Electrostatic effects and hydrogen exchange behaviour in proteins

J. Mol. Biol. (1987) 197, 111-130

Electrostatic

Effects and Hydrogen Behaviour in Proteins

Exchange

The pH Dependence of Exchange Rates in Lysozyme Muriel Delepierret, Christopher M. Dobson, Martin Karplus Flemming M. Poulsen$, David J. States and Randall E. Wedin Department of Chemistry Harvard University, 12 Oxford Street Cambridge, MA 02138, U.S.A. and Inorganic Chemistry Laboratory University of Oxford, South Parks Road Oxford OX1 3QR, England (Received 4 August

1986, and in revised form 3 March

1987)

The pH dependence of the exchange rates for a number of tryptophan and amide hydrogen atoms in hen egg-white lysozyme has been determined at temperatures well below the thermal denaturation temperature. The pH behaviour of each hydrogen is unique and can differ markedly from that of simple compounds. A model for electrostatic effects in proteins is described and used to explain a number of the features of the pH dependence of the exchange rates of certain hydrogens. The results indicate that exchange takes place from a conformation of the protein closely similar to that of the native protein, with local fluctuations providing the mechanism for exchange. For the more-buried hydrogens at low pH values there is a general increase in the exchange rates caused by the decreasing stability of the protein as calculated from the electrostatic model. The analysis shows how evidence from hydrogen exchange studies can be used to provide information about electrostatic interactions in localized regions of proteins. A description of the electrostatic model and some applications are given in the Appendix.

1. Introduction

undergo exchange at rates that can readily be measured experimentally. These rates are often orders of magnitude slower than the exchange rates of hydrogens in oligopeptides or unstructured polypeptides. Whilst the half-life of hydrogen exchange from the latter is normally a few seconds at 25°C and pH 3 to 5, hydrogen exchange from proteins can require months or even years. Given sufficient time, however, exchange will occur from proteins even for hydrogens that are shown by the crystal structure to be buried within hydrophobic regions, completely isolated from the solvent. The three-dimensional structure of the protein t*herefore retards hydrogen exchange without completely stopping it. Clearly, fluctuations in the protein structure are required to allow exchange of buried hydrogens to take place; fluctuations may also be important in the exchange of incompletely buried hydrogens.

The phenomenon of hydrogen exchange from globular proteins has been of interest to protein chemists since first reported 30 years ago (Linderstrom-Lang, 1955; Karplus & McCammon 1981; Barksdale and Rosenberg, 1982; Woodward et al., 1982; Englander & Kallenbach, 1984; Gregory & Rosenberg, 1986). In proteins, amide hydrogens bonded to the backbone nitrogen atoms, as well as hydrogen atoms bonded to side-chain nitrogens, can t Present address: DBpartement de Chimie Organique, Unit& d’Enseignement et de Recherche des Sciences Pharmaceutiques et Biologiques, Universitb RendDescartes, 4 Avenue de l’observatoire, F-75270 ParisCedex-06, France. $ Present address: Kemisk Afdeling, Carlsberg Laboratorium, Gamle Carlsbergvej 10, DK-2500, Valby. Denmark. 002%2836/W/

17011 I-20 $03.00/O

111

0 1987 Academic: Press Limited

112

M. Delepierre

The nature of the fluctuations involved in hydrogen exchange has been the subject of considerable controversy and interest. It has now become clear that more than one mechanism of exchange exists and that the relative importance of the various mechanisms depends on the experimental conditions (Gregory & Rosenberg, 1986). Under certain conditions, particularly at high temperature and extreme pH, the dominant process giving rise to exchange involves the reversible unfolding of the protein (Hilton & Woodward, 1979; et al., 1982; Woodward et al., 1982; Wedin Delepierre et al., 1983). Here the fluctuations making buried hydrogens accessible to solvent are those resulting in the co-operative unfolding of the protein, and the exchange reaction essentially takes place from the unfolded state of the molecule. This leads to similar exchange rates and activation energies for many of the hydrogens. Under different conditions, particularly at temperatures far from the denaturation temperature, it is thought that t’he fluctuations involved are more local in nature and that exchange takes place from a configuration of the protein closer to the native state. This is in accord with the correspondence of exchange data from solution and crystal studies of insulin and lysozyme (Tuchsen & Ottesen, 1979; Bentley et aE., 1983). For this case different hydrogens can have very different exchange behaviour. Both of these exchange mechanisms result in rates that are pH dependent. The chemical exchange rate for hydrogens in a protein can be expressed in the form:

km = ko,[OH-l+k,[H,O+l+k[H,Ol,

(1)

where k,,, k, and k are rate constants, respectively, for the base-catalysed, the acid-catalysed and the direct water exchange reactions. That the exchange reaction itself is both acid and base-catalysed is clearly seen in the study of amino acids and unstructured peptides. Second, the co-operative or local unfolding kinetics may depend on pH. Third, since the transition state for exchange can involve charged species, electrostatic interactions that vary with pH can influence the rates. It is this last feature that we examine in this paper to provide a better understanding of hydrogen exchange. The analysis suggests that hydrogen exchange in fact can serve as a probe for the electrostatic interactions that are implicated in a wide range of binding and catalytic properties of proteins. Electrostatics are of relevance to exchange because the interactions can influence the catalytic rate constants ko, and k,, which reflect the change in the free energy between the reactants and the transition state. The free energy of the charged transition state involved in the exchange reaction will be affected by the electrostatic potential at the particular location. Near a positively charged sidechain, for example, a negatively charged transition state will be stabilized by a favourable electrostatic interaction. The electrostatic interaction will tend to lead to opposite changes in k, and ken when the

et al.

