Low dielectric response in enzyme active site

The physico-chemical "anatomy" of the tautomerization through the DPT of the biologically important pairs of hypoxanthine with DNA bases: QM and QTAIM perspectives

The biologically important tautomerization of the Hyp·Cyt, Hyp·Thy and Hyp·Hyp base pairs to the Hyp·Cyt, Hyp·Thy and Hyp·Hyp base pairs, respectively, by the double proton transfer (DPT) was comprehensively studied in vacuo and in the continuum with a low dielectric constant (ε = 4) corresponding to hydrophobic interfaces of protein-nucleic acid interactions by combining theoretical investigations at the B3LYP/6-311++G(d,p) level of QM theory with QTAIM topological analysis. Based on the sweeps of the energetic, electron-topological, geometric and polar parameters, which describe the course of the tautomerization along the intrinsic reaction coordinate (IRC), it was proved that the tautomerization through the DPT is concerted and asynchronous process for the Hyp·Cyt and Hyp·Thy base pairs, while concerted and synchronous for the Hyp·Hyp homodimer. The continuum with ε = 4 does not affect qualitatively the course of the tautomerization reaction for all studied complexes. The nine key points along the IRC of the Hyp·Cyt↔Hyp·Cyt and Hyp·Thy↔Hyp·Thy tautomerizations and the six key points of the Hyp·Hyp↔Hyp·Hyp tautomerization have been identified and fully characterized. These key points could be considered as electron-topological "fingerprints" of concerted asynchronous (for Hyp·Cyt and Hyp·Thy) or synchronous (for Hyp·Hyp) tautomerization process via the DPT. It was found, that in the Hyp·Cyt, Hyp·Thy, Hyp·Hyp and Hyp·Hyp base pairs all H-bonds are significantly cooperative and mutually reinforce each other, while the C2H…O2 H-bond in the Hyp·Cyt base pair and the O6H…O4 H-bond in the Hyp·Thy base pair behave anti-cooperatively, i.e., they become weakened, while two others become strengthened.

Can DNA-binding proteins of replisome tautomerize nucleotide bases? Ab initio model study

Ab initio quantum-chemical study of specific point contacts of replisome proteins with DNA modeled by acetic acid with canonical and mutagenic tautomers of DNA bases methylated at the glycosidic nitrogen atoms was performed in vacuo and continuum with a low dielectric constant (ϵ ∼ 4) corresponding to a hydrophobic interface of protein-nucleic acid interaction. All tautomerized complexes were found to be dynamically unstable, because the electronic energies of their back-reaction barriers do not exceed zero-point vibrational energies associated with the vibrational modes whose harmonic vibrational frequencies become imaginary in the transition states of the tautomerization reaction. Additionally, based on the physicochemical arguments, it was demonstrated that the effects of biomolecular environment cannot ensure dynamic stabilization. This result allows suggesting that hypothetically generated by DNA-binding proteins of replisome rare tautomers will have no impact on the total spontaneous mutation due to the low reverse barrier allowing a quick return to the canonical form.

Experimentally assessing molecular dynamics sampling of the protein native state conformational distribution

The acute sensitivity to conformation exhibited by amide hydrogen exchange reactivity provides a valuable test for the physical accuracy of model ensembles developed to represent the Boltzmann distribution of the protein native state. A number of molecular dynamics studies of ubiquitin have predicted a well-populated transition in the tight turn immediately preceding the primary site of proteasome-directed polyubiquitylation Lys 48. Amide exchange reactivity analysis demonstrates that this transition is 10(3)-fold rarer than these predictions. More strikingly, for the most populated novel conformational basin predicted from a recent 1 ms MD simulation of bovine pancreatic trypsin inhibitor (at 13% of total), experimental hydrogen exchange data indicates a population below 10(-6). The most sophisticated efforts to directly incorporate experimental constraints into the derivation of model protein ensembles have been applied to ubiquitin, as illustrated by three recently deposited studies (PDB codes 2NR2, 2K39 and 2KOX2K392KOX). Utilizing the extensive set of experimental NOE constraints, each of these three ensembles yields a modestly more accurate prediction of the exchange rates for the highly exposed amides than does a standard unconstrained molecular simulation. However, for the less frequently exposed amide hydrogens, the 2NR2 ensemble offers no improvement in rate predictions as compared to the unconstrained MD ensemble. The other two NMR-constrained ensembles performed markedly worse, either underestimating (2KOX) or overestimating (2K39) the extent of conformational diversity.

