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J. Mol. Biol. (1996) 259, 828–839
Measurement and Modelling of Sequence-specific p Ka
Values of Lysine Residues in Calbindin D 9k
Tonu Kesvatera, Bo Jo ¨ nsson*, Eva Thulin and Sara Linse
Physical Chemistry 2 A pH titration study of calbindin D9k was performed using heteronuclearChemical Centre, University 1H-13C two-dimensional NMR spectroscopy. The protein was produced
with carbon-13 label in the side-chain of lysine residues, next to the titratingof Lund, POB 124, S-22100group. The site-specific pKa values of these lysine residues, ranging fromLund, Sweden10.1 to 12.1, were obtained from the analysis of pH-dependent chemicalshifts of 13C and 1H resonances. Ionization constants for both the Ca2 + -free(apo) and Ca2 + -loaded forms of the protein were determined. The protonuptake by lysine residues in the apo form was shifted up to 1.7 unitstowards high pH as compared to that for the model compound. Thebinding of calcium affected the pKa values of all lysine residues. The largestreduction of one pK unit was observed for Lys55, which is also the closestto the calcium binding sites. A threefold increase in protein concentration,from 0.5 to 1.5 mM, reduced the pKa values by 0.1 to 0.4 pK unit inagreement with the screening concept of ionic interactions. All the observedpKa shifts were site-specific, depending on the local electrostaticenvironment and were reproduced in Monte Carlo simulations based onthe three-dimensional structure of calbindin D9k and a dielectric continuummodel for the electrostatic interactions.
7 1996 Academic Press Limited
Keywords: calcium binding proteins; electrostatic interactions; pKa of*Corresponding author lysine residues; Monte Carlo simulations; nuclear magnetic resonance
Introduction
The folding of a polypeptide chain into afunctional protein results in multiple interactionsbetween ionizable groups and the pKa values ofthese residues differ from those of similarunperturbed groups in model compounds. Forexample, the pKa values of the carboxyl residues inbarnase increase by 0.4 unit on average upontransfer from a loose denatured conformation to thenative protein (Oliveberg et al., 1995). The pKa
perturbations are predominantly driven by electro-static factors such as protein charges and solventenvironment. The shifts are therefore sequence-specific, they vary from zero to several pK units and
each titrating group in a protein with its individualpKa value is a sensitive probe of the localelectrostatic potential. The titration behaviour ofionizable amino acid residues has therefore beenone of the classical targets for studies of electrostaticinteractions in proteins (Tanford & Kirkwood, 1957).
The pKa values of ionizable groups are intimatelylinked to protein function. Amino acid side-chainswith significantly shifted pKa values are often foundat or near the active sites of enzymes, with the shiftsbeing essential for the catalytic activity. Shifts of 2to 4 pKa units up or down the pH scale havebeen measured by means of UV or 1H NMRspectroscopy for papain (Lewis et al., 1981) andacetoacetate decarboxylase (Kokesh & Westheimer,1971). Active-site pKa shifts upon substrate bindinghave been inferred from the pH dependence of thecatalytic activity of the aspartic proteases pepsin,rhizopuspepsin and HIV-1 protease (Lin et al.,1992). The pKa values of ionizable groups in theligand binding pockets or at the interfaces ofinteracting proteins are often different in the freeand bound states. Accordingly, pH titration studieshave been successfully used for mapping thebinding surfaces involved in protein-ligand (Yu &
Permanent address: T. Kesvatera, Institute ofChemical Physics and Biophysics, Estonian Academy ofSciences, EE0026 Tallinn, Estonia.
Abbreviations used: FID, free induction decay;HSQC, heteronuclear single-quantum coherence; LB,Luria-Bertani; NMR, nuclear magnetic resonance; P43Gcalbindin, D9k with Pro43 replaced by Gly; pKa,negative logarithm of the acid dissociation constant;ppm, parts per million; TOCSY, total correlationspectroscopy.
0022–2836/96/240828–12 $18.00/0 7 1996 Academic Press Limited
pKa of Lysine Residues in Calbindin D9k 829
Fesik, 1994) and protein-protein (Kato et al., 1993;Szyperski et al., 1994) interactions.
Ionization behaviour of proteins has been asubject of considerable research effort in recentyears (Oliveberg et al., 1995; Schaller & Robertson,1995; Szyperski et al., 1994; Bartik et al., 1994; Odaet al., 1994; So�rensen & Led, 1994). The experimentaldata on pKa values are necessary for development ofreliable theoretical models for electrostatic inter-actions in proteins with a predictive capacity.Further, it is of great value to obtain data for aprotein at variable solvent conditions, since a theoryshould be able to reproduce not only the pKa shiftin a given environment, but also the change in theshift due to screening factors (e.g. altered protein orsalt concentration), ligand binding, mutations orother perturbations. Such experimental data are asrare as the theories capable of describing theinfluence of these factors. One exception is theovomucoid third domain that has been studiedwith respect to ionization equilibria for carboxylgroups at low and high ionic strength (Schaller &Robertson, 1995). Also, the pKa value of the catalytictriad histidine has been measured for eightsubtilisin mutants at different ionic strength values(Sternberg et al., 1987). The formulation of acomputational method that reproduces experimen-tally observed pKa shifts in response to ligandbinding and changes in the electrostatic environ-ment could lead to a better understanding ofbiological processes involving charge-charge inter-actions within and between proteins.
