,定量地考查了它们在蛋白质－蛋白质对接中作为打分函数评价近天然构象的能力。对7个蛋白质复合物体系的分析表明,就水化能而言,原子接触势模型（ACE）优于原子水化参数模型（ASP）,且修正的ACE模型具有更好的评价近天然构象的能力;水化能与静电能结合对评价能力有进一步的提高。最后,我们将静电和修正的ACE水化能结合作为打分函数用于36个蛋白质复合物体系的对接研究,进一步证实了这两种能量项的组合能有效地将近天然结构从分子对接模式中区分出来。     

Solvation effects in calculated electrostatic association free energies for the C3d‐CR2 complex and comparison with experimental data

The complement system is an integral part of the innate immune system that participates in the clearance of pathogens from the body. The association between complement protein fragment C3d and B or T cell‐receptor complement receptor (CR) 2 represents a crucial link between innate and adaptive immunities. The goal of this study is to predict association abilities of C3d and CR2 mutants by theoretically calculating electrostatic free energies of association and to assess the importance of solvation effects in the calculations. We demonstrate that calculated solvation free energy differences and Coulombic free energies of association are more sensitive than electrostatic free energies of association in solution and, thus, more accurate in predicting previously published experimental data for the association abilities (relative to the parent proteins) of specific C3d and CR2 mutants. We show that a proportional relationship exists between the predicted solvation free energy differences and the experimental data, while an inversely proportional relationship exists between the predicted Coulombic free energies of association and the experimental data. Our results yield new insights into the physicochemical properties underlying C3d‐CR2 association. We discuss the predictive validity of Coulombic, solvation, and solution electrostatic free energies of association and the generalization of our method for theoretical mutagenesis studies of other systems. This is a basic study, aimed toward improving our understanding of the theoretical basis of immune system regulation at the molecular level. Such insight can serve as the groundwork for the design of regulators with tailored properties, vaccines, and other biotechnology products. © 2010 Wiley Periodicals, Inc. Biopolymers 93:509–519, 2010. This article was originally published online as an accepted preprint. The “Published Online” date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com     

Pentacycloundecane lactam vs lactone norstatine type protease HIV inhibitors: binding energy calculations and DFT study

Background

Novel pentacycloundecane (PCU)-lactone-CO-EAIS peptide inhibitors were designed, synthesized, and evaluated against wild-type C-South African (C-SA) HIV-1 protease. Three compounds are reported herein, two of which displayed IC₅₀ values of less than 1.00 μM. A comparative MM-PB(GB)SA binding free energy of solvation values of PCU-lactam and lactone models and their enantiomers as well as the PCU-lactam-NH-EAIS and lactone-CO-EAIS peptide inhibitors and their corresponding diastereomers complexed with South African HIV protease (C-SA) was performed. This will enable us to rationalize the considerable difference between inhibitory concentration (IC₅₀) of PCU-lactam-NH-EAIS and PCU-lactone-CO-EAIS peptides.

Results

The PCU-lactam model exhibited more negative calculated binding free energies of solvation than the PCU-lactone model. The same trend was observed for the PCU-peptide inhibitors, which correspond to the experimental activities for the PCU-lactam-NH-EAIS peptide (IC₅₀ = 0.076 μM) and the PCU-lactone-CO-EAIS peptide inhibitors (IC₅₀ = 0.850 μM). Furthermore, a density functional theory (DFT) study on the natural atomic charges of the nitrogen and oxygen atoms of the three PCU-lactam, PCU-lactim and PCU-lactone models were performed using natural bond orbital (NBO) analysis. Electrostatic potential maps were also used to visualize the electron density around electron-rich regions. The asymmetry parameter (η) and quadrupole coupling constant (χ) values of the nitrogen and oxygen nuclei of the model compounds were calculated at the same level of theory. Electronic molecular properties including polarizability and electric dipole moments were also calculated and compared. The Gibbs theoretical free solvation energies of solvation (∆G_solv) were also considered.

