An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.     

Optimizing pKa computation in proteins with pH adapted conformations

pK(A) in proteins are determined by electrostatic energy computations using a small number of optimized protein conformations derived from crystal structures. In these protein conformations hydrogen positions and geometries of salt bridges on the protein surface were determined self-consistently with the protonation pattern at three pHs (low, ambient, and high). Considering salt bridges at protein surfaces is most relevant, since they open at low and high pH. In the absence of these conformational changes, computed pK(A)(comp) of acidic (basic) groups in salt bridges underestimate (overestimate) experimental pK(A)(exp), dramatically. The pK(A)(comp) for 15 different proteins with 185 known pK(A)(exp) yield an RMSD of 1.12, comparable with two other methods. One of these methods is fully empirical with many adjustable parameters. The other is also based on electrostatic energy computations using many non-optimized side chain conformers but employs larger dielectric constants at short distances of charge pairs that diminish their electrostatic interactions. These empirical corrections that account implicitly for additional conformational flexibility were needed to describe the energetics of salt bridges appropriately. This is not needed in the present approach. The RMSD of the present approach improves if one considers only strongly shifted pK(A)(exp) in contrast to the other methods under these conditions. Our method allows interpreting pK(A)(comp) in terms of pH dependent hydrogen bonding pattern and salt bridge geometries. A web service is provided to perform pK(A) computations.     

A parameterized, continuum electrostatic model for predicting protein pKa values

Recognizing the limits of trying to achieve chemical accuracy for pK(a) calculations with a purely electrostatic model, we include empirical corrections into the Poisson-Boltzmann solver macroscopic electrostatics with atomic detail (Bashford, Biochemistry 1990;29:10219-10225), to improve the reliability and accuracy of the model. The total number of parameters is kept to a minimum to maximize the robustness of the model for compounds outside of the fitting dataset. The parameters are based on: (a) the electrostatic interaction between functional groups close to the titratable site, (b) the electrostatic work required to desolvate the residue, and (c) the site-to-site interactions. These interactions are straightforward to calculate once the electrostatic field has been solved for each residue using the linearized Poisson-Boltzmann equation and are assumed to be linearly related to the intrinsic pK(a). Two hundred and eighty-six residues from 30 proteins are used to determine the empirical parameters, which result in a root mean square error (RMSE) of 0.70 for the entire set. Eight proteins with 46 experimentally known values were excluded from the parameterization to test the model. This test set had a RMSE of 1.08. We show that the parameterized model improves the results over other models, although like other models the error is strongly correlated with the degree to which a residue is buried. The parameters themselves indicate that local effects are most important for determining the pK(a), whereas site-to-site interactions are found to be less significant.     

Electrostatic effects in highly charged proteins: salt sensitivity of pKa values of histidines in staphylococcal nuclease

The pK(a) values of most histidines in small peptides and in myoglobin increase on average by 0.30 unit between 0.02 and 1.5 M NaCl [Kao et al. (2000) Biophys. J. 79, 1637]. The DeltapK(a) values reflect primarily the ionic strength dependence of the solvation energy; screening of Coulombic interactions contributes only in a minor way. This implies that Coulombic interactions are weak, or that attractive and repulsive contributions to the pK(a) values are balanced. To distinguish experimentally between these two possibilities, and to further characterize the magnitude and salt sensitivity of surface electrostatic interactions in proteins, the salt dependence of pK(a) values of histidines in staphylococcal nuclease was measured by (1)H NMR spectroscopy. Three of the four histidines titrated with significantly depressed pK(a) values, and the salt sensitivity of all histidine pK(a) values was substantial. In three cases, the pK(a) values increased by a full unit between 0.01 and 1.5 M KCl. Anion-specific effects were found; the pK(a) values measured under equivalent ionic strengths in SCN(-) and SO(4)(2-) were higher than in Cl(-); the order of the sensitivity of pK(a) values to anions was SCN(-) > Cl(-) > SO(4)(2-). Structure-based pK(a) calculations with continuum methods were performed to interpret the measured effects structurally and to test their ability to capture the experimental behavior. Calculations in which the protein interior was treated empirically with a dielectric constant of 20 reproduced the pK(a) values and their dependence on the concentration of Cl(-). According to the calculations, the pK(a) values are depressed because of unfavorable self-energies and repulsive Coulombic interactions. Their striking salt sensitivity reflects screening of weak, repulsive, Coulombic interactions among charges separated by more than 10 A. Long-range Coulombic interactions on the surfaces of proteins are weak, but they can add up to produce substantial electrostatic effects when positive and negative charges are not balanced.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

