Environmental effects on the protonation states of active site residues in bacteriorhodopsin.

Finite difference solutions of the Poisson-Boltzmann equation are used to calculate the pKa values of the functionally important ionizable groups in bacteriorhodopsin. There are strong charge-charge interactions between the residues in the binding site leading to the possibility of complex titration behavior. Structured water molecules, if they exist in the binding site, can have significant effects on the calculated pKa by strongly stabilizing ionized species. The ionization states of the Schiff base and Asp-85 are found to be strongly coupled. Small environmental changes, which might occur as a consequence of trans-cis isomerization, are capable of causing large shifts in the relative pKa values of these two groups. This provides an explanation for the protonation of Asp-85 and the deprotonation of the Schiff base in the M state of bacteriorhodopsin. The different behavior of Asp-85 and Asp-212 is discussed in this regard.     

Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility.

A new method for including local conformational flexibility in calculations of the hydrogen ion titration of proteins using macroscopic electrostatic models is presented. Intrinsic pKa values and electrostatic interactions between titrating sites are calculated from an ensemble of conformers in which the positions of titrating side chains are systematically varied. The method is applied to the Asp, Glu, and Tyr residues of hen lysozyme. The effects of different minimization and/or sampling protocols for both single-conformer and multi-conformer calculations are studied. For single-conformer calculations it is found that the results are sensitive to the choice of all-hydrogen versus polar-hydrogen-only atomic models and to the minimization protocol chosen. The best overall agreement of single-conformer calculations with experiment is obtained with an all-hydrogen model and either a two-step minimization process or minimization using a high dielectric constant. Multi-conformational calculations give significantly improved agreement with experiment, slightly smaller shifts between model compound pKa values and calculated intrinsic pKa values, and reduced sensitivity of the intrinsic pKa calculations to the initial details of the structure compared to single-conformer calculations. The extent of these improvements depends on the type of minimization used during the generation of conformers, with more extensive minimization giving greater improvements. The ordering of the titrations of the active-site residues, Glu-35 and Asp-52, is particularly sensitive to the minimization and sampling protocols used. The balance of strong site-site interactions in the active site suggests a need for including site-site conformational correlations.     

pH dependence of stability of the 10th human fibronectin type III domain: a computational study

We present detailed computational studies based on electrostatic calculations to evaluate the origins of pKa values and the pH dependence of stability for the 10th type III domain of human fibronectin (FNfn10). One of our goals is to validate the calculation protocols by comparison to experimental data (Koide, A.; Jordan, M. R.; Horner, S.; Batori, V.; Koide, S. Biochemistry 2001, 40, 10326-10333). Another goal is to evaluate the sensitivity of the calculated ionization free energies and apparent pKa values on local structural fluctuations, which do not alter the structural convergence to a particular architecture, by using a complete ensemble of solution NMR structures and the NMR average minimized structure of FNfn10 (Main, A. L.; Harvey, T. S.; Baron, M.; Boyd, J.; Campbell, I. D. Cell 1992, 71, 671-678). Our calculations demonstrate that, at high ionic strength, FNfn10 is more stable at low pH compared to neutral pH, in overall agreement with experimental data. This behavior is attributed to contributions from unfavorable Coulombic interactions in a surface patch for the pairs Asp7-Glu9 and Asp7-Asp23. The unfavorable interactions are decreased at low pH, where the acidic residues become neutral, and are further decreased at high ionic strength because of increased screening by salt ions. Elimination of the unfavorable interactions in the theoretical mutants Asp7Asn (D7N) and Asp7Lys (D7K) produce higher calculated stabilities at neutral pH and any ionic strength compared to the wild-type, in agreement with the experimental data. We also discuss subtleties in the calculated apparent pKa values and ionization free energies, which are not in agreement with the experimental data. This work demonstrates that comparative electrostatic calculations can provide rapid predictions of pH-dependent properties of proteins and can be significant aids in guiding the design of proteins with tailored properties.     