magnitude of the potential at a site in the protein is changed by alterations in the charge distribution consequent upon changes in the pH of the solution. A variety of continuum approaches has been proposed for the estimation of electrostatic effects Early in solvated macromolecules. models (Linderstrom-Lang, 1924, 1955; Scatchard, 1949) distributed charges uniformly over the surface of the molecule, but more recently models in which the charges are localized at specific sites in a homogeneously polarizable spherical molecule (Tanford, 1957) have been used; the treatment is based on the early formalism of Kirkwood (Kirkwood, 1934; Kirkwood & Westheimer, 1938). These models attempt to incorporate information concerning the known three-dimensional structure of a protein (Tanford & R,oxby, 1972; Orttung, 1969), but simplify the calculation by projecting the charges onto a spherical surface and by introducing correction factors for the depth and accessibility of the charges (Shire et al., 1974; Friend & Gurd, 1979). The sensitivity of the results to these empirical parameters makes it difficult to assess the validity of these models even though they have been applied to many systems (Matthew et al., 1985). Other workers have formulated electrostatic models that take account of the actual shape of a protein by introducing a charge grid (Orttung, 1978; Warwicker & Watson, 1982; Warwicker, 1986; Rogers et al., 1985; Klapper et al., 1986), but none of these models has been applied to the electrostatic effects on the titration curves. In the present’ study, we use a model (see Appendix; and States, 1983) that is intermediate between the spherical projection model of the Tanford-Roxby type and the grid model of the Orttung-Warwicker type. Like the Tanford-Roxby type model, the dielectric effect of the protein is represented in terms of a spherical core residing in a solvent with a Debye-Huckel ion atmosphere; like the OrttungWarwicker type models, the charged groups of the protein are positioned according to their X-ray coordinates. Thus, the charges can be located anywhere in the spherical core or the homogeneous solvent; both titratable groups and fixed partial charges can be included. As in the TanfordKirkwood formulation, intrinsic pK values are assigned to each titrating group and iterative calculations are performed to obtain a set of effective pK values; self energy corrections of the pK values can be introduced (States, 1983). Counterions are excluded from the impenetrable core region but are included in the solvent region by the Debye-Huckel approximation. The model thus incorporates the solvation of the titratable groups located external to the core and does not require accessibility weighting factors, Details of the model are given in the Appendix. Although there have been numerous experimental studies of the pH dependence of hydrogen exchange in proteins, relatively little has been done to analyse the contributing factors. One problem

pH Dependence of Exchange Rates in Lysozyme has been the lack of data providing results for specific residues, which have now become available from nuclear magnetic resonance (n.m.r.t) and tritium exchange studies. Two recent papers 1983; Tuchsen & (Matthew & Richards, Woodward, 198%) have been concerned specifically with the importance of electrostatic effects on hydrogen exchange. Both have used the TanfordKirkwood model as modified by Shire et al. (1974); the relationship of that model to the present formulation is discussed in the Appendix. Matthew & Richards (1983) considered the relation between electrostatic effects on the stability and local field and the pH dependence of amide hydrogen exchange in ribonuclease and the bovine pancreatic trypsin inhibitor. Tuchsen & Woodward focused on the ionic strength dependence of the rapidly exchanging surface amide hydrogens in the bovine pancreatic trypsin inhibitor and suggested that acid catalysis involves protonation of the carbonyl oxygen involved in the peptide bond to the amide group instead of the amide nitrogen itself. In this paper we report the pH dependence of the exchange rates of various side-chain tryptophan indole NH and main-chain amide hydrogens in lysozyme and compare them to those of model compounds. The degree to which calculations of electrostatic effects can explain these pH dependencies is then explored by use of the electrostatic model.

2. Materials and Methods Lysozyme from hen egg-white (EC 3.2.1.17) was obtained from the Sigma Chemical Company, and was further purified as described (Poulsen et al., 1980). Fourier transform n.m.r. spectra were recorded at the National Magnet Laboratory, MIT, at 270 MHz on a Bruker HX270 spectrometer and at 500 MHz on the home-built spectrometer of the NMR Facility. Spectra were also recorded in Oxford at 300 MHz on a Bruker WH300 and at 470 MHz using the home-built spectrometer of the Oxford Enzyme Group. Probe temperatures were maintained to within kO.5 deg.C and were determined before each experiment using a sample of ethylene glycol. Hydrogen exchange rates were measured at a protein concentration of 5.5 +_05 mM by determining the decrease in peak heights in the n.m.r. spectra following dissolution of the protein in ‘Hz0 (Wedin et al., 1982). Some experiments were carried out directly in the n.m.r. probe by dissolving lysozyme (lyophilized from a solution of the desired pH) in ‘HZ0 buffer and recording n.m.r. spectra at intervals. In most cases, however. the entire exchange process took place outside the spectrometer in a temperature-controlled water bath or dry block. Lyophilized lysozyme and ‘H,O solvent were separately equilibrated to the temperature of the experiment, and mixed rapidly at this temperature. Samples of protein solution were removed and the exchange process quenched by freezing the samples rapidly to 195 K. n.m.r. spectra were recorded immediately after thawing under conditions where exchange would be minimal. for example at 25°C after t Abbreviation resonance.

used: n.m.r., nuclear magnetic

113

adjusting the pH to 3% Exchange rates between lo-* s-r and lo-’ s-i could be measured in this way. No difference between the 2 methods of measuring exchange rates was observed for samples to which both techniques were applicable. The exchange rates for tryptophan in water were measured using saturation recovery methods (Waelder 6 Redfield, 1977). Electrostatic potentials at individual hydrogens in lysozyme were calculated using the model described in the Appendix. Co-ordinates of the hydrogen atoms were generated in a standard manner (Hoch et al., 1982) from the heavy-atom co-ordinates determined by refinement of the structure of lysozyme in tetragonal crystals (Artymiuk, unpublished results). The solvent& core transition radius (see Appendix) was chosen as 14.6 8, the radius at which the density of protein atoms has fallen to half the core value. The dielectric constants were taken as 10.0 (internal) and 78.0 (external). The calculations were carried out for an ionic strength of 0.1. Intrinsic pK values used for individual residues in the calculation are given in the Appendix. The effect of the electrostatic potential on the exchange reaction rates was calculated by use of a simple transition state formalism. We can write k,, and k, of eqn (1) in the form: k,, = k& eAE’-IHl’; k, = kg eAP”lR’l’,

