PROTEINS: Structure, Function, and Genetics 37:106–115 (1999) Ionization Behavior of Acidic Residues in Calbindin D9k Tõnu Kesvatera,1,2 Bo Jönsson,1* Eva Thulin,1and Sara Linse1 of Physical Chemistry 2, Lund University, Center for Chemistry and Chemical Engineering, Lund, Sweden 2National Institute of Chemical Physics and Biophysics, Akadeemia 23, Tallinn, Estonia 1Department ABSTRACT The ionization state of seven glutamate residues, one aspartate, and the C-terminal ␣-COOH group in bovine apo calbindin D9k has been studied by measurement and modeling of the pH titration curves and apparent pKa values. The observed pKa ranged from 3.0 to 6.5. Most of the observed acidic groups were half-ionized at lower pH values than those in unstructured proteins. As a rule, the ionization equilibria extended over a wider pH range than in the case of unperturbed single titrations, indicating a complex influence of protein charges on the charge state of each individual residue. Glu17, which is a backbone Ca2ⴙ-ligand in the N-terminal binding loop of calbindin D9k, was halfprotonated at pH 3.6 but manifested biphasic titration with apparent pKa values of 3.2 and 6.5. Complementary Monte Carlo simulations of the titration process and pKa values of the acidic groups in calbindin D9k reproduce the experimentally observed titration features, except for the pronounced double titration of Glu17. Discrepancies between the results from direct measurement and from modeling may be partly caused by changes in the protein structure when the net charge changes from ⴚ8 to ⴙ11 over the isoelectric point at pH 5. Proteins 1999;37:106–115. r 1999 Wiley-Liss, Inc. INTRODUCTION As a consequence of protein folding, the pKa values of titratable groups shift relative to their values in small model compounds or denatured proteins. In a folded protein, the specific arrangement of charged residues may cause a significant variation of the electrostatic potential throughout the protein. The electrostatic potential can be probed locally at many points of a protein by measuring the titration behavior of acidic and basic groups and provide rigorous tests of theoretical predictions of electrostatic effects in proteins. Computational algorithms for prediction of pKa values of titratable groups have been the focus of theoretical studies over the years. Traditionally, the protein is treated as a low-dielectric cavity in a high-dielectric environment. Recent theoretical studies have demonstrated that better results in accounting for the ionization behavior of proteins can be obtained by using a high-dielectric constant for the protein interior.1–5 Further studies about the state of ionic residues in proteins are thus highly motivated, and reliable determination of pKa values for individual titratable groups is necessary for developing the theoretical models for electrostatic interactions in proteins. r 1999 WILEY-LISS, INC. A common feature of the ubiquitous calmodulin-like proteins is the accumulation of negative charges on the protein surface, especially in the Ca2⫹ binding area. These proteins are of particular interest for theoretical structurebased modeling of long-range electrostatic interactions in proteins, because the pKa values of some of these acidic groups are expected to be strongly shifted toward high pH compared with the corresponding model compounds where the pKa perturbations due to ionic interactions are insignificant. The knowledge of pKa values of acidic residues is also helpful in understanding the function of EF-hand Ca2⫹ binding sites in a large number of regulatory or Ca2⫹ buffering proteins. However, the ionization behavior of acidic groups has not been reported yet for any of the ubiquitous calcium-dependent proteins belonging to the calmodulin superfamily. Bovine calbindin D9k is a small (75 residues, Mr 8,500) and well-characterized representative of the EF-hand proteins, which efficiently binds two Ca2⫹ ions.6 The excess negative charge in the binding area causes large upward pKa shifts for lysine residues2 located in the vicinity of Ca2⫹ binding sites, implying that the ionization equilibria of some carboxylate groups can be also shifted close to the physiologically relevant neutral pH values. Calbindin D9k is an excellent model or target for the experimental pKa measurements via nuclear magnetic resonance (NMR) spectroscopy because of its moderate size and remarkable stability in a variety of solvent conditions. In variance with the regulatory proteins of the calmodulin family, which undergo a significant conformational change on calcium binding, calbindin D9k has essentially the same structure in the absence and presence of metal ions in the binding sites. This is an advantage for theoretical calculations that can be sensitive to the variations in protein structure. In this study, we describe pKa measurements of nine acidic groups in calbindin D9k using 13C isotope labeling and two-dimensional heteronuclear NMR spectroscopy. MATERIALS AND METHODS Protein Preparation Calbindin D9k was expressed in Escherichia coli from a synthetic gene yielding a protein with bovine minor A Grant sponsor: Swedish Natural Science Council; Grant sponsor: The Royal Swedish Academy of Sciences; Grant sponsor: Estonian Science Foundation. *Correspondence to: Bo Jönsson, Physical Chemistry 2, Lund University, Center for Chemistry and Chemical Engineering, S-221 00 Lund, Sweden. E-mail: firstname.lastname@example.org Received 21 December 1998; Accepted 30 April 1999 PKA OF ACIDIC RESIDUES IN CALBINDIN D9K sequence except that residue 43 was changed to a glycine instead of a proline. The Pro43=Gly mutation was introduced to avoid the appearance of two sets of resonances in the NMR spectrum due