Mechanical Unfolding of a Titin Ig Domain: Structureof Transition State Revealed by Combining AtomicForce Microscopy, Protein Engineering and MolecularDynamics Simulations

Robert B. Best1†, Susan B. Fowler1†, Jose L. Toca Herrera1

Annette Steward1, Emanuele Paci2 and Jane Clarke1*

1Department of ChemistryUniversity of Cambridge, MRCCentre for Protein EngineeringLensfield Road, Cambridge CB21EW, UK

2Department of BiochemistryUniversity of ZurichWinterthurerstrasse 190, 8057Zurich, Switzerland

Titin I27 shows a high resistance to unfolding when subject to externalforce. To investigate the molecular basis of this mechanical stability,protein engineering F-value analysis has been combined with atomicforce microscopy to investigate the structure of the barrier to forcedunfolding. The results indicate that the transition state for forced unfold-ing is significantly structured, since highly destabilising mutations in thecore do not affect the force required to unfold the protein. As has beenshown before, mechanical strength lies in the region of the A0 andG-strands but, contrary to previous suggestions, the results indicateclearly that side-chain interactions play a significant role in maintainingmechanical stability. Since F-values calculated from molecular dynamicssimulations are the same as those determined experimentally, we can,with confidence, use the molecular dynamics simulations to analyse thestructure of the transition state in detail, and are able to show loss of inter-actions between the A0 and G-strands with associated A–B and E–F loopsin the transition state. The key event is not a simple case of loss of hydro-gen bonding interactions between the A0 and G-strands alone. Compari-son with F-values from traditional folding studies shows differencesbetween the force and “no-force” transition states but, nevertheless, theregion important for kinetic stability is the same in both cases. Thisexplains the correspondence between hierarchy of kinetic stability(measured in stopped-flow denaturant studies) and mechanical strengthin these titin domains.

q 2003 Elsevier Ltd. All rights reserved

Keywords: protein folding; AFM; titin; immunoglobulin; muscle*Corresponding author

Introduction

Some proteins experience significant mechanicalstress in vivo. Experimental studies of the effect offorce on various proteins show that there is a sig-

nificant range of mechanical strength.1 –8 All-bdomains from proteins of muscle or the extra-cellular matrix resist significantly higher forcesthan all-a, or mixed a/b proteins even where theymay be expected to experience stress in vivo (suchas the cytoskeletal protein spectrin). However,there is not a simple relationship between structureand strength. Even small changes in sequence canalter the dynamic force spectrum of a protein.9,10

Dissecting the forced unfolding pathways of pro-teins in detail should advance our understandingof the molecular basis for mechanical strength inproteins. In experimental studies of protein(un)folding the emphasis is on high-resolutioncharacterisation of all the species on the foldingpathway. States that are stable, the native anddenatured states and kinetic intermediates, as well

0022-2836/$ - see front matter q 2003 Elsevier Ltd. All rights reserved

† R.B.B. and S.B.F. contributed equally to this work.Present address: J. L. Toca Herrera, Centre for

Ultrastructure Research, Universitat fur BodenkulturWien, Gregor Mendel Str. 33, A-1180 Vienna, Austria.

E-mail address of the corresponding author:jc162@cam.ac.uk

Abbreviations used: AFM, atomic force microscopy;MD, molecular dynamics; Ig, immunoglobulin; TI I27,the 27th Ig-like domain from the I band of humancardiac titin; ‡f and ‡o, the transition states investigatedby force and denaturant unfolding, respectively.

doi:10.1016/S0022-2836(03)00618-1 J. Mol. Biol. (2003) 330, 867–877

as the rate-determining transition state, areaccessible to experimental techniques. Moleculardynamics (MD) simulations should be able, inprinciple, to shed light on the transitions betweenthem. However, since simulations are generallyperformed at far-from experimental conditions,the benchmarking of simulation by experiment isessential. An attractive feature of forced unfoldingexperiments is that direct comparison betweensimulation and experiment is facilitated by therebeing a well-defined reaction co-ordinate, the dis-tance between the N and C termini of the protein.

The protein that has been investigated mostextensively using atomic force microscopy (AFM)is the 27th immunoglobulin (Ig) domain of the Iband of titin (TI I27) (Figure 1).9,11 – 20 It wassuggested initially that on application of force thisprotein unfolds by the same pathway as that fol-lowed on addition of denaturant.11 The evidencewas twofold: the unfolding rate constant, extra-polated to zero force, was the same as that deter-mined by extrapolation to 0 M denaturant; and inboth cases the transition state lay very close to thenative state; forced unfolding is associated with ashort unfolding distance, ,3 A, and in denatur-ant-induced unfolding the bT† is high, .0.9.