Electrostatics of hydrogen exchange for analyzing protein flexibility

Electrostatic interactions at the protein-aqueous interface modulate the reactivity of solvent-exposed backbone amides by a factor of at least a billion fold. The brief (∼10 ps) lifetime of the peptide anion formed during the hydroxide-catalyzed exchange reaction helps enable the experimental rates to be robustly predictable by continuum dielectric methods. Since this ability to predict the structural dependence of exchange reactivity also applies to the protein amide hydrogens that are only rarely exposed to the bulk solvent phase, electrostatic analysis of the experimental exchange rates provides an effective assessment of whether a given model ensemble is consistent with the properly weighted Boltzmann conformational distribution of the protein native state.

DFT STUDY ON METAL CATIONIZATION AND O6-PROTONATION ON 2′-DEOXYGUANOSINE CONFIGURATION: CHANGES ON SUGAR PUCKERING AND STRENGTH OF THE N-GLYCOSIDIC BOND

Density functional theory (DFT) calculations were performed at the B3LYP/6-311++G (d, p) level to determine coordination geometries, absolute metal ion affinities, and free energies for all possible complexation stable products formed by monovalent metal cations including Li+ , Na+ , K+ with the nucleoside 2′-Deoxyguanosine. All computations indicate that the metal ion affinity (MIA) decreases on going from Li+ to Na+ and K+ for 2′-Deoxyguanosine. For example, the affinities for the metal ions described above are 75.2, 57.3, 43.4 kcal/mol, respectively.

Furthermore, the influence of metal cationization and O6 protonation on the strength of the N-glycosidic bond, torsion angles and angle of pseudorotation (P) have been studied. With respect to the results, it has been found that metal binding significantly change the values of the phase angle of pseudorotation (P) in the sugar unit of these nucleosides but, O6 -protonation do not significantly change the values of the torsion angles and angle of pseudorotation (P). In all modified forms, the length of the C1'–N9 bond increases. The Mulliken population analysis and natural bond orbital (NBO) analysis on atomic charges have been carried out on the optimized geometries.

Assessing the native state conformational distribution of ubiquitin by peptide acidity

At equilibrium, every energetically feasible conformation of a protein occurs with a non-zero probability. Quantitative analysis of protein flexibility is thus synonymous with determining the proper Boltzmann-weighting of this conformational distribution. The exchange reactivity of solvent-exposed amide hydrogens greatly varies with conformation, while the short-lived peptide anion intermediate implies an insensitivity to the dynamics of conformational motion. Amides that are well-exposed in model conformational ensembles of ubiquitin vary a million-fold in exchange rates which continuum dielectric methods can predict with an rmsd of 3. However, the exchange rates for many of the more rarely exposed amides are markedly overestimated in the PDB-deposited 2K39 and 2KN5 ubiquitin ensembles, while the 2NR2 ensemble predictions are largely consistent with those of the Boltzmann-weighted conformational distribution sampled at the level of 1%. The correlation between the fraction of solvent-accessible conformations for a given amide hydrogen and the exchange rate constant for that residue provides a useful monitor of the degree of completeness with which a given ensemble has sampled the energetically accessible conformational space. These exchange predictions correlate with the degree to which each ensemble deviates from a set of 46 ubiquitin X-ray structures. Kolmogorov-Smirnov analysis for the distribution of intra- and inter-ensemble pairwise structural rmsd values assisted the identification of a subensemble of 2K39 that eliminates the overestimations of hydrogen exchange rates observed for the full ensemble. The relative merits of incorporating experimental restraints into the conformational sampling process are compared to using these restraints as filters to select subpopulations consistent with the experimental data.

