Structure 14, 97–106, January 2006 ª2006 Elsevier Ltd All rights reserved DOI 10.1016/j.str.2005.09.012

Structural Interpretation of Hydrogen ExchangeProtection Factors in Proteins: Characterizationof the Native State Fluctuations of CI2

Robert B. Best1,2 and Michele Vendruscolo1,*1Department of ChemistryUniversity of CambridgeLensfield RoadCambridge, CB2 1EWUnited Kingdom

Summary

Protection factors obtained from equilibrium hydro-

gen exchange experiments are an important sourceof structural information on both native and nonnative

states of proteins. We present a method for determin-ing ensembles of protein structures by using hydro-

gen exchange data as restraints in molecular dynam-ics simulations in conjunction with an empirical

force-field. The method is applied to determine the en-semble of structures representing the native state of

chymotrypsin inhibitor 2 (CI2), including the rare, largefluctuations responsible for hydrogen exchange.

Introduction

The combination of empirical force-fields with experi-mental data from X-ray diffraction (Brunger et al., 1987;Kuriyan et al., 1991; Brunger and Adams, 2002) or NMRspectroscopy (Brunger et al., 1986; Nilges et al., 1988;Kanelis et al., 2001) for protein structure calculationhas proved to be an invaluable tool in structural biology.The force-field provides a detailed model for the energysurface of the protein, which, when combined with ex-perimentally derived restraints, allows high-resolutionstructures to be determined. These structures are ex-tremely useful in interpreting protein function, althoughthey are not expected to fully account for the importantrole played by the dynamics in this respect (Wand, 2001;Lindorff-Larsen et al., 2005). A technique capable of pro-viding information on such structural fluctuations is equi-librium hydrogen exchange (Woodward and Hilton, 1980;Bai et al., 1993; Arrington and Robertson, 2000; Clarkeand Itzhaki, 1998; Fersht, 1999; Englander, 2000), inwhich the rate of substitution of protein amide hydrogenatoms in a deuterium oxide solution is monitored. Underthe so-called EX2 conditions, the rate of amide hydrogenexchange is related to the free energy required to exposethe amide to the solvent. In cases in which the exchangeoccurs via local unfolding, rather than via a global unfold-ing transition, this exchange rate is a source of informa-tion on local structural fluctuations. The theoretical anal-ysis of hydrogen exchange measurements has beenused to rationalize the determinants of large conforma-tional fluctuations of proteins (Miller and Dill, 1995; Hilserand Freire, 1996; Sheinerman and Brooks, 1998; Baharet al., 1998; Garcia and Hummer, 1999; Viguera and Ser-rano, 2003; Dixon et al., 2004).

*Correspondence: mv245@cam.ac.uk2 Present address: Laboratory of Chemical Physics, NIDDK, National

Institutes of Health, Bethesda, Maryland 20892-0520.

Here, we propose a method that allows protectionfactors for local exchange to be used as low-resolutionstructural restraints in molecular dynamics simulationsin conjunction with an empirical force-field. After param-eterization on a set of proteins for which experimentalprotection factors are available, the method is applied tothe determination of the native state ensemble (NSE) ofthe chymotrypsin inhibitor 2 (CI2) protein. This methodinvolves determining the structures corresponding to therare, large fluctuations from the native state from wherelocal exchange takes place. The use of restraints de-rived from hydrogen exchange measurements makes itpossible to explore the regions of conformational spacecorresponding to these fluctuations, which may takeplace on a timescale of milliseconds or more, by usingdetailed molecular dynamics simulations. The NSE thatwe obtained allows a direct comparison to be made withthe transition state ensemble (TSE) determined by usingF values as restraints in molecular dynamics simula-tions. Our results suggest that the large equilibrium fluc-tuations leading to exchange-competent conformationscannot be related to the folding pathway of CI2.

Results

Microscopic Description of Protection Factors

The protection factor for residue i, Pexpi = kint

i =kexi , is the

ratio of the intrinsic rate, kinti , observed in an unstruc-

tured peptide (Hvidt and Nielsen, 1966; Bai et al., 1993;Fersht, 1999) to the observed amide hydrogen exchangerate, kex

i . Protection factors can be related to an apparentdifference in free energy, DGi = RT lnPexp