However, later analysis revealed that at moderateforces ($100 pN), below those required to unfoldthe protein completely (,200 pN), TI I27 unfoldsto form a meta-stable intermediate that is notobserved in the denaturant-induced unfolding.12

This intermediate is observed in simulations offorced unfolding that show that the A-strand isdetached from the body of the protein in theintermediate.16 Mutational studies confirmed thatthis intermediate is the “ground state” for forcedunfolding (Figure 2), so that the previous compari-son between the denaturant-induced and forcedunfolding pathways is invalid.17,18 We have pre-viously described a model intermediate in whichthe A-strand is deleted and shown, using a combi-nation of NMR and MD simulation that thismodel is folded and stable, and has essentially thesame structure as that of the wild-type protein.17

Here, we analyse the forced unfolding pathwayfurther. We have previously demonstrated thatprotein engineering F-value analysis can beapplied directly to the analysis of protein unfold-ing pathways in response to an external force.21

We show, by a combination of protein engineering,AFM and MD simulation, that the transition statefor forced unfolding is more native-like than thetransition state observed when unfolding isinitiated by addition of denaturants. We suggest,however, that the correlation between unfoldingrates of different titin Ig domains and their resist-ance to force is not coincidental: it is the sameregion of the protein that is responsible for kineticstability in both cases.

Results

All mutations destabilise TI I27 significantly

Mutations were chosen to probe differentregions of TI I27 (Figure 1). Each of these mutantshas been characterised in the isolated TI I27domain, both in terms of the effect on stabilityand the effect on the folding kinetics.22 All havebeen shown to destabilise the native state signifi-cantly (by 2.2–4.8 kcal mol21 (1 cal ¼ 4.184 J)).Since the AFM experiments measure the forcerequired to unfold the intermediate, I, the effect ofthe mutations on the stability of a model inter-mediate (DDGD-I), with the A-strand deleted (TII27-A)17 was determined (Table 1). For eachmutant, DDGD-I is similar to DDGD-N, reflecting theextremely native-like structure of I.17 The stability(DGD-N) of TI I27 in the polyprotein has beenshown to be the same as the stability of the isolateddomain.17

Most mutations do not significantly change theforce required to unfold the protein

The force required to unfold each mutant poly-protein was measured at a minimum of fourpulling speeds, and at least two separate data sets

Figure 1. TI I27 showing the position of the mutationsmade in this study.

†bT is defined as the ratio RTmkf/meq, where mkf andmeq are the dependence of folding rate and stability ondenaturant concentration. It is a measure of thetransition state position on a scale from 0 (close todenatured state) to 1 (close to the native state).40

868 Mechanical Unfolding of Titin

were collected at each pulling speed. Traces werecollected according to standard criteria23 (seeMaterials and Methods) and all peaks except forthe first and the last (protein detachment) wereused to determine unfolding forces. There was nodifference in the average number of peaks in atrace for wild-type and mutants. The mean of eachdata set was determined and the mean of thesemeans at each pulling speed is shown in Figure 3.Also shown on each graph in Figure 3 is the forcethat would be expected if all the loss in stabilityupon mutation were reflected in the unfoldingreaction; i.e. if the transition state energy were notaffected by mutation at all. It is clear that mostmutations have very little effect on the experimen-tally measured unfolding forces. Most mutants

have little effect on the dependence of the unfold-ing force on the pulling speed (most mutant datahave the same gradient as the wild-type data inFigure 3). V13A has significantly lower unfoldingforces than wild-type, but essentially the samegradient. V86A shows both a decrease in theunfolding forces, and a significant decrease in thegradient.

The data were analysed using a Monte Carloapproach, as described in Materials and Methods,to estimate an unfolding rate at zero force ðk0

uÞ andan unfolding distance (xu) that is related to thedistance along the unfolding trajectory betweenthe ground state (the unfolding intermediate inthe case of TI I27) and the transition state forunfolding (Figure 2 and Table 1).

F-Value analysis

A transition state F-value gives informationabout the structure of the transition state, and isdetermined by comparing the effect of mutationon the native state directly with the effect of themutation on the transition state for unfolding, andcan be determined from a comparison of unfoldingrates between wild-type and mutant:

F ¼ 1 2DDG‡-N

DDGD-N

� �ð1Þ

where DDGD-N is the change in free energy of theprotein on mutation, and:

DDG‡-N ¼ 2RT lnkwt

u

kmutu

� �ð2Þ

where kwtu and kmut

u are the unfolding rate constantsof wild-type and mutant proteins, respectively.

Figure 2. The forced unfolding pathway. Above,100 pN a stable unfolding intermediate is populated,the unfolding force is the force required to unfold thisintermediate, and k0

u is the unfolding rate constant ofthis intermediate, extrapolated to zero force. The unfold-ing distance xu reflects the distance from I to ‡.