NMR determination of pKa values in α-synuclein

The intrinsically unfolded protein α-synuclein has an N-terminal domain with seven imperfect KTKEGV sequence repeats and a C-terminal domain with a large proportion of acidic residues. We characterized pK(a) values for all 26 sites in the protein that ionize below pH 7 using 2D (1) H-(15) N HSQC and 3D C(CO)NH NMR experiments. The N-terminal domain shows systematically lowered pK(a) values, suggesting weak electrostatic interactions between acidic and basic residues in the KTKEGV repeats. By contrast, the C-terminal domain shows elevated pK(a) values due to electrostatic repulsion between like charges. The effects are smaller but persist at physiological salt concentrations. For α-synuclein in the membrane-like environment of sodium dodecylsulfate (SDS) micelles, we characterized the pK(a) of His50, a residue of particular interest since it is flanked within one turn of the α-helix structure by the Parkinson's disease-linked mutants E46K and A53T. The pK(a) of His50 is raised by 1.4 pH units in the micelle-bound state. Titrations of His50 in the micelle-bound states of the E46K and A53T mutants show that the pK(a) shift is primarily due to interactions between the histidine and the sulfate groups of SDS, with electrostatic interactions between His50 and Glu46 playing a much smaller role. Our results indicate that the pK(a) values of uncomplexed α-synuclein differ significantly from random coil model peptides even though the protein is intrinsically unfolded. Due to the long-range nature of electrostatic interactions, charged residues in the α-synuclein sequence may help nucleate the folding of the protein into an α-helical structure and confer protection from misfolding.     

The effect of heme-linked ionizable groups on cyanide binding to methemoglobin

The pH dependence of the kinetics of the binding of cyanide ion to methemoglobins A and S and to guinea pig and pigeon methemoglobins appears to be not directly correlated with the net charges on the proteins. The kinetics can, however, be adequately explained in terms of three sets of heme-linked ionizable groups with pK1 ranging between 4.9 and 5.3, pK2 between 6.2 and 7.9, and pK3 between 8.0 and 8.5 at 20 degrees C. pK1 is assigned to carboxylic acid groups, pK2 to histidines and terminal amino groups, and pK3 to the acid-alkaline methemoglobin transition. Kinetic second order rate constants have also been determined for the binding of cyanide ion by the four sets of methemoglobin species present in solution. The pKi values and the rate constants of methemoglobin S are strikingly different from those of methemoglobin A. This result is explained in terms of different electrostatic contributions to the free energy of heme linkage arising from differences in the environments of ionizable groups at the surfaces of the two molecules.     

Carboxyl pK(a) values, ion pairs, hydrogen bonding, and the pH-dependence of folding the hyperthermophile proteins Sac7d and Sso7d

Sac7d and Sso7d are homologous, hyperthermophile proteins with a high density of charged surface residues and potential ion pairs. To determine the relative importance of specific amino acid side-chains in defining the stability and function of these Archaeal chromatin proteins, pK(a) values were measured for the acidic residues in both proteins using (13)C NMR chemical shifts. The stability of Sso7d enabled titrations to pH 1 under low-salt conditions. Two aspartate residues in Sso7d (D16 and D35) and a single glutamate residue (G54) showed significantly perturbed pK(a) values in low salt, indicating that the observed pH-dependence of stability was primarily due to these three residues. The pH-dependence of backbone amide NMR resonances demonstrated that perturbation of all three pK(a) values was primarily the result of side-chain to backbone amide hydrogen bonds. Few of the significantly perturbed acidic pK(a) values in Sac7d and Sso7d could be attributed to primarily ion pair or electrostatic interactions. A smaller perturbation of E48 (E47 in Sac7d) was ascribed to an ion pair interaction that may be important in defining the DNA binding surface. The small number (three) of significantly altered pK(a) values was in good agreement with a linkage analysis of the temperature, pH, and salt-dependence of folding. The linkage of the ionization of two or more side-chains to protein folding led to apparent cooperativity in the pH-dependence of folding, although each group titrated independently with a Hill coefficient near unity. These results demonstrate that the acid pH-dependence of protein stability in these hyperthermophile proteins is due to independent titration of acidic residues with pK(a) values perturbed primarily by hydrogen bonding of the side-chain to the backbone. This work demonstrates the need for caution in using structural data alone to argue the importance of ion pairs in stabilizing hyperthermophile proteins.     