i , between the‘‘closed’’ state and the ‘‘open,’’ exchange-competentstate. If an amide hydrogen can only exchange whenthe protein is fully unfolded, then the apparent local sta-bility is equal to the global stability (DGi = DGD2N), andthe amide hydrogen is said to be undergoing ‘‘global’’exchange (we note, however, that the converse is nottrue). In this case, the protection factor does not give adirect indication about the local structure. The alterna-tive, ‘‘local’’ exchange occurs through localized fluctua-tions of the structure. Whether an amide hydrogen isexchanging locally or globally must be determined ex-perimentally, by using denaturant dependence (Bai andEnglander, 1996; Chu et al., 2002; Itzhaki et al., 1997),temperature dependence (Bai and Englander, 1996), ormutagenesis (Neira et al., 1997). When the exchange islocal, the origin of the free energy difference, DGi, islikely to be a combination of amide burial and hydrogenbonding, although little is known about the microscopicmechanism by which the amide hydrogen is exchangedwith deuterium (Woodward and Hilton, 1980). We usethe following phenomenological approximation to theprotection factors arising from local exchange (Vendrus-colo et al., 2003):

ln Psimi ðCÞ= bcNc

i ðCÞ+ bhNhi ðCÞ: (1)

The ‘‘protection’’ of the amide hydrogen of residue i ina particular conformation, C, relative to an unstructured

Structure98

peptide is written as a sum of the contributions fromburial (measured as the number of heavy atoms withina distance of 6.5 A from the amide nitrogen Nc

i (C)) andthe number of hydrogen bonds to the amide Nh

i , with re-spective weights bc and bh. The experimental protectionfactor can be compared to the average over an ensem-ble of conformations representing the state occupied bythe protein: �

ln Psimi

�=�bcNc

i + bhNhi

�: (2)

A more detailed justification for this equation is givenin Experimental Procedures. A cutoff of 2.4 A betweenthe donor hydrogen and the acceptor was used for iden-tifying a hydrogen bond; this cutoff provides similar ac-curacy to the combination of the distance between thedonor nitrogen and the acceptor and the angle conven-tionally used (de Loof et al., 1992). We found from initialtests that the choice of the threshold distance for count-ing, Nc

i , made little difference for the resulting ensem-bles. More complex expressions for ln Psim

i , including anonlinear dependence on the number of contacts anda dependence on the exposed surface area, did not per-form significantly better than those presented below,and so the simpler model of Equation 1 was retained.In this work, we use a definition of hydrogen bondingin which only native hydrogen bonds are considered,but this is not a necessary restriction. Tests with a non-native definition of hydrogen bonding did not make anappreciable difference in the cases discussed here.Nonnative interactions could be included within thesame framework if they are likely to be more important.

Equilibrium protection factors are a property of aBoltzmann ensemble of conformations, and no singleconformation is required, or indeed expected, to satisfyall of the observed protection factors simultaneously.The calculated protection factors of Equation 2 aretherefore taken as averages over M replicas of the mol-ecule, i.e.,

ln Psimi =

1

M

Xk

ln Psimi

�Ck

�; (3)

where the replicas have conformations Ck (k = 1, ., M).The horizontal bar distinguishes averaging over thenumber of replicas simulated from the thermal average.In most of the calculations described in this paper, weused M = 2, 4, and 8. We define a reaction coordinate,r, as the mean squared difference between experimen-tal and calculated protection factors,

r =X

i

�ln Psim

i 2 ln Pexpi

�2; (4)

and a pseudoenergy function that penalizes high valuesof the reaction coordinate (see below). The goal of theconformational samplingwith the experimental restraintsis to obtain an ensemble of conformations for which�

ln Psimi

�= ln Pexp

i : (5)

We note that the approach that we described is re-lated to the ‘‘umbrella sampling’’ method (Torrie and Val-leau, 1977; Allen and Tildesley, 1989; Muegge et al.,1997), since we use a biasing function to enhance thesampling of a region of conformational space (the par-

tially unfolded structures that give rise to exchange)that is not near a minimum in the force-field used.

Equation 2 has been already been used in a MonteCarlo study of native state exchange with a hard-spheremodel for the protein backbone (Vendruscolo et al.,2003). Restraints derived from hydrogen exchange mea-surements were recently used in low-resolution molec-ular dynamics simulations, in conjunction with a G�omodel, to generate a model of the structure of a FAT do-main folding intermediate (Dixon et al., 2004). By adopt-ing a full atomic representation and molecular dynamicssimulations including a detailed force-field, we providehere a more accurate method of structure determina-tion. The principal advantage of the present procedure,apart from providing a structural description at higherresolution, is that the hard-sphere model (Vendruscoloet al., 2003) and, to some extent, also G�o models donot contain any information about the energies of non-native conformations. Thus, when the hydrogen ex-change data require a particular region of structure tobe nonnative, the sampling is essentially determined en-tropically. Inclusion of an all-atom transferable force-field is therefore expected to give a more accurateweighting of nonnative states.