Table 1. Effect of mutation on the stability and unfolding of TI I27

MutantPosition

in proteinDDGD-I

a

(kcal mol21) xu (A)

k0u

b

(mean xu)(s21)

ExperimentalmechanicalF-valuec

SimulationmechanicalF-valued

ExperimentaldenaturantF-valuee

WT 3.3 1.5 £ 1024

V13A A0-strand 2.37 ^ 0.08 3.5 6.5 £ 1024 0.6 ^ 0.1 0.7 ^ 0.1 20.04 ^ 0.01I23A B-strand 2.89 ^ 0.09 3.0 5.3 £ 1025 1.2 ^ 0.1 0.9 ^ 0.1 0.82 ^ 0.03L41A C0-strandf 2.67 ^ 0.08 3.4 2.1 £ 1024 0.9 ^ 0.1 0.8 ^ 0.2 0.40 ^ 0.02L58A E-strand 3.61 ^ 0.11 3.3 8.3 £ 1025 1.1 ^ 0.1 0.9 ^ 0.1 0.79 ^ 0.04L60A E-strand 5.27 ^ 0.17 3.1 1.7 £ 1024 1.0 ^ 0.1 0.9 ^ 0.1 0.67 ^ 0.03F73L F-strand 3.06 ^ 0.12 2.9 8.0 £ 1025 1.1 ^ 0.1 0.7 ^ 0.1 0.72 ^ 0.02V86A G-strand 4.78 ^ 0.18 5.5 6.6 £ 1026g g 0.4 ^ 0.1 0.01 ^ 0.01

a Taken from Fowler et al.17 and refers to mutations made with the TI I27-A mutant as a model for the intermediate.b Values of k0

u calculated using Monte Carlo simulations using mean xu, (3.2 A).c F-values calculated by direct comparison of unfolding force, F, at a pulling speed of 500 nm s21; equation (4).d Fraction of native contacts at the transition state in the simulations.e Denaturant F-values taken from Fowler et al.22

f The C-D loop is formally termed the C0-strand in the accepted assignment of the structure of this type of domain.g Since V86A has a significantly different xu, it has been shown to unfold by a mechanism different from that used by the wild-

type,10 so k0u at mean xu and an experimental F-value cannot be determined. The k0

u quoted is taken from the direct Monte Carlo simu-lation of the data, but this cannot be compared to the k0

u for all other mutants, since it does not reflect the same unfolding transition.10

An experimental F-value for this mutant has been estimated to be <0.6.10

Mechanical Unfolding of Titin 869

Measuring DDGD-I

In the formalism above, the ground state forunfolding is assumed to be the native state N. Thisis not the case in TI I27. Upon application of force,TI I27 unfolds via a structured, meta-stable inter-mediate: N ! I ! ‡ ! D (Figure 2). Importantly,this intermediate is the ground state for the AFMmeasurements, thus the forces measured are theforces required to unfold I, not to unfold N.17 Tocarry out a F-value analysis, therefore, it isimportant to know the effect of mutation on thisground state. For such a system:

F ¼ 1 2DDG‡-I

DDGD-I

� �ð3Þ

We have characterised a mutant of TI I27 with theA-strand deleted (TI I27-A) and shown it to be agood model for I.17 Thus, DDGD-I was evaluated bymeasuring the effect of the mutations on TI I27-A,using equilibrium denaturation (Table 1). Notethat the mutations have a very similar effect onthe stability of I and N†. It would probably not bepossible to use multimers of TI I27-A directly forAFM experiments because the lack of a linker seg-ment would cause the domains to contact eachother. While a generic “unstructured” linker couldbe added, there is always the possibility of formingthe same backbone hydrogen bonding interactionsas the native A-strand.

Measuring DDG‡-I

In principle, the force data can be used to deter-mine the unfolding rate along this pathway atzero force, k0

u; directly and this can be used indetermination of DDG‡-I using equation (2). How-ever, there is significant error associated with thedirect determination of k0

u from the dynamic forcespectrum, since values of k0

u are strongly coupledto the unfolding distance between the intermediateand transition state (xu): small errors in xu cancause large changes in fitted unfolding rates.21 Ithas been shown that more accurate F-values canbe determined for mechanical unfolding datawhere wild-type and mutants have the same xu

within error, by evaluating DDG‡-I by one of threemethods, each of which essentially uses or assumesa fixed mean xu, and the F-values determined byall three methods are the same, within error.21 Theassumption of a fixed mean xu is akin to assumingthe same transition state, which is in any case afundamental requirement of F-value analysis.

(i) xu is fixed to a mean value and the MonteCarlo simulations are performed with thisparameter fixed. (Mean xu determined for wild-type and all mutants except V86A ¼ 3.2 A).

(ii) The unfolding forces for wild-type andmutant proteins can be compared directly at agiven pulling speed (equation (4); Materials andMethods).