Dissecting electrostatic interactions in Bacillus circulans xylanase through NMR-monitored pH titrations

NMR-monitored pH titration curves of proteins provide a rich source of structural and electrostatic information. Although relatively straightforward to measure, interpreting pH-dependent chemical shift changes to obtain site-specific acid dissociation constants (pK (A) values) is challenging. In order to analyze the biphasic titrations exhibited by the side chain (13)C(γ) nuclei of the nucleophilic Glu78 and general acid/base Glu172 in Bacillus circulans xylanase, we have revisited the formalism for the ionization equilibria of two coupled acidic residues. In general, fitting NMR-monitored pH titration curves for such a system will only yield the two macroscopic pK (A) values that reflect the combined effects of both deprotonation reactions. However, through the use of mutations complemented with ionic strength-dependent measurements, we are able to extract the four microscopic pK (Ai) values governing the branched acid/base equilibria of Glu78 and Glu172 in BcX. These data, confirmed through theoretical calculations, help explain the pH-dependent mechanism of this model GH11 xylanase by demonstrating that the kinetically determined pK (A) values and hence catalytic roles of these two residues result from their electrostatic coupling.     

Stabilization of a fibronectin type III domain by the removal of unfavorable electrostatic interactions on the protein surface

It is generally considered that electrostatic interactions on the protein surface, such as ion pairs, contribute little to protein stability, although they may play important roles in conformational specificity. We found that the tenth fibronectin type III domain of human fibronectin (FNfn10) is more stable at acidic pH than neutral pH, with an apparent midpoint of transition near pH 4. Determination of pK(a)'s for all the side chain carboxyl groups of Asp and Glu residues revealed that Asp 23 and Glu 9 have an upshifted pK(a). These residues and Asp 7 form a negatively charged patch on the surface of FNfn10, with Asp 7 centrally located between Asp 23 and Glu 9, suggesting repulsive electrostatic interactions among these residues at neutral pH. Mutant proteins, D7N and D7K, in which Asp 7 was replaced with Asn and Lys, respectively, exhibited a modest but significant increase in stability at neutral pH, compared to the wild type, and they no longer showed pH dependence of stability. The pK(a)'s of Asp 23 and Glu 9 in these mutant proteins shifted closer to their respective unperturbed values, indicating that the unfavorable electrostatic interactions have been reduced in the mutant proteins. Interestingly, the wild-type and mutant proteins were all stabilized to a similar degree by the addition of 1 M sodium chloride at both neutral and acidic pH, suggesting that the repulsive interactions between the carboxyl groups cannot be effectively shielded by 1 M sodium chloride. These results indicate that repulsive interactions between like charges on the protein surface can destabilize a protein, and protein stability can be significantly improved by relieving these interactions.     