to cis-trans isomerization of the Gly42-Pro43 peptide bond.7 The cells were first grown overnight in Luria-Bertani Medium (LB) medium, and 10 mL of the overnight culture was used to inoculate 250 mL of minimal medium. When the absorbance at 600 nm was 0.5, 60 mL of this middle culture was transferred into 500 mL of minimal medium, and cells were harvested 2–3 h after this final culture reached the lag phase, at which point the yield was at maximum.The minimal medium was made in the local tap water and 1 L contained: 6 g of Na2HPO4, 3 g of KH2PO4, 0.5 g of NaCl, 1 mM of MgSO4, 0.1 mM of CaCl2, 1 mg of Vitamin B1, and 18 µM of FeCl3. To prepare the medium, a mix of Na2HPO4, KH2PO4, and NaCl was autoclaved and supplemented by MgSO4 and CaCl2 from separately autoclaved stock solutions and Vitamin B1 and FeCl3 from separately sterile filtered stock solutions. All amino acids were added to the minimal media as sterile filtered free L-amino acids in relative amounts according to their frequencies of occurrence in proteins. The total amount of amino acids was 1.0 g/L in the middle culture and 0.5 g/L in the final growth medium. Carbon-13 labeled L-[␤-13C]aspartic and L-[␥-13C]glutamic acids were purchased from Cambridge Isotope Laboratories (Andover, MA), whereas unlabeled amino acids were purchased from Sigma. Purification of the protein and removal of calcium was performed as described by Johansson et al. (1990),8 and the purity was confirmed by agarose gel electrophoresis, sodium dodecyl sulfate (SDS) polyacrylamide gel electrophoresis, isoelectric focusing, and 1H NMR. The residual Ca2⫹ concentration after chelex 100 treatment was below 0.1 equivalents as judged from 1H NMR spectra and titrations in the presence of the chromophoric chelator quin 2. The total yield of purified Ca2⫹-free protein was 15 mg from 2 L of culture. Protein samples for titration experiments were made 0.5 mM in a 0.5-mL final volume containing 90% H2O and 10% 2H2O. NMR Spectroscopy Two-dimensional 13C-1H HSQC-TOCSY NMR spectra9–12 were recorded at 300 K on a Varian Unity Plus spectrometer operating at 599.89 MHz for 1H and 150.85 MHz for 13C. The spectral width was 8,000 Hz for protons and 4,300 Hz for carbon, and the digital resolution was 4,096 complex points in 2 and 128 real points in 1 and 128–256 FIDs were collected for each t1 point. Decoupling of the 13C nuclei during the acquisition period was achieved by using Garp-1 phase modulation.13 The DIPSI-2 mixing sequence14 with a mixing time of 80 ms was used. The water signal was suppressed by using pulsed field gradients.15,16 1H chemical shifts were referenced to the water signal at 4.75 ppm, and the 13C chemical shifts were measured relative to the spectrometer frequency. NMR spectra were processed on Sun or SiliconGraphics workstations using Felix95 (Biosym Technologies, San Diego, CA). 107 pH-Dependent Chemical Shift Measurements The pH titrations of calbindin D9k were performed starting at pH 6.0. The pH was adjusted by adding 0.2–1 µL amounts of concentrated HCl or NaOH with a Hamilton syringe to obtain accurate estimates of the added Na⫹ or Cl⫺ ions at each titration point. The pH of a sample was measured, and the adjustments were made in an NMR tube with use of the Radiometer PHM63 Digital pH meter with an Ingold U402-M3–57/200 electrode. The pH readings taken before and after the acquiring of NMR spectra were similar within 0.1 pH units, and the latter reading was used in data processing, uncorrected for isotope effects caused by the presence of 10% 2H2O. The pH of a 0.5 mM calbindin D9k sample from the current preparations, made in 10% 2H2O, 90% H2O, was always 6.0 ⫾ 0.1. After addition of a certain amount of 1 M of HCl to obtain a required pH of a sample, we observed the tendency that the pH of the sample was increasing by up to 0.1 pH units (probably because of some process related to a protein) during the 10–15 h of acquiring the NMR spectrum. It has been checked that most of this increase took place within 2–3 h after the pH adjustment. For this reason the pH reading of a sample after the acquiring NMR spectra was taken as a more correct value for the pH in a sample for which the spectrum was obtained. 1H-13C HSQC-TOCSY spectra were acquired at about 0.3 pH unit intervals between pH 2.4 and 7.6. Figure 1 shows the spectra at pH 7.0 and 2.4. The resonances in these spectra were identified by using proton resonance assignments for the P43G mutant of apo calbindin D9k at pH 5.25.17 In the test for reversibility of the titration the pH of a sample used for acquiring data at pH 2.4 was adjusted back to 5.25, and the spectrum obtained was essentially the same as at the start of titration. Determination of Titration Parameters Titration parameters were obtained by fitting the chemical shifts for ␤- or ␥-13C nuclei of aspartic acid, asparagine, glutamic acid ,or glutamine residues at different pH values by nonlinear least-squares analysis according to the equation for one-step titration: ␦obs ⫽ [␦HA ⫹ ␦A 10n(pH⫺pKa) ]/[1 ⫹ 10n(pH⫺pKa) ]. (1) Here, ␦obsis the observed chemical shift at a given pH value, ␦HA and ␦A are the asymptotes corresponding to chemical shift values for the protonated and unprotonated forms of a given residue, pKa is the negative logarithm of the apparent equilibrium constant for the observed protonation equilibrium, and n is the Hill parameter that accounts for the deviations from the unperturbed titration, caused by the influence of other titrating residues in the protein over the observed pH range. Four parameters, the apparent pKa value, n, and the chemical shifts at limiting pH values were optimized. Titration shift, ⌬␦, the change in the observed chemical shift upon titration from high to 108 T. KESVATERA ET AL. Fig. 1. 