Conclusions

A general trend is observed that the lactam species appears to have a larger negative charge distribution around the heteroatoms, larger quadrupole constant, dipole moment and better solvation energy, in comparison to the PCU-lactone model. It can be argued that these characteristics will ensure better eletronic interaction between the lactam and the receptor, corresponding to the observed HIV protease activities in terms of experimental IC₅₀ data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12929-015-0115-5) contains supplementary material, which is available to authorized users.     

Exploring QSAR of peripheral benzodiazepine receptor binding affinity of N,N-dialkyl-2-phenylindol-3-yl-glyoxylamides using physico-chemical descriptors

The present QSAR study has attempted to explore the structural and physicochemical requirements of ligands N,N-dialkyl-2-phenylindol-3-yl-glyoxylamides for binding with peripheral benzodiazepine receptor (PBR). The calculated partition coefficient values show parabolic relations with the PBR binding affinity, suggesting that the binding affinity increases with increase in the partition coefficient of the compounds until it reaches the critical value after which the affinity decreases. The critical value of logP is within range of 6.052-6.410. Furthermore, positive Wang-Ford.charge values of carbonyl oxygens of the glyoxamide moiety and negative Wang-Ford charge value of the glyoxamide nitrogen are conducive for the binding affinity. Again, the indole moiety should have favorable charge distribution. Higher values of the parameters dipole moment (Dipole) and moment of inertia (I_z) of the ligands are conducive for the binding affinity. The presence of hydrogen atom at R2 and cyclic moiety at R1 and R2 positions are detrimental to the binding affinity.     

Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.     

Accurate aqueous proton dissociation constants calculations for selected angiotensin-converting enzyme inhibitors

Studies that allow computing values of aqueous proton dissociation constants (pKa), gas phase proton affinities, and the free energy of solvation have been performed for six members of angiotensin-I-converting enzyme (ACE) inhibitor family (captopril, enalaprilat, imidaprilat, ramiprilat, perindoprilat, and spiraprilat). Density functional theory (DFT) calculations using PBE1PBE functional on optimized molecular geometries have been carried out to investigate the thermodynamics of gas-phase protonation. The conductor-like polarizable continuum model (CPCM) solvation method at various levels of theory was applied to calculate the free energy of solvation for the ACE inhibitors and their respective anions. The CPCM solvation calculations were performed on both gas-phase and solvent-phase optimized structures. The combination of gas-phase and solvation energies according to the thermodynamic cycle enabled us to compute accurate pKa values for the all studied molecules.     

Rapid boundary element solvation electrostatics calculations in folding simulations: successful folding of a 23-residue peptide.

Solvation effects play a profound role in the energetics of protein folding. While a continuum dielectric model of solvation may provide a sufficiently accurate estimate of the solvation effects, until now this model was too computationally expensive and unstable for folding simulations. Here we proposed a fast yet accurate and robust implementation of the boundary element solution of the Poisson equation, the REBEL algorithm. Using our earlier double-energy scheme, we included for the first time the mathematically rigorous continuous REBEL solvation term in our Biased Probability Monte Carlo (BPMC) simulations of the peptide folding. The free energy of a 23-residue beta beta alpha-peptide was then globally optimized with and without the solvation electrostatics contribution. An ensemble of beta beta alpha conformations was found at and near the global minimum of the energy function with the REBEL electrostatic solvation term. Much poorer correspondence to the native solution structure was found in the "control" simulations with a traditional method to account for solvation via a distance-dependent dielectric constant. Each simulation took less than 40 h (21 h without electrostatic solvation calculation) on a single Alpha 677 MHz CPU and involved more than 40,000 solvation energy evaluations. This work demonstrates for the first time that such a simulation can be performed in a realistic time frame. The proposed procedure may eliminate the energy evaluation accuracy bottleneck in folding simulations.