Several computational schemes or pKa values oftitratable side-chains have been developed. Most ofthese schemes use a dielectric continuum modeland only the electrostatic interactions between ioniccharges are treated explicitly. The electrostaticproblem is then solved within the Poisson-Boltzmann approximation or its linearized version(Bashford & Karplus, 1990; Antosiewicz et al., 1994).Yet, if we look at the ability to reproduce a wholeset of pKa values for titrable groups spread over anentire protein, most methods have failed to beat theso called null method which assigns each ionizableside-chain its model compound pKa value. As anexception, Antosiewicz et al. (1994) recentlypresented an approach that beats the null methodwhen a high dielectric constant is used for theprotein interior. Further investigations of theionization behaviour of proteins, both experimentaland theoretical, are thus highly motivated. They arefacilitated by the high number of proteins withknown three-dimensional structure and assigned1H NMR spectra.
Here we present an experimental and theoreticalstudy of site-specific pKa values of the ten lysineresidues in the apo and the calcium loaded forms ofcalbindin D9k. As a consequence of the net negativecharge of calbindin D9k, equal to −8 for the apo-format neutral pH, significant shifts of the lysine pKa
values to high pH are expected. The net charge ofthe protein and, accordingly, the pKa shifts can bemodified by binding two Ca2+. This modification is
relatively safe from the computational viewpoint,because the structure of calbindin does not changesignificantly upon calcium binding (Skelton et al.,1994, 1995). The theoretical approach is based on thetraditional dielectric continuum model. The electro-static problem is, however, solved using MonteCarlo simulation techniques thereby avoiding themean field approximation inherent in the Poisson-Boltzmann approach. The Poisson-Boltzmann ap-proximation is probably a reliable ansatz undermany experimental conditions. There do exist,however, some cases where it fails and this isusually in highly charged systems and withmultivalent ions present (Akesson & Jonsson, 1991).
Because of its small molecular weight (Mr 8500)and outstanding stability (Wendt et al., 1988),calbindin D9k serves as a suitable model forpH-titration study by two-dimensional NMR. Aprotein sample in which all lysine residues were 13Clabelled at the e-carbon was used and the ionizationof individual lysine residues was followed byrecording two-dimensional 13C-1H HSQC spectra atpH values ranging from 5.25 to 12.25. The strongsingle-bond coupling between 13C and 1H is utilizedfor sensitivity enhancement and makes it possibleto avoid the high protein concentrations (2 to 4 mM)often used in NMR studies of proteins. This is animportant point as increased protein concentrationleads to significant screening of electrostaticinteractions (Linse et al., 1995). One could expect allthe pKa values to move closer to those of modelcompounds with increasing protein concentration.This issue is addressed by evaluating theoreticallyand experimentally the pKa values at two differentprotein concentrations.
Results
In order to follow the titration behaviour of lysineresidues in calbindin D9k the influence of pH hasbeen studied on proton and carbon-13 chemicalshifts in two-dimensional 13C and 1H HSQC spectra.The P43G mutation has been introduced to avoidthe conformational heterogeneity observed for thewild-type calbindin due to the cis-trans isomeriz-ation of Pro43 (Chazin et al., 1989a). Figure 1 showsthe 13C-1H HSQC spectra for apo and Ca2+ forms ofcalbindin D9k recorded at neutral and alkaline pH.The cross-peaks for individual lysine residues areclearly distinguishable at neutral pH and the signalsmove significantly with changes in pH. Weakcross-peaks were observed for lysine residues 16, 25and 29 both in apo and Ca2+ form of calbindin D9k.Due to the spectral overlap and the low intensity ofresonances for Lys25 the pKa of this residue couldnot be determined unambiguously for the 0.5 mMapo protein. Significant broadening of resonanceswas observed for the apo calbindin at alkaline pHvalues, possibly caused by exchange effectsassociated with structural changes accompanyingthe deionization of lysine residues (Abildgaardet al., 1992). Lysine signals for the apo form showtendency to merge at high pH (Figure 1a), which
pKa of Lysine Residues in Calbindin D9k830
indicates the disappearance of the individualenvironment for most of the lysine side-chains,probably because the protein structure becomes
more loose. In contrast to this, the cross-peaks arestill clearly separated at pH 12.25 for theCa2+-loaded calbindin (Figure 1b), obviously be-
Figure 1. Lysine e-13CH2 finger-print regions of the 13C-1H HSQCNMR spectra of 0.5 mM apo (a) andCa2+ form (b) of calbindin D9k atneutral and alkaline pH and 300 K.