13C-1H HSQC-TOCSY spectra of 0.5 mM apo calbindin D9k at 300 K and pH 2.4 and 7.0. Assignments of ␣-protons are indicated. The 13C chemical shifts are given relative to spectrometer frequency 150.85 MHz for 13C. low pH, was calculated as ⌬␦ ⫽ ␦A⫺␦HA. The biphasic titration curve for Glu17 was analyzed according to the equation: ␦obs ⫽ 5[␦1 ⫹ ␦2 10(pH⫺pK1) ]/[1 ⫹ 10(pH⫺pK1) ] ⫹ ␦3 10(pH⫺pK2) 6 /[1 ⫹ 10(pH⫺pK2) ] (2) The reported standard errors characterize the precision of the data fitting, but not other possible errors, e.g., the accuracy of pH measurements or chemical shift readings. Theoretical Model and Monte Carlo Simulations The protein coordinates PDB3ICB from the Brookhaven Data Bank obtained from an X-ray diffraction study of the crystalline Ca2⫹-loaded protein18 were used. Each protein atom was represented as a hard sphere, impenetrable to any solvent ions unit charge on the -nitrogen. Carboxylic oxygens were given a charge of ⫺0.5, and lysine residues carried a positive unit charge on the -nitrogen, whereas all other protein atoms were kept neutral. The charges of all carboxyl groups were allowed to change according to the solution pH. The protein coordinates were kept fixed during the simulation, and the protein was placed in the center of a spherical cell to which counterions and salt ions were added in accordance with experimental conditions at each pH value. These ions were treated as mobile charged hard spheres confined to the cell, whose radius was determined by the protein concentration. This is in contrast to most other theoretical studies in which the protein usually is assumed to be at infinite dilution. Changing the protein concentration by a factor of 3 leads to pKa shifts of approximately 0.2 units for the lysine residues in calbindin D9k.2 The cell, including protein, counterions, and salt is always electroneutral. The number of counterions is given by the protein net charge, and increasing the cell radius (i.e., lowering the protein concentration) consequently leads to a reduced counterion concentration. This, of course, affects the electrostatic screening and in the limit of zero protein concentration all the screening is caused by the added salt. The interaction energy between charged species i and j is given by, u(ri j ) ⫽ qiq je 2/4⑀0⑀ri j u(ri j ) ⫽ ⬁ ri j ⱖ (i ⫹ j )/2 ri j ⬍ (i ⫹ j )/2 (3) PKA OF ACIDIC RESIDUES IN CALBINDIN D9K where q is a partial charge, e is the elementary charge, ⑀o is the permittivity of free space, i is the hard core diameter of particle i, and rij is the distance between the particles i and j. Only interactions between particles within the cell are taken into account. The dielectric constant, ⑀, was chosen as 77.8 at the experimental temperature of 300 K and was assumed to be uniform throughout the cell. The simulations were performed in the canonical ensemble with respect to salt ions and counterions with use of the traditional Metropolis Monte Carlo procedure.19 One million moves per mobile particle was attempted in each MC run. Half of that number was considered to be equilibration, and the second half was used for calculation of averages. The calculated fractional charges on the titrating residues were determined with an accuracy of ⫾0.001. In addition, the simulation cell was coupled to a proton bath to establish a constant pH in the system. After every tenth attempted move of the mobile charges, an attempt was also made to delete or insert a proton on a titrating residue. The proton is not explicitly inserted, but only the charges on the two carboxylic oxygens are neutralized. The opposite procedure takes place on a ‘‘proton deletion.’’ In reality, an addition of a proton to a carboxylate group means that acid (HCl) has been added to the solution. Hence in the simulation, a proton addition to a carboxylate group was always accompanied by the addition of a negative mobile charge to the cell to keep the system electroneutral. The acceptance or rejection of an attempt to change the ionization state of a particular carboxylate group was based on the trial energy, ⌬E ⫽ ⌬Ec ⫾ kT ln 10 (pH ⫺ pK0 ) (4) where ⌬Ec is the change in Coulomb energy due to the protonation or deprotonation, and K0 is the dissociation constant for the model compound.20 The plus sign is used when a residue is to be protonated, and the minus sign when it is to be deprotonated. In the theoretical analysis, the pKa of an ionizable group is taken as the pH value at which the group is half-protonated. The calculated pKa were corrected for the deviations of the activity coefficient for H⫹ from unity at low pH using a modified Widom technique.21,22 The main part of the correction originates from the increasing net positive charge on the protein, which gives rise to a significant electrostatic potential throughout the simulation cell. The calbindin preparation includes contaminant salt above the necessary counterions, about 10 times the concentration of protein, as estimated by atomic absorption spectroscopy measurements. This residual salt as well as the stepwise increase in salt concentration, resulting from addition of acid in the experimental determination of the titration curve, was taken into account in the simulations. RESULTS AND DISCUSSION The calcium-binding loop of the ubiquitous EF-hand proteins usually contains four acidic residues, which participate in coordination of the Ca2⫹ion. The free energy of calcium binding to this type of site is largely of electro- 109 static origin.23 Therefore, it is important to know the charge state and titration behavior of ionizable groups to understand the impact of overall electrostatic interactions on the structure and function of these proteins. The pKa