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.     

Some physicochemical properties of the antitumor drug thiotepa and its metabolite tepa as obtained by density functional theory (DFT) calculations

Density functional theory (DFT) using the B3LYP functional was applied to elucidate the molecular properties of the antitumor drug thiotepa and its main metabolite tepa. Aqueous solvent effects were introduced using the conductor-like polarizable continuum model (CPCM). The protocol for calculating the pK _a values obtained with different cavity models was tested on a series of aziridine and phosphoramide compounds. An efficient computational scheme has been identified that uses the CPCM model of solvation with a universal force field (UFF) cavity. The method has been used to evaluate the basicities of thiotepa and its metabolite. Our calculations show that the basicities of the aziridine moiety of thiotepa and tepa are dramatically reduced compared to free aziridine, indicating that highly acidic media are needed to produce substantial yields of the N-protonated form of the drug. Finally, the mechanisms of reaction of the drug and its metabolite are discussed based on our theoretical results. The calculations reproduce the experimental trends very satisfactorily.     

First-principles study of Carbz-PAHTDDT dye sensitizer and two Carbz-derived dyes for dye sensitized solar cells

Dimers of cytosine and its N¹-methylated counterpart were investigated in gas-phase and in various solvents including chloroform, dimethylsulfoxide, and water. The studies were performed at DFT/M06-2X/6-31+G(d,p) level of theory. Relative stabilities of tautomers of cytosine solvated explicitly by a small number of solvent molecules were evaluated. Further solvation effect calculations for homodimers were carried out with conductor-like polarizable continuum model (CPCM). H-NMR shifts and IR frequencies for optimized structures were calculated and compared with available experimental data.     

Mechanism of Long-Chain Free Fatty Acid Protonation at the Membrane-Water Interface

Long-chain free fatty acids (FFAs) play an important role in several physiological and pathological processes such as lipid fusion, adjustments of membrane permeability and fluidity, and the regulation of enzyme and protein activities. FFA-facilitated membrane proton transport (flip-flop) and FFA-dependent proton transport by membrane proteins (e.g., mitochondrial uncoupling proteins) are governed by the difference between FFA’s intrinsic pK_a value and the pH in the immediate membrane vicinity. Thus far, a quantitative understanding of the process has been hampered, because the pK_a value shifts upon moving the FFA from the aqueous solution into the membrane. For the same FFA, pK_a values between 5 and 10.5 were reported. Here, we systematically evaluated the dependence of pK_a values on chain length and number of double bonds by measuring the ζ-potential of liposomes reconstituted with FFA at different pH values. The experimentally obtained intrinsic pK_a values (6.25, 6.93, and 7.28 for DOPC membranes) increased with FFA chain length (C16, C18, and C20), indicating that the hydrophobic energy of transfer into the bilayer is an important pK_a determinant. The observed pK_a decrease in DOPC with increasing number of FFA double bonds (7.28, 6.49, 6.16, and 6.13 for C20:0, C20:1, C20:2, and C20:4, respectively) is in line with a decrease in transfer energy. Molecular dynamic simulations revealed that the ionized carboxylic group of the FFAs occupied a fixed position in the bilayer independent of chain length, underlining the importance of Born energy. We conclude that pK_a is determined by the interplay between the energetic costs for 1) burying the charged moiety into the lipid bilayer and 2) transferring the hydrophobic protonated FFA into the bilayer.     

Activation of the cisplatin and transplatin complexes in solution with constant pH and concentration of chloride anions; quantum chemical study

The thermodynamics of cisplatin and transplatin hydration is studied within the model of constant pH solution. Several implicit solvation models were chosen for the determination of pK_a and pK constants of the hydration reactions. The polarizable dielectric model (DPCM), integral equation formalism polarizable model (IEFPCM), and polarizable conductor model (CPCM) were combined with the ‘united atom model for Hartree-Fock’ (UAHF) method for cavity construction and the B3LYP/6-31++G(2dp,2pd) level of calculations for the determination of electronic energies. The results were compared with the COSMO-RS and SM8 model developed by Truhlar (with M06 and MPWX functionals and the charge model CM4). The RMS difference between experimental and calculated pK_a values of cis/transplatin, water, HCl, and NH₄⁺ was used to evaluate accuracy of calculations. The DPCM model was confirmed to perform the best. The predicted pK_a constants were used in Legendre transformation for the estimation of the ΔG’ energies in the constant-pH model. The dependence of the pK constant on pH is plotted and compared with experimental value at pH=7.4. The influence of various chloride concentrations on the molar fractions of dissolved forms of cisplatin is examined for the DPCM model. The increased ratio of cisplatin active aqua-forms is clearly visible for 4 mM chloride solution in comparison with 104 mM Cl^- concentration.     