Energetics of charge-charge interactions between residues adjacent in sequence

Statistical analysis of the residue separation between a pair of ionizable side chains within 4 ? of each other was performed on a set of 1560 non-homologous PDB structures. We found that the frequency of pairs of like charges (i.e., pairs consisting of acidic residues Asp and Glu or pairs consisting of basic residues Arg and Lys) is two orders of magnitude lower than the pairs of oppositely charged residues (salt-bridges). We also found that for pairs of like charges the distribution is skewed dramatically towards short residue separation (<3). On the basis of these observations, we hypothesize that at short residue separation the repulsion between charges does not contribute much to the protein stability and the effects are largely dominated by the long range charge-charge interactions with other ionizable groups in the protein molecule. To test this hypothesis, we incorporated various pairs of charged residues at position 63 and 64 of ubiquitin and compared the stabilities of these variants. We also performed calculations of the expected changes in the charge-charge interactions. A very good correlation between experimental changes in the stability of ubiquitin variants, and changes in the energy of charge-charge interactions provides support for the hypothesis that a pair of ionizable residues next to each other in sequence modulates protein stability via long range charge-charge interactions with the rest of the protein.     

Electrostatic contributions to residue-specific protonation equilibria and proton binding capacitance for a small protein

Charge-charge interactions in proteins are important in a host of biological processes. Here we use 13C NMR chemical shift data for individual aspartate and glutamate side chain carboxylate groups to accurately detect site-specific protonation equilibria in a variant of the B1 domain of protein G (PGB1-QDD). Carbon chemical shifts are dominated by changes in the electron distribution within the side chain and therefore excellent reporters of the charge state of individual groups, and the data are of high precision. We demonstrate that it is possible to detect local charge interactions within this small protein domain that stretch and skew the chemical shift titration curves away from "ideal" behavior and introduce a framework for the analysis of such convoluted data to study local charge-charge interactions and electrostatic coupling. It is found that, due to changes in electrostatic potential, the proton binding affinity, Ka, of each carboxyl group changes throughout the titration process and results in a linearly pH dependent pKa value. This result could be readily explained by calculations of direct charge-charge interactions based on Coulomb's law. In addition, the slope of pKa versus pH was dependent on screening by salt, and this dependence allowed the selective study of charge-charge interactions. For PGB1-QDD, it was established that mainly differences in self-energy, and not direct charge-charge interactions, are responsible for shifted pKa values within the protein environment.     

Electrostatic coupling between retinal isomerization and the ionization state of Glu-204: a general mechanism for proton release in bacteriorhodopsin.

The pKa values of ionizable groups that lie between the active site region of bacteriorhodopsin (bR) and the extracellular surface of the protein are reported. Glu-204 is found to have an elevated pKa in the resting state of bR, suggesting that it corresponds to the proton-releasing group in bR. Its elevated pKa is predicted to be due in part to strong repulsive interactions with Glu-9. Following trans-cis isomerization of the retinal chromophore and the transfer of a proton to Asp-85, polar groups on the protein are able to interact more strongly with the ionized state of Glu-204, leading to a substantial reduction of its pKa. This suggests a general mechanism for proton release in which isomerization and subsequent charge separation initially produce a new electrostatic balance in the active site of bR. Here it is proposed that those events in turn drives a conformational change in the protein in which the ionized state of Glu-204 can be stabilized through interactions with groups that were previously inaccessible. Whether these groups should be identified with polar moieties in the protein, bound waters, or Arg-82 is an important mechanistic question whose elucidation will require further study.     

Complete measurement of the pKa values of the carboxyl and imidazole groups in Bacillus circulans xylanase.