(2)

where k&, and ki are the exchange rate constants in the absence of direct electrostatic contributions, and AF and AF+ are the electrostatic free energies of activation. In the present calculations it is assumed that for the base(acid)-catalysed reaction a full negative(positive) charge is present in the transition state at the N atom involved in the exchange (i.e. the NE’ of the tryptophans and the N of the amide group). For the tryptophans model calculations were made that assumed that the charge was distributed equally over the 5-membered ring; the pH dependence obtained in the latter calculation was very similar to that for the model using the localized charge. The potential at a given site is nearly the same for the acid and base-catalysed step; i.e. the additional positive or negative charge present in the transition state has a small effect on the charge distribution of the rest of the protein in solution. Thus, we have AF+ = -AF- = AF and we can write eqn (1) in the form: k = k:,[OH-]‘+k;[H-]‘+k,,o,

(3)

where [H+]’ = [H+] eAFIRT;

[OH-]’

= [OH-]

~-‘~‘~r,

(4)

This means that the rate constant in the presence of the electrostatic potential term is equal to that in its absence with “effective” hydrogen and hydroxide ion concentrations equal to [H+]’ and [OH-]‘, respectively. We now assume that the pH profile (log k ver~w pH) of the rate constant in the protein would be identical to that of an amide or tryptophan without the electrostatic interaction; that is: kg,., = /UcoH;

k; = rU&;

kHIO = AkA,,,

(5)

where 1 is a structural factor (0 I 1< 1) that is assumed to be the same for the 3 contributions to the reaction and the primed constants correspond to the unhindered reactions. We can then obtain the pH profile of the reaction rate in the protein (other than for an additive constant log 1) by using the value for an amide or tryptophan at pH’ for the value at the corresponding pH. This description of the model makes clear the assumptions

114

M. Delepierre

et al.

inherent in the results. As we point out below, if the unfolding (deneturation) of the protein is the ratelimiting step (EXI) or if the equilibrium constant for the unfolding is pH dependent (EX2) (both of which occur in some pH ranges), the parameter 1 would be pH dependent and introduce an additional correction. No attempt was made in the present work to interpret in detail the absolute values of the exchange rates, i.e. to determine the values of 1, which are affected by factors such as the variations in solvent accessibility produced by fluctuations. Attention was focused only on the change of the exchange rates for a given hydrogen as a function of pH. Electrostatic potentials at individual sites in the

protein were calculated for different values of the solution pH. In conjunction with the known pH dependencies of the exchange rate of the indole NH of typtophan (Waelder & Redfield, 1977; Nakanishi et al., 1978) and of peptide amide hydrogen atoms (Molday et al., 1972) this permitted the pH dependence of the exchange rates of the

protein hydrogen atoms to be calculated. 2.0

3.0

4.0

5.0

6,O

PH

Figure 1. The dependence on pH of the hydrogen

3. Results (a) Side-chain hydrogens; tryptophan indole H”’ hydrogens

A study of the pH dependence of the exchange rate for the indole NH (H”‘) of the amino acid tryptophan was carried out at 47 “C, where the rates are sufficiently fast to be measured over a wide range using the saturation-recovery n.m.r. method described in Materials and Methods. The pH at which the exchange rate was at a minimum (pH,& was determined to be 4.4kO.2 (Fig. 1) and in agreement with earlier studies (Waelder et al., 1977; Nakanishi et al., 1978) a pH dependence of order 1.0 was found for both the acid and base-cataiysed reactions. Apparent activation energies at pH 3.8 (acid catalysis) and 5 1 (base catalysis) were determined to be 11.6 + 0.6 kcal mol- ’ (1 cal z 4.184 J) and 16.8 + 1.5 kcal mall ‘, respectively. The

PH,,,~, is therefore

temperature

dependent;

i.e. an

increase in temperature of 10 deg.C leads to a shift in the PH,,,~, of 0.06 unit to lower pH values. Exchange rates of HE’ hydrogens in the tryptophan residues of lysozyme were measured between pH 2 and pH 7 at temperatures between 12°C and 57 “C. The exchange rate of Trp62 was too rapid under all of these conditions to enable any measurements to be made by the techniques employed here. For the

other five tryptophan residues the exchange rates are much slower at pH 4-O ranging from 10m3 s- ’ to 1 s-l for 10-7 s-i, compared to approximately tryptophan itself. It proved possible to obtain reliable measurements for each of the five tryptophans; representative data are shown in Figure 1. For Trp63, -108, -111 and -123 the pH dependencies were well defined at 27°C; at higher temperatures the rates were too fast to measure accurately at the extremes of the pH range. For Trp28, however, the

exchange rates below 37°C were too slow for measurements to be obtained in reasonable times and the data presented are for this temperature. The pH dependencies obtained for the five

exchange rate constant (k, s-r) for He1 of tryptophan itself (V) and of Trp28 (n), Trp63 (+), Trp108 (A), Trplll (0) and Trp123 (0) of lysozyme. The experimental data for tryptophan are at 47 “C in 90 y0 H,O/lO”/O ‘H,O and the conthruous line is the pH dependence predicted by eqn (1) with a pHmi, of 4.4 and k HI0 -- 0. The experimental data for lysozyme are for unbuffered solutions in *H,O, at 37°C for Trp28 and at 27°C for the other tryptophan residues. The continuous lines here are smooth curves drawn through the experimental points.