Prediction of Secondary Ionization of the Phosphate Group in Phosphotyrosine Peptides

A computational approach, based on a continuum molecular electrostatics model, for the calculation of the pK_a values of secondary ionization of the phosphate group in phenyl phosphate derivatives is described. The method uses the ESP atomic charges of the mono-anionic and di-anionic forms of the ionizable phosphate group, computed with the use of the density functional method, and applies a new concept of the model group, being the reference state for the pK_a calculations. Both conformational flexibility and tautomeric degrees of freedom are taken into account in the calculations. The method was parameterized using experimentally available pK_a values of four derivatives of phenyl phosphates, and phosphotyrosine. Subsequently this parameterization was used to predict pK_a of the phosphate group in a short peptide Gly-Gly-Tyr(P)-Ala, and in a longer peptide consisting of 12 residues, the latter in water, and in a complex with a protein—phospholipase. The agreement between the computed and the experimental pK_a values is better than ±0.3 pH units for the optimized solute dielectric constant of 11–13. This approach is promising and its extension to other phospho-amino acids is in progress.     

Improving the accuracy of protein pKa calculations: Conformational averaging versus the average structure

Several methods for including the conformational flexibility of proteins in the calculation of titration curves are compared. The methods use the linearized Poisson-Boltzmann equation to calculate the electrostatic free energies of solvation and are applied to bovine pancreatic trypsin inhibitor (BPTI) and hen egg-white lysozyme (HEWL). An ensemble of conformations is generated by a molecular dynamics simulation of the proteins with explicit solvent. The average titration curve of the ensemble is calculated in three different ways: an average structure is used for the pK_a calculation; the electrostatic interaction free energies are averaged and used for the pK_a calculation; and the titration curve for each structure is calculated and the curves are averaged. The three averaging methods give very similar results and improve the pK_a values to approximately the same degree. This suggests, in contrast to implications from other work, that the observed improvement of pK_a values in the present studies is due not to averaging over an ensemble of structures, but rather to the generation of a single properly averaged structure for the pK_a calculation. Proteins 33:145–158, 1998. © 1998 Wiley-Liss, Inc.     

Proton transfer function of carbonic anhydrase: Insights from QM/MM simulations

Recent QM/MM analyses of proton transfer function of human carbonic anhydrase II (CAII) are briefly reviewed. The topics include a preliminary analysis of nuclear quadrupole coupling constant calculations for the zinc ion and more detailed analyses of microscopic pK_a of the zinc-bound water and free energy profile for the proton transfer. From a methodological perspective, our results emphasize that performing sufficient sampling is essential to the calculation of all these quantities, which reflects the well solvated nature of CAII active site. From a mechanistic perspective, our analyses highlight the importance of electrostatics in shaping the energetics and kinetics of proton transfer in CAII for its function. We argue that once the pK_a for the zinc-bound water is modulated to be in the proper range (~ 7.0), proton transfer through a relatively well solvated cavity towards/from the protein surface (His64) does not require any major acceleration. Therefore, although structural details like the length of the water wire between the donor and acceptor groups still may make a non-negligible contribution, our computational results and the framework of analysis suggest that the significance of such “fine-tuning” is likely secondary to the modulation of pK_a of the zinc-bound water. We encourage further experimental analysis with mutation of (charged) residues not in the immediate neighborhood of the zinc ion to quantitatively test this electrostatics based framework; in particular, Φ analysis based on these mutations may shed further light into the relative importance of the classical Grotthus mechanism and the “proton hole” pathway that we have proposed recently for CAII.     

Docking of 4‐oxalocrotonate tautomerase substrates: Implications for the catalytic mechanism

The enzyme 4‐oxalocrotonate tautomerase catalyzes the ketonization of dienols, which after further processing become intermediates in the Krebs cycle. The enzyme uses a general acid–base mechanism for proton transfer: the amino‐terminal proline has been shown to function as the catalytic base and Arg39 has been implicated as the catalytic acid. We report the results of molecular docking simulations of 4‐oxalocrotonate tautomerase with two substrates, 2‐hydroxymuconate and 5‐carboxymethyl‐2‐hydroxymuconate. pK_a calculations are also performed for the free enzyme. The predicted binding mode of 2‐hydroxymuconate is in agreement with experimental data. A model for the binding mode of 5‐carboxymethyl‐2‐hydroxymuconate is proposed which explains the lower catalytic efficiency of the enzyme toward this substrate. The pK_a predictions and docking simulations support residue Arg39 as the general acid for the enzyme catalysis. © 1999 John Wiley & Sons, Inc. Biopoly 50: 319–328, 1999     