Dissecting the electrostatic interactions and pH-dependent activity of a family 11 glycosidase

Previous studies of the low molecular mass family 11 xylanase from Bacillus circulans show that the ionization state of the nucleophile (Glu78, pK(a) 4.6) and the acid/base catalyst (Glu172, pK(a) 6.7) gives rise to its pH-dependent activity profile. Inspection of the crystal structure of BCX reveals that Glu78 and Glu172 are in very similar environments and are surrounded by several chemically equivalent and highly conserved active site residues. Hence, there are no obvious reasons why their apparent pK(a) values are different. To address this question, a mutagenic approach was implemented to determine what features establish the pK(a) values (measured directly by (13)C NMR and indirectly by pH-dependent activity profiles) of these two catalytic carboxylic acids. Analysis of several BCX variants indicates that the ionized form of Glu78 is preferentially stabilized over that of Glu172 in part by stronger hydrogen bonds contributed by two well-ordered residues, namely, Tyr69 and Gln127. In addition, theoretical pK(a) calculations show that Glu78 has a lower pK(a) value than Glu172 due to a smaller desolvation energy and more favorable background interactions with permanent partial charges and ionizable groups within the protein. The pK(a) value of Glu172 is in turn elevated due to electrostatic repulsion from the negatively charged glutamate at position 78. The results also indicate that all of the conserved active site residues act concertedly in establishing the pK(a) values of Glu78 and Glu172, with no particular residue being singly more important than any of the others. In general, residues that contribute positive charges and hydrogen bonds serve to lower the pK(a) values of Glu78 and Glu172. The degree to which a hydrogen bond lowers a pK(a) value is largely dependent on the length of the hydrogen bond (shorter bonds lower pK(a) values more) and the chemical nature of the donor (COOH > OH > CONH(2)). In contrast, neighboring carboxyl groups can either lower or raise the pK(a) values of the catalytic glutamic acids depending upon the electrostatic linkage of the ionization constants of the residues involved in the interaction. While the pH optimum of BCX can be shifted from -1.1 to +0.6 pH units by mutating neighboring residues within the active site, activity is usually compromised due to the loss of important ground and/or transition state interactions. These results suggest that the pH optima of an enzyme might be best engineered by making strategic amino acid substitutions, at positions outside of the "core" active site, that electrostatically influence catalytic residues without perturbing their immediate structural environment.     

A fast and accurate computational approach to protein ionization

We report a very fast and accurate physics-based method to calculate pH-dependent electrostatic effects in protein molecules and to predict the pK values of individual sites of titration. In addition, a CHARMm-based algorithm is included to construct and refine the spatial coordinates of all hydrogen atoms at a given pH. The present method combines electrostatic energy calculations based on the Generalized Born approximation with an iterative mobile clustering approach to calculate the equilibria of proton binding to multiple titration sites in protein molecules. The use of the GBIM (Generalized Born with Implicit Membrane) CHARMm module makes it possible to model not only water-soluble proteins but membrane proteins as well. The method includes a novel algorithm for preliminary refinement of hydrogen coordinates. Another difference from existing approaches is that, instead of monopeptides, a set of relaxed pentapeptide structures are used as model compounds. Tests on a set of 24 proteins demonstrate the high accuracy of the method. On average, the RMSD between predicted and experimental pK values is close to 0.5 pK units on this data set, and the accuracy is achieved at very low computational cost. The pH-dependent assignment of hydrogen atoms also shows very good agreement with protonation states and hydrogen-bond network observed in neutron-diffraction structures. The method is implemented as a computational protocol in Accelrys Discovery Studio and provides a fast and easy way to study the effect of pH on many important mechanisms such as enzyme catalysis, ligand binding, protein-protein interactions, and protein stability.     

Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient

Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.     

Protonation states and pH titration in the photocycle of photoactive yellow protein

Photoactive yellow protein (PYP) undergoes a light-driven cycle of color and protonation states that is part of a mechanism of bacterial phototaxis. This article concerns functionally important protonation states of PYP and the interactions that stabilize them, and changes in the protonation state during the photocycle. In particular, the chromophore pK(a) is known to be shifted down so that the chromophore is negatively charged in the ground state (dark state) even though it is buried in the protein, while nearby Glu46 has an unusually high pK(a). The photocycle involves changes of one or both of these protonation states. Calculations of pK(a) values and protonation states using a semi-macroscopic electrostatic model are presented for the wild-type and three mutants, in both the ground state and the bleached (I(2)) intermediate state. Calculations allowing multiple H-bonding arrangements around the chromophore also have been carried out. In addition, ground-state pK(a) values of the chromophore have been measured by UV-visible spectroscopy for the wild-type and the same three mutants. Because of the unusual protonation states and strong electrostatic interactions, PYP represents a severe test of the ability of theoretical models to yield correct calculations of electrostatic interactions in proteins. Good agreement between experiment and theory can be obtained for the ground state provided the protein interior is assumed to have a relatively low dielectric constant, but only partial agreement between theory and experiment is obtained for the bleached state. We also present a reinterpretation of previously published data on the pH-dependence of the recovery of the ground state from the bleached state. The new analysis implies a pK(a) value of 6.37 for Glu46 in the bleached state, which is consistent with other available experimental data, including data that only became available after this analysis. The new analysis suggests that signal transduction is modulated by the titration properties of the bleached state, which are in turn determined by electrostatic interactions. Overall, the results of this study provide a quantitative picture of the interactions responsible for the unusual protonation states of the chromophore and Glu46, and of protonation changes upon bleaching.     