pKa of Lysine Residues in Calbindin D9k 831
Figure 2. Region of a 1H-13CHSQC spectrum of 1.5 mM cal-bindin D9k showing the behavior ofa cross-peak for Lys55 upon deami-dation of Asn56.
cause the Ca2+ are supporting the structure in thestrongly alkaline solution. This is in accordancewith stability studies of calbindin D9k showing thatthe calcium form is more stable than the apo formagainst denaturation with urea (Wendt et al., 1988)and that increased negative surface charge leads toreduced stability (Akke & Forsen, 1990). For lysineresidues 7, 16, 29 and 72 two e-CH2 protonresonances were observed in the Ca2+ form atneutral pH. However, the gradual degeneracy ofthese proton resonances took place with increasingpH, and distinct peaks could be observed only forLys16 at pH 12.25 (Figure 1b).
The assignments of cross-peaks were based onthe previously published sequence-specific 1Hassignments at pH 5.25 for the apo form (Skeltonet al., 1990) and at pH 6.0 for the Ca2+ form (Kordelet al., 1989) of calbindin D9k. Further assignmentduring the titration was obtained by tracing thecross-peaks through the series of pH-dependentspectra registered at approximately 0.5 pH unitintervals and confirmed by comparison with atitration followed by 1H TOCSY for the apo form at1.65 mM protein concentration. At pH valuesbetween 10 and 11 two cross-peaks were observedfor Lys55, one vanishing and the other appearing(Figure 2). This was interpreted as a change in theside-chain environment resulting from the deami-dation, which is reported to occur at high pH for theneighbouring residue Asn56 (Chazin et al., 1989b).
Figure 3 illustrates the titration of lysine residuesin the Ca2+ form of calbindin as followed by 13C
(Figure 3a) and 1H (Figure 3b) resonances. As aresult of lysine titrations between pH 10 and 12 thenet charge on calbindin D9k varies and under thesecircumstances significant changes in protein confor-mation or in specific interactions between thespatially close ionizable residues could result inperturbed (broadened or biphasic) titration curves.Figure 3 shows, however, that over the observed pHrange the dependences of chemical shifts can bedescribed as simple sigmoidal one-step titrations.Indirect effects on chemical shift changes with pHother than the ionization itself are negligible. Thetitration behaviour of Lys29 in the apo form ofcalbindin D9k is somewhat exceptional, since theproton resonance titration shift of this residue(E0.2 ppm) is significantly smaller than that for theother lysine residues (0.3 to 0.5 ppm) in calbindinD9k (Figure 3b). For Lys55 most of the pH-dependent part of the titration is obtained in thepresence of Asp56 (deamidated Asn56). Thereversibility of the titration has been tested asfollows. In a sample of the 0.5 mM Ca2+-loadedprotein that has been used throughout all theexperiments from pH 6.0 to 12.25 the pH wasadjusted back to 10.03 and the spectrum wasobtained. The data indicated by arrows in Figure 3aand b show the absence of significant hysteresis inpH titration of Ca2+-loaded calbindin D9k.
The pKa values calculated from titration shifts fornon-degenerated proton resonances, when avail-able, agreed within 0.01 to 0.05 pK unit. Theagreement between pKa values determined from 13C
pKa of Lysine Residues in Calbindin D9k832
and 1H chemical shifts is generally good (seeTable 1) and the difference does not exceed 0.1 pKa
unit on average. As an exception, pKa for Lys29 inthe apo form of calbindin, determined from 13Cdata, is 0.2 to 0.4 unit smaller than that from the 1Hdata. It has been suggested that in variance with thetitration behaviour of the carbon resonance theproton chemical shift may be susceptible to factorsother than the ionization state of an adjacentgroup (Oda et al., 1994). However, no significantperturbation of the titration curve for the 1Hresonance of the e-CH2 group in Lys29 can beobserved in Figure 3b.
Simulations were performed for the apo andcalcium loaded forms at the same protein concen-trations and at the same pH interval as in theexperiments. During the course of the titration ofapo calbindin at 0.5 mM protein concentration, theprotein net charge varies between the original −8 atpH 7 to −15.2 at pH 12.5. Table 2 shows thetheoretically determined pKa values for the threedifferent cases studied. The site specific pKa valueswere determined as the pH at half occupancy. Theaccuracy of the calculated pKa values was betterthan 20.03 of a pK unit and was achieved after 104
moves for equilibration and another 105 moves perparticle for analysis. The computational effort israther modest and a full titration curve is obtainedin less than one hour on an ordinary work station.The simulation time increases approximatelyquadratically with the salt concentration, butnumerical approximations can be implemented inorder to reduce the simulation time at high saltconcentrations.