tryptophan residues of lysozyme are very different from each other. Three of the residues, Trp28, -111 and - 123, have a reasonably well-defined pHmi,; that of Trp28 is close to that of tryptophan itself but for Trplll and particularly Trp123 the pH,. is displaced to lower pH values. For Trp28 the slopes representing both acid and base catalysis are significantly less than 1.0, resulting in little change in the exchange rate between pH 3.7 and 5.2. For Trp63 and Trp108 the pH-dependent behaviour is similarly less sensitive to pH compared with tryptophan itself; for TrplOS the exchange rate scarcely changes between pH 4 and 6. Although the absolute rates are temperature dependent, the general features of variation with pH are not significantly affected by temperature, provided that the temperature does not exceed about 50°C (see Fig. 2). The full temperature dependence at one pH value, 3.8, has been analysed in detail elsewhere (Wedin et al., 1982). The effects of ionic strength on the pa-dependent behaviour were also found to be small, The counterions present in a 5 mM solution of lysozyme are at least 0.05 M in the pH range studied here. Addition of up to O-5 M-KC1 had little effect (see Fig. 2), although as the ionic strength increases the pH dependence curves shift slightly to higher pH values. No differences lysozyme

in exchange in unbuffered

rates were found between solutions compared with

pH Dependence of Exchange Rates in Lysozyme

2.0

"

"

3.0

4.0

"

5.0

'

6-O

'J

115

7.0

PH

Figure 2. Temperature dependence of the variation in k with pH for (a) TrplOS and (b) Trp123 of lysozyme. The data are for solutions at 27 “C ( x ), 37 “C (A) and 47°C (a), Rates indicated by circled symbols are for unbuffered solutions; the remainder are for solutions buffered in 0.15 M-d,-acetate. Rates indicated by + are at 47°C in the presence of 0.5 M-NaCl. The lines through the points are smooth curves.

solutions buffered with 0.15 M-acetate, except for increased the exchange rate Trp63 where significantly in the presence of buffer. In addition, the exchange rates reported here were essentially independent of protein concentration indicating that effects of aggregation, known to occur at higher pH values (Imoto et al., 1972), could be neglected at pH values below 6. The electrostatic potentials at the NE’ atoms of the six tryptophan residues were calculated as described above as a function of pH; the results are plotted in Figure 3. In each case, the potential becomes less positive with increasing pH, reflecting the decreasing positive charge on the protein (the isoelectric point of lysozyme is calculated to be 11.2; see Appendix). Above pH 7 little change in potential takes place until pH 9, reflecting the absence of ionizable groups with pK values between 6.3 and 9.8 other than the N terminus, which is distant from all tryptophan residues (see Table A2 in Appendix). The large effect above pH 9.5 for Trplll reflects its close proximity to Tyr23 (see Fig. 4). Below pH 7 the major effects on the electrostatic potentials arise from the proximity of carboxylate residues, notably Glu35. Glu35, positioned within the core in a region of low dielectric constant, causes major perturbations to the potentials of Trp63 and TrplOS, and to a lesser extent to all the other residues, between pH 5 and

-4”

3

’ 4

’ 5

’ 6

’ 7

’ El

’ 9

’ IO

PH

Figure 3. The dependence on pH of the electrostatic potential (in pK units) at W’ for Trp28 (n), Trp62 ( x ), Trp63 (+), TrplOS (A), Trplll (0) and Trp123 (@). Calculations were carried out at intervals of 0.5 pH unit as described in the text.

7. Below pH 4 a number of residues titrate, but only Asp52, also in the region of low dielectric constant, produces major effects on the tryptophans, notably on the nearby Trp63 and TrplOS. In over the pH range of interest to summary, hydrogen exchange, electrostatic effects are calculated to be most pronounced for Trp63 and Trpl08; the other four residues show smaller effects that are similar to each other. From the electrostatic potentials given in Figure 3, the effect on the pH dependence of the were exchange of tryptophan HE’ hydrogens calculated using the procedure derived in Materials and Methods (eqns (3) to (5)). The resulting curves that are to be compared with that for tryptophan (see Fig. 1) are shown in Figure 5. That for Trp123 has the pH,. shifted by approximately 1 unit to a low pH value, but is otherwise relatively little changed. This reflects the almost constant potential of + 1 experienced between pH 4 and 9. The curves for Trp28 and Trpll 1 are very similar, as expected from the potentials shown in Figure 3, and have a shift of the pH,i” similar to that of Trp123. A slight flattening of these curves between pH 5 and 7, resulting in the effective slopes of the basecatalysed part of the exchange curve being less than 1.0, can be attributed to the decrease in electrostatic potential observed in this pH range (see

M. Delepierre et al.

116

Figure 4. Stereo projection to in the text.

of the structure

of lysozyme showing backbone heavy atoms and the side-chains referred

Fig. 3). The curve for Trp62 is also similar, except slightly lessfor a smaller shift in pH,i”, reflecting positive potentials over most of the pH range.

the pH range 3 to 7 as Asp52 and then Glu35 ionize. For Trp108 the potential changes by approximately 1 unit for each unit change in pH, so that kobs is nearly independent of pH. Comparison of the experimental data in Figure 1 with the predicted pH dependencies of Figure 5

Marked differences occur in the curves for Trp63 and TrplOS. In both cases the potentials in Figure 3 become markedly and steadily more negative over

I

Cd) 1

(c) 32-

-z B

/*

’ o-

/* *\

I

I

1

I

I

I

,/

/ %-.-.-.J

-I I

2

I

I

4

I

I

6

I

1

8

.

