Proc. Nati. Acad. Sci. USAVol. 91, pp. 10430-10434, October 1994Biochemistry

Characterization of the transition state of protein unfolding by useof molecular dynamics: Chymotrypsin inhibitor 2AUJUN LI AND VALERIE DAGGETTDepartment of Medicinal Chemistry, BG-20, University of Washington, Seattle, WA 98195

Communicated by A. R. Fersht, July 12, 1994

ABSTRACT Temperature-induced unfolding of chymo-trypsin inhibitor 2 in water was investigated by moleculardynamics smulations. The major transition state of unfoldingwas Identified on the bass of structural and conformationalchanges in the protein during the unfoldig reaction. Thenative tertiary contacts in the hydrophobic core were consid-erably disrupted in the transition state, whereas the secondarysuture was partially intact. The extent of structural changeof the protein around a particular residue was representedquantitatively by the ratio ofthe number ofcontacts the residuemakes in the transition state relative to the native state, 4MD,which allows quantitative comparison with the experimentallydetermined F values. For the region of the unfolding trajec-tory that is identified as the transition state, the 4Om and Ovalues are in good agreement, sugging that the transitionstate identified in the unfolding smulation corresponds to thatprobed with protein engineering methods. Although specula-tive, the transition state identified in the simulation is consistentwith available experimental data and provides an in-depth viewof what the transition state o unfolding may look like.

For a typical elementary chemical reaction, the transitionstate represents structures around the saddle point of thepotential energy surface of the reacting system (1). Proteinfolding and unfolding are far more complicated than anelementary chemical reaction, as the nature of the barrierinvolves changes in many low-energy noncovalent interac-tions and the possibility of many transition states withentropy playing a major role in the process. If one transitionstate has a much higher barrier than all the others, then thisreaction step is rate limiting and, by convention, is consid-ered as the transition state of the overall reaction (2). Evenifone can successfully identify a single transition state for theoverall process, the transition state will be an ensemble ofstructures due to the importance of low-energy noncovalentinteractions (2). The transition state in protein folding/unfolding potentially involves the entire protein and, in anycase, will not be localized to a particular bond as in a chemicalreaction (3, 4).The transition state of unfolding of the barley chymotryp-

sin inhibitor 2 (C12) has been investigated by Fersht andcoworkers (5-8). Kinetic measurements indicate that thetransition state is a high-energy form of the native state inwhich stabilizing interactions present in the native state aredisrupted (5). Protein engineering methods have been appliedto probe the structure of the hydrophobic core of the proteinin the transition state (6, 9). These studies suggest that theedges of the core are significantly weakened in the transitionstate, while the center of the core remains partially intact.One particular residue, Val-38, is special in that it is moreburied in the transition state than it is in the native state.CI2 is an 83-residue protein. The structure of the first 19

residues is not resolved by either x-ray crystallography (10)

or two-dimensional NMR studies (11-15). The structure of apseudo-wild-type form of C12 in which these residues havebeen omitted has recently been solved to 1.7-A resolution(Fig. 1) (17). These 19 amino acids do not contribute to thestability and activity of the protein, and a truncated form ofthe protein omitting these residues was used for the proteinengineering experiments (9). The secondary structure of theremaining 64 residues, according to the (4, Or) angles (18, 19),consists of an 11-residue a-helix and three (-strands (see Fig.1). The packing of the a-helix against the (3-sheet forms theonly hydrophobic core.Although C12 is a single-domain protein, we divide the

protein into two regions, for reasons that will become clearlater. The first region (residues 20-42) consists of the N-ter-minal strand and the a-helix, and the second region (residues43-83) consists ofthe (3-sheet and the loop. The hydrophobiccore may be considered as being formed by the packing ofregion 1 against region 2. The hydrogen bonds denoted by thedashed lines in Fig. 1, together with the hydrophobic inter-actions, stabilize the packing of region 1 against region 2.