(iii) The pulling speeds are compared for wild-type and mutant proteins at a given force.

The experimental F-values, determined usingmethod (ii) are reported in Table 1. Note thatF-value analysis is valid only where the mutationdoes not change the mechanism for unfolding.This can be assumed to be true for most of themutants described here, where the mutation doesnot change the dependence of force on pullingspeed (i.e. they have the same xu, as wild-typewithin error). For the mutant V86A, however,there is evidence that the mutation changes theunfolding mechanism, since the pulling speeddependence is significantly different from that ofthe wild-type, a F-value cannot be determinedusing this analysis. This mutant has been discussedin detail elsewhere.10

Determining “limiting forces” where F 5 1,or F 5 0

The limiting conditions describing F ¼ 1 andF ¼ 0 can be determined as follows for eachmutant and are shown for each mutant in Figure 3.

Upper limit, F ¼1

Where the mutation is in a region of the proteinthat is as fully formed in ‡ as in I, then the barrierto unfolding, DG‡-I, will remain the same heightand the force required to unfold the mutant willbe the same as wild-type. Thus the wild-type datadefine the limiting case for forces expected forF ¼ 1. Where mutant unfolding forces fall close tothe wild-type forces we can say that F < 1.

Lower limit, F ¼0

Where the mutation is in a region that is com-pletely unfolded in ‡, the change in the heightof the free energy barrier is equal to the fullloss in free energy of I upon mutation (i.e.DDG‡-I ¼ DDGD-I). This F ¼ 0 limit will depend onhow destabilising the mutation is, and can bedetermined from the wild-type data and equation

† It should be noted that throughout we assume that TII27-A is a good model for I. If this assumption were notcorrect then the F-values determined would have anassociated error. It is possible that the effect of amutation on the ground state under force will bedifferent from that measured in solution, but it is notpossible to measure this. Although the denatured state isdifferent in the equilibrium and pulling experiments, it isreasonable to suppose that the effect of a conservativemutation as described here will be the same on the twodenatured states. It has been shown that this holds truefor the mutant V13A (see10). The same was not true of themutant V86A, which is discussed in detail elsewhere.10

However, since for the other mutants there is nodifference between DG‡-I for WT and mutants(DDG‡-I < 0) the absolute value of DDGD-I is actuallyunimportant, since DDG‡-I/DDGD-I is also <0.

870 Mechanical Unfolding of Titin

(4) (Materials and Methods). Where mutantunfolding forces fall close to this limit we can saythat F < 0.

To have confidence in the ability of the experi-mental data to distinguish these cases, the mutantswere chosen such that DDGD-I was .2 kcal mol21.Where the unfolding forces fall between these twolimits, the mutant has a partial F-value.

Identification of the transition state forunfolding in MD simulations

MD simulations of forced unfolding were per-formed at three different forces (300, 350 and400 pN) as described (see Materials and Methods).In all simulations, a meta-stable intermediate is

evident, at an N–C distance (rNC) of approximately53 A. At forces of 300 pN or lower, this inter-mediate does not unfold further, within the 3 nstimescale of the simulations. This state correspondsto the TI I27-A model intermediate characterisedextensively by simulation and experiment.17

At higher forces, the protein unfolds further (see,for example Figure 5 of Fowler et al.17). In somesimulations complete unfolding is preceded by aslow unfolding phase detected at rNC ,57.5 Acorresponding to a rearrangement of the A0 andG-strands with formation of non-native hydrogenbonds between them, before the structure is dis-rupted completely. The transition state for forcedunfolding (‡f) is assumed to be the last configur-ation before the protein starts stretching at high

Figure 3. Most mutations do not affect either the mean unfolding force or the pulling speed dependence of theunfolding force. (Wild-type data, filled circles and continuous line; mutant data, open circles and broken line). The fitof the data using a mean value of xu (3.2 A) is shown, except for V86A, where the dependence of unfolding force onthe pulling speed is significantly different. The dotted line represents the force expected if the F-value were 0, whereDDG‡-I ¼ DDGD-I.

Mechanical Unfolding of Titin 871

speed under force. Being an unstable state, it is notpossible to sample it extensively. However, sincewe performed multiple simulations, we were ableto collect a considerable number (263) of theseunstable configurations for analysis, all character-ised by an rNC between 56 A and 58 A. Averageproperties of these conformations show that theprotein remains quite native-like at the transitionstate for forced unfolding; the RMSD from nativestate is between 3 A and 5 A (3.9 A on average),while the radius of gyration (Rg) increases by 5%and the solvent-accessible surface increases by 8%.

Evaluating F-values in MD simulations

It has been shown that a F-value can be deter-mined from MD simulations of unfolding bymeasuring the fraction of native contacts remain-ing in a transition state structure.24 FMD is calcu-lated as the fraction of native contacts in thetransition state structures, compared to the fractionpresent in the unfolding intermediate. FMD valuescalculated for the same residues as those measuredexperimentally are reported in Table 1.