2

RH Figure 5. The dependence on pH of k for HE’ of a tryptophan experiencing the electrostatic potentials described in the text for (a) Trp28, (b) Trp62, (c) Trp63, (d) Trpl68, (e) Trplll and (f) Trp123.

calculated

as

117

pH Dependence of Exchange Rates in Lysozynze

-5IIII

I

I

I

I

1

-,_(e)

-5I

2

I

I

4

I

I

I

2

6

4

6

PH

Figure 6. Comparison of the calculated and experimental dependence on pH of k for (a) tryptophan itself and for (b) Trp28, (c) Trp63, (d) TrplO8, (e) Trplll and (f) Trp123 of lysozyme. The experimental data are as shown in Fig. 1. The calculated curves differ from those of Fig. 5 in that log 1 (eqn (5)) f or each residue has been chosen to enable comparison with the experimental data to be made. In addition, the calculated potentials have been scaled by a factor of 0.7; this improves the agreement with the experimental data (seethe text).

shows marked similarities between the two. This is clearer in Figure 6 where the experimental data are superimposed on the predicted pH dependence. In this Figure, the predicted k values have been divided by constants (log 2 in eqn (5)) that represent the degrees of protection to exchange of the various H” hydrogens by factors other than electrostatic effects arising from the protein environment. Some correlation of such constants with static accessibilities has been noted (Wedin et al., 1982). In addition, the potentials used in Figure 6 were scaled by a factor of 0.7 relative to those used in Figure 5, This does not affect the qualitative picture but gives slightly

better quantitative agreement with the experimental data; such a change could have been introduced into the potential calculation by the use of a somewhat larger value of the dielectric constant for the protein interior. For four of the tryptophan residues (Trp63, -108, -111 and -123) the agreement is excellent and all the major features of the experimental data are reproduced by the predicted curves. For Trp63 the experimental exchange data do not extend to sufficiently high pH for any effects of Glu35 to be observed; the predicted pH dependence is dominated by the ionization of Asp52. For TrplOS, however, the

118

M. Delepierre

experimental data are available at pH values at which the effect of the ionization of Glu35 is predicted to be becoming significant’. The general form of the calculated pH dependence is followed well for this residue although some differences in the details of the behaviour are apparent. In particular, the local maximum in the exchange rate for Trp108 predicted to occur at about pH 6 is not observed experimentally. Further, at low pH values the experimental exchange rates increase somewhat more rapidly than the predicted rates. For the fifth tryptophan, Trp28, the agreement is much less good. If the theoretical curve is aligned with the experimental data between pH 5 and pH 8 the exchange rate at low pH values is much faster than predicted. A similar but less pronounced effect is also seen for Trpl Il. This behaviour is attributed to the fact that the exchange rat’e here depends on the reversible unfolding of the protein, which is made much more likely by the decrease in thermal stability of the protein at low pH (see below).

et al

Table 1 Exchange

rates for amide

hydrogen

atoms

1% kS Residue?

pH 3.0

pH 5.0

pH 7.0

LeU8

-6.9

Ala9 Ala10 Ala1 1 Met12 Lys13 Ala31 Thr40

-7.2 -7.1

-5.7 -6.3 -6.7

-3.5 -4.5 - 5.1

- 7.3 -7.0 - 7.1 -7.0 -6.2 -7.2 -7.1 -7.0 -6.6 -6.5 -7.2 -7.4 - 7.0 -7.3

-6.3 -6.X - 64 -7.2 -4.7 -6.9 -6.6 -6.9 -5.5 -5.4 -6.7 -7.1 -7.3 - 74

-4.4

ASP52 Tyr53 Ser60 Cys76

Ile78 Val92

Ala95 Lys9S Ile9X

t Assignments

-6.1 -4.1 -5.9 -5.4 -5.2 -3.7 -5.4

-6.1 -6.0 -5.1

of resonances are given by Delepierre

et al.

(1984).

(b) Main-chain

hydrogens;

amide hydrogens

The pH dependence of the exchange rates of model amides resembles that of tryptophan in that it is of order 1.0 for both acid and base-catalysed reactions (Molday et al., 1972). The pH at which the exchange rates are at a minimum differs from that of tryptophan, and varies by over 1 pH unit with the nature of the adjacent residues; the data of Molday et al. (1972) have been used here. The pH dependencies of the hydrogen exchange rates have been measured for 17 amide hydrogens, whose assignments have been described (Delepierre et al., 1984), over the pH range 2.5 to 8.5 and at various temperatures. The most detailed data are for 37°C and these are summarized in Table 1. The amides studied here are amongst the slowest to exchange. As with the tryptophan indole H”‘, the pH curves for the amides are characteristic for each residue; representative data are given in Figure 7. The spread of rate constants between the different amide hydrogens observed here is less than that between the tryptophan HE’, reflecting the fact that only the most slowly exchanging hydrogens have been studied. The pH dependencies are very similar for many of the different residues although some differences do exist (see Fig. 7). The PH,,,~, values in virtually all cases were in the range 3.5 to 4.2. Further examination of the data in Table 1 and Figure 7 shows that the exchange rates at higher pH values differ somewhat more from residue to residue than those at low pH. For all of the residues studied the exchange rates at pH 3-O are between 10-6.5 $-l and 10-7.4 s-1 ~ whereas at pH 7.0 the . rates vary between 10W3” s-l and 10W6” s-r. The possible significance of this behaviour will be discussed below. Electrostatic potentials at the amide nitrogen for all the residues of lysozyme were calculated as a

$ At 37”C, k(s-‘) was determined from a smooth curve of pH dependence drawn through experimental points. For all these residues. the minimum rate of exchange is between 3.0 and 5.0.