pK(a) values for side-chain carboxyl groups of a PGB1 variant explain salt and pH-dependent stability

Determination of pK(a) values of titrating residues in proteins provides a direct means of studying electrostatic coupling as well as pH-dependent stability. The B1 domain of protein G provides an excellent model system for such investigations. In this work, we analyze the observed pK(a) values of all carboxyl groups in a variant of PGB1 (T2Q, N8D, N37D) at low and high ionic strength as determined using (1)H-(13)C heteronuclear NMR in a structural context. The pK(a) values are used to calculate the pH-dependent stability in low and high salt and to investigate electrostatic coupling in the system. The observed pK(a) values can explain the pH dependence of protein stability but require pK(a) shifts relative to model values in the unfolded state, consistent with persistent residual structure in the denatured state. In particular, we find that most of the deviations from the expected random coil values can be explained by a significantly upshifted pK(a) value. We show also that (13)C backbone carbonyl data can be used to study electrostatic coupling in proteins and provide specific information on hydrogen bonding and electrostatic potential at nontitrating sites.     

The pKa Cooperative: a collaborative effort to advance structure-based calculations of pKa values and electrostatic effects in proteins

The pK(a) Cooperative (http://www.pkacoop.org) was organized to advance development of accurate and useful computational methods for structure-based calculation of pK(a) values and electrostatic energies in proteins. The Cooperative brings together laboratories with expertise and interest in theoretical, computational, and experimental studies of protein electrostatics. To improve structure-based energy calculations, it is necessary to better understand the physical character and molecular determinants of electrostatic effects. Thus, the Cooperative intends to foment experimental research into fundamental aspects of proteins that depend on electrostatic interactions. It will maintain a depository for experimental data useful for critical assessment of methods for structure-based electrostatics calculations. To help guide the development of computational methods, the Cooperative will organize blind prediction exercises. As a first step, computational laboratories were invited to reproduce an unpublished set of experimental pK(a) values of acidic and basic residues introduced in the interior of staphylococcal nuclease by site-directed mutagenesis. The pK(a) values of these groups are unique and challenging to simulate owing to the large magnitude of their shifts relative to normal pK(a) values in water. Many computational methods were tested in this first Blind Prediction Challenge and critical assessment exercise. A workshop was organized in the Telluride Science Research Center to objectively assess the performance of many computational methods tested on this one extensive data set. This volume of Proteins: Structure, Function, and Bioinformatics introduces the pK(a) Cooperative, presents reports submitted by participants in the Blind Prediction Challenge, and highlights some of the problems in structure-based calculations identified during this exercise.     

Improved pKa calculations through flexibility based sampling of a water-dominated interaction scheme