Parameter Fitting

The coefficients bc and bh were found by a fit to ex-perimental data. We used native state exchange datafrom seven proteins with well-characterized hydrogen-exchange data (see legend to Figure 1). The most

Figure 1. Fitting of the Parameters bc and bh

Contour plots of the mean square deviation as a function of bc and bh

between protection factors calculated from unbiased 1 ns native

state simulations in CHARMM/EEF1 (Lazaridis and Karplus, 1999)

and their corresponding experimental values. Simulations were car-

ried out for the following seven proteins: barnase (Clarke et al.,

1993), horse heart cytochrome c (Milne et al., 1998), staphylococcal

nuclease (Loh et al., 1993), ribonuclease H (Chamberlain et al., 1996),

equine lysozyme (Morozova et al., 1995), human a-lactalbumin

(Schulman et al., 1995), and basic pancreatic trypsin inhibitor (Kim

et al., 1993). The optimal values of the parameters are indicated by

a solid, black square.

Structural Interpretation of Protection Factors99

Figure 2. ‘‘Jack-Knife’’ Test

Contour plots of the mean square deviation

between protection factors calculated from

biased simulations of BPTI by using hydro-

gen exchange restraints with varying values

of the parameters bc and bh.

(A–D) The panels show the mean square devi-

ation from experimental data for the two-

thirds of the data used in the restraints for

simulations with (A) one, (B) two, (C) four,

and (D) eight replicas. A large region of pa-

rameter space is satisfied because these

data were used as restraints; the solid, black

squares indicate the position of the optimal

parameters.

(E–H) Panels show the deviations for the pro-

tection factors back-calculated from the re-

maining one-third of the data for (B) one, (D)

two, (F) four, and (G) eight replicas: this

case provides a more limited range of suit-

able values for the parameters. The optimal

parameters are indicated by solid, red circles.

(I–L) The right-hand column shows plots of

the calculated protection factors against the

experimental data for the optimal parameter

values only: black squares indicate the data

used in the restraint, and red circles indicate

the ‘‘free’’ data.

straightforward method of calibration is to optimize thefit of protection factors calculated by using Equation 1from the crystal structures to the experimental values.These structures, however, represent only a small partof the entire native state ensemble; the latter also in-cludes conformations accessed through the rare fluctu-ations giving rise to exchange (Bai et al., 1995; Bai andEnglander, 1996). In order to improve the descriptionof the native state ensemble, we constructed a slightlylarger ensemble by carrying out molecular dynamicssimulations of the native state. Figure 1 shows the devi-ation in the training set, averaged over all of the proteins,from experimental data as a function of the parametersbc and bh. The graph indicates that the optimal parame-ters are bc = 0.35 and bh = 2. This result is consistent withthose determined for a simpler model with only thebackbone atoms represented, for which bc = 1 andbh = 5 (Vendruscolo et al., 2003). In both cases, a singlehydrogen bond contributes much more to the protectionfactor than a single burial ‘‘contact.’’ The smaller value ofbc in the all-atom method results from the number of na-tive contacts per residue being approximately threetimes larger than in the Ca model. The smaller value ofbh is due to the partial double counting introduced byour definitions of burial and hydrogen bonding.

Due to the possible limitations of fitting parameters tothe native state ensembles determined by molecular dy-namics simulations, which are unlikely to sample ade-quately the true fluctuations giving rise to exchange,we used additional simulations restrained by the protec-tion factor data in a jack-knife test. Simulations werecarried out with two-thirds of the data as restraints,and protection factors were back-calculated for the re-maining one-third of the data (the actual restraint imple-mentation is described below). Using this method, it wasalso possible to include the effect of ensemble averag-ing, by imposing the restraints as an average over a num-ber of copies of the system. Figure 2 shows the compar-

ison with experiment as a function of the parameters forone protein (BPTI). In all cases, a sizeable region of pa-rameter space provides a significant agreement with ex-periment for the data used in the restraints (Figures 2A–2D): only very small values of the parameters, requiringvery compact structures, are forbidden. However, theoptimal region is much smaller for the back-calculatedvalues and is similar to that calculated by using nativestate data only (Figures 2E–2H); the addition of replicasincreases the size of the optimal region, but the best-fitparameters are essentially the same. This result is simi-lar for the other proteins studied (data not shown). Theagreement between experimental and protection fac-tors and those calculated from simulations with the op-timal parameter values is illustrated by the scatter plotsin Figures 2I–2L. The correlation coefficients betweenthe experimental data and the protection factors usedin the restraint are 0.92–0.93 in all cases, and the corre-lation with the protection factors left out of the con-straint are in the range 0.79–0.88.