In this paper we report the study of the transition state ofunfolding of C12 by molecular dynamics (MD) simulations.Various unfolding simulations have now been performed[reviewed recently by Daggett and Levitt (20)]. The advan-tage of computer simulations is the ability to investigate theconformational characteristics of the protein at every pointalong the unfolding pathway. These structures can clearly tellus how the protein molecule changes from its native foldedstructure to the unfolded structure.Due to the ambiguities in defining the transition state for

such a complicated process, we will rely on structural char-acteristics in locating this state. Specifically, we define thetransition state as the ensemble of structures populatedimmediately prior to the onset of a large structural change.We have two main reasons for using a structural definition asopposed to an energetic one. First, computation of smallfree-energy differences for such a complicated process insolution is not currently possible. Second, delineation ofstructural features is the strength of force-field methods, andthese structural features are easily viewed, interpreted, andunderstood. Here we discuss how the transition state wasidentified and then compare its structural characteristics withthe available experimental data.

METHODSThe starting conformation for the simulation was the crystalstructure of the pseudo-wild-type C12 (referred to simply asthe wild type) solved by Harpaz et al. (17). The potentialenergy function (M. Levitt, M. Hirshberg, R. Sharon, andV.D., unpublished work) will be described elsewhere. Pro-tocols (21) for MD, as implemented within ENCAD (22), havebeen described in detail.

Abbreviations: CI2, chymotrypsin inhibitor 2; MD, molecular dy-namics; rmsd, root-mean-square deviation.

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The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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Fio. 1. Ribbon representation of the main-chain fold of thecrystal structure of C12 (16) with the regions of secondary structureindicated and the residues involved given in parentheses. The Nterminus and the c-helix are defined as region 1; the loop and the,-sheet are defined as region 2. The five-hydrogen bonds betweenregions 1 and 2 are represented by dashed lines. MIDAS PLUS(University of California, San Francisco) (16) was used for allcomputer graphics figures.

Three simulations ofC12 were performed, one at 298 K andtwo at 498 K. The procedure for the 298 K and the main 498K simulations was as follows. The protein was first mini-mized for 1000 cycles to reduce any bad contacts prior toperforming MD. Then, water molecules were added aroundthe protein to fill a rectangular box, with walls at least 8 Aaway from any protein atom, resulting in a total of 2392 watermolecules. The density of the solvent was set to the exper-imental value for the temperature of interest (21, 23), andperiodic boundary conditions were employed. Various min-imization and MD cycles were performed to prepare thesystem (21). The 298 K simulation was performed for 8 x 10Wsteps (1.6 ns) and the 498 K simulation was continued for 1.1x 106 steps (2.2 ns).The only difference between the second 498 K simulation

and that described above was that the protein was notminimized in vacuo prior to addition of solvent. Changing thepreparation protocol is equivalent to changing the random-number seed for MD and sends the molecule on a differentdynamic trajectory. The C" root-mean-square deviation(rmsd) between the two starting structures forMD was 0.8 A.This simulation proceeded for 0.5 ns. The purpose of thissimulation was to test the reproducibility ofthe main featuresof the first 498 K simulation.

RESULTS AND DISCUSSIONNative Dynamics. Before the unfolding simulation was

performed, the dynamic behavior of C12 in water at roomtemperature (298 K) was investigated. The protein was verystable under these conditions. The C" rmsd from the crystalstructure remained <2 A at all times during the 1.6-nssimulation (Fig. 2), with a 1.6-A coordinate-averaged devia-tion during the last 200 ps. Other structural and dynamic

1.2Time, ns

FIG. 2. Ca rmsd from the crystal structure as a function of timefor the native (298 K) and unfolding (498 K) simulations. (Inset) Thefirst 400 ps of the 498 K curve.