Discussion

Choice of mutants

In any F-value analysis, the choice of mutation iscritical.25 The mutation should not be likely tocause any significant perturbation of the nativestate structure, nor should it be expected to have asignificant effect on the stability of the denaturedstate. To this end, the mutation should be a con-servative deletion, removing specific interactions,not adding new ones and not changing the chemi-cal (polar/non-polar) nature of the side-chain. Themutations described here all meet these criteriaand were chosen to probe all regions of TI I27 with-out bias to regions of low or high F-values indenaturant. The effect of the mutation on thestability of the domain in the eight module proteinused for AFM experiments is the same as in thesingle module.17 All mutants were chosen to havea significant change in DGD-I, so that any change inforce upon mutation is likely to be outside theerror of the wild-type data.

Most mutations do not change xu andku

0 significantly

It is apparent that most of the mutants do notchange the dependence of the force on the pullingspeed significantly (the slope of Figure 3), with theexception of V86A, which changes this slope (andthus xu) significantly (Figure 3). Thus to determineaccurate F-values DDG‡-I was determined by directcomparison of wild-type and mutant data, for allmutants except V86A, as outlined in Materials andMethods.21 Most mutants have the same k0

u, withinerror, as wild-type (i.e. F < 1). This is qualitatively

apparent from direct comparison of the data withwild-type (Figure 3). None of the mutants has Fequal or close to zero. Only V13A has a signifi-cantly reduced F-value (F < 0.6). Interestingly,although I23A has F close to 1 (within error), themean force required to unfold this mutant is higherat all pulling speeds than that required for thewild-type. This mutant may really have F . 1. Iftrue, this would suggest that this mutationdestabilises the transition state more than the inter-mediate and might indicate that the structurearound residue 23 is more compact in ‡f than in I;that is, residue 23 may be stabilized in ‡f relativeto I due to the formation of additional (possiblynon-native) packing interactions.

It is not possible to calculate a F-value directlyfor V86A in the G-strand, since there is evidencethat the mechanism for unfolding is changing inthis mutant. It has been shown that this mutant is,in fact, unfolding directly from the native state;thus, the unfolding distance (xu) is significantlylonger than for the wild-type and the othermutants.10 However, the change in unfoldingmechanism indicates that mutation of this side-chain changes the unfolding activation energy, i.e.it is likely that this mutation has more effect onthe ground state for unfolding than on thetransition state. This side-chain is apparently lessstructured in ‡f than in I (i.e. F , 1). It has beenestimated that the F-value for this V86A mutant is<0.6.10

Structure of the transition state

The picture from the experimental F-values isclear: the transition state for forced unfolding (‡f)is very native-like, except in the A-strand andthe region encompassing the A0-strand and theC-terminal section of the G-strand. While thenumber of mutants is naturally limited by the tech-nique, experience from solution F-value analysisshows that F-values always follow a smoothpattern. Thus, it would be extremely unlikely forthe residues “in between” those probed to havevery different F-values. This is especially truewhen all the measured F-values are close to unity,as this would be difficult to reconcile with anyresidues in between (which must contact some ofthe residues which were probed) having lowF-values.

Residues 41, 58 and 60 probe the “upper”,C-terminal part of the core (Figure 1) and contactresidues in the B, C, D, E and F-strands and theC–D loop region. The F-values of 1 indicate thatmutations in this region affect the stability of ‡f tothe same extent as the intermediate (and,incidentally, the native state). The structure of thisregion is not perturbed by force, before thetransition state barrier is overcome.

Residues 23 and 73 probe the “lower”,N-terminal part of the core (Figure 1) and contactresidues in the B, C, E and F-strands, the F-Gloop and, interestingly, the early part of the

872 Mechanical Unfolding of Titin

G-strand. The high F-values indicate that thisregion of the core remains completely structuredin the transition state. They also indicate that theN-terminal portion of the G-strand remainsattached to the protein. V4A, in the A-strand,which is in contact with residues 23 and 73, isalready detached in the unfolding intermediate,so the F-values do not reflect loss of thesecontacts.

Residues 13 and 86 in the A0 and C-terminalregion of the G-strand, are in contact close to theC terminus of the protein. They are in contact alsowith residues in the A–B and E–F loops. The inter-mediate F-value of V13A indicates that this regionis partially, but not completely, unstructured in ‡f.There are insufficient data from these experimentalresults to indicate what the partial F-value ofV13A represents, a weakening of all contacts, or acomplete disruption of some part of the structure,with some contacts remaining intact. Since theseare single-molecule experiments, it is possible tosay definitively that the partial F-value does notresult from parallel pathways; since the distri-bution of forces in the unfolding experiments isthe same as for other mutants and wild-type, thereis no indication of a bimodal distribution of forcesthat would be expected from parallel pathways(data not shown).