In Equation 1, Nci can be calculated by using either na-

tive contacts only or both native and nonnative contacts,without an appreciable difference in the resulting opti-mal parameters bc and bh. This result is to be expectedfor native state hydrogen exchange, but inclusion ofnonnative contacts should be important when hydrogenexchange is measured for other states of the protein(e.g., intermediates), or in situations where persistentnonnative interactions could be expected to give riseto protection. The latter, for example, may be the caseof protection for protein-protein or protein-membraneassociation (Halskau et al., 2002) or in amyloid fibrils(Hoshino et al., 2002).

The Native State Fluctuations of CI2 Determinedfrom Hydrogen Exchange

The native state equilibrium hydrogen exchange of chy-motrypsin inhibitor 2 (CI2) was chosen as a test case,

Structure100

since it is very well understood experimentally (Itzhakiet al., 1997; Neira et al., 1997); exchange mechanisms(local, global, or mixed) have been determined for allsites. Since our model cannot easily be related to globalor mixed exchange, only protection factors for locallyexchanging protons were used as restraints in the sim-ulations. For this purpose, the original literature assign-ments of local and global exchange were used, al-though, in several cases, these did not determine themechanism explicitly. It should be noted, however, thatsimilar parameters were obtained when the data set wasrestricted to only those proteins with a well-establishedexchange mechanism. In addition, the protection factorfor L32 was omitted since it is extrapolated from data athigh denaturant concentration. Simulations biased bywild-type hydrogen exchange data were carried outwith one, two, four, and eight replicas.

In Figure 3, the back-calculated protection factors arecompared with the experimental values. The back-cal-culated data are averaged over all replicas and overtime, by using the equilibrated portion of the simulation.Thus, the results for a single replica are only time-aver-aged. For all of the simulations (one, two, four, and eightreplicas), a good agreement is obtained with the exper-imental protection factors used as restraints (Figure 3A).It is also interesting to compare the results with the datanot used in the simulations (Figure 3B). Globally ex-changing amides do not fall close to the back-calculatedline, while many of the residues undergoing mixed ex-change are quite similar to the calculated protection fac-tors. This latter result is consistent with local exchangemaking a significant contribution to the observed pro-tection factor, since, in these cases, the rates of localand global exchange must be comparable. The protec-tion factors predicted from the structures that we deter-mined for the residues with missing exchange data arelower than the measured protection factors. This resultis consistent with these residues being in less protectedregions of the structure; thus, the exchange rates maybe too rapid to be measured. We also note, however,that variations in the intrinsic exchange rate (in additionto the protection factors) will also affect the overall rate.

The use of replicas is an important aspect of thismethod, as described above. Using just two replicas in-stead of one results in a marked increase in fluctuations(Figure 4); the fluctuations for four and eight replicas aresimilar to those obtained for two replicas, suggestingthat four is a suitable number, at least in the applicationthat we present here, to be used in restrained simula-tions. Convergence of the values that we determinedto characterize structural fluctuations and other struc-tural properties for ensembles with sufficient members,in addition to the crossvalidation tests described above,gives us confidence that the various ensembles result ina similar conformational sampling.

The sampling method that we presented is designedto access the conformations that correspond to largefluctuations. This aspect is illustrated by showing thelargest fluctuation per residue observed in the ensemble(see Figure 4). The relatively small values of the fluctua-tions that we observed are consistent with the study ofItzhaki et al. (1997), in which no evidence was foundfor exchange-competent, partially folded conformations(Neira et al., 1997). By clustering the structures by rmsd,

we found no evidence of nonnative ‘‘excited states’’(corresponding to intermediates) of significant popula-tion (Bai et al., 1995; Bai and Englander, 1996). The pres-ent simulation method, however, also generates someconformations that are significantly more unfoldedthan the native state, as shown in Figures 4 and 5E.

Transition State EnsembleWe determined the transition state ensembles of CI2 byusing two series of simulations, with one (Paci et al.,2003, 2004) and four replicas, respectively. Restrainedsimulations were carried out at a pseudotemperatureof 400 K, at which the average experimental F valueswere found to be closest to the average back-calculatedF values for all residues. In this type of method, a varia-tion of the pseudotemperature is used both to enhancesampling efficiency and to favor the presence of higher-energy nonnative structures (Paci et al., 2003). The en-semble for the four-replica case was slightly more het-erogeneous than in the single copy case, but it had thesame general structural features. In the following, we fo-cus on the four-replica ensemble, but similar results areobtained for the single replica case, as expected for

Figure 3. Protection Factors for CI2

(A and B) Comparison of experimental protection factors for CI2

(Itzhaki et al., 1997; Neira et al., 1997) with those back-calculated

from the simulations. (A) The experimental protection factors for

local exchange used in the simulation (filled, black circles) are com-

pared to those back-calculated from simulations with one, two, four,

and eight replicas (black lines). (B) Protection factors calculated

from the four-replica simulation are compared to the local exchange

data used as a bias (filled, black circles), data from mixed exchange

(open squares), and data from global exchange (open circles).