properties were in good agreement with the NMR solutiondata (unpublished work). These results indicated that thenative protein was well behaved and that the more specula-tive unfolding simulations could be performed.The Unfoding Simulation. The unfolding simulation was

performed at a temperature of 498 K for 2.2 ns. Hightemperature was used to speed up the reaction; CI2 isextremely stable at neutral pH, with a Tm > 80"C (8). Thereare two plateaus in the rmsd curve; the first spans from 0.3to 0.9 ns and the second from 1.2 to 2.2 ns (Fig. 2). In the firstplateau, the tertiary structure was disrupted but most of thenative secondary structure was retained. This region corre-sponds to a transient unfolding intermediate. After 1.2 ns theprotein lost all of its native secondary and tertiary structureand became fully unfolded. A full discussion ofthe unfoldingofCI2 will be presented elsewhere. Here we will concentrateon the transition state of unfolding, which, as will be seenlater, occurred before 300 ps (Fig. 2 Inset).

Early Events In Unfolding. The initial rapid increase in theCa rmsd was mainly due to the disruption of the hydrophobiccore. As an indication of this disruption, the hydrogen bondlabeled Od in Fig. 1 broke almost immediately (5 ps). At about25 ps, hydrogen bonds () and C) broke; after that, the Carmsd entered a slowly increasing phase (Fig. 2). The Cterminus moved toward the center of the loop, where itformed a strong hydrogen bond with the side chain ofArg-67.As a result, the interaction between (-strands 2 and 3 wasstrengthened. The N terminus moved away from the hydro-phobic core and became almost fully solvated, exposing thisportion of the hydrophobic core to solvent.Between 230 and 280 ps, there was a large jump in Ca

rmsd, from 4 to 6 A. This jump was caused by the furtherexpansion of the hydrophobic core and the breaking ofhydrogen bonds i) and CD. The structure of the proteinchanged very rapidly and most of the native tertiaryhydrophobic contacts were lost during this time period. Theorientation of the a-helix also changed, as its axis rotatedfrom being parallel to the 13-strands to an angle of about 450at 300 ps. The hydrophobic residues on the helix and the3-sheet reorganized, the helix packed against the middle

portion of the 13-sheet and formed a new, smaller, and moredynamic hydrophobic cluster.

Characterization of the Transition State. The major transi-tion state of protein folding/unfolding is believed to be adistorted form of the native state (24), and experimentalresults support this assumption (2, 5, 6). This suggests that

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10432 Biochemistry: Li and Daggett

the transition state should occur early in the unfoldingsimulation.

Structural changes. The transition state is kinetically andthermodynamically unstable, and we expect the structure ofthe protein to change rapidly once it passes the majortransition state. The first structural change was relativelysmall and occurred very early (25 ps) (Fig. 2 and discussedabove). This rearrangement was triggered by the local dis-ruption ofthe hydrophobic core and the breaking ofhydrogenbonds (X) and ® (Fig. 1). The second change occurred ataround 230 ps and was characterized by the further openingof the hydrophobic core and the breaking of the last twohydrogen bonds between regions 1 and 2. The second changewas large and took longer to occur, and after it had occurredthe protein quickly unfolded to another state, which webelieve is a transient intermediate (see the conformationalanalysis below). This suggests that the second structuralchange may be the major transition state.

Conformational changes. The C't rmsd shown in Fig. 2 iswith respect to the crystal structure. Another way of classi-fying the various states in the unfolding pathway is to analyzethe Co rmsd between the structures themselves (25, 26). Thedifference between points is a close approximation to theactual deviation between structures, and structures belong-ing to the same state should cluster together in the rmsdspace. Such a cluster plot is shown in Fig. 3 with pointsconnected sequentially in time.Three distinct clusters are observed: the first cluster spans