function of pH. As in the case of the tryptophan NE’ atom, the potentials were positive at low pH (between 0.54 and 3.74 at pH 2), less positive or negative at high pH (between I.59 and - 4.72 at pH 9), and changed most rapidly between pH 3 and 7. Plots for the six residues with experimental data presented in Figure 7 are given in Figure 8. They are representative of the behaviour of the amides as a whole. The main features of Figure 8 resemble closely those seen in Figure 3. As for the tryptophan N”’ atoms, ionization of the buried Glu35 and Asp52 has marked effects for a large number of amides. Ionization of exposed carboxylates (e.g. Asp48) is less important because of the high dielectric constant of the medium. The predicted pH dependence of the amides obtained from calculated the electrostatic potentials given in Figure 8 are shown in Figure 7. There are two notable features. The first is the pronounced shift in the pH,. to lower pH. As the pHmi, values for model amides are lower than that of the HE’ of tryptophan, this results in predicted PH,,,~, values below 2 for most of the amides of lysozyme, whether on the surface of the protein or buried in the interior. The second feature is that for a number of amides the pH dependence is predicted to be complex. The behaviour of Asp52 is an example of this; the exchange rate is predicted to be nearly equal at pH 2 and pH 5 but to pass through a local maximum close to pH 3. The behaviour is similar to that predicted for the He1 of TrplO8, and is again a consequence of the Glu35 and Asp52 ionizations (see Fig. 8). The pH dependence of Tyr53 and Ser60 again can also be correlated with these ionizations. Further examination of Figure 7 shows that for

pH Dependence of Exchange Rates in Lysozyme

119

-4 (b)

/ -6/

. .

/

. . -8 7

9

I

I

1

3

5

7

PH

Figure 7. Experimental and calculated dependence of k on pH for (a) Asp52, (b) Ser60, (c) Va192, (d) Tyr53, (e) Cys76 and (f) Ala95. The experimental data are for unbuffered solutions at 37°C. The calculated values of log k for each residue have been adjusted by a constant term log1 (eqn (5)) to give best agreement with experimental data at pH values above 4. 4,

1

pH values above 5 there is very good correlation between experimental and predicted exchange rates; in particular, the experimental observation of an order less than 1.0 for base catalysis is predicted for all amides. This arises from the steady change in the potentials to less-positive values as the pH is increased and the protein becomes less positively charged. As with H”’ of Trp28, however, the correlation between the predicted and experimental pH dependence is less good at pH values below 5; in particular the predicted low values of pHmi, are not observed experimentally for the amides studied in this work.

4. Discussion The pH dependence of the exchange rates of the H”’ hydrogens of the five tryptophan residues of lysozyme investigated here correlates well with the calculated PH

Figure 8. The dependence on pH of the electrostatic potentials (in pK units) at the amide N for Asp52 (e), Tyr53 (O), Ser60 (A), Cys76 (+), Va192 (0) and Ala95 ( x ). Calculations were carried out at 0.5 pH unit intervals as described in the text.

electrostatic

interactions

within

the

protein. Of particular significance is the observation that the complex exchange behaviour predicted to occur for the hydrogen atoms of Trp63 and Trp108, because of the effects of ionization of the nearby carboxylate groups of Asp52 and Glu35, offers an explanation of the unusual experimental behaviour

120

M. Delepierre

observed for these residues. The electrostatic interactions involving these active-site residues are shown to be most important because of their location within the low dielectric region of the protein. The only serious discrepancy between the experimental exchange behaviour and the electrostatic predictions for the HE’ hydrogens is that the increase in exchange rate at lower pH values is not correctly predicted for Trp28. A similar discrepancy, however, is observed for essentially all the amide hydrogen atoms observed here. For these hydrogens, the electrostatic calculations predict low values of pHmi, compared to model compounds; these are attributable to the net positive charge existing on lysozyme over the whole pH range relevant to the hydrogen exchange measurements. An explanation for this difference between the experimental observations and theoretical predictions can, however, be found in terms of the decreasing thermal stability of the protein at low pH values. It is clearly established that at least two different processes contribute to hydrogen exchange in lysozyme (Wedin et al., 1982; Gregory et aE., 1982; Bentley et al., 1983). One of these involves local fluctuations in the structure, but the other involves the co-operative unfolding of the protein. The relative importance of the two mechanisms differs for different hydrogens. In particular, the more slowly exchange takes place via the local fluctuations the more likely is the unfolding mechanism to be significant. The contributions of the two mechanisms also vary with the conditions under which measurements are made. For example, exchange via an unfolding mechanism is most likely to be dominant at temperatures close to the temperature than at lower denaturation temperatures. The relative importance of the two exchange mechanisms has previously been examined in detail for the tryptophan HE1 exchange (Wedin et al., 1982; Bentley et al., 1983). The unfolding mechanism is of greatest importance for Trp28, which exchanges most slowly via the local t-luctuation mechanism; even for this residue unfolding does not significantly influence the exchange rate at pH 3.8 except for temperatures above 55°C. Analogous behaviour is found for exchange rates of the amide hydrogens; some results for the temperature dependence are shown in Figure 9. The increase in the slope of the Arrhenius plot at higher temperatures is attributed to the contribution of the unfolding mechanism, which has a high activation energy. At pH 3.8 this mechanism contributes even at 37°C for the slowly exchanging amides considered in this paper. The significance of this mechanism will decrease at higher pH values because of the increasing rapidity of the exchange through base catalysis and the slight increase in the stability of the protein between pH 4 and 8; detailed measurements of the stability of lysozyme as a function of pH have been made by Pfeil and

et al.