Mechanism of DNA methylation: the double role of DNA as a substrate and as a cofactor

Methylation of cytosine residues in the DNA is one of the most important epigenetic marks central to the control of differential expression of genes. We perform quantum mechanical calculations to investigate the catalytic mechanism of the bacterial HhaI DNA methyltransferase. We find that the enzyme nucleophile, Cys81, can attack C6 of cytosine only after it is deprotonated by the DNA phosphate group, a reaction facilitated by a bridging water molecule. This finding, which indicates that the DNA acts as both the substrate and the cofactor, can explain the total loss of activity observed in an analogous enzyme, thymidylate synthase, when the phosphate group of the substrate was removed. Furthermore, our results displaying the inability of the phosphate group to deprotonate the side chain of serine is in agreement with the total, or the large extent of, inactivity observed for the C81S mutant. In contrast to results from previous calculations, we find that the active site conserved residues, Glu119, Arg163, and Arg165, are crucial for catalysis. In addition, the enzyme-DNA adduct formation and the methyl transfer from the cofactor S-adenosyl-L-methionine are not concerted but proceed via stepwise mechanism. In many of the different steps of this methylation reaction, the transfer of a proton is found to be necessary. To render these processes possible, we find that several water molecules, found in the crystal structure, play an important role, acting as a bridge between the donating and accepting proton groups.

Sidechain conformational dependence of hydrogen exchange in model peptides

Peptide hydrogens that are exposed to solvent in protein X-ray structures exhibit a billion-fold range in hydroxide-catalyzed exchange rates, and these rates have previously been shown to be predictable by continuum dielectric methods to within a factor of 7, based on single protein conformations. When using a protein coil library to model the Boltzmann-weighted conformational distribution for the various N-acetyl-[X-Ala]-N-methylamides and N-acetyl-[Ala-Y]-N-methylamides, the acidity of the central amide in the individual conformers of each peptide spans nearly a million-fold range. Nevertheless, population averaging of these conformer acidities predicts the standard sidechain-dependent hydrogen exchange correction factors for nonpolar model peptides to within a factor of 30% (10(0.11)) with a correlation coefficient r=0.91. Comparison with the analogous continuum dielectric calculations for the other N-acetyl-[X-Y]-N-methylamides indicates that deviations from the isolated residue hypothesis of classical polymer theory predict appreciable errors in the exchange rates for conformationally disordered peptides when the standard sidechain-dependent hydrogen exchange rate correction factors are assumed to be independently additive. Although electronic polarizability generally dominates the dielectric shielding for the approximately 10ps lifetime of peptide ionization, evidence is presented for modest contributions from rapid intrarotamer conformational reorganization of Asn and Gln sidechains.

Redox potential of the Rieske iron-sulfur protein quantum-chemical and electrostatic study

Quantum-chemical study of structures, energies, and effective partial charge distribution for several models of the Rieske protein redox center is performed in terms of the B3LYP density functional method in combination with the broken symmetry approach using three different atomic basis sets. The structure of the redox complex optimized in vacuum differs markedly from that inside the protein. This means that the protein matrix imposes some stress on the active site resulting in distortion of its structure. The redox potentials calculated for the real active site structure are in a substantially better agreement with the experiment than those calculated for the idealized structure. This shows an important role of the active site distortion in tuning its redox potential. The reference absolute electrode potential of the standard hydrogen electrode is used that accounts for the correction caused by the water surface potential. Electrostatic calculations are performed in the framework of the polarizable solute model. Two dielectric permittivities of the protein are employed: the optical permittivity for calculation of the intraprotein electric field, and the static permittivity for calculation of the dielectric response energy. Only this approach results in a reasonable agreement of the calculated and experimental redox potentials.

Peptide conformer acidity analysis of protein flexibility monitored by hydrogen exchange