values for lysine residues have been estimated for apo and holo forms of both calmodulin24 and calbindin D9k.2,25However, the individual pKa values of acidic groups have not been determined for any of the calcium-binding proteins belonging to the EF-hand family. This study describes an attempt to measure the pKa values of acidic residues in Ca2⫹-free calbindin D9kusing 13C labeling and heteronuclear NMR spectroscopy. Electrostatic interactions, known as determinants of the individual pKa values in proteins, are highly dependent on the presence of screening factors. To minimize the screening, no buffer or salt was added to the protein sample, except for controlled amounts of acid (HCl) or alkaline (NaOH), which were taken into account in Monte Carlo simulations of the titration process.Because the protein itself, an amphoteric polyelectrolyte, is a screening factor for ionic interactions,26 it was important to keep the concentration of calbindin D9k as low as possible. It was also established, that below the isoelectric point at about pH 5, the solubility of calbindin D9k abruptly decreases to ⬍1 mM, and well-resolved homonuclear TOCSY NMR spectra could not be acquired within a time period of 24 h. 13C labeling of acidic residues was therefore used to increase the sensitivity of NMR experiments and to facilitate the use of 0.5 mM protein concentration in the present titration experiments. 13C Labeling Selective 13C-labeling of acidic residues in a protein via expression in E. coli is complicated because of transamination reactions. E. coli strains exist with lesions to prevent metabolic conversion of aspartic acid to asparagine,27 but not those to prevent interconversion of glutamate and glutamine. The use of the general transaminase-deficient E. coli strain did not prevent the conversion of 13C-labeled glutamate to glutamine in Bacillus circulans xylanase.28 Because calbindin D9k contains 13 glutamates and only 4 aspartates, our protocol for the production of calbindin D9k in the presence of 13C-labeled aspartic and glutamic acid did not include any protective means against their metabolic conversion to respective amines during the expression in E. coli. As a result, the 13C label was also found in asparagine and glutamine residues of calbindin D9k, but eight acidic amino acids were 13C-enriched enough to be identified in NMR spectra and followed throughout the titration. It is conspicuous that all the acidic residues that were significantly labeled are half-ionized at pH values below the isoelectric point of approximately 5. The acidic groups with low apparent pKa values can be considered as those of primarily structural importance for a protein.29 Chemical Shift Assignments The 1H-13C HSQC-TOCSY experiments were used in pH titration to provide correlations between the ␥-13C (Glu, 110 T. KESVATERA ET AL. TABLE I. Experimentala and Simulatedb Titration Parameters of Acidic Residues and the C-Terminal ␣-Carboxyl Group in the Apo Form of Bovine Calbindin D9k at 0.5 mM Protein Concentration and 300 Kc Ionizable group Glu4 Glu5 Glu11 Glu17g Glu26g Asp47 Glu48 Glu64g ␣-COOH ⌬␦(13C), ppm 4.01 ⫾ 0.06 4.50 ⫾ 0.09 3.92 ⫾ 0.08 2.85 2.09 ⫾ 0.12 0.76 ⫾ 0.10 3.02 ⫾ 0.14 3.62 ⫾ 0.03 4.04 ⫾ 0.24 4.04 ⫾ 0.07 0.44 ⫾ 0.02 Experimental n pKa 0.80 ⫾ 0.02 0.77 ⫾ 0.02 0.70 ⫾ 0.03 0.98 ⫾ 0.07 0.68 ⫾ 0.05 0.58 ⫾ 0.06 0.78 ⫾ 0.02 1.17 ⫾ 0.10 3.77 ⫾ 0.02 3.40 ⫾ 0.02 4.74 ⫾ 0.02 3.62h 3.21 ⫾ 0.06 6.46 ⫾ 0.16 4.08 ⫾ 0.04 3.04 ⫾ 0.09 4.62 ⫾ 0.06 3.84 ⫾ 0.02 3.20 ⫾ 0.05 pKa shiftd pKae nf Simulated pKa shiftd pKaexp ⫺ pKasim ⫺0.63 ⫺1.00 ⫹0.34 ⫺0.78 ⫺1.19 ⫹2.06 ⫺0.32 ⫺0.96 ⫹0.22 ⫺0.56 ⫺0.60 4.2 3.7 4.1 4.9 0.52 0.60 0.44 0.30 ⫺0.2 ⫺0.7 ⫺0.3 ⫹0.5 ⫺0.43 ⫺0.30 ⫹0.64 ⫺1.28 3.9 2.5 4.2 3.9 3.6 0.50 0.55 0.61 0.55 0.72 ⫺0.5 ⫺1.5 ⫺0.2 ⫺0.5 ⫺0.2 ⫹0.18 ⫹0.54 ⫹0.42 ⫺0.06 ⫺0.40 aThe experimental titration parameters, including pKa values, n values, and titration shifts, were determined from the titration behavior of chemical shifts for aspartate ␤-13C, glutamate ␥-13C, and of the ␥-13C NMR resonances of the C-terminal Gln75 residue (␣-COOH). bThe protein coordinates with accession number 3ICB from the Brookhaven Data Bank for the crystalline Ca2⫹-loaded calbindin D18 were used. 9k cThe estimated initial salt concentration in a protein sample for titration experiments was 0.5 mM at pH 6.0 due to residual salt in a purified protein. An increase in ionic strength due to added HCl or NaOH during the titration was taken into account in Monte Carlo simulations. dpK shift from the model compound pK values, pK –pK : pK is 4.0 for Asp, 4.4 for Glu, and 3.8 for ␣-COOH.20 a 0 a 0 0 eIn simulations the pK of an ionizable group is defined as the pH value at which the group is half-protonated. a fThe Hill parameter (n) values for simulated titration curves were determined using Equation 1. gResidues located in calcium-binding loops of calbindin D : Glu64 in the C-terminal loop, Glu26 and Glu17 in the N-terminal loop; the backbone 9k carbonyl oxygen of Glu17 provides a calcium ligand in the Ca2⫹-loaded form of calbindin D9k . hThe experimentally observed pH value corresponding to a half-protonated state of Glu17. Gln) or ␤-13C (Asp, Asn) and the main-chain ␣-protons, as well as side-chain protons of respective residues. Because of the dilution of the carbon-13 label by transamination reactions and the overlap of resonances in the recorded NMR spectra, only 8 of 17 acidic amino acid residues present in calbindin D9k could be identified by using the proton resonance assignments for the apo calbindin D9k at pH 5.25.17 Thus, it was possible to unambiguously identify and follow the titration behavior of residues Glu4, Glu5, Glu11, Glu17, Glu26, Asp47, Glu48, Glu64 and the Cterminal ␣-carboxyl group of Gln75. In