Ionizable groups play critical roles in biological processes. Computation of pK(a)s is complicated by model approximations and multiple conformations. Calculated and experimental pK(a)s are compared for relatively inflexible active-site side chains, to develop an empirical model for hydration entropy changes upon charge burial. The modification is found to be generally small, but large for cysteine, consistent with small molecule ionization data and with partial charge distributions in ionized and neutral forms. The hydration model predicts significant entropic contributions for ionizable residue burial, demonstrated for components in the pyruvate dehydrogenase complex. Conformational relaxation in a pH-titration is estimated with a mean-field assessment of maximal side chain solvent accessibility. All ionizable residues interact within a low protein dielectric finite difference (FD) scheme, and more flexible groups also access water-mediated Debye-Hückel (DH) interactions. The DH method tends to match overall pH-dependent stability, while FD can be more accurate for active-site groups. Tolerance for side chain rotamer packing is varied, defining access to DH interactions, and the best fit with experimental pK(a)s obtained. The new (FD/DH) method provides a fast computational framework for making the distinction between buried and solvent-accessible groups that has been qualitatively apparent from previous work, and pK(a) calculations are significantly improved for a mixed set of ionizable residues. Its effectiveness is also demonstrated with computation of the pH-dependence of electrostatic energy, recovering favorable contributions to folded state stability and, in relation to structural genomics, with substantial improvement (reduction of false positives) in active-site identification by electrostatic strain.     

Calbindin D(9k): a protein optimized for calcium binding at neutral pH.

The binding of calcium ions by EF-hand proteins depends strongly on the electrostatic interactions between Ca(2+) ions and negatively charged residues of these proteins. We have investigated the pH dependence of the binding of Ca(2+) ions by calbindin D(9k). This protein offers a unique possibility for interpretation of such data since the pK(a) values of all ionizable groups are known. The binding is independent of pH between 7 and 9, where maximum calcium affinity is observed. An abrupt decrease in the binding affinity is observed at pH values below 7. This decrease is due to protonation of acidic groups, leading to modification of protein charges. The pH dependence of the product of the two macroscopic Ca(2+)-binding constants can be formally described by the involvement of two acidic groups with pK(a) = 6.6. Monte Carlo calculations show that the reduction of Ca(2+) binding is strictly determined by variable electrostatic interactions due to pH-dependent changes not only in the binding sites, but also of the overall charge of the protein.     

Molecular mechanisms of pH-driven conformational transitions of proteins: insights from continuum electrostatics calculations of acid unfolding

The acid unfolding of staphylococcal nuclease (SNase) is very cooperative (Whitten and García-Moreno, Biochemistry 2000;39:14292-14304). As many as seven hydrogen ions (H+) are bound preferentially by the acid-unfolded state relative to the native (N) state in the pH range 3.2-3.9. To investigate the mechanism of acid unfolding, structure-based pKa calculations were performed with a variety of continuum electrostatic methods. The calculations reproduced successfully the H+ binding properties of the N state between pH 5 and 9, but they systematically overestimated the number of H+ bound upon acid unfolding. The calculated pKa values of all carboxylic residues in the N state were more depressed than they should be. The discrepancy between the observed and the calculated H+ uptake upon acid unfolding was not improved by using high protein dielectric constants, structures relaxed with molecular dynamics, or other empirical modifications implemented previously by others to maximize agreement between measured and calculated pKa values. This suggests an important role for conformational fluctuations of the backbone as important determinants of pKa values of carboxylic groups. Because no global or subglobal conformational changes have been observed previously for SNase under acidic conditions above the acid-unfolding region, these fluctuations must be local. The acid unfolding of SNase does not seem to involve the disruption of the N state by accruement of intramolecular repulsive interactions, nor the protonation of key ion paired carboxylic residues. It is more consistent with modest contributions from many H+ binding groups, with an important role for local conformational fluctuations in the coupling between H+ binding and the global structural transition.     

Discrete charge calculations of potentiometric titrations for globular proteins: sperm whale myoglobin, hemoglobin alpha chain, cytochrome c.

The modified Tanford-Kirkwood theory of Shire et al. for intramolecular electrostatic interactions has been applied to hydrogen ion equilibria of sperm whale ferrimyoglobin, human hemoglobin α-chain and horse cytochrome c. The model employs two sets of parameters derived from the crystalline protein structures, first, the atomic coordinates of charged amino acid residues and, second, static accessibility factors to reflect their solvent exposure. In addition, a consistent set of intrinsic pK values (pK_int) for the individual groups is employed. The theoretical pK values at half-titration for individual groups in each protein correspond to the available observed pK values, and the theoretical titration curves compare closely with experimental potentiometric curves.