First-principles prediction of the pK(a)s of anti-inflammatory oxicams

The gas- and aqueous-phase acidities of a series of oxicams have been computed by combining M05-2X/6-311+G(3df,2p) gas-phase free energies with solvation free energies from the CPCM-UAKS, COSMO-RS, and SMD solvent models. To facilitate accurate gas-phase calculations, a benchmarking study was further carried out to assess the performance of various density functional theory methods against the high-level composite method G3MP2(+). Oxicams are typically diprotic acids, and several tautomers are possible in each protonation state. The direct thermodynamic cycle and the proton exchange scheme have been employed to compute the microscopic pK(a)s on both solution- and gas-phase equilibrium conformers, and these were combined to yield the macroscopic pK(a) values. Using the direct cycle of pK(a) calculation, the CPCM-UAKS model delivered reasonably accurate results with MAD ~ 1, whereas the SMD and COSMO-RS models' performance was less satisfactory with MAD ~ 3. Comparison with experiment also indicates that direct cycle calculations based on solution conformers generally deliver better accuracy. The proton exchange cycle affords further improvement for all solvent models through systematic error cancellation and therefore provides better reliability for the pK(a) prediction of compounds of these types. The latter approach has been applied to predict the pK(a)s of several recently synthesized oxicam derivatives.     

Concerted electron-proton transfer (EPT) in the oxidation of tryptophan with hydroxide as a base

Tryptophan is unique among the redox-active amino acids owing to its weakly acidic indolic proton (pK(a) ≈ 16) compared to the -O-H proton of tyrosine (pK(a) = 10.1) or the -S-H proton of cysteine (pK(a) = 8.2). Stopped-flow and electrochemical measurements have been used to explore the roles of proton-coupled electron transfer and concerted electron-proton transfer (EPT) in tryptophan oxidation. The results of these studies have revealed a role for OH(-) as a proton acceptor base in EPT oxidation of N-acetyl-tryptophan but not for other common bases. The reorganizational barrier for (N-acetyl-tryptophan)(+/?) self-exchange is also estimated.     

Thermodynamic cycle for the calculation of ab initio pKa values for hydroxamic acids

A thermodynamic cycle to calculate pK_a values (Minus log of acid dissociation constants) of hydroxamic acids is presented. Hydroxamic acids exist mainly as amide isomers in the aqueous medium. The amide form of hydroxamic acids has two deprotonation sites and may yield either an N-ion or an O-ion upon deprotonation. The thermodynamic cycle proposed includes the gas-phase N–H deprotonation of the hydroxamic acid, the solvent phase transformation of the N-ion to the O-ion and the solvation of the hydroxamic acid molecule and the O-ion in water. The CBS-QB3 method was employed to obtain gas-phase free energy differences between 12 hydroxamic acids and their respective anions. The aqueous solvation Gibbs free energy changes were calculated at the HF/6-31G(d)/CPCM and HF/6-31+G(d)/CPCM levels of theory using HF/6-31+G(d)/CPCM geometries. For the proton, literature values of the gas-phase free energy of formation and the solvation free energy change were used. The free energy change for the transformation of the N-ion to O-ion in the aqueous medium was calculated by employing CBS-QB3/CPCM in the aqueous medium. For this, the hydroxamic acids were divided in two classes according to the substituent at the carbonyl carbon. A common transformation free energy difference for aliphatic substituted hydroxamic acids and a separate common transformation free energy difference for aromatic substituted hydroxamic acids were obtained. The pK_a calculation yielded a root mean square error of 0.32 pK_a units.     