from 10 to 230 ps (with an approximate radius of 1 A), thesecond from 250 to 850 ps (radius 2.5 A), and the third from1335 to 2200 ps (radius 4 A). Consistent with our previousclaim, structures in each of the two plateaus of the Co, rmsdcurve (Fig. 2) are indeed similar to one another, and thereforeeach cluster represents a distinct state. However, the heter-ogeneity in the various states is also evident, as shown by thespread of the clusters. The protein lost all its secondary andtertiary structure in the last cluster, and this cluster corre-sponds to a fully unfolded state. The second cluster corre-sponds to a transient intermediate (250-850 ps). As men-tioned above, there were two major structural changes thatoccurred between 10 and 230 ps, but structures in this timeperiod form only one cluster in the Cc, rmsd space, at least inthe two-dimensional representation. This suggests again thatthe barrier for the first structural change, if it exists, is small.Hence, the major barrier must be the second structuralchange, which occurred at about 230 ps and corresponds tothe further disruption of the hydrophobic core. The portionofthe trajectory from 230 to 250 ps represents the progressionfrom the transition state to the intermediate.

-2

la 60<

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.10

-14.5 0 5 10 15

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FIG. 3. Two-dimensional projection of the Co rmsd space. Thedeviation is calculated between structures along the trajectory withpoints connected sequentially in time.

The driving force for the protein to pass over the transitionstate to the intermediate and fully unfolded state is entropicin nature. This entropy is reflected in the two-dimensionalprojection in Fig. 3; the heterogeneity of the ensemblemaking up the various conformational states is proportionalto the entropy, or ways of folding the chain. The heteroge-neity gets progressively larger in going from the native to theintermediate and the unfolded state, indicating also an in-crease in entropy. Therefore, there must be a rapid increasein entropy in the period 230-250 ps, and it is likely that thecurve of free energy versus time has a maximum centeredbefore, but very close to, the 230-ps time point.Based on the above discussion, we think that the transition

state for the unfolding of C12 was reached before 230 ps.Since the conformational change ofthe protein prior to 230 pswas slow, any structure in the time period 200-230 ps wouldbe a fair representation of the major transition state. In thefollowing, we will use the computed average structure be-tween 220 and 225 ps to represent the transition state; as wewill see later, this structure gives the best agreement withexperiment.Comparison with Experiment. Fersht and coworkers (6, 7)

have determined (DF values spanning all regions ofC12, where(F = AAGtu/AAGF1u (F, folded; U, unfolded; t, transitionstate) (27). In particular, we focus on the 4sF values for 10hydrophobic-core mutants (6).The experimentally measured AAGU-F values are propor-

tional to the number of methyl/methylene groups in thecrystal structure within a 6-A radius of the mutation (9). Inlight of this, it is reasonable to assume that AAGtu isproportional to the number of contacts, ANTS, the mutatedgroup makes in the transition state. From structural andconformational analyses, we concluded that the transitionstate could be represented by the average structure for theperiod 220-225 ps of the MD simulation; hence, ANTS can becalculated directly. The ratio ANTs/ANN, designated 4SD,should be equivalent, within perhaps a proportionality con-stant, to (F. Since the crystal and solution structures of C12are slightly different (15), we used the NMR solution struc-ture as a reference for the native state.The difference in the number of contacts for a particular

residue was calculated for each reference structure for boththe wild-type and mutant forms ofC12 to give ANN and ANTS.The mutants were constructed by merely swapping theresidue of interest, preserving the original side-chain orien-tation, and minimizing briefly (10 steps). As with SIF, a 4)value close to 1 indicates that the structure at the site ofmutation is almost the same as that in the native state,

1.5 -

-4Cis

.o4 j

1.0 i

0.5

0.o1

L27A 139VV38A 148A

I48VV66A

Mutations

L68A 176AV70A 148A/176V

FIG. 4. Comparison ofthe calculated X)D (o) and experimentallymeasured OF (e) values. Each Oh point represents an average of 10values obtained from 10 snapshots in the simulation time period220-225 ps. The error bars represent the standard deviation of theOhm value when 10 individual snapshots are used instead of a singleaverage structure.