Discussion
Ionization constants of unassigned mono- anddimethylated lysine residues have recently beenreported for calmodulin (Zhang & Vogel, 1993) andcalbindin D9k (Zhang et al., 1994). The observed pKa
values for the Ca2+-free proteins were in the range9.87 to 10.55 for calmodulin and 9.7 to 10.7 forcalbindin, in 0.15 and 0.10 M KCl, respectively. Thebinding of Ca2+ was found to reduce the pKa valuesof the modified lysine residues in both proteins, tothe range 9.29 to 10.23 for calmodulin and 9.3 to 10.9for calbindin D9k (Zhang & Vogel, 1993; Zhang et al.,1994). The observed pKa shifts relative to the modelcompound value were small because the electro-static interactions were strongly screened due to thehigh salt concentration.
In the present work we have measured the site-specific pKa values of chemically unmodified lysineresidues in both the apo and Ca2+ forms of calbindinD9k. In order to minimize the screening of electro-static interactions, low concentration of protein hasbeen used and no salt was added, except for thecontrolled amounts of NaOH, that were accountedfor in Monte Carlo simulations. We have been ableto follow the chemical shifts of all lysine residues asa function of pH except for the Lys25 in the 0.5 mMapo calbindin. The lysine pKa values (except that forLys16 in the Ca2+ loaded form) are shifted towardshigh pH as compared with those for the modelcompound (Figure 3). This is in good agreementwith the simulated pKa values in Table 2, butdisagrees with the earlier observation (Zhang et al.,1994) that the pKa values for half of the methylated
Figure 3. pH dependence of 13C (a) and 1H (b) chemical shifts of the lysine e-13CH2 resonances in the Ca2+ form of0.5 mM calbindin D9k at 300 K. The fitted titration curves are shown by continuous lines. The data indicated by arrowsshow the chemical shifts for the protein sample that has been used throughout the measurements from pH 6.0 to 12.25and then adjusted back to pH 10.03.
Tabl
e1.
pKa
valu
esof
lysi
nere
sidu
esin
Ca2+
and
apo
form
sof
calb
ind
inD
9kat
0.5
mM
and
1.5
mM
prot
ein
conc
entr
atio
nan
d30
0K
pKa
Ca2+
-for
m,
0.5
mM
prot
ein
Ap
o-fo
rm,
0.5
mM
prot
ein
Ap
o-fo
rm,
1.5
mM
prot
ein
Res
idue
1 H13
CM
eana
1 H13
CM
eana
1 H13
CM
eana
Lys
110
.61
20.
0410
.58
20.
0710
.60
20.
0510
.60
20.
0510
.58
20.
0410
.59
20.
0410
.50
20.
0210
.47
20.
0310
.49
20.
02L
ys7
11.3
92
0.03
11.3
12
0.03
11.3
52
0.03
11.3
02
0.02
11.5
22
0.06
11.3
62
0.03
11.1
72
0.02
11.2
72
0.03
11.2
22
0.03
Lys
1210
.39
20.
0811
.06
20.
0711
.00
20.
0711
.01
20.
0611
.13
20.
0811
.06
20.
0710
.87
20.
0410
.88
20.
0210
.88
20.
03L
ys16
10.0
62
0.05
10.1
22
0.06
10.0
92
0.06
11.0
22
0.02
11.1
52
0.05
11.0
62
0.03
10.7
92
0.03
10.9
62
0.02
10.8
92
0.02
Lys
2511
.90
20.
0511
.72
20.
0611
.81
20.
06no
tob
serv
ed10
.78
20.
1910
.76
20.
1410
.77
20.
16L
ys29
11.0
52
0.03
10.8
82
0.06
10.9
92
0.04
11.6
42
0.09
11.2
02
0.02
11.2
82
0.03
11.3
72
0.12
11.1
42
0.04
11.2
02
0.06
Lys
4110
.95
20.
0610
.83
20.
0510
.89
20.
0610
.94
20.
0310
.92
20.
0210
.93
20.
0310
.86
20.
0410
.78
20.
0410
.82
20.
04L
ys55
11.4
32
0.04
11.3
32
0.06
11.3
92
0.05
12.1
42
0.12
12.1
02
0.13
12.1
22
0.13
11.7
32
0.07
11.8
02
0.09
11.7
62
0.08
Lys
7110
.72
20.
0410
.73
20.
0510
.72
20.
0510
.71
20.
0110
.75
20.
0410
.72
20.
0210
.68
20.
0.3
10.7
12
0.06
10.6
92
0.04
Lys
7211
.01
20.
0510
.91
20.
0710
.97
20.
0611
.33
20.
0811
.33
20.
0711
.33
20.