Thus, in the transition state for unfolding, theA-strand is entirely detached from the rest of theprotein, while the A0 and G-strand have lost someof their interactions, but are not detached com-pletely. In particular, the G-strand is apparentlycompletely structured towards the N-terminal partof the strand. The experimental F-values can becompared directly with the F-values computedfrom the MD simulation. In all cases, the experi-mental and simulated F-values are the same,within error (Table 1). Thus, the simulations canbe used with confidence to compare the structureof the transition state with the native state in moredetail.

Transition state structures from a number ofsimulations were analysed. All these structuresshowed similar features. The RMSD from thewild-type protein (residues in the B-F strandsonly) varies between 1.7 A and 3.7 A, with mostvariation in the relatively mobile C–D loop. Thecontacts between strands B and E, E and D, and Cand F are maintained, as are all hydrogen bondsbetween these strands. The core structure isunaffected. In all structures, the A-strand isdetached completely from the protein, as is thecase in the unfolding intermediate. The main struc-tural difference between the intermediate (I) andnative (N) structures and the transition state is theposition of the G-strand. In N and I, there arehydrogen bonds between G and A0, and G packsbetween the A–B and E–F loops. In the transitionstate structures, the G-strand is pulled “up”, awayfrom the A0-strand (Figure 4). All hydrogen bondsbetween G and A0 are lost, although some side-chain contacts between A0 and G remain. The con-

tacts between the G-strand and the A–B and E–Floops are weakened significantly. However, theG-strand retains both hydrogen bonding and side-chain contacts with the F-strand. The A0-strandretains cross-sheet contacts with residues in theB-strand but loses some with both the A–B andE–F loops, which change structure following lossof the packing interactions with the G-strand.Interestingly, a mutant of TI I27 that has a Cys toSer mutation at position 63, in the E–F loop, thatcontacts both V13 and V86 has been shown torequire a lower unfolding force than wild-type TII27, with a significantly lower k0

u (2 £ 1023 s21) butsimilar xu (2.9 A).18 Although a quantitative com-parison of these data is not possible, as they referto a five-domain construct in which there are twokinds of domains, with two or three othermutations compared to the wild-type describedhere, the results are consistent with the partialbreaking of contacts between the E-F loop and theA0 and G-strands.

Our results are entirely consistent with theprevious suggestions that the A0 –G region acts asa “mechanical clamp”.12 – 14,18 However, in contrastto earlier suggestions, the mechanical strengthdoes not rest solely in the hydrogen bonding net-work between the A0 and G-strands.14 Side-chaininteractions between the strands and between theA0 and G-strands and other regions of the protein,in particular with the A–B and E–F loops alsoplay a critical role in determining mechanicalstrength.26

Comparison with the transition state fromdenaturant-induced unfolding

An extensive F-value analysis of TI I27 has beenreported, in the absence of applied force, usingdenaturant-induced unfolding/refolding.22 Thisprotein has one of the most structured transitionstates yet described (called ‡0) (Figure 5). Inessence, ‡0 is an expanded form of the native state,with no region fully structured; no mutant has aF-value of 1 but a number of residues have highF-values (0.7–0.8) with the nucleus centred aroundresidues 23, 34, 58 and 73 from the B, C, E andF-strands. Mutants in the A-strand (such as V4A)and the loops (such as L41A) have intermediateF-values, inferring that they are less well struc-tured than the core, but still ordered to someextent. Only the A0 and G-strands and associatedA-B and E-F loops are completely unstructured,and have F ¼ 0.

The transition state for forced unfolding (‡f) ismore structured than ‡0. All the core residuesreported for ‡f in this study have significantlylower F-values in ‡0 (Table 1). Most of the proteinis unchanged in structure by the applied force,which acts to detach the A-strand completely, andthen to disrupt the structure in the region of theA0 and G-strands, breaking contacts between thesestrands, and between these strands and the associ-ated loops. However, this region still maintains

Mechanical Unfolding of Titin 873

some structure in ‡f, unlike ‡0, where the F-valuesare close to zero (Table 1). The only region that ismore structured in ‡0 is the A-strand, which haspartial F-values (<0.4).

It is now clear that the unfolding pathways arenot the same;17,18 TI I27 unfolds via an intermediatethat is not populated on the denaturant-inducedunfolding pathway, and the transition states havedifferent structures. It is easy to understand whythis should be so, force acts on specific regions ofthe protein, namely the N and C termini, whereasdenaturant has a more global effect. However,there is evidence that there are common determi-nants of the unfolding kinetics in the different

pathways.11 In an investigation of the forcedunfolding of two titin domains, I27 and its neigh-bour I28, it was observed that I28, which is muchless stable than I27, unfolded at significantly higherforces than I27, and that this correlated with thesignificantly lower unfolding rate (at 0 M denatur-ant) of I28.27 Furthermore, the hierarchical unfold-ing of a number of titin domains corresponds wellto the unfolding hierarchy observed in denatur-ant-unfolding studies.28,29 Why are some modulessuch as TI I28 kinetically more stable than TI I27when we compare unfolding both by denaturantand by force?