Structural Interpretation of Protection Factors101

Figure 4. Structural Heterogeneity of the Native State Ensemble

(A–D) Root mean square fluctuations per residue calculated over all

replicas for hydrogen exchange-biased simulations of CI2 with (A)

one, (B) two, (C) four, and (D) eight replicas. The shaded regions in-

dicate the mean rms fluctuation over the entire ensemble; the max-

imum fluctuation for each residue is shown by a broken line in each

case.

proteins with a single dominant folding pathway (Daviset al., 2002).

Figure 5A compares F values back-calculated fromthe four-replica ensemble with the experimental data.In almost all cases, good agreement is obtained, verify-ing the self-consistency of the data. The main exceptionis A16, for which the experimental value is 1.1 (a value of1.0 was used as a restraint). The slightly lower value (F =0.82) calculated for this residue is probably due to thelimitation of counting only native contacts. A closer ex-amination of the ensemble reveals that although thelong-range native interactions (between residues 16–49,16–57) are substantially weakened, there is a strength-ening of local interactions (16–8, 16–11, 16–13, 16–19)through nonnative contacts. Inclusion of these contactswould raise the calculated F value for A16. The resultingtransition state ensemble is illustrated by a set of repre-sentative structures in Figure 5F.

Discussion

The application of restraints derived from hydrogen ex-change data to CI2 results in an ensemble of native con-formations, characterized by an average rmsd from thecrystal structure of 2.7 A when either four or eight repli-cas are used (see Figure 4). This relatively small value ofthe rmsd is anticipated, since native-like conformationshave the largest statistical weight in the native state.However, much larger fluctuations related to hydrogenexchange do exist in the ensemble that we determined(see the maximum fluctuations in Figure 4). We alsonote that the inclusion of global exchange restraintswould result in an even larger NSE. This important prop-erty of the native state ensemble is shown by a sample ofconformations showing significant local deviations fromthe native state in Figure 5E.

Determination of a transition state ensemble for fold-ing from experimental F values results in a much less

Figure 5. Transition State Ensemble of CI2

(A) The F values calculated from the CI2 TSE

determined by four-replica simulations (black

line) are compared with the experimental F

values. The white area surrounding the solid

line represents one standard deviation from

the mean, where the average is taken across

the ensemble.

(B and C) In (B), the largest root mean square

fluctuation for each residue is shown for the

native ensemble determined from hydrogen

exchange data, while, in (C), the root mean

square deviation of the TSE determined

from F values from the native state is plotted.

The main secondary structure elements of

the protein are indicated between (B) and (C).

(D–F) On the right, structures corresponding

to the different ensembles are shown: (D)

the native structure of CI2; (E) structures rep-

resentative of large fluctuations from the na-

tive ensemble determined from hydrogen ex-

change data; (F) representative structures

from the transition state ensemble deter-

mined by using a F value bias for four-replica

simulations. All structures are colored from

the N terminus to the C terminus with a blue-

green-red gradient.

Structure102

native-like, and more heterogeneous, ensemble, with anaverage rmsd from the native state of 7.8 A. This value isslightly larger than that (about 5.0 A) reported by Dag-gett and coworkers (Day et al., 2002), probably due tothe enhancement in the sampling realized through theuse of replicas in the present calculations. A number ofrepresentative structures from this ensemble, shown inFigure 5F, illustrate the heterogeneous nature of theTSE. Pairwise interaction energies (see Figure S1 in theSupplemental Data available with this article online)computed from the NSE and crystal structure are similar,while, for the TSE, there is an overall weakening of inter-actions, but not in a uniform manner. Interactions withinthe a helix remain quite strong, while there is a markedweakening of interactions within the b sheet. Theseresults are qualitatively consistent with those found fortransition states identified from high-temperature un-folding simulations with explicit (Daggett et al., 1996) andimplicit (Lazaridis and Karplus, 1997) solvent models.