Excited-state intramolecular proton transfer in 2-(2'-arylsulfonamidophenyl)benzimidazole derivatives: the effect of donor and acceptor substituents

A series of water-soluble 2-(2'-arylsulfonamidophenyl)benzimidazole derivatives containing electron-donating and accepting groups attached to various positions of the fluorophore pi-system has been synthesized and characterized in aqueous solution at 0.1 M ionic strength. The measured pK(a)'s for deprotonation of the sulfonamide group of monosubstituted derivatives range between 6.75 and 9.33 and follow closely Hammett's free energy relationship. In neutral aqueous buffer, all compounds undergo efficient excited-state intramolecular proton transfer (ESIPT) to yield a strongly Stokes-shifted fluorescence emission from the phototautomer. Upon deprotonation of the sulfonamide nitrogen at high pH, ESIPT is interrupted to yield a new, blue-shifted emission band. The peak absorption and emission energies were strongly influenced by the nature of the substituents and their attachment positions on the fluorophore pi-system. The fluorescence quantum yield of the ESIPT tautomers revealed a significant correlation with the observed Stokes shifts. The study provides valuable information regarding substituent effects on the photophysical properties of this class of ESIPT fluorophores in an aqueous environment and may offer guidelines for designing emission ratiometric pH or metal-cation sensors for biological applications.     

Proton-coupled electron transfer from tryptophan: a concerted mechanism with water as proton acceptor

The mechanism of proton-coupled electron transfer (PCET) from tyrosine in enzymes and synthetic model complexes is under intense discussion, in particular the pH dependence of the PCET rate with water as proton acceptor. Here we report on the intramolecular oxidation kinetics of tryptophan derivatives linked to [Ru(bpy)(3)](2+) units with water as proton acceptor, using laser flash-quench methods. It is shown that tryptophan oxidation can proceed not only via a stepwise electron-proton transfer (ETPT) mechanism that naturally shows a pH-independent rate, but also via another mechanism with a pH-dependent rate and higher kinetic isotope effect that is assigned to concerted electron-proton transfer (CEP). This is in contrast to current theoretical models, which predict that CEP from tryptophan with water as proton acceptor can never compete with ETPT because of the energetically unfavorable PT part (pK(a)(Trp(?)H(+)) = 4.7 ? pK(a)(H(3)O(+)) ≈ -1.5). The moderate pH dependence we observe for CEP cannot be explained by first-order reactions with OH(-) or the buffers and is similar to what has been demonstrated for intramolecular PCET in [Ru(bpy)(3)](3+)-tyrosine complexes (Sjo?din, M.; et al. J. Am. Chem. Soc.2000, 122, 3932. Irebo, T.; et al. J. Am. Chem. Soc.2007, 129, 15462). Our results suggest that CEP with water as the proton acceptor proves a general feature of amino acid oxidation, and provide further experimental support for understanding of the PCET process in detail.     

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.     

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.     

Deprotonation of lithiated benzenes

The deprotonation energies of all possible lithiobenzenes (C(6)Li(n)H(6-n), n = 0-5) were computed at B3LYP/6-311+G(d,p). Based on natural population analysis, the conjugate bases can be thought of as salts between a polyanionic phenyl core and associated lithium cations. The most stable structures maximize the electrostatic attraction between these two species, typically by positioning the lithium cations to bridge in the ring plane across two adjacent carbanion centers. Favorable deprotonation occurs when the formal carbanion centers are adjacent to each other and then the proton is removed from an adjacent carbon. The deprotonation free energies range from 365.0 to 397.2 kcal mol(-1), with most of them less than the deprotonation free energy of benzene (391.8 kcal mol(-1)).     

Thermochemical properties of the ammonia-water ionized dimer probed by ion-molecule reactions

The thermochemical properties of some small clusters such as the (H2O)2*+ dimer have already been investigated by both experimental and theoretical methods. The recent method to selectively prepare the ammonia-water ionized dimer [NH3, H2O]*+ (and not its proton transfer isomer [NH4+, OH*]) allowed us to study its chemical reactivity. This study focuses on the charge and proton transfer pathways: Ion-molecule reactions in the cell of an FT-ICR mass spectrometer were carried out with a range of organic compounds. Examination of the reactivity of the [NH3, H2O]*+ ionized dimer versus ionization energy and proton affinity of the neutral reagents shows a threshold in the reactivity in both instances. This leads to a bracketing of thermochemical properties related to the dimer. From these experiments and in agreement with ab initio calculations, the adiabatic recombination energy of the [NH3, H2O]*+ dimer was evaluated at -9.38 +/- 0.04 eV. The proton affinity bracketing required the reevaluation of two reference gas-phase basicity values. The results, in good agreement with the calculation, lead to an evaluation of the proton affinity of the [NH2*, H2O] dimer at 204.4 +/- 0.9 kcal mol(-1). These two experimental values are respectively related to the ionization energy of NH3*+ and to the proton affinity of NH2* by the difference in single water molecule solvation energies of ionized ammonia, of neutral ammonia, and of the NH2* radical.     

