An evaluation of the use of hydrogen exchange at equilibrium toprobe intermediates on the protein folding pathwayJane Clarke and Alan R Fersht
Background: Methods have been developed recently for probing localfluctuations of protein structure using H/2H-exchange of amide protons atequilibrium. It has been suggested that equilibrium exchange methods canidentify the order of events in folding pathways and detect folding cores. Wehave applied the procedure of measuring the effects of denaturant on the H/2H-exchange of amide protons of barnase, the folding pathway of which is wellestablished.
Results: The addition of relatively low concentrations of denaturant causes themechanism of exchange of amide protons of barnase to change from EX2 toEX1 for the residues that require global unfolding for exchange to occur. Thischange of mechanism, which would have been missed by some of the standardtests, causes artefacts that could be easily misinterpreted. We also present thethermodynamic argument that measurements at equilibrium cannot give theorder of events in folding.
Conclusions: Measurement of H/2H-exchange of amide protons at equilibrium,when applied correctly, is an excellent method for analyzing the equilibriumdistribution of unfolded and partly folded states. It cannot, in theory and inpractice, be used for determining protein folding pathways by itself.
IntroductionAmide protons that are buried within a protein, or formintramolecular hydrogen bonds, are protected againstexchange with protons of solvent. The structure anddynamics of a folded protein at equilibrium can be probedby monitoring the rate of exchange of amide protons withsolvent deuterons (e.g. see [1–6]). There are two generalpathways that allow access of the solvent to the protectedprotons of the ‘closed state’ (C) of the native protein viaan ‘open state’ (O): local exchange, in which there arefluctuations of structure in a local structural element, andglobal exchange, in which the protein undergoes largescale unfolding [2,3,5,7–10], as shown in equation 1:
ko kint kcCH OH OD CD (1)
kc D2O ko
The intrinsic rate constant for chemical exchange from theopen state, kint in equation 1, varies with conditions andnature of the amide group, ko is the first-order rate con-stant for the opening of the folded protein, kc for itsclosing. The mechanism of exchange has two limitingcases, depending on the relative values of kint and the rateconstant kc for reprotection of the open state [7,9,11]. Inthe more commonly observed EX2 process, the chemicalexchange process is slower than reprotection and is part ofthe rate-determining step. The overall rate constant for
exchange, kex, is equal to the product of kint and the appar-ent equilibrium constant for the formation of the openstate. The ratio kex : kint is the apparent equilibrium con-stant for the formation of the open or exchangeable state,and so the free energy for formation of the state is definedby equation 2:
�Gappex = –RT ln(kex) (2)kint
In the other limiting case, EX1, kint is much higher thanthe rate constant for reprotection and so the formation ofthe exchangeable state is rate determining. There is acrossover between EX1 and EX2 when the rate constantfor reprotection is similar to kint.
It has been suggested recently that the effect of denatu-rant on �Gapp
ex might be a probe of the pathway of proteinfolding [12,13]. There is an approximately linear relation-ship between free energies of unfolding in guanidiniumchloride (GdmCl) solutions and GdmCl concentration [14]as shown in equation 3:
�Gu = �GuH2O – m[GdmCl] (3)
where m is a variable that includes a term proportional tothe increase in surface exposure of the protein on unfold-ing and �Gu
H2O is the free energy of unfolding in water.
Address: Centre for Protein Engineering, MRCCentre, Hills Road, Cambridge CB2 2QH, UK.
Bai et al. [13] fitted the variation of �Gappex with [GdmCl]
for the exchange of protons of cytochrome c to equation 4:
�Gappex = –RTln(Kl + K0
g exp (m[GdmCl]/RT)) (4)
where K1 is the apparent local equilibrium constant for for-mation of the exchangeable state, K0
g is the global unfold-ing equilibrium constant of exchange at 0 M GdmCl. Incytochrome c the mechanism remains EX2 throughout therange of denaturant [15], so that the rate of exchangedepends on the local or global stability. They were able toidentify regions with individual global �Gapp
ex and m values,which they suggest represent partially unfolded states onthe folding pathway.