Comparisons of the unfolding pathways of

Figure 4. Structures along the forced unfolding pathway. (a) These structures are snapshots from a typical MDunfolding trajectory. (b) Overlay of five representative transition state structures (in blue) with the structure of the“model” intermediate TI I27-A (in red).17

Figure 5. The same region of the protein determines the kinetic stability along both the forced and denaturant-induced unfolding pathways. (a) A summary of results on ‡f, described here. (b) A summary of F-value data takenfrom Fowler & Clarke for ‡0.22 The F-values are coloured from low (,0) in red to high (,0.7) in blue, with nucleusresidues shown in dark blue.

874 Mechanical Unfolding of Titin

Ig-like proteins have strongly suggested that theyall fold (and unfold) by similar mechanisms.22,30 – 32

Thus, it is reasonable to suppose that the same istrue of the closely related TI I27 and I28. Comparethe results from the protein engineering analysisof TI I27 by the two methods (Figure 5). Thethermodynamic stability depends largely on theprotein core, yet mutations in the core have littleeffect on the unfolding rates or unfolding forces,since it is the least perturbed region in either ‡0 or‡f. The A-strand has relatively little importance indetermining the kinetic stability. This is eitherbecause it is detached completely in the unfoldingintermediate (in forced unfolding) or remainsattached (in ‡0). The only region that is crucial indetermining the kinetic stability of the protein,whichever unfolding regime is under inspection,is the A0–G region towards the C terminus of theprotein. Thus, the relative stability of this region,which will depend on the specific interactions ofside-chains, will largely determine the kineticstability of a titin domain, whether unfolded byforce or by chemical denaturant. This explainswhy both AFM and denaturant studies observethe same unfolding hierarchy in TI I27 and TI I28,and suggests that denaturant-based studies will beuseful in understanding the assembly of titindomains. Despite the common determinants ofunfolding kinetics, the similarity between thechemical and denaturant-induced unfolding ratesmust now be interpreted as a coincidence: theproteins are unfolding from a different groundstate via a differently structured transition state, toa very different denatured state; only the height ofthe free energy barrier is similar.

Conclusion

Our aim has been to characterise all speciesalong the forced unfolding pathway, combiningAFM, protein engineering and MD simulation toget a detailed picture with atomic resolution.Here, we have shown that protein engineeringF-value analysis can be applied directly to AFMexperiments and that, where this analysis is inagreement with simulation, MD simulations canbe used to describe species along the pathway indetail (Figure 4). Simulations show that the nativestate lengthens slightly (N–C distance) upon appli-cation of force, but TI I27 retains essentially thesame structure with nearly all native-state contactsretained. Next, the A-strand detaches from thebody of the protein and the intermediate is formed.This intermediate has a structure very similar tothat of the native protein with only the residuesthat contact the A-strand directly losing native con-tacts. The transition state for forced unfolding isalso very native-like. The hydrogen bonds and anumber of side-chain contacts between the A0 andG-strands and the A–B and E–F loops are broken.Once the transition state is reached, unfolding

proceeds rapidly and the structure no longerresists applied force.

The unfolding pathway following addition offorce is demonstrably different from that followedupon addition of denaturant. However, the sameregion of the protein is largely responsible fordetermining the kinetic stability along both unfold-ing pathways, which suggests why the hierarchy ofunfolding rates of titin domains at 0 M denaturantis reflected in their resistance to force. Thus, whileAFM is essential to allow us to probe the mechan-ical unfolding pathway, “bulk solution” studiesmay give information on the modular assembly ofa mechanical protein, where the determinants ofkinetic stability are the same for both pathways.This is unlikely to be the case for all proteins.

Materials and Methods

Construction and purification of proteins

The method of construction, production and purifi-cation of multimodular repeats of wild-type TI I27 andmutants using a custom designed multiple cloningsystem has been described: in the final construct, thedomains are linked in tandem with a two-residue linker(corresponding to the restriction site) separating them.33

All “polyproteins” had two cysteine residues inserted atthe C terminus to facilitate attachment to the AFM stageand a His6 tag at the N terminus to facilitate purification.This tag was not removed in our constructs. All proteinswere stored in PBS (10 mM sodium phosphate (pH 7.4),137 mM NaCl, 2.7 mM KCl) at 4 8C in the presence of0.1% (w/v) sodium azide.