-81 2.9

I 3.0

3.1

I 3.2

(I/T) x IO3

Figure 9. The dependence on temperature of k at pH 3.8 for Cys76 (0) and Va192 (+). The continuous lines are smooth curves through the experimental points. Privalov (1976). On the other hand, its significance will increase at lower pH because the protein stability decreases very markedly below pH 3.5 (Pfeil & Privalov, 1976). This decrease in stability is in accord with the electrostatic model (see Appendix, Fig. A4). The predictions for hydrogen exchange described so far (Figs 6 and 7) in this paper are based on the assumption that it takes place from a state of the protein close to the native state, through a mechanism that involves no more than local fluctuations. Exchange from the unfolded state would be expected to have a pH dependence close to that of simple compounds, and to yield similar rates for the hydrogen atoms of different amide groups (see the results for pH 3 in Table 1). By taking the contribution of an unfolding mechanism into account in this way it is possible to predict the overall form of the exchange behaviour. Figure 10 shows schematically an example of such It correlates well an approach for H”’ of Trplll. with the pH dependence of the hydrogen exchange over the whole pH range for which experimental data are available. The contribution of the unfolding mechanism clearly provides an explanation in the case of the slowly exchanging hydrogens studied here for the observed deviation at low pH from the predictions based on the electrostatic model with only local unfolding. Further, recent results with bovine pancreatic trypsin inhibitor (BPTI) show that for rapidly exchanging surface hydrogens, very low pH minima can be observed in some cases (Tuchsen & Woodward, 1985b). Preliminary data reveal that this is also the case with lysozyme (C. M. Dobson, C. Redfield & E. Tuchsen, unpublished results); for these hydrogens the unfolding mechanism is not dominant even at low pH values. Other explanations for the exchange behaviour of the buried hydrogens at low pH cannot, however, be excluded at this stage. For example, exchange could take place from a state significantly different from the native but not from the completely unfolded

pH Dependence of Exchange Rates in Lysozyme

--8c,

234567234567

htlllll PH

Figure 10. Calculations illustrating the possible contributions of an unfolding mechanism to hydrogen exchange, using data for Trplll as an example. The contributions of the exchange from the folded state ( - - - ) and via the unfolding mechanism ( -. -. - ) are indicated. The continuous line represents the resulting pH dependence of the exchange rate, k. For exchange from the folded state, the calculated pH dependence shown in Fig. 5 was used. For exchange via the unfolding mechanism, the pH dependence was calculated making use of the results of Pfeil & Privalov (1976). (a) and (c) show the results for an EXI mechanism (assuming that the pH dependence of the unfolding rate k, follows that of Kd, the equilibrium constant for denaturation); (b) and (d) show the results for an EX2 mechanism (assuming that the pH dependence of k,, the rate constant for exchange from the unfolded state, is the same as that of tryptophan itself). In (a) and (b) it was assumed that the 2 processes had equivalent rates at pH 3, and in (c) and (d) at pH 3.9.

state; in addition, the uncatalysed exchange, via H,O rather than OH- and HsO+, could be of greater importance in proteins than in simple compounds. Also, as mentioned in the Introduction, it has been suggested for the amides (Tuchsen & Woodward, 19856) that the acid-catalysed exchange involves protonation of the carbonyl oxygen of the peptide bond to the amide group, instead of the amide group itself, as assumed here; of course such a possibility does not arise for the tryptophan H”‘. The success of electrostatic models in explaining features of the pH dependence of the exchange rates of more exposed residues such as Trp63 and Trp108 strongly suggests that exchange takes place under the conditions described here, for these residues at least, from an environment very close to that of the native structure. The electrostatic potentials are relatively geometry

short range and dependent on the specific of the system. If the fluctuations

permitting exchange involved significant structural changes, it would be expected that agreement with

121

the results of calculations using the native structure would be poor. Electrostatic effects are well established as determinants of the pK values of ionizable groups in proteins (Tanford & Roxby, 1972). The present work demonstrates that they can be important as one of the factors influencing the pH dependence of hydrogen exchange rates. Electrostatic interactions are also thought to be essential to the function of proteins, for example in the catalytic activity of enzymes (Perutz, 1978). The unusual electrostatic environment of the active site of lysozyme is clearly illustrated by the unique pH behaviour of the exchange rates of the HE’ hydrogens of Trp63 and Trpl08. Thus, studies of the pH dependence of hydrogen exchange rates in proteins can be used more generally as a probe of electrostatic interactions in proteins. They should be useful in the testing of theoretical models for the calculation of electrostatic potentials, and eventually may contribute to a better understanding of electrostatic effects in enzyme catalysis. This work was supported in part by grants from the National Science Foundation, the National Institute of Health and the U.K. Science and Engineering Research Council. Fellowships are acknowledged from the Royal Society and the Centre National de la Recherche Scientifique (to M.D.) from the Carlsberg Foundation of Copenhagen (to F.M.P.), and from the National Science Foundation and the Danforth Foundation (to R.E.W.). C.M.D. is a member of the Oxford Enzyme Group. References Barksdale,

A. & Rosenberg, A. (1982). In Methods of Analysis (Glick, D., ed.), vol. 28, pp. I113, Wiley, New York. Bentley, G. A., Delepierre, M., Dobson, C. M., Mason, S. A., Paulsen, F. M. & Wedin, R. E. (1983). J. Mol. Biol. 170, 243-247. Delepierre, M. Dobson, C. M., Selvarajah, S., Wedin, R. E. & Paulsen, F. M. (1983). J. &foZ. Biol. 168, Biochemical

687-692.