Studies on mutants of barnase have shown which protonsexchange by a local unfolding pathway, which by globalunfolding and which by a mixture of the two pathways inthe absence of denaturant [16,17]. The protons thatexchange by a local unfolding pathway have the sameexchange rate constants in mutants whose stability variesby up to 6 kcal mol–1, and so must be exchanging from thefully folded state. Protons in barnase that exchange by aglobal unfolding pathway are characterized by having�Gapp
ex = the free energy of unfolding measured bycalorimetry under the same conditions.
Here, we analyze the effect of increasing denaturantupon the exchange kinetics of amide protons in wild-type barnase. Protein engineering experiments haveallowed the characterization of a folding intermediate ofbarnase that is more stable than the unfolded state atequilibrium [18]. Some regions of the protein have sig-nificant structure in the folding intermediate and transi-tion state whereas other regions appear to be folded onlyafter the rate determining step. Barnase should, there-fore, be an ideal test protein to evaluate methodsdesigned to observe folding intermediates. We find thatanalysis of the exchange data by the simple model givesan apparent m value for exchange that is the same for allbut a few protons in all regions of barnase and is similarto that observed by equilibrium denaturation experi-ments. A deeper analysis, however, reveals a change inthe mechanism of exchange at higher denaturant concen-trations. This complicates the analysis considerably,because the apparent differences in m value can beattributed to differences in exchange pathway and mech-anism. This suggests that the method cannot be used inisolation as a probe for folding intermediates. We discusswhether partially folded states which are observed bythis method are on the folding pathway. All the evidenceon barnase suggests that exchange of the highly pro-tected protons occurs from the fully unfolded state orfrom fluctuations of the folded state and not from thefolding intermediate.
ResultsOver half the backbone amide protons of barnaseexchange in the dead time of the experiments. Theresidues with measurable exchange rates are found princi-pally in the main helix and sheet regions of folded barnaseand are mostly involved in hydrogen bonds. The rate con-stants of exchange are given in Table 1. In general,protons exchange more rapidly at higher concentrations ofGdmCl, but the exchange rate constants of globallyexchanging residues show a greater dependence on denat-urant concentration. At 0 M GdmCl, the measured rateconstants vary by more than four orders of magnitude, andthe rate constants of some globally exchanging protonscould not be determined as there was no decrease inintensity of the cross peaks in the duration of the experi-ment. At 1 M GdmCl, in contrast, all rate constants ofexchange are similar (0.017–0.043 min–1, mean =0.024 min–1, standard deviation = 0.006). Table 1 lists thepathway by which exchange occurs at 0 M denaturant,global, local or a mixed pathway, as identified in previousstudies [16,17]. Figure 1 has representative experimentalresults of the decay of cross-peak intensity of four residuesin helix 1. One of these residues has been shown toexchange by global unfolding, two by local unfolding andone by a mixed pathway at 0 M GdmCl.
DiscussionWe have found that there is a change with increasing[GdmCl] from the EX2 to the EX1 mechanism for H/2H-exchange of protons in barnase that require global unfold-ing for exchange. Ignoring the change in mechanismwould lead to artefactual results. Some of the standardtests for detecting such changes fail. Since these resultsare relevant to hydrogen exchange methods in general, wediscuss these in detail first. We then show that even whenthe method does correctly identify fluctuations, the resultscannot in principle determine the order of events on theprotein folding pathway.
Exchange of all residues moves towards a global unfoldingpathway with increasing denaturant concentrationThe relative importance of the local and global exchangepathways depends strongly upon experimental conditions[12,13,19]. The local unfolding pathway predominates formost protons under conditions where the protein is stable(at physiological pH and temperature and in the absenceof denaturant). For wild-type barnase, for example, only13 of the 106 exchangeable backbone amide protonsexchange by a global unfolding pathway at 33°C [16,17].These globally exchanging protons are characterized bybeing buried in the core of the protein. Global unfoldingevents become more important at higher temperatures, atextremes of pH, and in the presence of denaturant (e.g.see [12,20–23]). In this discussion, we define ‘locally’,‘globally’ and ‘mixed’ exchanging residues according totheir behaviour in the absence of denaturant (Tables 1,2).
244 Folding & Design Vol 1 No 4
Research Paper H/2H-exchange and the barnase folding pathway Clarke and Fersht 245
Table 1
Rate constants of exchange of amide protons in wild-type barnase.