It has been proposed that hydrogen exchange can beused to infer information on protein folding pathways,since it reports on large fluctuations from the nativestate, which may conceivably be the initial steps of un-folding pathways (Bai et al., 1995; Bai and Englander,1996; Kim et al., 1993). For proteins that exhibit foldingintermediates, this approach has proved useful (Kimet al., 1993; Englander, 2000). However, in other cases,the most probable fluctuations from the native statemay not be those that result in productive unfolding(Clarke et al., 1993). F values, which report on the kinet-ically relevant residues for folding, provide a more directdescription of folding pathways, at least in the case oftwo-state proteins. It has previously been concluded inthe case of CI2, based on a comparison of experimentalprotection factors and F values, that protection factorscannot be used to single out the residues identified byF value analysis as being important for folding (Itzhakiet al., 1997; Neira et al., 1997).

We have carried out a structural comparison betweenthe ensembles of structures representing both the na-tive state and the transition state ensembles. If the hy-pothesis that fluctuations from the native state shouldbe the first steps leading toward unfolding (via the tran-sition state) is valid in the case of CI2, then the residuesthat exhibit the largest fluctuations in the native ensem-ble should be the first to unfold, and should therefore bethe least native-like in the transition state. Figure 5Bshows the largest fluctuations for each residue in the na-tive state derived from protection factors, which wouldbe those hypothesized to unfold first. In Figure 5C, thermsd per residue from the native state is shown. Resi-dues undergoing large native fluctuations are not thosethat are the most unfolded in the transition state. The lin-ear correlation coefficient between the maximum nativestate fluctuations and the rmsd from the native structurefor each residue is 20.07 for the four-replica ensembles.This effect can be seen more clearly when the rmsd perresidue from the crystal structure is compared for indi-vidual structures in the NSE and TSE. We calculatedthe pairwise linear correlation between the rmsd profilesof each pair of structures, one from each of the nativeand transition state ensembles. In an all-against-all com-parison of the NSE and TSE, the correlations are all weakand lay in the interval [20.5, 0.5], with an average

of 0.06. A restricted comparison of the TSE with theNSE structures with the largest overall rmsd (in the top10%) does not improve the correlation; the average cor-relation coefficient is 0.05 (distributions of correlationcoefficients are available as Supplemental Data). Forcomparison, the average correlation of rmsd profiles ofmembers of the NSE with each other is 0.95, and the cor-relation of members of the TSE with each other is 0.45.The latter value is lower as a result of the greater struc-tural heterogeneity of the TSE compared with the NSE.

Further analysis reveals that the a helix, which is oneof the most native-like elements of structure in theTSE, is one of the most fluctuating structural elementsin the native state. Similarly, the termini of the protein,which are largely disordered in the transition state,show approximately average fluctuations within the na-tive state. Thus, an explicit comparison of experimen-tally determined ensembles supports the conclusionssuggested for CI2 by a direct comparison of experimen-tal data (Itzhaki et al., 1997; Neira et al., 1997). In addi-tion, the ensembles that we determined reveal detailsthat are not immediately evident from inspection of theexperimental data. For example, the fact that the N ter-minus of the helix undergoes some of the largest nativestate fluctuations in the protein is not directly apparentfrom the protection factor data, although it is fully con-sistent with them. Further, while the native a helix isclearly defined by the F values as being substantiallyformed in the transition state ensemble, the structureof other regions of the protein with lower F values isnot obvious from the experimental data alone; combin-ing the information from all of the experimental F valuesas simulation restraints permits a self-consistent de-scription of the transition state ensemble.

Thus, equilibrium hydrogen exchange does not ap-pear to be correlated with the folding pathway of CI2,which folds in a two-state fashion. This technique, how-ever, has provided considerable information about thefolding mechanism of proteins with intermediate states(Bai et al., 1995; Bai and Englander, 1996; Kim et al.,1993). Indeed, we are currently in the process of apply-ing the approach that we described to the determinationof the intermediate state in the folding of Im7 and of theintermediate state of lysozyme, which is possibly thespecies that gives rise to the amyloid aggregation ofthis protein.

The technique that we presented provides insight intothe cooperativity of the fluctuations that give rise to localexchange. The covariance matrix of atom-atom fluctua-tions (averaged over residues) for the CI2 native ensem-ble (Figure 6) shows that there are both strong positiveand negative correlations present within the native statefluctuations. For example, the motions of atoms withineach element of secondary structure (the a helix andstrands b1–b3) are positively correlated with one anothersince the secondary structure elements form locally sta-ble and cooperative units. In addition, the motions ofatoms within each b strand are positively correlated withthose in the other b strands (particularly for strands b1

and b2) since they are all part of the same b sheet. Thefluctuations of the a helix are mostly anticorrelatedwith those of the b sheet, indicating the presence of a‘‘breathing’’ motion. The data are presented in an alter-native format as a graph in Figure 6B: this emphasizes

Structural Interpretation of Protection Factors103

Figure 6. Correlations in the Structural Fluctuations of CI2

(A) Covariance matrix for fluctuations within the native ensemble of

CI2 determined by using protection factor data (with four replicas).