Delepierre, M., Dobson, C. M., Howarth, M. A. & Paulsen, F. M. (1984). Eur. J. Biochem. 145, 389-395. Englander, S. W. & Kallenbach, N. B. (1984). @m-t. Rev. Biophys. 16, 521-655. Friend, S. & Gurd, F. R. N., (1979). Biochemistry, 18, 4613-4619. Gregory, R. B. & Rosenberg, A. (1986). Methods Enzymol. 131, 448-508. Gregory, R. B., Knox, D. G., Percy, A. J. & Rosenberg, A. (1982). Biochemistry, 21, 6523-6530. Hilton, B. D. & Woodward, C. K. (1979). Biochemistry, 18, 5834-5842. Hoch, J. C., Dobson, C. M. & Karplus, M. (1982). Biochemistry, 21, 1118-1125. Imoto, T., Johnson, L. N., North, A. C. T., Phillips, D. C. & Rupley, J. A. (1972). The Enzymes, 7, 665-668. Karplus, M. & McCammon, A. (1981). CRC Crit. Rev. Biochem.

Kirkwood, Kirkwood,

9, 293-349.

J. G. (1934). J. Chem. Phys. 2, 351-361. J. G. & Westheimer, F. H. (1938). J. Chem. Phys. 6, 506-512. Klapper, I., Magstrom, R., Fine, R., Sharp, K. & Honig, B. (1986). Proteins, 1, 47-53.

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Linderstrom-Lang, K. (1924). C. R. Trav. Lab. Carlsberg, 15, 7-14. Linderstrom-Lang, K. (1955). Chem. Sot. Spec. Publ. 2, l-24. Matthew, J. B. & Richards, F. M. (1983). ,I Biol. Chem. 258, 3039-304-4. Matthew, J. B., Gurd, F. R. N., Flanagan, M. A., March, K. L. & Shire, S. J. (1985). CRC Grit. Rev. Biochem. 18, 91-197. Molday, R., Englander, S. W. & Kallen, R. G. (1972). Biochemistry, 12, 150-158. Nakanishi, M., Nakamura, H., Hirakawa, A., Tsubor, M., Nagamura, T. & Saijo, Y. (1978). J. Amer. Chem. Sot. 100, 272-276. Orttung, W. H. (1969). J. Amer. Chem. Sot. 91, 162-167. Orttung, W. H. (1978). J. Amer. Chem. Sot. 100, 43694375. Peru& M. (1978). Science, 201, 1187-l 191. Pfeil, W. $ Privalov, P. I,. (1976). Biophys. Chem. 4, 23-32. Poulsen, F. M., Hoch, J. C. & Dobson, C. M. (1980). Biochemistry, 19, 2597-2607. Rogers, N. K., Moore, G. R. & Sternberg, M. J. E. (1985), J. Mol. Biol. 182, 613-616. Edited

Scatchard, G. (1949). Ann. N. Y. Acad. Sci. 51. 660-672. Shire, S.. Hanannia, G. I. H. & Gurd, F. R. N. (1974). Biochemistry, 13, 2967-2974. States, D. J. (1983). Ph. D. thesis, Harvard University. Tanford, C. (1957). J. Amer. Chem. Sot. 79, 5340-5347. Tanford, C. & Roxby, R. (1972). Biochemistry, 11, 21922198. Res. Tuchsen. E. & Ottesen, M. (1979). Carlsberg. CommurL. 44, l-10. Turhsen. E. & Woodward, C. K. (1985a). J. Mol. Biol. 185, 405-419. Tuchsen. E. & Woodward, C. K. (19856). J. Mol. Biol. 185, 421-430. 16, Waelder, S. F. & Redfield, A. C. (1977). Biopolymers, 623-629. Warwicker. ,J. (1986). J. Theor. Biol. 121, 199-210. Warwicker, ,J. & Watson, H. C. (1982). J. Mol. Biol. 157, 671-679. Wedin. R. E., Delepierre, M., Dobson, C. M. & Poulson, F. M. (1982). Biochemistry, 21, 1098-1103. Woodward, C., Simon, I. & Tuchsen, E. (1982). Mol. Cell Biochem. 48, 135-160.

by A. Fersht

APPENDIX

A Model for Electrostatic Effects in Proteins D. J. States and M. Karplus are important Electrostatic interactions determinants of macromolecular chemistry (Perutz, 1978). Electric fields couple directly to electronic structure and consequently can have immediate relevance to the chemistry of catalysis. Moreover, the long range of the electrostatic interactions suggests that they are critical to the overall structure and to the solvation of macromolecules (Kauzmann, 1959; Warshel & Russell, 1984; Matthew et al., 1985; Honig & Hubbell, 1986). The complex effects resulting from electrostatic forces have long been recognized and there are a number of early efforts to model such phenomena (Linderstrom-Lang, 1924; Hill, 1956; Tanford & Kirkwood, 1957; Kauzmann, 1959). LinderstromLang (1924) considered proteins to be impenetrable spheres with charges uniformly distributed over their surface. The limitations of this model led Hill (1956) and Tanford & Kirkwood (1957) to apply the Kirkwood-Westheimer formalism (Kirkwood, 1934; Kirkwood & Westheimer, 1938) to proteins. They assumed the protein to be an impenetrable sphere of low dielectric constant in a high dielectric constant solvent and located the charges at discrete sites at a fixed distance beneath the surface of that

sphere. Since at the time of this work, structural data for proteins were not available. they considered a number of models with simple distributions of charge. Interactions between the charged groups modified their behaviour and qualitatively accounted for the titration curves of proteins. In the course of this work it was noted that the depth at which charges were located was critical in determining the resultant electrostatic properties of the system. Information concerning the positions of charges obtained from X-ray structures of proteins was incorporated into the Tanford-Kirkwood model by Orttung (1970) and Tanford & Roxby (1972). They projected the charges onto a spherical shell. The projection scheme resulted in artifactual foreshortening of the distance between some charge centres, the need to readjust or exclude sites from the calculation and the introduction of the depth of the charges as a fitting parameter. Gurd and coworkers (Shire et al., 1974; Friend & Gurd, 1979) improved the projection procedure by using the actual distances between the charges in the calculation. In contrast to Tanford & Roxby (1972), they assumed that all of the charges are on the