Rate constant of exchange (min–1)*
p2H 6.8‡ p2H 7.8‡
Residue† 0 M 0.26 M 0.51 M 0.73 M 1.02 M 1.20 M 0.51 M 1.02 M GdmCl GdmCl GdmCl GdmCl GdmCl GdmCl GdmCl GdmCl
*For some residues, accurate rate constants could not be determinedaccurately because the rate of decay was too slow or too fast, oroverlapping cross peaks could not be de-convoluted under theexperimental conditions. †Residues that exchange at 0 M denaturant
by a global exchange mechanism are identified in bold, those thatexchange by a local unfolding mechanism are underlined, and thosethat exchange by a mixed mechanism are shown in plain typeface.‡Using: p2H = p2Hread + 0.4.
At low concentrations of denaturant, the rate constants ofexchange of those protons that exchange by local unfold-ing exhibit low dependence on [denaturant]. But thosethat exchange by global unfolding show a strong depen-dence on [denaturant], reflecting the global stability of theprotein. Figure 2a shows the effect of GdmCl on theexchange rate constants of four residues in helix 1 thatexchange by local unfolding (residues 10 and 11), globalunfolding (residue 14) and ‘mixed’ (residue 15) exchangepathways. As the concentration of denaturant increases,the pathway of the locally exchanging protons movestoward global exchange. The move towards globalexchange is manifested as a convergence of �Gapp
ex (deter-mined from equation 2, with values of the intrinsicexchange rate constant taken from [24]) to a single, global,denaturant-dependent value (Fig. 2b). Residue 10, thefirst protected residue in the helix, appears to exchange bylocal unfolding throughout the range of [denaturant].
Nearly all residues display the same exchange behaviour andfit to the same apparent m valueThe value of �Gapp
ex for residues in all regions of the proteinmoves towards a single global value at higher denaturantconcentrations (Fig. 3, upper panels; Table 2). The meanvalue of �Gapp
ex at 1.2 M GdmCl is 5.4 kcal mol–1
(± 0.6 kcal mol–1 standard deviation). This convergence of�Gapp
ex implies that EX2 conditions apply [13]. An apparentm value for the global exchange component is obtained byfitting the data to equation 4 (Table 2). Some residues donot appear to have reached global unfolding under theseconditions and so a global m value cannot be obtainedaccurately: in fitting the curves to equation 4, it is thevalues of �Gapp
ex at high denaturant that define the global mvalue, if any residues have not reached global unfolding,the apparent m value obtained will be too low. Mostapparent m values are about 4 kcal mol–1 M–1 (mean = 3.6,standard deviation ± 0.9), which is the value obtained forwild-type barnase from equilibrium denaturation experi-ments in GdmCl [25]. The exceptions are a few very lowm values, which are all for residues that appear toexchange locally at high [GdmCl] (Table 2; Figs 3,4).
In summary, the same exchange behaviour and the sameapparent value of m is found across the whole molecule.There is no evidence from exchange kinetics for individ-ual cooperative unfolding substructures, which is in con-trast to the experiments on cytochrome c. The unfoldingreaction that leads to global exchange is a cooperativeevent that involves the whole molecule. At first sight,
246 Folding & Design Vol 1 No 4
Figure 1
Representative examples of exchange kinetics of four residues in helix1 at different concentrations of GdmCl. At 0 M GdmCl, residues 10and 11 exchange by a local unfolding pathway, residue 14 by a globalunfolding pathway, and residue 15 by a mixture of the two pathways(see text).
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Research Paper H/2H-exchange and the barnase folding pathway Clarke and Fersht 247
Table 2
Apparent free energies of exchange of amide protons in wild-type barnase.