Electrostatic interactions in proteins can be dissected experimentally by determining the pKa values of their constituent ionizable amino acids. To complement previous studies of the glutamic acid and histidine residues in Bacillus circulans xylanase (BCX), we have used NMR methods to measure the pKa s of the seven aspartic acids and the C-terminus of this protein. The pKa s of these carboxyls are all less than the corresponding values observed with random coil polypeptides, indicating that their ionization contributes favorably to the stability of the folded enzyme. In general, the aspartic acids with the most reduced pKa s are those with limited exposure to the solvent and a high degree of conservation among homologous xylanases. Most dramatically, Asp 83 and Asp 101 have pKa s < 2 and thus remain deprotonated in native BCX under all conditions examined. Asp 83 is completely buried, forming a strong salt bridge with Arg 136. In contrast, Asp 101 is located on the surface of the protein, stabilized in the deprotonated form by an extensive network of hydrogen bonds involving an internal water molecule and the neutral side-chain and main-chain atoms of Ser 100 and Thr 145. These data provide a complete experimental database for theoretical studies of the ionization behavior of BCX under acidic conditions.     

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.     

Coupled molecular dynamics and continuum electrostatic method to compute the ionization pKa’s of proteins as a function of pH. Test on a large set of proteins

A computational method, to predict the pKa values of the ionizable residues Asp, Glu, His, Tyr, and Lys of proteins, is presented here. Calculation of the electrostatic free-energy of the proteins is based on an efficient version of a continuum dielectric electrostatic model. The conformational flexibility of the protein is taken into account by carrying out molecular dynamics simulations of 10 ns in implicit water. The accuracy of the proposed method of calculation of pKa values is estimated from a test set of experimental pKa data for 297 ionizable residues from 34 proteins. The pKa-prediction test shows that, on average, 57, 86, and 95% of all predictions have an error lower than 0.5, 1.0, and 1.5 pKa units, respectively. This work contributes to our general understanding of the importance of protein flexibility for an accurate computation of pKa, providing critical insight about the significance of the multiple neutral states of acid and histidine residues for pKa-prediction, and may spur significant progress in our effort to develop a fast and accurate electrostatic-based method for pKa-predictions of proteins as a function of pH.     

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.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Electrostatic interactions in an integral membrane protein

The effects of charge-charge interactions on the midpoint reduction potential (E(m)()) of the primary electron donor (P) in the photosynthetic reaction center of Rhodobacter sphaeroides were investigated by introducing mutations of ionizable amino acids at selected sites. The mutations were designed to alter the electrostatic environment of P, a bacteriochlorophyll dimer, without greatly affecting its structure or molecular orbitals. Two arginine residues at homologous positions in the L and M subunits [residues (L135) and (M164)], Asp (L155), Tyr (L164), and Cys (L247) were changed independently. Arginine (L135) was replaced by Lys, Leu, Gln, or Glu; Arg (M164), by Leu or Glu; Asp (L155), by Asn; Tyr (L164), by Phe; and Cys (L247), by Lys or Asp. The R(L135)E/C(L247)K double mutant also was made. The shift in the E(m)() of P/P(+) was measured in each mutant and was compared with the effect predicted by electrostatics calculations using several different computational approaches. A simple distance-dependent dielectric screening factor reproduced the effects remarkably well. By contrast, microscopic methods that considered the reaction field in the protein and solvent but did not include explicit counterions overestimated the changes in the E(m)() considerably. Including counterions for the charged residues reduced the calculated effects of the mutations in molecular dynamics calculations. The results show that electrostatic interactions of P with ionizable amino acid residues are strongly screened, and suggest that counterions make major contributions to this screening. The screening also could reflect penetration of water or other relaxations not taken into account because of incomplete sampling of configurational space.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.     