The amide hydrogens that are exposed to solvent in the high-resolution X-ray structures of ubiquitin, FK506-binding protein, chymotrypsin inhibitor 2, and rubredoxin span a billion-fold range in hydroxide-catalyzed exchange rates which are predictable by continuum dielectric methods. To facilitate analysis of transiently accessible amides, the hydroxide-catalyzed rate constants for every backbone amide of ubiquitin were determined under near physiological conditions. With the previously reported NMR-restrained molecular dynamics ensembles of ubiquitin (PDB codes 2NR2 and 2K39) used as representations of the Boltzmann-weighted conformational distribution, nearly all of the exchange rates for the highly exposed amides were more accurately predicted than by use of the high-resolution X-ray structure. More strikingly, predictions for the amide hydrogens of the NMR relaxation-restrained ensemble that become exposed to solvent in more than one but less than half of the 144 protein conformations in this ensemble were almost as accurate. In marked contrast, the exchange rates for many of the analogous amides in the residual dipolar coupling-restrained ubiquitin ensemble are substantially overestimated, as was particularly evident for the Ile 44 to Lys 48 segment which constitutes the primary interaction site for the proteasome targeting enzymes involved in polyubiquitylation. For both ensembles, “excited state” conformers in this active site region having markedly elevated peptide acidities are represented at a population level that is 10² to 10³ above what can exist in the Boltzmann distribution of protein conformations. These results indicate how a chemically consistent interpretation of amide hydrogen exchange can provide insight into both the population and the detailed structure of transient protein conformations.

Metal and substrate binding to an Fe(II) dioxygenase resolved by UV spectroscopy with global regression analysis

The addition of divalent metal ions or substrate taurine to TauD, an alpha-ketoglutarate-dependent dioxygenase, alters its UV absorption, as clearly observed by monitoring the protein's difference spectra. Binding of metal ions leads to a decrease in absorption at approximately 297 nm and modulation of other features. A separate signature with enhanced absorption at approximately 295 nm is identified for binding of taurine. These narrow ( approximately 700 cm(-1)) and intense ( approximately 0.5mM(-1) cm(-1)) spectral changes are attributed to ligand-induced protein conformational changes affecting the environment of aromatic residues. The changes in the UV difference spectra were exploited to assess directly the thermodynamics and kinetics of ligand interactions in wild-type TauD and selected variants. This approach holds promise as a new tool to probe ligand-induced conformational changes in a wide range of other proteins. Experimental and quantification approaches for a reliable analysis of protein absorption below 320 nm are presented.

Polarization and polarizability assessed by protein amide acidity

Hydroxide-catalyzed exchange rate constants were determined for those amides of FK506-binding protein (FKBP12), ubiquitin, and chymotrypsin inhibitor 2 (CI2) that are solvent-accessible in the high-resolution X-ray structures. When combined with previous hydrogen exchange results for the rubredoxin from Pyrococcus furiosus, the acidity of these amides was calculated by continuum dielectric methods as a function of the nonpolarizable electrostatic parameter set, internal dielectric, and the charge distribution of the peptide anion. The CHARMM22 parameter set with an internal dielectric value of 3 and an ab initio-derived anion charge distribution yielded an rmsd value of 7 for the 56 amide exchange rate constants ranging from 10(0.67) to 10(9.0) M(-1) s(-1). The OPLS-AA parameter set yielded comparably robust predictions, while that of PARSE, AMBER parm99, and AMBER ff03 performed more poorly. The small value for the optimal internal dielectric, combined with the brief lifetime of the peptide anion intermediate and the uniformity of the correlation between predicted and observed amide acidities, is consistent with electronic polarizability providing the dominant contribution to dielectric shielding. By construction, nonpolarizable force fields do not model electric field attenuation by electronic polarizability. Accurate prediction of the total electrostatic energy by such force fields necessitates the hyperpolarization of the atomic charge values in order to match the average electric field energy density (1/2)epsilon(tau)E(2)(tau) when epsilon(tau) is set to the in vacuo dielectric value of 1. The resulting predictions of the experimental hydrogen exchange data demonstrate the substantial systematic errors in the predicted electrostatic potential that can arise when dielectric shielding due to electronic polarizability is neglected.

Testing geometrical discrimination within an enzyme active site: constrained hydrogen bonding in the ketosteroid isomerase oxyanion hole