Graphical analysis of pH-dependent properties of proteins predicted using PROPKA

Background  

Charge states of ionizable residues in proteins determine their pH-dependent properties through their pK_a values. Thus, various theoretical methods to determine ionization constants of residues in biological systems have been developed. One of the more widely used approaches for predicting pK_a values in proteins is the PROPKA program, which provides convenient structural rationalization of the predicted pK_a values without any additional calculations.     

pK(a) values for the unfolded state under native conditions explain the pH-dependent stability of PGB1

Understanding the role of electrostatics in protein stability requires knowledge of these interactions in both the folded and unfolded states. Electrostatic interactions can be probed experimentally by characterizing ionization equilibria of titrating groups, parameterized as pK_a values. However, pK_a values of the unfolded state are rarely accessible under native conditions, where the unfolded state has a very low population. Here, we report pK_a values under nondenaturing conditions for two unfolded fragments of the protein G B1 domain that mimic the unfolded state of the intact protein. pK_a values were determined for carboxyl groups by monitoring their pH-dependent ¹³C chemical shifts. Monte Carlo simulations using a Gaussian chain model provide corrections for changes in electrostatic interactions that arise from fragmentation of the protein. Most pK_a values for the unfolded state agree well with model values, but some residues show significant perturbations that can be rationalized by local electrostatic interactions. The pH-dependent stability was calculated from the experimental pK_a values of the folded and unfolded states and compared to experimental stability data. The use of experimental pK_a values for the unfolded state results in significantly improved agreement with experimental data, as compared to calculations based on model data alone.     

Catalytic subunit of cAMP-dependent protein kinase: Electrostatic features and peptide recognition

The electrostatic field was calculated for the mammalian cAMP-dependent protein kinase (PKA) catalytic subunit (C-subunit) complexed with a 20-residue peptide from a heat stable protein kinase inhibitor (PKI: 5–24). The electrostatic field was also calculated for the C-subunit complexed with a modeled heptapeptide substrate that has been used extensively in structure/function studies for the C-subunit. Perturbations in the electrostatic free energy were calculated when single ionizable active site residues were mutated to alanine. These perturbations in electrostatic free energy were correlated to changes in the binding energy measured in a charge-to-alanine scan of the homologous yeast C-subunit by M. J. Zoller and C. S. Gibbs [(1991) Journal of Biological Chemistry, Vol. 266, pp. 8923–8931; C. S. Gibbs and M. J. Zoller (1991) Biochemistry, Vol. 30, p. 22]. This analysis indicated that the substrate binding parameters primarily depend on electrostatic interactions between a substrate or inhibitor and the C-subunit. Amino acid replacements that led to large perturbations in the electrostatic field are listed in the text. pK_a shifts were also calculated for the substrate's phosphate accepting atom, the serine hydroxyl oxygen, when the active site ionizable residues were changed to structurally similar uncharged amino acids. The theoretical mutation of three active site residues caused large shifts in this parameter: E91Q, D166N, and D184N. The calculated pK_a shifts for these mutants indicate that the rate of phosphotransfer should be markedly reduced in these cases. This prediction has been experimentally confirmed for the D166N mutant. The correlation between calculated electrostatic free energy changes and measured binding energy, and pK_a shifts with phosphotransfer for C-subunit mutants were within experimental error of the measurements. The calculations of electrostatic energy and ΔpK_a have identified previously unconsidered active site residues in the mammalian C-subunit that contribute to binding energy and phosphotransfer. © 1996 John Wiley & Sons, Inc.     

On the protonation equilibrium for the benzimidazole derivative Hoechst 33258: an electronic molecular orbital study

Hoechst 33258 and its deprotonated forms have been examined in the gas-phase and in solution using quantum mechanical methods. Ab initio calculations at the HF level have been used to investigate the more relevant geometrical trends of such species, while proton affinities and gas-phase basicities were derived from B3LYP and MP2 electronic energies. Solvation energies were calculated using a dielectric continuum model: MST. The Delta(p)K(a) values were estimated by combining the gas-phase basicities and the free energies of solvation. Comparison of these Delta(p)K(a) values with experimentally reported data have been used to highlight the advantages and limitations of this strategy.     