Charge substitution shows that repulsive electrostatic interactions impede the oligomerization of Alzheimer amyloid peptides

The strong pH dependence of A beta oligomerization could arise from favorable intermolecular charge-charge interactions between His and carboxylate groups, or, alternatively, by mutual electrostatic repulsion of peptide molecules. To test between these two possibilities, the pH dependence of the oligomerization of A beta and three charge substitution variants with Asp, Glu and His substituted by Ala is measured. All four peptides oligomerize, as detected by thioflavin T fluorescence, turbidity, and amyloid fibril formation; therefore, specific charge-charge interactions are nonessential for oligomerization. The strong negative correlation between net charge and oligomerization indicates that electrostatic repulsion between A beta monomers impedes their association.     

Structural basis of perturbed pKa values of catalytic groups in enzyme active sites

In protein and RNA macromolecules, only a limited number of different side-chain chemical groups are available to function as catalysts. The myriad of enzyme-catalyzed reactions results from the ability of most of these groups to function either as nucleophilic, electrophilic, or general acid-base catalysts, and the key to their adapted chemical function lies in their states of protonation. Ionization is determined by the intrinsic pKa of the group and the microenvironment created around the group by the protein or RNA structure, which perturbs its intrinsic pKa to its functional or apparent pKa. These pKa shifts result from interactions of the catalytic group with other fully or partially charged groups as well as the polarity or dielectric of the medium that surrounds it. The electrostatic interactions between ionizable groups found on the surface of macromolecules are weak and cause only slight pKa perturbations (<2 units). The sum of many of these weak electrostatic interactions helps contribute to the stability of native or folded macromolecules and their ligand complexes. However, the pKa values of catalytic groups that are found in the active sites of numerous enzymes are significantly more perturbed (>2 units) and are the subject of this review. The magnitudes of these pKa perturbations are analyzed with respect to the structural details of the active-site microenvironment and the energetics of the reactions that they catalyze.     

Residual electrostatic effects in the unfolded state of the N-terminal domain of L9 can be attributed to nonspecific nonlocal charge-charge interactions

Residual electrostatic interactions in the unfolded state of the N-terminal domain of L9 (NTL9) were found by Kuhlman et al. [(1999) Biochemistry 38, 4896-4903]. These residual interactions are analyzed here by the Gaussian-chain model [Zhou, H.-X. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 3569-3574]. The original model is made more realistic by replacing "standard" model-compound pK(a) values for ionizable groups by those measured by Kuhlman et al. in peptide fragments of NTL9. The predicted pH dependence of the unfolding free energy is in agreement with experiment over the pH range of 1-7 at ionic strengths of 100 and 750 mM. This indicates that the residual electrostatic effects in the unfolded state of NTL9 can be attributed to nonspecific nonlocal charge-charge interactions.     

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA.

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

Optimization of the electrostatic interactions in proteins of different functional and folding type

The 3-dimensional optimization of the electrostatic interactions between the charged amino acid residues was studied by Monte Carlo simulations on an extended representative set of 141 protein structures with known atomic coordinates. The proteins were classified by different functional and structural criteria, and the optimization of the electrostatic interactions was analyzed. The optimization parameters were obtained by comparison of the contribution of charge-charge interactions to the free energy of the native protein structures and for a large number of randomly distributed charge constellations obtained by the Monte Carlo technique. On the basis of the results obtained, one can conclude that the charge-charge interactions are better optimized in the enzymes than in the proteins without enzymatic functions. Proteins that belong to the mixed αβ folding type are electrostatically better optimized than pure α-helical or β-strand structures. Proteins that are stabilized by disulfide bonds show a lower degree of electrostatic optimization. The electrostatic interactions in a native protein are effectively optimized by rejection of the conformers that lead to repulsive charge-charge interactions. Particularly, the rejection of the repulsive contacts seems to be a major goal in the protein folding process. The dependence of the optimization parameters on the choice of the potential function was tested. The majority of the potential functions gave practically identical results.     