0711
.12
20.
0311
.10
20.
0411
.12
20.
04a
The
mea
nva
lues
are
calc
ulat
edas
wei
ghte
dav
erag
esof
the
pKa
valu
esob
tain
edfr
omth
epH
dep
ende
nce
of13
Can
d1 H
reso
nanc
esof
the
e-13
CH
2gr
oups
inly
sine
resi
dues
.
pKa of Lysine Residues in Calbindin D9k834
Table 2. Simulated pKa values of lysine residues in Ca2+
and apo forms of calbindin D9k at 0.5 mM and 1.5 mMprotein concentration and 300 K
Ca2+-form, Apo-form Apo-formResidue 0.5 mM protein 0.5 mM protein 1.5 mM protein
Lys1 11.99 12.10 11.93Lys7 12.29 12.53 12.32Lys12 11.77 12.02 11.84Lys16 11.35 11.90 11.71Lys25 12.77 13.21 12.85Lys29 11.51 11.81 11.61Lys41 10.87 11.02 10.84Lys55 12.12 12.95 12.86Lys71 11.09 11.22 10.99Lys72 11.82 11.95 11.84
the simulations predict a shift of 1.7 pK units,while the experimental value is 0.2. This is probablydue to the fact that the terminal residues areflexible in solution (Kordel et al., 1993) and theirconfiguration may be different from that in crystal.Another possible reason is that the recombinantcalbindin has an extra methionine as a N-terminalresidue, which will change the conformation ofLys1.
The pKa shifts are due to electrostatic charge-charge interactions within the protein and with thesurrounding ions. It is easy to obtain an estimate ofthe static contribution to the electrostatic potentialfrom the protein using the charge distribution atneutral pH and from the electrostatic potential at aparticular site (i.e. the z-nitrogen of lysine) one mayestimate a ‘‘static’’ pKa shift. These calculated staticshifts are too large and range from 1 to 3 pK unitsat neutral pH. The screening from salt andcounterions will reduce these pK shifts by 0.3 to 0.7unit. The division of the total shift into a static andscreening contribution is arbitrary since the proteincharge varies with pH. Still, this simplifiedapproach captures the relative trend in pKa shiftsamong lysine residues and provides an insight intohow the pKa values of ionizable groups in a proteinare perturbed by the surroundings, and the trend isthe same as seen in the experiments and MonteCarlo simulations for calbindin D9k.
As a result of the binding of two Ca2+ the pKa
values are shifted down-pH, towards the unper-turbed value of 10.4, in agreement with theCoulomb law and previous results obtained forcalbindin D9k with mono- and dimethylated lysineresidues (Zhang et al., 1994). The average shift uponcalcium binding is 0.30 and 0.31 in experiment andsimulation, respectively. The largest changes in pKa
are observed, both experimentally and theoretically,for Lys55 and Lys16, which are close to thenegatively charged Ca2+ sites in the protein (Figure5a). A significant change is also observed for Lys29.For the lysine residues 1, 41 and 71, which are at thelargest distances from the calcium sites, the
lysine residues were shifted towards acidic pH ascompared with those for unperturbed modelcompound, despite the high net negative charge oncalbindin. One possible explanation could be thatthe reference pKa value of dimethylated lysine issignificantly lower than 10, a value reported byHuque & Vogel (1993).
The pKa values of apo calbindin in the presentstudy span a range of approximately 1.5 units. Thelargest shift from the model compound valueobserved in the apo form in this work was 1.72 pKa
units for Lys55. The pKa shift of 2.5 units wasobtained for the same residue in the simulations. Itappears that the simulated shifts are overestimatedby 0.7 unit on average (see Figure 4). This issomewhat surprising since we use a high dielectricconstant throughout the system. The theoreticaloverestimate of the pK shifts could be due to anunderestimate of the salt content and the initial saltconcentration could be higher than 5 mM. The useof a higher salt concentration in the simulationwould of course reduce the pK shifts. A factorthat works in the opposite direction is thedeamidation of Asn56, which was not taken intoaccount in simulations. The largest discrepancybetween theory and experiment is, not unexpect-edly, seen for the N-terminal Lys1, for which
Figure 4. Comparison of experimental (light shadowing) and calculated (dark shadowing) pKa values of lysineresidues in Ca2+ free (a) and Ca2+-loaded (b) forms of calbindin D9k at 0.5 mM protein concentration and 300 K.
pKa of Lysine Residues in Calbindin D9k 835
Figure 5. Comparison of experimental (light shadowing) and calculated (dark shadowing) pKa shifts of lysine residuesupon Ca2+ binding (a) and increasing protein concentration (b) from 0.5 to 1.5 mM of apo calbindin D9k.
experimental and theoretical changes in pKa arenegligible.