addition, the chemical shift changes of residues Gln22, Gln33, and Gln67 with changing pH were followed. The side-chain proton resonances, although helpful in making positive identification of 13C resonances, did not provide titration curves for reliable pKa determination for all the observed residues because of the overlap of resonances in NMR spectra at several pH values. The titration parameters for individual residues reported in this work were therefore determined from the pH dependence of their carbon-13 chemical shifts. The experimental measurements were complemented by Monte Carlo simulations of the titration process and pKa values. The results are summarized in Table I. Titration Shifts The chemical shifts of the 13C nuclei, located next to the ionizing carboxyl groups in the side chains of aspartates and glutamates, decrease with decreasing pH. Titration shifts were observed in the range from 2.85 to 4.50 ppm. These upfield titration shifts with decreasing pH are consistent with those observed for the chemical shifts of ␤and ␥-13C resonances of aspartates and glutamates in other proteins, e.g., human immunodeficiency virus protease30 or bovine pancreatic trypsin inhibitor.31 The titration shift of 3.62 ppm for Asp47 may be underestimated (and the experimental pKa value overestimated) because the low pH limit of the titration curve was not observed in the pH range under the study. All the titration curves in Figure 2 are better described at their high-pH ends. Therefore, all the reported experimental pKa values, to a different extent, should be considered as ‘‘upper estimates.’’ Apart from Asp47, this particularly concerns residues Glu5, Glu17, and the C-terminal ␣-COOH, which are characterized by low pKa values and ‘‘uncompletely covered’’ low-pH ends of their titration curves. The upfield titration shift of 0.45 ppm with decreasing pH, characterized by an apparent pKa of 3.20 ⫾0.05, was registered for the ␥-13C nucleus of the Gln75 side chain and assigned as resulting from the change in the ionization state of the C-terminal ␣carboxyl group of Gln75. This titration shift may include conformation-mediated influences resulting from the titration of the relatively distant ␣-carboxyl group. Similar titration shift of 0.58 ppm with an apparent pKa of 3.17 ⫾ 0.10 for the ␥-13C resonance of Gln67, is probably dominated by conformational consequences of the change in ionization state of ␣-carboxyl group of Gln75. The ␥-13C resonance frequency of the Gln33 residue was independent of pH in the observed range. Multiple-Site Titration Figure 2 shows theoretical unperturbed titration curves for each ionizable group with its model compound pK0 value. The shape of experimental titration curve for the side-chain carboxyl group of Glu26 and the C-terminal PKA OF ACIDIC RESIDUES IN CALBINDIN D9K 111 Fig. 2. Experimental (circles, thick line) and simulated (dashed line) titration curves and pKa (experimental values underlined) for acidic groups in apo calbindin D9k at 300 K. Unperturbed titrations with corresponding model compound pK0 values (Asp 4.0, Glu 4.4, and ␣-COOH 3.8), and the n equal to 1 are given by thin curves. ␣-COOH group is close to the ideal single-proton titration. The experimental titration curves for the rest of the observed ionizing residues, however, extend over a significantly wider pH range than those for unperturbed model compounds and display Hill coefficient values less than unity. The titration range is even larger for the simulated titration curves and can be clearly seen for all the studied ionizable groups in Figure 2. The Hill coefficient values for simulated titrations, as a rule, are lower than for experimental titration curves (Table I). The negative cooperativity, as manifested by the Hill parameter, both in theory and experiment, can be explained as an effect due to other acidic residues that undergo a change in their ionization state in the observed pH range, resulting in modulation of the Coulomb interaction over the long distances. Because of the monotonically delayed titration behavior, it is not possible, by analyzing the experimental titration curves in terms of limited number of strongly interacting ionizable groups,32,33 to unambiguously identify particular ionizing groups affecting the titration of each individual residue. In contrast to the titration of other residues, the pH dependence of [␥-13C] chemical shift of Glu17 shows a distinguished biphasic titration curve, pointing to the strongly coupled titration of two acidic groups. Theoretical structure-based modeling of the titration of this residue does not explicitly reproduce the pronounced two-step titration observed in the experiment, and significant differences in predicted and determined ionization step are observed from pH 2.5 to 6. However, the Hill parameter for the simulated titration curve of Glu17, equal to 0.30, is significantly lower than for other residues observed in this work. This confirms that, to some extent, the theoretical model is still capable of reproducing electrostatic effects arising from structural features of calbindin D9k that cause the titration of Glu17 to take place under the strong influence of the electrostatic field created by nearby resi- 112 T. KESVATERA ET AL. dues. Another explanation for the biphasic titration behavior of Glu 17 could be a conformational change taking place at pH 4.5–5. This would also explain the discrepancy observed between experimental and theoretical results. Apparent pKa Values of Acidic Groups in Apo Calbindin D9k The protonation-deprotonation equilibria of ionizable groups in unstructured peptides are largely determined by their intrinsic properties and are usually not significantly affected by