Enzymes are classically proposed to accelerate reactions by binding substrates within active-site environments that are structurally preorganized to optimize binding interactions with reaction transition states rather than ground states. This is a remarkably formidable task considering the limited 0.1-1 A scale of most substrate rearrangements. The flexibility of active-site functional groups along the coordinate of substrate rearrangement, the distance scale on which enzymes can distinguish structural rearrangement, and the energetic significance of discrimination on that scale remain open questions that are fundamental to a basic physical understanding of enzyme active sites and catalysis. We bring together 1.2-1.5 A resolution X-ray crystallography, (1)H and (19)F NMR spectroscopy, quantum mechanical calculations, and transition-state analogue binding measurements to test the distance scale on which noncovalent forces can constrain the structural relaxation or translation of side chains and ligands along a specific coordinate and the energetic consequences of such geometric constraints within the active site of bacterial ketosteroid isomerase (KSI). Our results strongly suggest that packing and binding interactions within the KSI active site can constrain local side-chain reorientation and prevent hydrogen bond shortening by 0.1 A or less. Further, this constraint has substantial energetic effects on ligand binding and stabilization of negative charge within the oxyanion hole. These results provide evidence that subtle geometric effects, indistinguishable in most X-ray crystallographic structures, can have significant energetic consequences and highlight the importance of using synergistic experimental approaches to dissect enzyme function.

Semi-continuum electrostatic calculations of redox potentials in photosystem I

The midpoint redox potentials (E(m)) of all cofactors in photosystem I from Synechococcus elongatus as well as of the iron-sulfur (Fe(4)S(4)) clusters in two soluble ferredoxins from Azotobacter vinelandii and Clostridium acidiurici were calculated within the framework of a semi-continuum dielectric approach. The widely used treatment of proteins as uniform media with single dielectric permittivity is oversimplified, particularly, because permanent charges are considered both as a source for intraprotein electric field and as a part of dielectric polarizability. Our approach overcomes this inconsistency by using two dielectric constants: optical epsilon(o)=2.5 for permanent charges pre-existing in crystal structure, and static epsilon(s) for newly formed charges. We also take into account a substantial dielectric heterogeneity of photosystem I revealed by photoelectric measurements and a liquid junction potential correction for E(m) values of relevant redox cofactors measured in aprotic solvents. We show that calculations based on a single permittivity have the discrepancy with experimental data larger than 0.7 V, whereas E(m) values calculated within our approach fall in the range of experimental estimates. The electrostatic analysis combined with quantum chemistry calculations shows that (i) the energy decrease upon chlorophyll dimerization is essential for the downhill mode of primary charge separation between the special pair P(700) and the primary acceptor A(0); (ii) the primary donor is apparently P(700) but not a pair of accessory chlorophylls; (iii) the electron transfer from the A branch quinone Q(A) to the iron-sulfur cluster F(X) is most probably downhill, whereas that from the B branch quinone Q(B) to F(X) is essentially downhill.

Dielectric relaxation in proteins: the computational perspective

In photoexcitation and electron transfer, a new dipole or charge is introduced, and the structure is adjusted. This adjustment represents dielectric relaxation, which is the focus of this review. We concentrate on a few selected topics. We discuss linear response theory, as a unifying framework and a tool to describe non-equilibrium states. We review recent, molecular dynamics simulation studies that illustrate the calculation of dynamic and thermodynamic properties, such as Stokes shifts or reorganization free energies. We then turn to the macroscopic, continuum electrostatic view. We recall the physical definition of a dielectric constant and revisit the decomposition of the free energy into a reorganization and a static term. We review some illustrative continuum studies and discuss some difficulties that can arise with the continuum approach. In conclusion, we consider recent developments that will increase the accuracy and broaden the scope of all these methods.

Spatial distribution of dielectric shielding in the interior of Pyrococcus furiosus rubredoxin as sampled in the subnanosecond timeframe by hydrogen exchange

Experimental pK values of ionizable sidechains provide the most direct test for models representing dielectric shielding within the interior of a protein. However, only the strongly shifted pK values are particularly useful for discriminating among models. NMR titration studies have usually found only one or two such shifted pK values in each protein, so that the fitting of the experimental data to a uniform internal dielectric (epsilon(int)) model is not well constrained. The observed variation among proteins for such epsilon(int) estimates may reflect nonuniformity of dielectric shielding within each protein interior or qualitative differences between individual proteins. The differential amide kinetic acidities for a series of metal-substituted rubredoxins are shown to be consistent with Poisson-Boltzmann predictions of dielectric shielding that is relatively uniform for all of the amides that are sensitive to the metal charge, a region which corresponds to roughly 1/3 of the internal volume. The effective epsilon(int) values near 6 that are found in this study are significantly lower than many such estimates derived from sidechain pK measurements. The differing timeframes in which dielectric relaxation can respond to the highly transient peptide anion as compared to the longer lived states of the charged sidechains offers an explanation for the lower apparent dielectric constant deduced from these measurements.