An effect of screening the electrostatic inter-actions was observed by comparing the pKa valuesat two different protein concentrations. Threefoldincrease in protein concentration from 0.5 to 1.5 mMresults in decrease of pKa values in the apocalbindin D9k by 0.15 unit on average (Figure 5b).This result is of general significance because therather high protein concentrations (2 to 4 mM) oftenused in NMR analyses will markedly screen theelectrostatic interactions. The largest protein con-centration-dependent pKa shift is observed forLys55, which is closest to an area with high negativesurface charge at calcium binding sites. The pKa
values of the most distant lysine residues, Lys41and Lys71, are closest to the model compoundvalue and are also least affected by screeningcaused by increased protein and salt concentrations.
The pKa shifts due to increased protein concen-tration are more uniform in the simulations than inthe experiment (see Figure 5b). The average shift is0.15 pK unit in experiment and 0.19 unit insimulations. Lys25 is an exception in simulationswith the shift twice as large as the average value,but we lack experimental data for this residue in0.5 mM apo calbindin D9k.
The titration behaviour of Lys29 in the apo formof calbindin D9k is somewhat exceptional anddeserves specific attention. The proton resonancetitration shift corresponding to a side-chain ioniz-ation of this residue is smaller than that for the otherlysine residues in calbindin D9k (Figure 3b).However, the e-CH2 proton resonance of Lys29 inthe apo form displays an additional titration withpKa around 5.7 (Figure 6a), probably manifestingthe ionization of one of the neighbouring acidicgroups, Glu26 or Asp47, which can be found within
Figure 6. pH titration behaviour of proton (a) and carbon-13 (b) resonances of e-13CH2 group of lysine 29 in apo andCa2+ forms of calbindin D9k at 300 K as followed by homonuclear (TOCSY) and heteronuclear (HSQC) two-dimensionalNMR spectroscopy. r, 1.65 mM apo calbindin (TOCSY); q, 1.5 mM apo calbindin (HSQC); w, 0.5 mM apo calbindin(HSQC); W, 0.5 mM Ca2+calbindin (HSQC).
pKa of Lysine Residues in Calbindin D9k836
8 A from the ionizable group of Lys29 in the X-raystructure. The total titration shift from the acidic toalkaline limit of the biphasic titration is around0.3 ppm for the apo protein. In variance with this,a single titration is displayed by the e-protonresonance of Lys29 in the Ca2+ form of calbindinD9k, with a titration shift of 0.3 ppm (Figure 6a).Carbon-13 resonance of the e-CH2 group of Lys29shows a single titration with a typical titration shiftboth for the apo and Ca2+ forms of the protein(Figure 6b). The absence of acidic pKa for the protonresonance in the Ca2+ form might be caused by ashift of the corresponding ionization equilibriumtowards low pH upon Ca2+ binding, which reducesthe net negative charge of the protein. Alternatively,it may result from the structural change upon Ca2+
binding, which moves the Lys29 side-chain awayfrom the carboxylic group in question.
Correlations between observed and calculatedpKa values of lysine residues in apo and Ca2+-loadedcalbindin D9k are characterized by correlationcoefficients (r) of 0.71 and 0.72, respectively. Similarcorrelations for basic ionizable groups in BPTI andlysozyme (Antosiewicz et al., 1994) yielded r-valuesof 0.08 and 0.26 at a protein dielectric constant valueof 4 and 20, respectively. We assume that theagreement between theory and experiment does notdepend so much on whether the Monte Carlomethod or Poisson-Boltzmann approach is used.The value of the dielectric constant seems to bemore critical and a high dielectric constant tends toyield a better agreement. An important point is acareful reproduction in theoretical calculations ofexperimental conditions during the titration and toaccount for screening factors, such as electrolyte andprotein concentrations.
Conclusions
The pKa values of lysine residues in calbindin D9k
are shifted to high pH, as compared to thecorresponding model compound value, due to thenet negative charge of the protein. The shifts aresite-specific, depending on the local electrostaticenvironment. The binding of two calcium ions tocalbindin reduces the pKa shifts and so does anincrease in protein concentration. The effect ofcalcium binding is a direct manifestation ofCoulomb law, while the effect of increased proteinand salt concentrations is compatible with screeningconcepts. The experimental shifts are reproduced byMonte Carlo simulations. In particular, the changesdue to calcium binding and protein concentrationincrease are well described. The simulations, basedon a uniform dielectric continuum model, certainlybeat the so-called ‘‘null method’’, which assumesunperturbed pKa values in the native protein. Ingeneral, we consider the assumption of a fixedprotein structure the most severe approximation inthe theoretical scheme. pH-dependent structuralchanges are, of course, expected to affect the pKa
values, but fortunately appear to be of minorsignificance for calbindin D9k at alkaline pH values.