Highly perturbed pKa values in the unfolded state of hen egg white lysozyme

The majority of pK_a values in protein unfolded states are close to the amino acid model pK_a values, thus reflecting the weak intramolecular interactions present in the unfolded ensemble of most proteins. We have carried out thermal denaturation measurements on the WT and eight mutants of HEWL from pH 1.5 to pH 11.0 to examine the unfolded state pK_a values and the pH dependence of protein stability for this enzyme. The availability of accurate pK_a values for the folded state of HEWL and separate measurements of mutant-induced effects on the folded state pK_a values, allows us to estimate the pK_a values of seven acidic residues in the unfolded state of HEWL. Asp-48 and Asp-66 display pK_a values of 2.9 and 3.1 in our analysis, thus representing the most depressed unfolded state pK_a values observed to date. We observe a strong correlation between the folded state pK_a values and the unfolded state pK_a values of HEWL, thus suggesting that the unfolded state of HEWL possesses a large degree of native state characteristics.     

Peptides and Peptoids - A Systematic Structure Comparison

A systematic analysis of the conformational space of the basic structure unit of peptoids in comparison to the corresponding peptide unit was performed based on ab initio MO theory and complemented by molecular mechanics (MM) and molecular dynamics (MD) calculations both in the gas phase and in aqueous solution.The calculations show three minimum conformations denoted as C_7ß, a_D and a that do not correspond to conformers on the gas phase peptide potential energy hypersurface. The influence of aqueous solvation was estimated by means of continuum models. The MD simulations indicate the a_D form as the preferred conformation in solution both in cis and trans peptide bond orientations.     

Combined DFT and electrostatics study of the proton pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase is a redox-driven proton pump which converts atmospheric oxygen to water and couples the oxygen reduction reaction to the creation of a membrane proton gradient. The structure of the enzyme has been solved; however, the mechanism of proton pumping is still poorly understood. Recent calculations from this group indicate that one of the histidine ligands of enzyme's Cu_B center, His291, may play the role of the pumping element. In this paper, we report on the results of calculations that combined first principles DFT and continuum electrostatics to evaluate the energetics of the key energy generating step of the model—the transfer of the chemical proton to the binuclear center of the enzyme, where the hydroxyl group is converted to water, and the concerted expulsion of the proton from δ-nitrogen of His291 ligand of Cu_B center. We show that the energy generated in this step is sufficient to push a proton against an electrochemical membrane gradient of about 200 mV. We have also re-calculated the pK_a of His291 for an extended model in which the whole Fe_a3-Cu_B center with their ligands is treated by DFT. Two different DFT functionals (B3LYP and PBE0), and various dielectric models of the protein have been used in an attempt to estimate potential errors of the calculations. Although current methods of calculations do not allow unambiguous predictions of energetics in proteins within few pK_a units, as required in this case, the present calculation provides further support for the proposed His291 model of CcO pump and makes a specific prediction that could be targeted in the experimental test.     

A density functional study towards substituent effects on anion sensing with urea receptors

Effects of substituents on anion binding in different urea based receptors have been examined using density functional (B3LYP/6-311+G**) level of theory. The complexes formed by a variety of substituted urea with a halide anion (fluoride) and an oxy-anion (acetate) have been calculated. The stronger complexes were predicted for receptors with fluoride ion than that of acetate ion, however, in water the preference was found to be reversed. The pK _a calculations showed the preferred sites of deprotonation for positional isomers, while interacting with anions. The position of the substituent in the receptor, however, could change the preferred sites of deprotonation compared to the site predicted with pK _a values.      

Proton translocation in hydrogen bonds with large proton polarizability formed between a Schiff base and phenols

OH…N ? O^?…H⁺N hydrogen bonds formed between N-all-transretinylidene butylamine (Schiff base) and phenols (1:1) are studied by IR spectroscopy. It is shown that both proton limiting structures of these hydrogen bonds have the same weight with Δ pK_a (50%) = (pK_a protonated Schiff base minus pK_a phenol) = 5.5. With the largely symmetrical systems, continua demonstrate that these hydrogen bonds show great proton polarizability. In the Schiff base + tyrosine system in a non-polar solvent the residence time of the proton at the tyrosine residue is much larger than that at the Schiff base. In CH₂CCl₂ these hydrogen bonds show, however, still proton polarizability, i.e., the position of the proton transfer equilibrium OH…N ? O^?…H⁺N is shifted to and fro as function of the nature of the environment of this hydrogen bond. Consequences regarding bacteriorhodopsin are discussed.