specific influences from other residues. The pKa values normally observed in such peptides are 4.0 for an aspartic acid side chain, 4.4 for glutamic acid side chain, and 3.8 for a C-terminal ␣-carboxyl group. Individual ionizable groups in folded proteins are usually characterized by apparent pKa that are significantly different from their intrinsic values in unstructured model peptides, the shifts from intrinsic pK0 values being largely caused by site-specific electrostatic interactions. The ionization constants for acidic groups observed in apo calbindin D9k were found to deviate from their model compound values as illustrated in Figure 3. Experimental pKa for Glu11 and Glu48 are shifted toward high pH by 0.34 and 0.22 pK units, respectively. Local electrostatic environment of the remaining observed ionizable groups favors their deprotonated state in a folded protein, thus causing their apparent pKa values to be shifted toward low pH, with the shifts ranging from 0.32 to 1.0 pK units. Reduced pKa values of these carboxyl groups can be explained as resulting from global electrostatic effects due to protein charges. Most of these ionizable groups are distant from the calciumbinding sites, and they titrate under conditions in which the protein carries a net positive charge dominated by cationic lysine side chains. It should then be expected that among the acidic residues that were not accessible through 13C-labeling are residues titrating under the influence of net negative charge of the protein, and some of them probably display pKa values significantly shifted toward high pH. The data obtained in this work do not allow the discussion about involvement of hydrogen-bonding effects. Some information about hydrogen bonds could be obtained by inspection of the pH effects on backbone amide proton chemical shifts, which we do not possess here. Obtaining these data is a part of ongoing studies. The pKa shifts of ionizable residues, whether acidic groups or lysines, from their model compound values are interpreted as resulting from the cumulative effect of ionic charges from all over the protein molecule. Partial charges and dipoles are not included. The theoretical model also neglects H-bonds and conformational changes. However, lysines and acidic residues ionize in different electrostatic environments. The onset of a proton uptake by lysines at strongly alkaline pH occurs under the influence of 18 negatively charged acidic groups. When all the lysines are protonated at about pH 9, the net charge of the protein is still ⫺8, assuming that the N-terminal ␣-NH2 uptakes a proton between pH 7 and 8. The ionization of acidic groups, on the other hand, involves Fig. 3. Experimental (filled bars) and simulated (empty bars) pKa shifts from corresponding model compound values for Asp and Glu residues and the C-terminal ␣-COOH group in apo calbindin D9k at 300 K. the change of protein net charge from ⫺7 to ⫹10, with isoelectric pH around 5. The measured and modeled pKa shifts, as illustrated in Figure 3, are in fair agreement. For residues Glu5, Glu26, and Glu64, the observed and predicted pKa values agree within 0.3 pK units and for residues Glu4, Asp47, Glu48, and ␣-COOH the agreement is within 0.4–0.5 pK units. For Glu11 the predicted pKa shift is in opposite direction to what was observed in experiment, with the difference of 0.64 units in pKa values. The major disagreement between the measured and predicted titration behavior is observed for Glu17, which is a backbone Ca2⫹-ligand in the Nterminal calcium binding loop. According to the measurements, this residue is half-protonated at pH 3.6 but manifests a biphasic titration with apparent pKa values of 3.2 and 6.5 (Table I). In Figure 2 the comparison is made between the pH values corresponding to the half-protonated state in experiment and simulation. Analogously, the pH dependence of the chemical shift of ␥-13C resonance of Gln22 can be also described as a two-step titration with apparent pKa values of 4.13 ⫾ 0.18 and 6.20 ⫾ 0.16 and the total titration shift of 0.51 ppm. It is not possible, however, from the present data to decide whether the apparent pKa of 6.2 for Gln 22 manifests the titration of the Glu 17 residue. Neither is it possible to tell whether the apparent pKa of 6.5 is a characteristic of only Glu17 or reports the change in ionization state of some other nearby acidic residue. In either case the events resulting in 20% neutralization with apparent pKa of about 6.5 of a Ca2⫹-ligating residue Glu17 in the N-terminal calcium-binding loop are most probably significant for the physiological activity of calbindin D9k. Impact of pH Change on Protein Structure Computational approaches to the calculation of pKa values in a protein usually rely on the assumption that the structure of the protein is well established ,and it does not change over the pH range used in titration experiments. Calbindin D9k has been reported to have similar structure both in crystal and solution, which does not respond significantly to the specific binding of two calcium ions34or changes in solvent and temperature.35 In agreement with PKA OF ACIDIC RESIDUES IN CALBINDIN D9K Fig. 4. A diagram showing side chain carboxyl groups for aspartate and glutamate residues in a set of 33 structures of apo calbindin D9k at pH 5.3 by NMR spectroscopy. The backbone is shown for one of the structures. The pKa values were measured for residues shown by dashed circles. this, no significant changes in calbindin D9k structure were observed at pH values up to 12.2,25The Hill coefficient for lysine titrations did not significantly deviate from unity, and the theoretical pKa values for lysine residues in calbindin D9k, calculated for the structure of protein