Proton transfer dynamics of GART: the pH-dependent catalytic mechanism examined by electrostatic calculations

The enzyme glycinamide ribonucleotide transformylase (GART) catalyzes the transfer of a formyl group from formyl tetrahydrofolate (fTHF) to glycinamide ribonucleotide (GAR), a process that is pH-dependent with pK(a) of approximately 8. Experimental studies of pH-rate profiles of wild-type and site-directed mutants of GART have led to the proposal that His108, Asp144, and GAR are involved in catalysis, with His108 being an acid catalyst, while forming a salt bridge with Asp144, and GAR being a nucleophile to attack the formyl group of fTHF. This model implied a protonated histidine with pK(a) of 9.7 and a neutral GAR with pK(a) of 6.8. These proposed unusual pK(a)s have led us to investigate the electrostatic environment of the active site of GART. We have used Poisson-Boltzmann-based electrostatic methods to calculate the pK(a)s of all ionizable groups, using the crystallographic structure of a ternary complex of GART involving the pseudosubstrate 5-deaza-5,6,7,8-THF (5dTHF) and substrate GAR. Theoretical mutation and deletion analogs have been constructed to elucidate pairwise electrostatic interactions between key ionizable sites within the catalytic site. Also, a construct of a more realistic catalytic site including a reconstructed pseudocofactor with an attached formyl group, in an environment with optimal local van der Waals interactions (locally minimized) that imitates closely the catalytic reactants, has been used for pK(a) calculations. Strong electrostatic coupling among catalytic residues His108, Asp144, and substrate GAR was observed, which is extremely sensitive to the initial protonation and imidazole ring flip state of His108 and small structural changes. We show that a proton can be exchanged between GAR and His108, depending on their relative geometry and their distance to Asp144, and when the proton is attached on His108, catalysis could be possible. Using the formylated locally minimized construct of GART, a high pK(a) for His108 was calculated, indicating a protonated histidine, and a low pK(a) for GAR(NH(2)) was calculated, indicating that GAR is in neutral form. Our results are in qualitative agreement with the current mechanistic picture of the catalytic process of GART deduced from the experimental data, but they do not reproduce the absolute magnitude of the pK(a)s extracted from fits of k(cat)-pH profiles, possibly because the static time-averaged crystallographic structure does not describe adequately the dynamic nature of the catalytic site during binding and catalysis. In addition, a strong effect on the pK(a) of GAR(NH(2)) is produced by the theoretical mutations of His108Ala and Asp144Ala, which is not in agreement with the observed insensitivity of the pK(a) of GAR(NH(2)) modeled from the experimental data using similar mutations. Finally, we show that important three-way electrostatic interactions between highly conserved His137, with His108 and Asp144, are responsible for stabilizing the electrostatic microenvironment of the catalytic site. In conclusion, our data suggest that further detailed computational and experimental work is necessary.     

A fast and simple method to calculate protonation states in proteins.

A simple model for electrostatic interactions in proteins, based on a distance and position dependent screening of the electrostatic potential, is presented. It is applied in conjunction with a Monte Carlo algorithm to calculate pK(alpha) values of ionizable groups in proteins. The purpose is to furnish a simple, fast, and sufficiently accurate model to be incorporated into molecular dynamic simulations. This will allow for dynamic protonation calculations and for coupling between changes in structure and protonation state during the simulation. The best method of calculating protonation states available today is based on solving the linearized Poisson-Boltzmann equation on a finite difference grid. However, this model consumes far too much computer time to be a practical alternative. Tests are reported for fixed structures on bacteriorhodopsin, lysozyme, myoglobin, and calbindin. The studies include comparisons with Poisson-Boltzmann calculations with dielectric constants 4 and 20 inside the protein, a model with uniform dielectric constant 80 and distance-dependent dielectric models. The accuracy is comparable to that of Poisson-Boltzmann calculations with dielectric constant 20, and it is considerably better than that with epsilon = 4. The time to calculate the protonation at one pH value is at least 100 times less than that of a Poisson-Boltzmann calculation. Proteins 1999;36:474-483.