Residue *Position of †Exchange ‡�Gappex
‡�Gappex
§ApparentH-bond pathway in 0 M GdmCl in 1.2 M GdmCl m
protecting proton (in 0 M GdmCl) kcal mol–1 kcal mol–1 kcal mol–1 M–1
(donor-receptor)10 �1–�1 Local 6.4 4.9 1.0
11 �1–�1 Local 8.5 5.4 3.3
12 �1–�1 Local 7.2 5.0 2.9
13 �1–�1 Local 9.6 6.2 3.4
14 �1–�1 Global # 5.1 4.1
15 �1–�1 Mixed 9.8 5.3 4.2
16 �1–�1 Local 7.3 6.0 1.4
17 �1–�1 Local 7.9 5.4 2.4
19 Buried Mixed 12.1 6.9 3.2
25 Tertiary Global # 4.5 4.8
26 Loop–sidechain Local 7.9 5.3 3.0
30 �2–�2 Mixed # 5.6 3.7
31 �2–�2 Local 8.5 5.8 3.1
33 �2–�2 Local 8.5 4.8 3.2
35 Turn–�2 Local 8.2 5.4 4.0
36 Turn–turn Local 5.8 4.2 2.0
44 �3–�3 Local 6.2 4.8 2.0
45 �3–�3 Local 7.9 5.8 3.0
46 �3–�3 Mixed 10.4 5.6 3.8
49 Turn–�3 Mixed 10.0 5.8 3.7
50 Tertiary Global 11.1 6.3 3.3
51 Buried Mixed 9.5 5.3 3.5
52 Tertiary Global 11.1 5.7 3.7
53 �1–�2 Mixed 10.3 6.3 3.8
56 �1–�2 Mixed 9.6 5.0 4.1
71 Sidechain–loop Local 7.4 5.3 3.3
72 �2–�3 Global # 5.4 4.3
73 �2–�1 Global # 5.2 2.9
74 �2–�3 Global # 5.4 4.0
76 �2–�3 Mixed # 5.0 5.6
87 �3–�4 Local 10.0 6.6 4.0
88 �3–�2 Mixed 10.2 4.9 4.1
89 �3–�4 Global # 4.4 4.8
89 �3–�4 Global # 4.4 4.8
90 �3–ß2 Global # 4.9 4.1
91 �3–�4 Global 11.2 6.2 3.7
94 �4–turn Local 7.7 5.8 2.1
95 �4–sidechain Local 8.3 4.8 3.8
97 �4–�3 Global # 5.0 4.4
98 �4–�5 Global 11.0 5.6 4.0
99 �4–�3 Global 10.2 5.7 3.6
107 �5–�4 Local 7.9 5.9 2.2
*Hydrogen bonds observed in the crystal structure [37]. †Exchangepathway at 0 M GdmCl, determined by comparing exchange rates ofwild-type and mutant proteins [16,17]. Global exchange, ��Gex ≈��GU–F. Local exchange, ��Gex ≈ 0. Mixed exchange, 0 < ��Gex <��GU–F. Residues that have not moved completely to global exchange
at 1 M GdmCl (see text) are shown in bold. ‡�Gappex determined using
equation 2. §Apparent m values determined from the fit of �Gappex
against [GdmCl] using equation 4. #Exchange rate constants forcertain slow exchanging residues could not be determined at 0 MGdmCl.
these results appear to fit the simple analysis and, interest-ingly, we cannot observe a folding intermediate. Upondeeper analysis, however, the system becomes consider-ably more complex — see below.
Mechanism of exchangeThe predominant exchange mechanism that has beenobserved under most experimental conditions is the EX2limit [9,15], where kc >> kint and kex = K.kint, where K =ko/kc. Under EX2 conditions, therefore, the observedexchange rate constant, kex, depends on the stability(either local or global) of the structural element protect-
ing the proton from exchange and on the intrinsicexchange rate of the proton, which has a p2H dependence[7,24,26]. At the other extreme, under EX1 conditions,where kc << kint, kex = ko, exchange depends only on therate of opening, or unfolding, and is no longer directlyproportional to stability, or intrinsic exchange rate (andhence pH). Exchange under EX1 conditions has beenobserved only rarely, under extreme conditions[21,23,27].