A multistate empirical valence bond description of protonatable amino acids

The multistate empirical valence bond (MS-EVB) model, which was developed for molecular dynamics simulations of proton transport in water and biomolecular systems, is extended for the modeling of protonatable amino acid residues in aqueous environments, specifically histidine and glutamic acid. The parameters of the MS-EVB force field are first determined to reproduce the geometries and energetics of the gas phase amino acid-water clusters. These parameters are then optimized to reproduce experimental pK(a) values. The free energy profiles for acid ionization and the corresponding pK(a) values are calculated by MS-EVB molecular dynamics simulations utilizing the umbrella sampling technique, with the center of excess charge coordinate chosen as the dissociation reaction coordinate. A general procedure for fitting the MS-EVB parameters is formulated, which allows for the parametrization of other amino acid residues with protonatable groups and the subsequent use of the MS-EVB approach for molecular dynamics simulations of proton transfer processes in proteins involving protonation/deprotonation of the protonatable amino acid groups.     

Proton-coupled electron transfer reactions at a heme-propionate in an iron-protoporphyrin-IX model compound

A heme model system has been developed in which the heme-propionate is the only proton donating/accepting site, using protoporphyrin IX-monomethyl esters (PPIX(MME)) and N-methylimidazole (MeIm). Proton-coupled electron transfer (PCET) reactions of these model compounds have been examined in acetonitrile solvent. (PPIX(MME))Fe(III)(MeIm)(2)-propionate (Fe(III)~CO(2)) is readily reduced by the ascorbate derivative 5,6-isopropylidine ascorbate to give (PPIX(MME))Fe(II)(MeIm)(2)-propionic acid (Fe(II)~CO(2)H). An excess of the hydroxylamine TEMPOH or of hydroquinone similarly reduces Fe(III)~CO(2), and TEMPO and benzoquinone oxidize Fe(II)~CO(2)H to return to Fe(III)~CO(2). The measured equilibrium constants, and the determined pK(a) and E(1/2) values, indicate that Fe(II)~CO(2)H has an effective bond dissociation free energy (BDFE) of 67.8 ± 0.6 kcal mol(-1). In these PPIX models, electron transfer occurs at the iron center and proton transfer occurs at the remote heme propionate. According to thermochemical and other arguments, the TEMPOH reaction occurs by concerted proton-electron transfer (CPET), and a similar pathway is indicated for the ascorbate derivative. Based on these results, heme propionates should be considered as potential key components of PCET/CPET active sites in heme proteins.     

Computational electrochemistry: aqueous two-electron reduction potentials for substituted quinones

The electrode potentials of some quinone derivatives in aqueous solution have been calculated. The calculations are carried out at the Hartree–Fock and B3LYP levels with the inclusion of entropic and thermochemical corrections to yield free energies of redox reactions. The Polarisable Continuum Model (PCM) is used to describe the solvent. The average error of calculation of electrode potentials is less than 0.03 V and is decreased compared to the average error of methods presented previously. The role of relaxation energies and frequency calculations in improving the results has been investigated.     