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Proc. Nati. Acad. Sci. USA 91 (1994) 10433

Table 1. Calculated solvent-accessible surface area (A2) forselected residues in the crystal structure (Xtal) and the transitionstate (TS)

Residue Xtal TS ATS - AxwLeu-27 7.4 52.1 44.7Val-38 63.0 58.5 -4.5Ile-39 0.5 58.9 58.2Ile-48 30.9 82.5 51.6Val-66 0.0 33.7 33.7Ile-68 1.9 44.8 42.9Val-70 19.5 90.3 70.8lle-76 5.0 31.5 26.6

The residues correspond to those whose IP values have beendetermined. TS represents the period 220-225 ps of the unfoldingsimulation; ATS - Axtaw = the difference in the solvent-accessiblesurface area of the transition state and the crystal structure.

whereas a 4Dm value close to 0 means that the structure isconsiderably disrupted. A 4)MD value larger than 1 indicatesthat the residue is more buried in the transition state than itis in the native state.4X) values for the 10 mutations are shown in Fig. 4

together with the experimentally measured OF values. Giventhe approximate nature of the comparison, the overall agree-ment between 4Dm and OF is excellent. Val-38 is of specialinterest and resides on the edge of the hydrophobic core,pointing toward solvent. The OF value for the mutationVal-38 -- Ala (V38A) is -0.15 and was interpreted as being>1 and therefore more buried in the transition state than it isin the native state (6). The calculated OMD value is also >1,indicating that the number of contacts this residue makes inthe transition state is indeed higher than in the native state.The change in solvent-accessible surface area for each of themutated residues in the transition state relative to the crystalstructure is given in Table 1. The solvent exposure increasedupon unfolding for all residues except Val-38. Reproducingthe unexpected behavior of Val-38 lends support to thecontention that the simulation represents the actual unfoldingprocess.To further test the choice of the transition state and the

validity of comparing 4<i with OF, we calculated 4)1mvalues for various time periods, spanning the length of thesimulation. The best agreement was found for the period220-225 ps, with an average deviation from the experimentalOF value of 0.12 per data point.

Structure of the Transition State. Based on the abovediscussion, we conclude that the average structure between

(Crvstal Structure

220 and 225 ps is a fair representation of the transition state.Fig. 5 shows how this structure compares with the crystalstructure. Only the side chains in the hydrophobic core areshown explicitly. The residues whose 4mD values have beendetermined are colored according to their SDF values (yellow,(DF < 0.3; red, 0.3 ' OF < 0.6; purple, 4) > 1), whereas otherhydrophobic residues in the core are shown in green. Thehydrophobic core in the transition state is considerablydisrupted compared with the crystal structure. There is a gapbetween the hydrophobic residues in regions 1 and 2; this gapis dynamic but is not filled by water molecules and thereforerepresents a state in which previously favorable packinginteractions are disrupted and uncompensated. The red resi-dues (intermediate ODF values) retain some hydrophobic pack-ing interactions. The yellow residues, however, are exposed tosolvent and make few interactions with neighboring residues.The transition-state model is relatively compact; the radius

of gyration increased 10% from the crystal structure, com-pared with a 44% increase for the unfolded state. The Nterminus is almost fully solvated in the transition state. Thehelix is essentially intact but experiences some fraying andmakes few interactions with the rest of the structure. The(3-structure is more disrupted, however. The central portionofthe sheet formed by (strands 1 and 2 is partially intact, andthe top of the sheet (as depicted in Fig. 5) has interstranddistances that have increased 6 A relative to the crystalstructure. The interactions between (-strands 2 and 3 at its Cterminus are strengthened due to the breaking of interactionsbetween (-strand 3 and the N terminus. The Ca rmsd of thetransition-state structure with respect to the crystal (10) andsolution (15) structures is 3.4 and 3.8 A, respectively.While we have focused on hydrophobic core mutations,