A sensitive method of detecting a change from EX2 toEX1 is to analyze the relative effect of p2H on theexchange rates of all the amide protons in a protein[17,28]. As kint depends on only the OH–-catalyzed reac-tion above pH 5 [10,29], kex is proportional to [OH–] for anEX2 exchange mechanism as shown by equation 5:
logk pHex
1 = log KpH1 + log(koint[OH–]1) (5)
where koint is the intrinsic second-order rate constant for
exchange. Thus, a plot of the logarithm of the rate con-stants for exchange at one pH against those for anotheralkaline value (equation 6) yields a line of slope 1.0, if theequilibrium constant for opening, KpH, does not changewith pH.
logk pHex
1 = logk pHex
2 + pH1 – pH2 (6)
But for exchange by an EX1 mechanism, kex is indepen-dent of kint and so kex should not vary in a similar mannerwith pH. Thus, a plot of log kex for individual residues atone value of pH against those for a different pH is diag-nostic for the mechanism of exchange; a straight linewith slope of 1.0 shows EX2, deviation from the slope of1.0 indicates deviation from an EX2 mechanism. AnEX1 mechanism should give a slope of zero if there is nochange of opening rate constant with pH. Betweenthese limits, exchange will result in an intermediateslope. This is a sensitive test for a move from EX2behaviour since it surveys all protons, and it hasdetected a deviation from EX2 to EX1 behaviour for theglobally exchanging residues of barnase as the protein isdestabilized [17]. (Note that the switch from EX2towards EX1 for barnase is not directly related to themain refolding rate constant, but rather to the overallstability of the protein, implying that the re-protectionstep is not the same as the refolding from the folding
248 Folding & Design Vol 1 No 4
Figure 2
The effect of [GdmCl] on (a) the rate constants of exchange (kex), and(b) the apparent free energy of exchange (�Gapp
ex ) of four residues inhelix 1. Data in (b) were fitted to equation 4.
-4.5
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app
Figure 3
The dependence of �Gappex (upper panels) and log kex (lower panels) on
the concentration of denaturant. The results are grouped according tothe region of the protein, and representative protons from each regionare shown together in plot H. Exchange pathway of proton at 0 Mdenaturant is denoted: global exchanging residues are joined withsolid lines, local exchanging residues with dotted lines, and residuesthat exchange by a mixed pathway by a dashed line.
Research Paper H/2H-exchange and the barnase folding pathway Clarke and Fersht 249
intermediate — for a discussion of this point see [17].This means that these data cannot be analyzed simply interms of kinetic constants, as has been possible for otherproteins [23].)
The mechanism of exchange of globally exchanging protonsmoves from EX2 to EX1 with increasing denaturantconcentrationIt is crucial to detect possible changes in the mechanismof exchange for analysis of the effect of denaturant onH/2H exchange. The mechanism of globally exchangingprotons in mutants that are destabilized by ∼2 kcal mol–1
moves away from EX2 behaviour at 33°C, p2H ∼7.6 [17].As barnase is destabilized by approximately 4 kcal mol–1
between 0 and 1 M GdmCl [25], it is likely that the glob-ally exchanging residues do not exchange by the EX2mechanism at high denaturant concentrations. Whereasall residues exchange by an EX2 mechanism at 0 Mdenaturant (Fig. 5, top panel; see footnote 1), we findthat the globally exchanging residues exchange by anEX1 mechanism at 0.5 M GdmCl, whereas the locallyexchanging residues retain EX2 (Fig. 5, middle panel).At 1 M denaturant, however, almost all residues havemoved to a global exchange pathway and hence allexchange by an EX1 mechanism (Fig. 5, bottom panel).Seven residues, 10, 12 and 16 in helix 1, 36 in loop 2, 44in helix three, and 94 and 107 at the edges of the �-sheet, appear to retain some local exchanging characteris-tics. Residues in the first helix are shown in Figure 5(bottom panel), but residues 36, 44, 94 and 107 exchangetoo rapidly at the higher pH to allow rate constants ofexchange to be determined.
All residues have a single rate constant of exchange at high[GdmCl], which results in an apparently converging value of∆Gapp
exThe value of �Gapp
ex for residues in all regions of theprotein appears, at first sight, to move to a single global�Gapp
ex at higher denaturant concentrations (Fig. 3, toppanels). But it is seen in a plot of kex against [GdmCl]that all the residues exchange with the same rate con-stant at higher denaturant concentrations (Fig. 3, lowerpanels; Table 1), which is a consequence of the changeto an EX1 mechanism. The small ‘spread’ of values of�Gapp
ex derived from equation 2 reflects the spread ofintrinsic rate constants of exchange under these condi-tions (200–9 000 min–1, for the protons observed in thisexperiment at 30°C p2H 6.8), and is not, as might beinterpreted, a sign that all residues are exchanging, byglobal unfolding, by an EX2 mechanism. Importantly,again, all regions of the protein behave in the samefashion: we show in Figure 3h ‘typical’ mixed and locallyexchanging residues from all regions of the protein, andthere is no evidence for different behaviour from earlyand late folding regions of the protein.