Comprehensive Conformational Analysis of the Nucleoside Analogue 2‘-β-Deoxy-6-azacytidine by DFT and MP2 Calculations

A comprehensive conformational analysis of isolated 2'-beta-deoxy-6-azacytidine (d6AC), an analogue of therapeutically active 6-azacytidine (6AC), has been performed by means of ab initio calculations at the MP2/6-311++G(2df,pd)//DFT B3LYP/6-31G(d,p) level of theory. Among the 81 conformers located within a 7.83 kcal/mol Gibbs energy range at T = 298.15 K, 38 contain syn-oriented bases with respect to 2'-deoxyribose; the other conformers include anti-oriented bases. Energetic analysis of these conformers shows that conformational equilibrium of isolated d6AC at T = 298.15 K is shifted to syn conformation with a syn/anti ratio estimated as 61.4%:38.6%. As far as the sugar conformation is concerned, 40 conformers contain north (N) (with 0.3 degrees < or = P < or = 40.1 degrees), and the rest possess south (S) (with 157.1 degrees < or = P < or = 207.0 degrees) puckers, where P is the pseudorotational angle of the furanose ring. The S/N occupancy ratio is estimated as 80.2%:19.8% (T = 298.15 K). The two most stable conformers are energetically quasidegenerate and correspond to both C2'-endo/syn conformers differing only by orientation of the O3'H hydroxyl group. They are both stabilized by means of similar intramolecular H-bonds, i.e., O5'H...O2, C2'H2...O2, and C2'H2...O5'. As examined by AIM criteria, from 1 to 3 H-bonds per conformer were identified among 13 possible interactions: O5'H...O2, O5'H...N6, O3'H...O5', O5'H...O3', C1'H...O2, C2'H2...O2, C2'H2...O5', C3'H...O2, C3'H...N6, C5'H1...O2, C5'H2...O2, C5'H1...N6, and C5'H2...N6. The biological effect of d6AC is conceived as an inhibition of replicative DNA polymerase caused by an unusual orientation of the sugar residue against the base in the only A form DNA-like conformer.

Calculation of redox properties: understanding short- and long-range effects in rubredoxin

In this computational study we show that for rubredoxin, a small and comparatively simple iron-sulfur protein, it is possible to combine a full ab initio description of the electronic structure of the protein in explicit solvent with sampling of the relevant time scale of the protein dynamics by using a hybrid method based on a force field molecular dynamics/density functional theory scheme. Applying this scheme within the framework of Marcus theory we are able to reproduce the experimental redox potential difference of 60 mV between a mesophilic and thermophilic rubredoxin within an accuracy of 20 mV and explain it in terms of short-range contributions from a few residues close to the metal center. We also compute the reorganization free energy for oxidation of the protein obtaining 720 meV for the mesophilic and 590 meV for thermophilic variant. Decomposition of the reorganization energy by using the classical force field shows that this quantity is largely determined by the solvent, with both short-range (an oxidation induced change of coordination number) and long-range (dielectric) contributions. The 130 meV higher value for the mesophilic form is analyzed in terms of detailed differences in the solvent structure around the metal center and the dielectric response. These results underline the importance of a molecular description of the solvent and of a correct inclusion of the polarization effects.

Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction Center Using a Microstate Description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.

Factors influencing the energetics of electron and proton transfers in proteins. What can be learned from calculations

A protein structure should provide the information needed to understand its observed properties. Significant progress has been made in developing accurate calculations of acid/base and oxidation/reduction reactions in proteins. Current methods and their strengths and weaknesses are discussed. The distribution and calculated ionization states in a survey of proteins is described, showing that a significant minority of acidic and basic residues are buried in the protein and that most of these remain ionized. The electrochemistry of heme and quinones are considered. Proton transfers in bacteriorhodopsin and coupled electron and proton transfers in photosynthetic reaction centers, 5-coordinate heme binding proteins and cytochrome c oxidase are highlighted as systems where calculations have provided insight into the reaction mechanism.