Positive correlations are shown in the upper-left half of the matrix,

and the absolute value of negative correlations is shown in the

lower-right half. Secondary structure elements are indicated along

the axes.

(B) The same covariance data presented as a graph: all residue-

residue correlations of a magnitude greater than 0.56 were used to

define edges between nodes representing the residues of the pro-

the grouping of parts of the structure whose fluctuationsare correlated. One would expect that, in larger proteinsin which different subunits of structure may be more in-dependent, correlated effects would be stronger.

Conclusions

We have presented a method for using equilibrium hy-drogen exchange data in conjunction with a transferableforce-field in molecular dynamics simulations, and wehave demonstrated its application for the determinationof an ensemble of structures representing the native fluc-tuations of chymotrypsin inhibitor 2, including the rare,large ones that give rise to local hydrogen exchange.

In cases in which independent sets of experimentaldata exist for the same state of a protein, it is possibleto make an explicit comparison between the ensemblesgenerated by the different methods and those obtainedfrom hydrogen exchange. For example, hydrogen ex-change protection factors (Gorski et al., 2004), chemicalshifts (Spence et al., 2004), and F values (Capaldi et al.,2002) are known for the folding intermediate of Im7; an-other example is the drkN SH3 domain for which bothhydrogen exchange (Crowhurst et al., 2002) and numer-ous other NMR measurements, including NOE- andPRE-derived distances, are available (Choy et al., 2002;Crowhurst and Forman-Kay, 2003).

Given the large body of hydrogen exchange dataavailable, we anticipate that the technique that we pre-sented will be generally applicable to provide quantita-tive structural information for a variety of protein states,relevant to protein folding (Clarke et al., 1997; Li andWoodward, 1999; Maity et al., 2003; Ferraro and Robert-son, 2004), membrane binding (Halskau et al., 2002;Takeuchi et al., 2004), and protein aggregation (Hoshinoet al., 2002).

Experimental Procedures

Alternative Derivation of Equation 2

Equation 2 can be justified by using the right-hand side as an approx-

imation of the free energy of opening (Vendruscolo et al., 2003), as-

suming that the exchange takes place between fully ‘‘closed’’ and

fully ‘‘open’’ states. However, even though we are using protection

factors calculated from intrinsic exchange rates in unstructured

peptides, the method is still applicable in the more general case of

partial opening, as we show here. We start by writing the simulated

protection factor in conformation C as:

Psimi ðCÞ=

kinti

ksimi ðCÞ

; (6)

where kinti is the intrinsic rate of exchange in an unstructured peptide

(Bai et al., 1993), and ksimi ðCÞ is the simulated rate of exchange from

conformation C. In order to define Psimi ðCÞ, we require that�

Psimi

�= Pexp

i ; (7)

where Pexpi is the rate of exchange observed experimentally. The

equilibrium average is defined as CPsimi D =

PC pðCÞPsim

i ðCÞ, where

tein; the threshold was chosen to maximize the information in the

graph. The thick and thin edges represent positive and negative cor-

relations, respectively. Elements of secondary structure are identi-

fied by node shading (see legend). This representation illustrates the

strong positive correlations between the b strands and within the

a helix.

Structure104

p(C) is the Boltzmann weight of conformation C. It is convenient to

express the sum over C as a sum over Nci and Nh

i :

�Psim

i

�=X

Nci;Nh

i

p�Nc

i ;Nhi

� kinti

k�Nc

i ;Nhi

�; (8)

where p�Nc

i ;Nhi

�is the Boltzmann probability for the amide hydro-

gen of residue i of having Nci native contacts and Nh

i native hydrogen

bonds, and k�Nc

i ;Nhi

�is the rate of exchange when the number of na-

tive contacts is Nci and the number of native hydrogen bonds is Nh

i .

While p�Nc

i ;Nhi

�in the present scheme is found by simulation, the

dependence of the rate on the conformation, k�Nc

i ;Nhi

�, is unknown

and must be postulated. We assume that the rate k�Nc

i ;Nhi

�of resi-

due i can be factorized into an ‘‘intrinsic part,’’ kinti , and a ‘‘conforma-

tional part,’’ f�Nc

i ;Nhi

�, such that:

k�Nc

i Nhi

�= kint

i f�Nc

i ;Nhi

�: (9)