Standard methods for diagnosing EX2 may be misleadingIt is important to note that two of the standard methodsfor proving that EX2 conditions apply would have givenus misleading results here.
First, the ratio of k pH1ex : k pH2
ex . A tenfold increase in the rateconstant of exchange with a rise of 1 pH unit is expectedunder EX2 conditions, providing there is no change in sta-bility on changing the pH (equation 5). This is sometimes
250 Folding & Design Vol 1 No 4
Figure 4
Apparent m values determined by plotting�Gapp
ex against [GdmCl] according to equation4. Residues that exchange by a globalpathway at 0 M GdmCl are shown in filledbars, by a local pathway with open bars, andby a mixed pathway with stippled bars. Thoseresidues that have not moved to a globalpathway in 1 M GdmCl are shown hatched.
1It might appear from these data that the globally exchanging residuesare deviating from EX2 at 0 M GdmCl — with the exception of only twofaster exchanging points, protons of residues 50 and 52, all fall within
the range observed for the local pathway, and so it seems safer toassume that at the lower pH there is no significant difference inmechanism between the two sets.
applied to just the slowest exchanging residues in theprotein. The four globally exchanging residues with theslowest exchange rate at pH 6.8 (circled in Fig. 5, centrepanel) do have kpH1
ex : kpH2ex ratios approximating 10. But
these protons are not representative, and so exchange inthe whole protein must be analyzed.
Second, comparison of values of �Gappex with free energies
of unfolding, �GU–F. The EX2 mechanism implies that�Gapp
ex tends to a common value at high [denaturant] forthe exchange of the slowly exchanging protons thatrequire global unfolding. This should equal �GU–F.Under EX1 conditions, however, �Gapp
ex should not beconstant. But the misapplication of equation 2 to EX1conditions gives errors that need not be that large. Allthe protons that exchange from the fully unfolded stateby the EX1 mechanism do so with the same rate con-stant, that for opening. Misapplication of equation 2then leads to a spread of values that reflects the range ofkint for those protons. The range of kint for all protons ofbarnase is equivalent to 3.6 kcal mol–1. For the experi-mentally observable residues, however, this reduces toapproximately 2.3 kcal mol–1, and for the globallyexchanging residues, to approximately 2.0 kcal mol–1.Thus, values of �Gapp
ex that appear, within experimentalerror, to be converging may be as found here simply areflection of a move from EX2 to EX1 and a commonvalue of kex.
Two other points emerge from this analysis. Firstly, it isimportant to distinguish global from locally exchangingresidues. Had we taken our results at 0.5 M GdmCl as asingle unit, for example, then a fit of all the data inFigure 5 (central panel) to a linear function gives a slopeof 0.8. It is only upon separating the residues into theirclasses that we are able to distinguish a move from EX2for the global and mixed protons. Further, the test formechanism must always be applied at the most extremeexperimental conditions; extrapolation from intermediateconditions is insufficient.
Research Paper H/2H-exchange and the barnase folding pathway Clarke and Fersht 251
Figure 5
Plots of pH dependence of exchange at different concentrations ofdenaturant. The value of log kex at p2H1 is plotted against the log kexat p2H2 for the same residue. Residues that exchange by local (�n),global (�) and mixed (�u) exchange pathways determined in 0 Mdenaturant are distinguished. At 0.5 M GdmCl global residues thathave a kex(p
2H1)/kex(p2H2) ratio of ∼10 are circled (see text). A slope
of 1.0 indicates an EX2 exchange mechanism, a slope of 0 indicatesthe EX1 limit has been reached. At 0 M GdmCl, all residues areexchanging by the same EX2 mechanism (see footnote 1). In 1.0 MGdmCl, all residues shown except residues 10, 12 and 16 appear tobe exchanging by an EX1 mechanism. The data in the top panel aretaken from [17]. These data were acquired at 33°C over a longer timeperiod than the present study, which allowed rate constants for all theglobally exchanging residues to be measured.