Proton binding to proteins: a free-energy component analysis using a dielectric continuum model

Proton binding plays a critical role in protein structure and function. We report pK(a) calculations for three aspartates in two proteins, using a linear response approach, as well as a "standard" Poisson-Boltzmann approach. Averaging over conformations from the two endpoints of the proton-binding reaction, the protein's atomic degrees of freedom are explicitly modeled. Treating macroscopically the protein's electronic polarizability and the solvent, a meaningful model is obtained, without adjustable parameters. It reproduces qualitatively the electrostatic potentials, proton-binding free energies, Marcus reorganization free energies, and pK(a) shifts from explicit solvent molecular dynamics simulations, and the pK(a) shifts from experiment. For thioredoxin Asp-26, which has a large pK(a) upshift, we correctly capture the balance between unfavorable carboxylate desolvation and favorable interactions with a nearby lysine; similarly for RNase A Asp-14, which has a large pK(a) downshift. For the unshifted thioredoxin Asp-20, desolvation by the protein cavity is overestimated by 2.9 pK(a) units; several effects could explain this. "Standard" Poisson-Boltzmann methods sidestep this problem by using a large, ad hoc protein dielectric; but protein charge-charge interactions are then incorrectly downscaled, giving an unbalanced description of the reaction and a large error for the shifted pK(a) values of Asp-26 and Asp-14.

Influence of the solvent structure on the electrostatic interactions in proteins

The proper estimation of the influence of the many-body dynamic solvent microstructure on a pairwise electrostatic interaction (PEI) at the protein-solvent interface is very important for solving many biophysical problems. In this work, the PEI energy was calculated for a system that models the interface between a protein and an aqueous solvent. The concept of nonlocal electrostatics for interfacial electrochemical systems was used to evaluate the contribution of a solvent orientational polarization, correlated by the network of hydrogen bonds, into the PEI energy in proteins. The analytical expression for this energy was obtained in the form of Coulomb's law with an effective distance-dependent dielectric function. The asymptotic and numerical analysis carried out for this function revealed several features of dielectric heterogeneity at the protein-solvent interface. For charges located in close proximity to this interface, the values of the dielectric function for the short-distance electrostatic interactions were found to be remarkably smaller than those determined by the classical model, in which the solvent was considered as the uniform dielectric medium of high dielectric constant. Our results have shown that taking into consideration the dynamic solvent microstructure remarkably increases the value of the PEI energy at the protein-solvent interface.

Anomalous Microscopic Dielectric Response of Dipolar Solvents and Water

This paper reports measurements of static microscopic dielectric response of several dipolar solvents to charge redistribution in a fluorescent probe. Contrary to recent predictions of dielectric theories and computer simulations of bulk liquids, the observed dielectric response of most solvents conforms to the macroscopic continuum description even at atomic distances, as if these solvents had no spatial intermolecular structure. Such conformance is observed for several probes when the contribution of specific probe-solvent interactions to the response is negligible. However, water, formamide, and glycerol exhibit anomalous responses even though such a probe is used. We discuss a possible reason for the macroscopic-like behavior and a connection between the anomaly and fluctuating structures formed by anomalous solvents near the hydrophobic surface of the probe.

Solvation forces on biomolecular structures: a comparison of explicit solvent and Poisson-Boltzmann models

Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without expensive sampling required by explicit solvent models. In particular, the Poisson-Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless, dielectric material, and the mobile ions as a continuous distribution of charge. Polar solvation forces and energies obtained from the PBE are often supplemented with simple solvent-accessible surface area (SASA) models of nonpolar solvation. Given the recent development of methods that enable the use of PBE and SASA forces in molecular dynamics simulations, it is important to determine the ability of these implicit solvent models to accurately reproduce the solvation forces of more detailed explicit solvent simulations. In this article, we compare PBE and SASA solvation forces with explicit solvent forces for several snapshots from eight trajectories of static conformations of intestinal fatty acid binding protein. The results from this comparison show that current implementations of the PBE are capable of generating polar solvation forces that correlate well with explicit solvent forces but systematically overestimate the magnitude of the interaction. However, SASA-based nonpolar forces are found to have no significant correlation with nonpolar explicit solvent forces. Nevertheless, due to the small magnitude of the nonpolar forces in the current system, a good correlation is still obtained for total solvation forces. The good correlation of implicit solvent forces with more detailed explicit solvent models is encouraging and implies that the systematic errors identified in these models could be corrected by appropriate parameterization of the force fields.