We then require k�Nc

i ;Nhi

�to be close to 0 for large Nc

i or for Nhi = 1,

and to tend to kinti for small Nc

i and for Nhi = 0. In practice, we assume

that a residue is protected either if it is buried or if it forms a hydrogen

bond. In the EX2 mechanism, k�Nc

i ;Nhi

�should decrease slowly with

Nci because, in this case, it is possible to have a small Nc

i without ex-

changing. Therefore, we define

fcðNci Þ= expð2 bcNc

i Þ: (10)

Similarly, for hydrogen bonds, we define

fh

�Nh

i

�= exp

�2 bhNh

i

�; (11)

which we use to factorize f�Nc

i ;Nhi

�into a ‘‘burial’’ part and a ‘‘hydro-

gen bonding’’ part:

f�Nc

i ;Nhi

�= f�Nc

i

�f�Nh

i

�: (12)

From Equation 8, the protection factor measured in the simula-

tions is therefore

�ln Psim

i

�=

*ln

kinti

ksimi

+=�bcNc

i + bhNhi

�: (13)

Thus, by making the assumptions given by Equations 10 and 11, the

simulated protection factor of Equation 2 can be interpreted as an

average over an ensemble of partially open conformations.

Hydrogen Exchange Restraint Implementation

The ‘‘biased molecular dynamics’’ method of Paci and Karplus

(1999) was used to drive the system toward the experimental values.

To summarize, a reaction coordinate, r, is defined as the mean

square deviation of experimental from calculated protection factors

(Equation 4). The restraint energy

Wðr; tÞ=(a

2ðr 2 raÞ

2 if rðtÞ> ra

0 if rðtÞ% ra

; (14)

where

raðtÞ= min0%t%t

rðtÞ (15)

is then added to the standard CHARMM19/EEF1 (Lazaridis and Kar-

plus, 1999) polar hydrogen force-field. This energy term is non-zero

only when r is larger than the lowest value reached since the start

of the simulation; thus, the system moves in the direction of better

agreement by spontaneous fluctuation. The force constant a con-

trols the relative weight of the restraint with respect to the force-

field. In all cases, the force constant a (see Experimental Proce-

dures) was increased, from 10 to 100 and then to 1000, with

a 500 ps simulation time at each value to slowly improve agreement

between experimental and calculated protection factors; finally,

a 1 ns simulation was preformed with a = 1000, which was used

for analysis.

Molecular dynamics simulations were carried out starting with

each copy of the system from a structure equilibrated at 300 K in

the CHARMM19/EEF1 force-field, and velocities were randomly as-

signed from a Maxwell-Boltzmann distribution at 300 K with a differ-

ent random seed for each copy. An initial equilibration simulation

was run, during which the agreement between calculated and exper-

imental data, represented by their mean squared deviation, r, was

allowed to converge. Following this, an extended period of dynam-

ics was run for the purpose of data collection and averaging. The

multiple copy simulations were implemented by running a number

of copies of the program, communicating via MPI, analogous

to a method described previously (Best and Vendruscolo, 2004;

Lindorff-Larsen et al., 2005).

Transition State Ensemble

An ensemble representative of the transition state of CI2 was deter-

mined from molecular dynamics simulations restrained by F values

(Paci et al., 2003, 2004) obtained experimentally (Daggett et al.,

1996). Briefly, the F value of residue i is defined in structural terms

as the fraction of native contacts made in conformation C by that

residue with all residues apart from its immediate neighbors:

Fsimi ðCÞ=

niðCÞnnat

i

; (16)

where niðCÞ and nnati are the number of native contacts made by res-

idue i in conformation C and the total number in the native state, re-

spectively. Contacts are defined as the number of side chain heavy

atoms within a distance of 6.5 A, and they are counted by using a dif-

ferentiable function (Paci et al., 2003). A biased molecular dynamics

method similar to that used for hydrogen exchange is then used to

drive the system toward agreement with the experimental data

(Paci et al., 2003). An extension of this method was also used, in

which the experimental restraint is applied to the average F value

for each residue, calculated over a number of copies of the system.

In this case, an additional restraint was enforced on the average F

value for all residues, in order to keep all replicas close to the tran-

sition state (Davis et al., 2002).

Supplemental Data

Supplemental Data including other comparisons between the native

state ensemble and the transition state ensemble are available at

http://www.structure.org/cgi/content/full/14/1/97/DC1/.

Acknowledgments

We thank Jane Clarke, Chris Dobson, Alan Fersht, Joerg Gsponer,

Martin Karplus, and Emanuele Paci for helpful comments on the

manuscript and the Leverhulme Trust (R.B.B. and M.V.) and the

Royal Society (M.V.) for supporting this work.

Received: August 22, 2005

Revised: September 20, 2005

Accepted: September 21, 2005

Published: January 10, 2006

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