Differences in apparent m values reflect only differences inthe pathway and mechanism of exchangeAt higher denaturant concentrations, therefore, twoprocesses take place. Firstly, the exchange mechanism ofamide protons that exchange by local unfolding in 0 Mdenaturant moves towards global exchange. Secondly, athigher concentrations of denaturant, the mechanism ofglobally exchanging protons moves away from an EX2mechanism. This is consistent with our observations onmutant proteins [17]. What are the consequences of theseobservations to the analysis? The change of exchangemechanism means that these data cannot be used todetermine true m values which relate stability, �Gex, to[denaturant], as exchange is no longer directly related tostability. No deductions can be made about the stabilityof partly unfolded states that may be present at low con-centrations at equilibrium, since at higher denaturantconcentrations exchange rates are not directly related toprotein stability, but are related to the rate of unfolding.The rate constants of exchange in conditions that areclose to EX1 reflect the opening rate constants, which arethemselves dependent on [denaturant]. Observed differ-ences in the apparent m values reflect differences in thepathway and mechanism of exchange at higher concentra-tions of denaturant (Fig. 4). Although this method hasidentified some partially unfolded states in cytochrome c,where there is no change from EX2 to EX1 [13,15], it failsto give information on barnase and cannot be used blindlyto detect partially unfolded states. Further, as discussedbelow, it gives no information on the order of events inprotein folding.
Analysis of local exchange behaviour∆Gapp
ex may not be a true estimate of local stabilityIf we assume an EX2 behaviour, the change in freeenergy between open and closed form (equation 1),�Gapp
ex , can be determined for the globally exchangingresidues from equation 2 using experimentally derivedintrinsic rate constants [24]. It is important to note,however, that �Gapp
ex may not be an accurate measure-ment of local stability for locally exchanging residues.The values of the intrinsic rate constants of exchange,kint, determined using unstructured peptides [24] havebeen shown to be valid for unfolded barnase and for theglobally exchanging residues in the folded protein, whichexchange from the fully unfolded state [17,30]. Thesame values of kint may not, however, be a true intrinsicexchange rate in the folded protein [12] as localexchange may not occur from fully unfolded conforma-tions and kint is strongly dependent on the solvent expo-sure. The ‘apparent’ free energy of exchange, �Gapp
ex , ofthe solvent exposed, locally exchanging residue 12 inhelix 1, in 0 M GdmCl, for instance, at 7.2 kcal mol–1, islower than the �Gapp
ex of two adjacent, more buried,locally exchanging residues 11 and 13 (= 8.5 and9.6 kcal mol–1 respectively).
Locally exchanging residues may show some dependence on[denaturant] in their exchange behaviourThe exact nature of the local fluctuations that allowproton exchange are unclear [3,8,12,31]. It is possible thatsome local fluctuations may involve significant unfoldingprocesses [31]. The local stability, and thus exchangekinetics, may show some denaturant dependence. Forresidue 10 of barnase, for example (Fig. 2), althoughexchange appears to be by a local or mixed pathwaythroughout the range of [GdmCl], exchange rate constantsshow a dependence on denaturant concentration through-out the whole range and give a low, but significant appar-ent m value of 1.0 kcal mol–1 M–1. In barnase, exchangefrom loop regions is very rapid, presumably through a localexchange pathway. Exchange from loop regions of barnasecannot be measured under the same conditions at whichexchange rates are obtained for the globally exchangingresidues [32]. It is probable that all the residues in a loopexchange in the same local unfolding process, and, as theunfolding is presumably very rapid, with local stabilitylow, the local exchange would continue throughout a longrange of denaturant before the global pathway is observed.In this case, the whole loop would display the same lowapparent m value, yet this would not mean that the loopacted as a cooperative unfolding unit on the foldingpathway, simply that global unfolding had not beenreached.