crystals that were obtained at neutral pH, were found to be in good agreement with experimental data.2 The solution structure of apo calbindin D9k is not a single well-defined protein configuration but a set of 33 structures (1clb.pdb), whose statistical weights are unknown. Figure 4 shows the side chain carboxyl groups of acidic residues in these structures. Except for Glu11,Glu35, and Glu60, configurations of side chains of acidic groups are not well defined. In many cases, their configurations occur in two to four groups, and for Glu17 and Asp58 the side chain carboxyl groups are more or less uniformly spread over the sphere with a diameter of 10–12 Å. This may indicate the conformational lability of these side chains in the solution. Because the overall charge state of a protein as well as the charge states of individual residues are gradually changing with changing the pH, the configuration of side chains can also vary with pH, particularly in the calcium-binding area. At present, we can see no reliable way of accounting for these structural changes in theoretical calculations. The use of a rigid structure of a calcium-loaded calbindin in theoretical pKa calculations is an approximation that neglects structural changes due to calcium binding and changing pH. The failure to exactly reproduce the biphasic titration curve for Glu17 in theoretical calculations may be intrinsic to a model but may also result from this neglect. The side chain of Glu17 seems to be the least well-defined in the apo calbindin D9k structures. 113 The results of the present study indicate that calculations based on the crystal structure of the calcium-loaded protein can reproduce the main features of titration behavior of acidic residues, including apparent pKa values and broadened titration curves. Differences in measured and modeled titration behavior of acidic residues may arise partly from shortcomings of the theoretical model for electrostatic interactions in proteins. However, it is also highly possible that some changes in protein structure take place with decreasing pH. It is relevant that neutralization of all the acidic groups in calbindin D9k, while pH is changing from neutral to strongly acidic values, causes the change in the overall charge of the protein by 18 units, from ⫺7 to ⫹11, assuming the N-terminal ␣-NH2 group (pKa ⱖ 7.5) protonated at pH 7. The change includes reversal of the net charge from negative to positive values over the isoelectric point at about pH 5. It may not be reasonable to expect that the structure of a protein will remain resistant to such a large change in the net charge. An indication of possible structural change is that the experimental titration curves for acidic residues in calbindin D9k are characterized by distinctly higher Hill parameter values than simulated titrations, obtained under the assumption of protein structure being constant at variable pH. It is reasonable to expect that while the change in the overall charge takes place during the titration, the protein structure will respond to this change to maintain optimal interaction between the groups still remaining ionized in a new electrostatic environment. On the basis of the comparison of solution structures of apo and calcium-loaded calbindin D9k, it has been suggested that such changes in the spatial arrangement of the side chains of some acidic residues occur on calcium binding.36It is also possible that changes in configuration of side chains of ionizable residues take place with changing pH to compensate the changes in the charge state of their own or other titratable groups. This may be the case for Glu17, the backbone carbonyl group of which is a calcium ligand in the Nterminal binding site, highly populated by acidic residues. The biphasic titration observed for this residue in experiment, but not explicitly reproduced in the theoretical calculations, may well be a manifestation of the change in side-chain configuration around pH 5. At similar overall three-dimensional structure of a protein, differences in positions of particular ionizable side chains can cause significant differences in their pKa values.5 It is important that the onset of titration of Glu17 at near-neutral pH, down to the pH where this residue is protonated in 20% of the protein, is remarkably well reproduced in simulations (Fig. 2). This observation suggests that at high pH limit of titration the side chain of Glu17 is in a configuration given by crystal structure. When 20% of Glu17 is protonated, the change in side-chain configuration takes place, resulting in a charge distribution of the protein molecule that favors the ionization step of this residue being unchanged between pH 5 and 4 while further titration takes place with a different pKa value at lower pH values. However, because the simulations, in general, fairly agree with the experimental data, the changes in the net charge of calbindin D9k, either resulting from calcium 114 T. KESVATERA ET AL. binding or caused by changes in pH, are apparently balanced not to result in large fluctuations of the overall charge distribution or the global structure of the protein. This assumption is supported by a recent remarkable observation that the overall charge distribution of a protein catalyst acetylcholinesterase remained stable despite the change in its net charge by a factor of 2.37 The Dielectric Constant In pKa simulations according to the electrostatic continuum model we use a high dielectric constant throughout the system, including the protein interior. This may appear a rather drastic approximation, but previous Monte Carlo simulations of this model accurately reproduce experimentally observed shifts in the calcium-binding affinity