Reorganization free energies for long-range electron transfer in a porphyrin-binding four-helix bundle protein

To explore the possibility of electron transport in a recently designed four-helix bundle protein (Cochran, F. V.; et al. J. Am. Chem. Soc. 2005, 127, 1346), we have computed the reorganization free energy for (i) oxidation of a single Ru-porphyrin cofactor and (ii) electron self-exchange between two Ru-porphyrin cofactors binding to the solvated protein. Sampling the classical electrostatic energy gap for 20 ns, we find that the fluctuations are well described by Gaussian statistics and obtain reorganization free energies of 0.90 +/- 0.04 eV for oxidation and 1.36 +/- 0.08 eV for self-exchange. The latter is 0.1-0.2 eV higher than the experimental estimate for interprotein electron self-exchange in cytochrome b5. As in natural electron carriers, inner-sphere reorganization is very small, 88 meV for self-exchange between two model cofactors computed at the density functional level of theory. Decomposing the outer-sphere reorganization free energy, we find that the solvent (aqueous ionic solution) is the primary outer-sphere medium for oxidation, contributing 0.60 eV (69%). The protein contributes only 0.27 eV (31%). For self-exchange, the solvent contribution, 0.68 eV (54%), and the protein contribution, 0.59 eV (46%), are almost equally important. The large solvent contribution is due to the slow decay of dipole reorientation of the solvent as a function of distance to the cofactor, implying that the change in the electric field upon electron transfer is not as effectively screened by the four-helix bundle protein. However, ranking the residues according to their free energy contributions, it is suggested that the reorganization free energy can be decreased by about 0.2 eV if two glutamine residues in the vicinity of the cofactor are mutated into less polar amino acids.     

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.     

Stepwise hydration and multibody deprotonation with steep negative temperature dependence in the benzene.+ -water system

We studied the stepwise hydration and solvent-mediated deprotonation of the benzene*+ cation (Bz*+) and found several unusual features. The solvent binding energies DeltaH on-1,n for the reactions Bz*+(H2O)n-1 + H2O --> Bz*+(H2O)n are nearly constant at 9 +/- 1 kcal mol-1 for n = 1 to 8. We observed a remarkable sudden decrease in the entropy of association accompanying the formation of Bz*+(H2O)7 and Bz*+(H2O)8, indicating strong orientational restraint in the hydration shells of these clusters consistent with the formation of cagelike structures. We observed the size-dependent deprotonation of Bz*+ in a cooperative multibody process, where n H2O molecules (n >/= 4) can remove a proton from Bz*+ to form protonated water clusters. We measured, for the first time, the temperature dependence of such a process and found a negative temperature coefficient of a magnitude unprecedented in any chemical reaction, of the form k = AT-67+/- 4, or in an Arrhenius form having an activation energy of -34 +/- 1 kcal mol-1. The temperature effect may be explained by Bz*+ and four H2O molecules needing to be assembled from gas-phase components to form the reactive species. Such large temperature effects may be therefore general in solvent cluster-mediated reactions.     

Stepwise hydration of ionized aromatics. Energies, structures of the hydrated benzene cation, and the mechanism of deprotonation reactions

The stepwise binding energies (DeltaHdegree(n-1,n)) of 1-8 water molecules to benzene(.+) [Bz(.+)(H2O)n] were determined by equilibrium measurements using an ion mobility cell. The stepwise hydration energies, DeltaHdegree(n-1,n), are nearly constant at 8.5 +/- 1 kcal mol-1 from n = 1-6. Calculations show that in the n = 1-4 clusters, the benzene(.+) ion retains over 90% of the charge, and it is extremely solvated, that is, hydrogen bonded to an (H2O)n cluster. The binding energies and entropies are larger in the n = 7 and 8 clusters, suggesting cyclic or cage-like water structures. The concentration of the n = 3 cluster is always small, suggesting that deprotonation depletes this ion, consistent with the thermochemistry since associative deprotonation Bz(.+)(H2O)(n-1) + H2O-->C6H5. + (H2O)nH+ is thermoneutral or exothermic for n > or = 4. Associative intracluster proton transfer Bz(.+)(H2O)(n+1) + H2O-->C6H5.(H2O)nH+ would also be exothermic for n > or = 4, but lack of H/D exchange with D2O shows that the proton remains on C6H6(.+) in the observed Bz(.+)(H2O)n clusters. This suggests a barrier to intracluster proton transfer, and as a result, the [Bz(.+)(H2O)n]* activated complexes either undergo dissociative proton transfer, resulting in deprotonation and generation of (H2O)nH+, or become stabilized. The rate constant for the deprotonation reaction shows a uniquely large negative temperature coefficient of K = cT(-67+/-4) (or activation energy of -34+/- 1 kcal mol-1), caused by a multibody mechanism in which five or more components need to be assembled for the reaction.     