Relationship between exchange at equilibrium and thefolding pathwayIt is a fundamental tenet of kinetic and thermodynamicanalysis that measurements of the equilibrium distributionof intermediates give only the relative thermodynamicproperties of the intermediates and not the pathwaybetween them. This is a consequence of the first law ofthermodynamics: one cannot derive a kinetic mechanismfrom an equilibrium analysis because the free energy of aparticular molecule at equilibrium depends only on thestate of the molecule and is independent of the pathwayby which it is formed. The value of �Gapp
ex or the equilib-rium constant between particular open and closed states ofa protein derived from hydrogen exchange at equilibriumis just such a thermodynamic measurement and does notgive information on when that state is formed on apathway. For example, consider the exchange from a reac-tion sequence as shown in equation 7:
K1 K2N I U (7)
kint kint
where an intermediate, I, is formed from a native struc-ture, N, with formation constant K1 (=[I]/[N]), and the
252 Folding & Design Vol 1 No 4
unfolded state, U, has formation constant K1K2 (=[U]/[N]), and I and U are ‘open’ states for exchange. Therate constant for the exchange of a particular residue ifrom state I is given by ki
ex = kiintK1, and that of residue j
from state U by kjex = kj
intK1K2. Suppose, instead, that I isan off-pathway state, as shown in equation 8:
1/K1 K1K2I N U (8)
kint kint
formed with the same equilibrium constants; K1 =[I]/[N],K1K2 = [U]/[N]. Again, the rate constant for the exchangeof a particular residue i from state I is given by ki
ex = kiintK1,
and that of residue j from state U by kjex = kj
intK1K2. Thus,identical values of �Gapp
ex are obtained for both pathways.
All that equilibrium exchange measurements under EX2conditions can do is to rank equilibrium unfolding statesor fluctuations in the order of their energies. They cannot,as has been proposed [33,34], identify which parts of theprotein fold first or form a nucleation core. The slowestexchanging proteins are simply those that require thelargest change in energy of formation of the state fromwhich exchange takes place. Any agreement betweenthose protons and a folding nucleus is purely fortuitous.Indeed, it has been shown for barnase that there is not adirect correspondence between early formation of struc-ture and slow exchange [16]. The only significant correla-tion is between slow exchange and a high degree of burialof the protons in the structure.
Materials and methodsSample preparationUniformly 15N-labelled wild-type barnase was prepared as describedpreviously [16]. The exchange buffer was 50 mM deuterated imidazole,in 2H2O, adjusted to p2H 6.8 or 7.9 with 5 M HCl, and containingGdmCl at concentrations between 0 and 1.2 M (p2H values reported arecorrected using p2H = p2Hread + 0.4 where p2Hread is observed pHusing a glass electrode [35]). The concentration of GdmCl at which50% of the protein is unfolded, [GdmCl]50%, is 2 M in water at 25°C andpH 6.3, i.e. at all experimental concentrations barnase is expected to be> 99% folded form. The experiments at 0 and 0.25 M GdmCl were per-formed in the presence of 0.5 M NaCl [24]. 20 mg of lyophilized proteinwere dissolved rapidly in the deuterated exchange buffer, centrifuged,and transferred to an NMR tube. The final pH was measured using aglass electrode at 30°C at the end of the experiment. A series of experi-ments at p2H 6.8 were performed at increasing concentrations ofGdmCl. Experiments were also performed at p2H 7.9 to ascertain themechanism of exchange at higher denaturant concentrations.
NMR experiments and data analysisThe exchange experiments were performed as described previously[16]. 1H-15N HSQC spectra [36] were acquired on a Bruker AMX500spectrometer. Spectra were acquired with increasing delays for up to 4days, with about 30 experiments performed in the first 24 hours. Thetime point for an experiment was taken to be half way through theacquisition time.
The spectra were processed and the volume integrals of the crosspeaks were calculated using the Bruker program UXNMR. The datawere transferred to a Macintosh computer and the decays were fittedto a single exponential, using the program KaleidaGraph (AbelbeckSoftware). In cases where the rate of exchange was very slow, and thedecay could not be fitted to an exponential, but where an initial ratecould be determined, a rate constant was calculated from the ratio ofthe initial rate to the estimated amplitude of the decay.
AcknowledgementsWe are grateful to Dr SW Englander for providing us with the equations forthe analysis shown in equation 4.
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