Quantification of helix-helix binding affinities in micelles and lipid bilayers

A theoretical approach for estimating association free energies of alpha-helices in nonpolar media has been developed. The parameters of energy functions have been derived from DeltaDeltaG values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of alpha-helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of alpha-helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.

Photoelectric studies of the transmembrane charge transfer reactions in photosystem I pigment-protein complexes

The results of studies of charge transfer in cyanobacterial photosystem I (PS I) using the photoelectric method are reviewed. The electrogenicity in the PS I complex and its interaction with natural donors (plastocyanin, cytochrome c(6)), natural acceptors (ferredoxin, flavodoxin), or artificial acceptors and donors (methyl viologen and other redox dyes) were studied. The operating dielectric constant values in the vicinity of the charge transfer carriers in situ were calculated. The profile of distribution of the dielectric constant along the PS I pigment-protein complex (from plastocyanin or cytochrome c(6) through the chlorophyll dimer P700 to the acceptor complex) was estimated, and possible mechanisms of correlation between the local dielectric constant and electron transfer rate constant were discussed.

pH-dependent redox potential: how to use it correctly in the activation energy analysis

The activation barrier (the activation free energy) for the reaction's elementary act proper does not depend on the presence of reactants outside the reaction complex. The barrier is determined directly by the concentration-independent configurational free energy. In the case of redox reactants with pH-dependent redox potential, only the pH-independent quantity, the configurational redox potential enters immediately into expression for activation energy. Some typical cases of such reactions have been discussed (e.g., simultaneous proton and electron detachment, acid dissociation followed by oxidation, dissociation after oxidation, and others). For these mechanisms, the algorithms for calculation of the configurational redox potential from the experimentally determined redox potentials have been described both for the data related to a dissolved reactant or to a prosthetic group of an enzyme. Some examples of pH-dependent enzymatic redox reactions, in particular for the Rieske iron-sulfur protein, have been discussed.

Catalysis of electron transfer during activation of O2 by the flavoprotein glucose oxidase

Two prototropic forms of glucose oxidase undergo aerobic oxidation reactions that convert FADH(-) to FAD and form H(2)O(2) as a product. Limiting rate constants of k(cat)K(M)(O(2)) = (5.7 +/- 1.8) x 10(2) M(-1).s(-1) and k(cat)K(M)(O(2)) = (1.5 +/- 0.3) x 10(6) M(-1).s(-1) are observed at high and low pH, respectively. Reactions exhibit oxygen-18 kinetic isotope effects but no solvent kinetic isotope effects, consistent with mechanisms of rate-limiting electron transfer from flavin to O(2). Site-directed mutagenesis studies reveal that the pH dependence of the rates is caused by protonation of a highly conserved histidine in the active site. Temperature studies (283-323 K) indicate that protonation of His-516 results in a reduction of the activation energy barrier by 6.0 kcal.mol(-1) (0.26 eV). Within the context of Marcus theory, catalysis of electron transfer is attributed to a 19-kcal.mol(-1) (0.82 eV) decrease in the reorganization energy and a much smaller 2.2-kcal.mol(-1) (0.095 eV) enhancement of the reaction driving force. An explanation is advanced that is based on changes in outer-sphere reorganization as a function of pH. The active site is optimized at low pH, but not at high pH or in the H516A mutant where rates resemble the uncatalyzed reaction in solution.

Probing protein electrostatics with a synthetic fluorescent amino acid

Electrostatics affect virtually all aspects of protein structure and activity and are particularly important in proteins whose primary function is to stabilize charge. Here we introduce a fluorescent amino acid, Aladan, which can probe the electrostatic character of a protein at multiple sites. Aladan is exceptionally sensitive to the polarity of its surroundings and can be incorporated site-selectively at buried and exposed sites, in both soluble and membrane proteins. Steady-state and time-resolved fluorescence measurements of Aladan residues at different buried and exposed sites in the B1 domain of protein G suggest that its interior is polar and heterogeneous.