Stability of the mutants

Each mutation was made in a model of the foldingintermediate (with the A-strand deleted, TI I27-A) andthe effect of the mutation on the free energy of unfolding(DDGD-I) determined by equilibrium denaturation in PBSat 25 8C using guanidinium chloride as a denaturant asdescribed.11 We have shown that TI I27 has the samestability in the polyprotein as an isolated domain, sothat measurements of DDG in the isolated domain are areasonable approximation of the effect of the mutationin the polyprotein.7

AFM

The proteins were adsorbed onto a freshly evaporatedgold surface and excess protein was removed bythorough washing with PBS. All experiments werecarried out in PBS at ambient temperature (this wasmeasured to be in the range 20–25 8C for allexperiments). Force measurements were made with aMolecular Force Probe (Asylum Research, Santa Barbara,CA), as described.7 Briefly, the AFM cantilever tip wasused to pick up the N-terminal end of the protein bynon-specific adhesion, and then retracted from the sur-face at a constant speed, measuring the force exerted bythe polyprotein in the process. A range of pulling speedsbetween 100 nm s21 and 5000 nm s21 was used (in orderto obtain kinetic information; see below). Silicon nitridecantilevers (Thermomicroscopes, Sunnyvale CA) with a

Mechanical Unfolding of Titin 875

spring constant of ,0.03 N m21 were used and cali-brated using the method implemented in the MFP soft-ware. In this, the spring constant is found from theresponse of the cantilever to background “white”noise.34 The criteria for selecting force-extension traceshave been described.23 These are aimed at eliminatingunusual traces that might arise, for example, from twoproteins becoming attached to the cantilever. Typically, atrace from a single polyprotein gives rise to a number ofsudden rupture events (with a peak force at the point atwhich rupture occurs), one for the cooperative unfoldingof each module. The unfolding force is defined to be themaximum force at the peak immediately before eachunfolding event. All peaks from acceptable traces wereused to determine the unfolding force at a given pullingspeed, using the Igor software (Wavemetrics, LakeOswego, OR) of the MFP. At least 40 peaks were countedat any given pulling speed to determine a mean unfold-ing force and at least two (usually three) repeat experi-ments were carried out at each pulling speed. The meanof the means of experiments carried out on differentdays with different cantilevers is shown in Figure 3. Themotivation for this is to reduce the effect of systematicerrors in spring constant calibration.

Analysis of AFM data

The dependence of unfolding force on pulling speedwas used to determine the unfolding kinetics using asimple two-state model (representing unfolding from Ito D).35 The model describes the unfolding energy barrierby an extrapolated unfolding rate at zero force, k0

u, and adistance from the native state to the transition state, xu.The value of xu is (inversely) related to the slopes of theplots in Figure 3 and k0

u to the intercepts. A Monte Carlosimulation approach11,35 was used to solve for the par-ameters that best describe the data, taking into accountthe non-linear loading of the folded modules due tothe elasticity of the unfolded protein: this was modelledby a worm-like chain model with parametersobtained from fits to the actual force-extension traces(the persistence length, a measure of the backboneflexibility, was 0.35 nm).

F-Value analysis21

For mutants with the same dependence of the force onthe pulling speed as wild-type (all except V86A), F wascalculated directly at a pulling speed of 500 nm s21 (asjudged from individual fits of the force versus pullingspeed dependence):

DF�xuA ¼ 2RT lnkwt

u

kmutu

� �¼ DDG‡-I ð4Þ

where A is Avogadro’s number.We have shown that, since the forced unfolding

pathway involves an intermediate, a three-state analysisis formally more correct to determine absolute values ofkI!‡ and xI!‡.

10 However, since we are comparing wild-type and mutants, which have the same unfoldingmechanism, we have used a two-state analysis asdescribed,21 which is simpler and gives exactly the sameresults.

Molecular dynamics simulations

The simulations analysed here have been described indetail previously17 and the method used has been

described in full elsewhere.36 Briefly, to unfold the pro-tein, a constant force is applied parallel with the reactionco-ordinate, the distance between the N and C termini(rNC). Nine simulations were performed, three at each ofthree different forces (300, 350 and 400 pN). TheCHARMM program37 and potential38 were used withcontinuum representation of the solvent.39

To calculate F-values from the simulation, an all-side-chain definition is used, where F is the fraction of nativecontacts formed by that side-chain.24 This can be used toanalyse a single structure or an ensemble of structures.

Acknowledgements

We thank Professor Martin Karplus for helpfuldiscussion. This work was supported by theWellcome Trust and the MRC. J.C. is a WellcomeTrust Senior Research Fellow; R.B.B. is supportedby the Cambridge Commonwealth Trust.

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Edited by C. R. Matthews

(Received 18 February 2003; received in revised form 8 May 2003; accepted 8 May 2003)

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