Materials and Methods
Protein preparation
The P43G mutant form of calbindin D9k was expressedin Escherichia coli from a synthetic gene yielding a proteinwith bovine minor A sequence except that residue 43 isa glycine instead of a proline. The cells were first grownovernight in LB medium and 10 ml of the overnightculture was used to inoculate 250 ml minimal medium.When the absorbance at 600 nm was 0.5, 60 ml of thismiddle culture was transferred into 500 ml minimalmedium and cells were harvested two to three hours afterthis final culture reached the lag phase, at which point theyield was at maximum. All amino acids were added to theminimal media as free L-amino acids in relative amountsaccording to their frequencies of occurrence in proteins.The total amount of amino acids was 1.0 g/l in the middleculture and 0.5 g/l in the final growth medium.Carbon-13 labelled l-lysine (the e-carbon next to thetitrating amino group) was purchased from CambridgeIsotope Laboratories (Andover, Massachusetts), whileunlabelled amino acids were purchased from Sigma.Purification of the protein and removal of calcium wasperformed as described by Johansson et al. (1990) and thepurity was confirmed by agarose gel electrophoresis,SDS/polyacrylamide gel electrophoresis, isoelectric fo-cusing and 1H NMR. The residual Ca2+concentration afterchelex treatment was below 0.1 equivalent as judged from1H NMR spectra and titrations in the presence of thechromophoric chelator quin 2. The total yield of purifiedCa2+ free protein was 15 mg from two litre culture.Protein samples for titration experiments were made0.5 mM or 1.5 mM in a 0.5 ml final volume containing 90%H2O and 10% 2H2O. The protein was transferred intoCa2+-loaded form by addition of three equivalents ofcalcium.
NMR spectroscopy
Two-dimensional 13C-1H HSQC NMR spectra (Bax et al.,1990; Norwood et al., 1990) were recorded at 300 K on aGE Omega 500 spectrometer operating at 500.11 MHz for1H and 125.76 MHz for 13C. The spectral width was5000 Hz in both dimensions and the digital resolution was4096 complex points in v2, and 128 real points in v1 and128 to 256 FIDs were collected for each t1 point.Decoupling of the 13C nuclei during the acquisition periodwas achieved using Garp-1 phase modulation (Shakaet al., 1985). The water signal was suppressed usinga low-power presaturation pulse of 1.3 seconds. The13C chemical shift was measured relative to thespectrometer frequency. Two-dimensional 1H TOCSYspectra (Braunschweiler & Ernst, 1983; Rance, 1987) wereacquired with the DIPSI-2 mixing sequence (Shaka et al.,1988) and a mixing time of 80 ms.
pH titration
13C-1H HSQC spectra were recorded for carbon-13labelled apo- and Ca2+-forms of calbindin mutant P43G atpH values ranging from 5.25 to 12.25 at ca 0.5 pH unitintervals in the region of lysine titrations. The pH wasadjusted by adding 0.2 to 1 ml amounts of concentratedHCl or NaOH with a Hamilton syringe in order to obtainaccurate estimates of the added Na+ or Cl− at each titrationpoint. The pH of a sample was determined before andafter NMR measurements and the two values agreed
pKa of Lysine Residues in Calbindin D9k 837
within 0.1 pH unit. The pH value was taken as thereading of the Radiometer PHM63 Digital pH meter withan Ingold U402-M3-57/200 electrode and was notcorrected for isotope effects caused by the 10% 2H2O.
The pKa values were determined by fitting theexperimental chemical shift versus pH data to theequation that describes a one-step titration:
dobs = [dHA + dA10(pH−pKa)]/[1 + 10(pH−pKa)] (1)
where dobs is the observed 1H chemical shift and dHA, dA are
the chemical shift values for the protonated andunprotonated species.