on mutations of the protein as well as changes in salt and protein concentration.22,23,26,38 Recent studies1–5 of the titration behavior of proteins support the use of a high dielectric permittivity for the protein interior. Molecular simulations also support the notion of a high dielectric permittivity of the protein interior.39 These results are in agreement with the ideas advocated by Warshel and co-workers40–42 emphasizing that protein charges have to be stabilized one way or another. One possibility is that the charges are located on the surface of the protein and stabilized by the aqueous solvent. An ‘‘interior’’ charge, on the other hand, has to be stabilized by other nearby charges or polar groups. To describe the latter type of stabilization in a macroscopic model is difficult, if not impossible, but one possible way to approximate the effect is to assume a high dielectric response also from the protein interior. The detailed microscopic information concerning hydrogen bonds, partial solvation, etc. will be lost, and the ‘‘interior’’ dielectric permittivity becomes in this case just an additional fitting parameter. An easy and accurate way out of this dilemma is to assume a uniform dielectric permittivity equal to the value of pure water for the whole solution. A second aspect of this problem is at what separation between two charges can we expect the macroscopic theory to be valid? Previous experimental and theoretical results for the calcium- binding properties of calbindin seem to indicate that the macroscopic theory is valid down to separations below one nanometer.23 This notion is also supported by titration data for diamines and dicarboxylic acids.43 The effective dielectric screening between the two nitrogens (3.4 Å apart) in 1,2-diaminoethane is 26, whereas for 1,5-diaminopentane it is already close to 70. The separation between the charged nitrogens in the latter molecule is about 6 Å. Similar results are also observed for polycarboxylic acids. It turns out that the titration pattern for polyacrylic acid is well reproduced in a continuum model44 while it fails completely for more highly charged chains such as polyfumaric acid and polymaleic acid (M. Borkovec and G. Koper, personal communication). From the X-ray structure of Ca2⫹-loaded calbindin D9k we find that of the acidic residues studied in this work it is only Glu17 and Asp47 that have any additional charged groups within 5 Å distance. The carboxylic oxygens of Glu27 are approximately 4.5 Å from those of Glu17 and the positively charged nitrogen of Lys25 is only 3.5 Å away from the carboxylate group of Asp47. In the latter case we should expect a significant upward shift of Lys25 and a downward shift of Asp47. This is indeed born out in the experiments.2 It is interesting to note that despite the short separations between Lys25 and Asp47 in the X-ray structure both shifts are reasonably well reproduced in the theoretical modeling. A possible explanation for the good agreement is that their separation is increased by a few Ångströms compared with the X-ray structure. Thus, we might conclude that a macroscopic continuum model assuming a high dielectric response from the protein interior adequately describes the ionic interactions in calbindin D9k. Prospects of pKa Determination The agreement between theory and experiment is not perfect; for some residues even the sign of the predicted pKa shift is wrong. Overall, the comparison is of the same quality as obtained from other macroscopic models.1 The pKa values of six residues at the binding sites of calbindin D9k have been recently calculated by using Debye-Hückel theory.45 A reasonable prediction was made for Asp 19 to have a pKa of 4.22 in the apo form. The rest of predicted pKa values, in the range from 9 to 22, seem to be far too unrealistic. Unfortunately, none of these residues could be followed in our present study. However, all titratable acidic groups in calbindin D9k were included in calculations. Simulated pKa values span the range from 2.5 (Asp47) to 6.0 (Glu60). The ongoing work has shown that the pKa values can be determined for all the acidic residues in calbindin D9k. The agreement between the measurement and modeling in the present study would of course improve slightly by using the interior dielectric permittivity as a fitting parameter. No further information should, however, be gained by such an attempt. Structural changes in the protein on pH change are not taken into account in our model and neither are nonelectrostatic effects on the intrinsic dissociation constant, pK0. That is, we assume that the pK0 values of glutamic acid and aspartic acid are the same in folded calbindin D9k as in small model peptides. These are theoretical or modeling problems that should be discussed together with the experimental difficulties of identifying and following every single titrating group in a protein. Note that this has to be done over a wide pH range actually passing through the pI. Previously2 we were successful in determining the apparent pKa values for all 10 lysine residues in calbindin D9k using 13C enrichment. In the present work we were able to identify nine apparent pKa values for acidic groups, but nine escaped our efforts. The correctness of the assignment of both the acidic groups and the lysines has been verified by using homonuclear 1H TOCSY NMR experiments. The remaining nine glutamic and aspartic acid residues will be studied by using a different labeling strategy, e.g., 15N labeling. Depending on the method in use the number of peaks in NMR spectra can be huge, and the risk of making errors in assignments of resonances at variable pH is not negligible. 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