Energetics of radical transfer in DNA photolyase

Charge separation and radical transfer in DNA photolyase from Escherichia coli is investigated by computing electrostatic free energies from a solution of the Poisson-Boltzmann equation. For the initial charge separation 450 meV are available. According to recent experiments [Aubert et al. Nature 2000, 405, 586-590] the flavin receives an electron from the proximal tryptophan W382, which consequently forms a cationic radical WH(*)(+)382. The radical state is subsequently transferred along the triad W382-W359-W306 of conserved tryptophans. The radical transfer to the intermediate tryptophan W359 is nearly isoenergetic (58 meV uphill); the radical transfer from the intermediate W359 to the distal W306 is 200 meV downhill in energy, funneling and stabilizing the radical state at W306. The resulting cationic radical WH(*)(+)306 is further stabilized by deprotonation, yielding the neutral radical W(*)306, which is 214 meV below WH(*)(+)306. The time scale of the charge recombination process yielding back the resting enzyme with FADH(*) is governed by reprotonation of W306, with a calculated lifetime of 1.2 ms that correlates well with the measured lifetime of 17 ms. In photolyase from Anacystis nidulans the radical state is partially transferred to a tyrosine [Aubert et al. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 5423-5427]. In photolyase from Escherichia coli, there is a tyrosine (Y464) close to the distal tryptophan W306 that could play this role. We show that this tyrosine cannot be involved in radical transfer, because the electron transfer from tyrosine to W306 is much too endergonic (750 meV) and a direct hydrogen transfer is likely too slow. Coupling of specific charge states of the tryptophan triad with protonation patterns of titratable residues of photolyase is small.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

黄嘌呤异构体质子转移异构化反应机理的理论研究

采用量子化学密度泛函B3LYP/6-31G(d,p)和M06-2X/6-311++G(d,p)方法对黄嘌呤两种酮式异构体X(1,3,7)与X(1,3,9)间质子转移引起的互变异构反应机理进行了计算研究,获得了异构化反应过程的反应焓﹑活化吉布斯自由能和质子转移反应的速率常数等参数。水相计算采用极化连续(PCM)模型。结果表明,由于可能的氢迁移顺序差异,分子内由X(1,3,7)向X(1,3,9)异构化可能共有16条反应通道,涉及11个中间体和20个过渡态,其主反应通道速控步骤的活化吉布斯自由能为183.10k J/mol,速率常数为5.17×10-20s-1,其余各通道速控步骤活化吉布斯自由能均较高,而且整体水溶剂效应不利于质子转移的发生。     

Internal energies of analyte ions generated from different matrix-assisted laser desorption/ionization matrices

A transfer of energy into the internal modes of the matrix and analyte is expected to occur during matrix-assisted laser desorption/ioniziation (MALDI) processes. Both the physical and thermochemical properties of the MALDI matrix used can influence the ion internal energy and analyte ion fragmentation. Here we report the effect of several MALDI matrices on the relative internal energy of the 2'-deoxyadenylyl-(3',5')-2'-deoxyguanosine (AG) anion. Relative internal energies were probed by low-energy collision-induced dissociation in a Fourier transform ion cyclotron resonance mass spectrometer. Sublimation temperatures of the matrices under study were also determined and found to lie between 409 and 455 K. Analyte ion internal and initial kinetic energies did not correlate with matrix sublimation temperatures. In contrast, a strong correlation between the relative internal energy of the analyte anions and the gas-phase basicity of the matrix anions was found. These results suggest that gas-phase proton transfer reactions play an important role in MALDI analyte ion formation and influence their internal energy and fragmentation behavior. Copyright 2000 John Wiley & Sons, Ltd.