Theoretical model
The protein coordinates PDB3ICB from the BrookhavenData Bank obtained from an X-ray diffraction study of thecrystalline Ca2+ loaded protein (Szerbenyi & Moffat, 1986)were used. Each protein atom was represented as a hardsphere, impenetrable to any solvent ions. Negativelycharged carboxylic oxygen atoms were given a charge of−0.5, while positively charged lysine residues carried apositive unit charge on the z-nitrogen. The lysine chargeswere allowed to change according to the solution pH asdescribed below. The protein coordinates were kept fixedduring the simulation, and the protein was placed in thecentre of a spherical cell to which counterions and saltions were added in accordance with experimentalconditions. These ions were treated as mobile chargedhard spheres confined to the cell, whose radius wasdetermined by the protein concentration. The cell,including protein, counterions and salt is alwayselectroneutral. The number of counterions is given by theprotein net charge and increasing the cell radius (i.e.lowering the protein concentration) consequently leads toa reduced counterion concentration. This, of course,affects the electrostatic screening and in the limit of zeroprotein concentration all the screening is given by theadded salt. Thus, the cell model approximation gives anopportunity to study how the protein concentrationaffects the titration curve. This is in contrast to most othertheoretical studies, which usually assume the protein tobe at infinite dilution. The interaction energy betweencharged species i and j is given by:
u(rij ) = qiqje2/4pe0erij rije(si + sj )/2
u(rij ) = a rij < (si + sj )/2
where q is a partial charge, e is the elementary charge, e0
is the permittivity of free space, si is the hard corediameter of particle i, and rij is the distance between theparticles i and j. Only interactions between particleswithin the cell are taken into account. The dielectricconstant, e, was chosen as 77.8 at the experimentaltemperature of 300 K. A schematic diagram of the systemis given in Figure 7. The dielectric constant was assumedto be uniform throughout the cell. This may appear arather drastic approximation, but previous Monte Carlosimulations of this model accurately reproduce exper-imentally observed shifts in the calcium binding affinityof several calcium binding proteins upon mutations of theprotein as well as changes in salt and proteinconcentration (Svensson et al., 1991, 1993; Linse et al.,1995). A recent theoretical study (Antosiewicz et al., 1994)of the titration behaviour of proteins support the use ofa high dielectric permittivity for the protein interior.Molecular simulations also support the notion of a highdielectric permittivity of the protein interior (Smith et al.,1993).
Figure 7. Schematic picture of the protein and mobileions in the simulation cell coupled to a proton bath. Thefree ions are shown as open circles with a sign indicatingthe charge. The protein atoms are shaded circles and thetwo calcium binding sites are shown as filled circles.
Monte Carlo simulations
The simulations were performed in the canonicalensemble with respect to salt ions and counterions, usingthe traditional Metropolis Monte Carlo procedure(Metropolis et al., 1953). In addition, the simulation cellwas coupled to a proton bath in order to establish aconstant pH in the system. After every tenth attemptedmove of the mobile charges, an attempt was also made todelete/insert protons on a lysine residue. In reality, adeletion of a proton from a lysine means that alkali(NaOH) has been added to the solution. Hence in thesimulation, a proton deletion on a lysine residue wasalways accompanied by the addition of a positive mobilecharge to the cell in order to keep the systemelectroneutral. The acceptance/rejection of an attempt tochange the ionization state of a particular lysine wasbased on the trial energy:
DE = DEC2kT ln10(pH-pK0)
where DEC is the change in Coulomb energy and K0 is thedissociation constant for the model compound. In thisstudy we have chosen a value of 10.4 for lysine residues(Nozaki & Tanford, 1967). The plus sign is used when aresidue is to be protonated and the minus sign when itis to be deprotonated. The successive addition of alkali inthe experimental determination of the titration curvemeans that the ionic strength increases with pH. Thisstepwise increase in salt concentration was taken intoaccount in the simulations in order to mimick theexperimental conditions as closely as possible. At highpH, the activity coefficient for OH− starts to deviate fromunity and the calculated pK values have to be corrected
pKa of Lysine Residues in Calbindin D9k 838
for this effect. This was accomplished by a modifiedWidom technique (Widom, 1963; Svensson et al., 1991).The main part of the correction originates from theincreasing net negative charge on the protein, which givesrise to a significant electrostatic potential throughout thesimulation cell. The magnitude of the correction amountsto 0.1 to 0.2 pK unit at the highest pH. One can, of course,at very high protein and hydroxide concentrations call theexperimental pH determination in question. It has to bepointed out also that the desalted calbindin preparationstill includes contaminant salt, about ten times theconcentration of protein, as estimated by atomicabsorption spectroscopy measurements. This residual salthas been taken into account in the simulations.
The X-ray structure is obtained for the calcium loadedform, but was used in the simulations of both apo andcalcium loaded forms, which at first sight may seeminconsistent. In principle, it would be correct to usesolution structures from NMR studies. In practice, this isnon-trivial since the NMR structure is not a singlewell-defined protein configuration, but a set of configur-ations, whose statistical weights are unknown (Kordelet al., 1993). However, comparison of the structuresobtained from NMR and from X-ray for the calciumloaded form of calbindin shows only minor differences(Kordel et al., 1993). The same is true for the apo andcalcium loaded forms according to NMR studies (Skeltonet al., 1994, 1995). A consequence of the use of a rigidprotein structure is that pH-induced changes in thestructure will be neglected.
AcknowledgementsWe thank Dr Goran Carlstrom for the assistance in
NMR measurements and Dr Torbjorn Drakenberg forhelpful discussions. We are grateful to Drs Sture Forsenand Walter Chazin for their support and interest in thiswork. The Swedish Natural Science Research Council(NFR, grant numbers K 10178-301, 305, 306) and SwedishRoyal Academy of Sciences are gratefully acknowledgedfor financial support.
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Edited by A. R. Fersht
(Received 29 November 1995; received in revised form 26 March 1996; accepted 3 April 1996)