our model of the transition state can also be evaluated in lightof the structural interpretations of the more recent SF valuesdetermined by Otzen et al. (7). Their studies have led to thefollowing conclusions regarding the structure ofthe transitionstate: the a-helix is the most structured portion ofthe protein,with OF values ranging from 0.3 to 0.7; the (3-P2 region isunstructured (with our secondary structure definitions, thiscorresponds to interactions between the N-terminal extendedstrand and (3), the (3~-P4 interaction is partially formed (thiscorresponds to 31-(P2 in our terminology), and the active-siteloop and turns are mostly unstructured. Our model of thetransition state is in very good agreement with these conclu-sions. We do indeed find that the a-helix is the most struc-tured portion of the protein. The (3structure is significantlydisrupted, although portions of (structure remain intact.

Transition State

FIG. 5. Comparison of the structure ofthe transition state with the crystal structure. Only the residues in the hydrophobic core are explicitlyshown. The residues whose OF values have been determined are colored according to their OF values (yellow, OF < 0.3; red, 0.3 '4OF < 0.6;purple, OF > 1); other hydrophobic residues are shown in green.

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10434 Biochemistry: Li and Daggett

The N terminus has become fully exposed to solvent and nolonger interacts with other segments of the protein.

Reproducibility of the Unfolding Pathway. In a real unfold-ing experiment, each protein molecule may unfold via its ownpathway. Though the majority of the pathways are probablysimilar, some of them may differ from others considerably.So far we have been discussing the transition state of un-folding of C12 based on only one trajectory. To test that themain features of this trajectory were reproducible and rep-resentative, we repeated the simulation, using a slightlydifferent preparation procedure. The detailed order of theunfolding events differs between the two simulations. How-ever, despite the many ways that a chain can unfold, C12appeared to pass through essentially the same transition statein the two simulations, as based on structural grounds andcomparisons of (DF and Dmi[ (data not presented). While theresults of only two simulations cannot disprove the notion ofparallel transition states, they do suggest that the conforma-tional ensemble of the transition state is limited.

Concluions. The major transition state for the unfolding ofC12 was identified on the basis of structural changes andconformational analysis ofthe structures during the unfoldingprocess. The hydrophobic packing and some ofthe hydrogenbonds stabilizing the core were considerably weakened in thetransition state. The last two hydrogen bonds between re-gions 1 and 2 played an important role in maintaining theupper portion ofthe hydrophobic core. The breaking ofthesetwo hydrogen bonds occurred concomitantly with opening ofthe core and initiated the progression from the transition stateto a transient intermediate. The secondary structure in thetransition state was partially intact. The overall structure ofthe transition state is closer to that of the native state than itis to the intermediate or the unfolded state. However, it isinteresting and somewhat unexpected that the transition stateoccurs so late in the simulation (-225 ps); in fact, manysimulations do not proceed past 200-250 ps.The structure of the protein in the vicinity of a particular

residue in the transition state was quantitatively character-ized by the ratio of the numberof contacts the residue makesin the transition state and the native state. These ratios agreewell with the experimentally measured OF values (6), sug-gesting that the simulation yields a reasonable description ofthe actual unfolding process.Our results indicate that the rate-determining step in tem-

perature-induced unfolding of CI2 involves the disruption ofthe hydrophobic core and some aspects of the secondarystructure. This phenomenon was first proposed by variousexperimentalists (28-30), and experimental studies on thefolding and unfolding of CI2 (6) provide further support forthis idea. It is likely that this is a general phenomenon for bothtemperature- and chemical-induced denaturation. Con-versely, the last event in protein refolding must be theconsolidation of these hydrophobic cores.

We thank Alan Fersht for stimulating discussions, for introducingus to CI2, and for providing us with the crystal structure and otherexperimental data prior to publication. We thank David Baker and

Keith Laidig for useful comments on the manuscript. We are gratefulto the Department of Medicinal Chemistry for providing start-upfunds.

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