Anna L. Mallam and Sophie E. Jackson- Folding Studies on a Knotted Protein

doi:10.1016/j.jmb.2004.12.055 J. Mol. Biol. (2005) 346, 1409–1421

Folding Studies on a Knotted Protein

Anna L. Mallam and Sophie E. Jackson*

Chemistry DepartmentLensfield Road, CambridgeCB2 1EW, UK

0022-2836/$ - see front matter q 2005 E

Abbreviations used: MTase, methAdoMet, S-adenosylmethionine; SAaccessible surface area; CD, circularE-mail address of the correspond

[email protected]

YibK is a 160 residue homodimeric protein belonging to the SPOUTclass ofmethyltransferases. Proteins in this group all display a unique topologicalfeature; the backbone polypeptide chain folds to form a deep trefoil knot.Such knotted structures were completely unpredicted, it being thoughtimpossible for a protein to fold efficiently in this way. However, they arebecoming more common and there are now a growing number of examplesin the Protein Data Bank. These intriguing knotted structures represent anew and significant challenge in the field of protein folding. Here, wepresent an initial characterisation of the folding of YibK, one of the smallestknotted proteins to be identified. This is the first detailed folding study on aknotted protein to be reported. We have established conditions underwhich the protein can be denatured reversibly in vitro using urea, therebyshowing that molecular chaperones are not required for the efficientfolding of this protein. A series of equilibrium unfolding experiments wereperformed over a 400-fold range of protein concentration. Both secondaryand tertiary structural probes show a single, protein concentration-dependent unfolding transition, and data are most consistent with athree-state equilibrium denaturation model involving a monomericintermediate. Thermodynamic parameters obtained from the fit of thedata to this model indicate that the intermediate is a stable species withappreciable secondary and tertiary structure; whether the topological knotremains in the intermediate state is still to be shown. Together, these resultsdemonstrate that, despite its complex knotted structure, YibK is able to foldefficiently and behaves remarkably similarly to other dimeric proteinsunder equilibrium conditions.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: protein folding; fluorescence; circular dichroism; dimer thermo-dynamics; topological knot

Introduction

The past two decades have seen the foldingpathways of many proteins characterised in greatdetail, using both experimental and computationalapproaches. These studies have been biasedtowards small, monomeric proteins, lacking indisulphide bridges, cofactors and cis proline resi-dues because they represent simple folding sys-tems. As a result, many models for the differentmechanisms by which small proteins fold havebeen proposed and tested.1,2 A newly identifiedclass of proteins, however, challenges currentfolding theories. These proteins contain trefoil

lsevier Ltd. All rights reserve

yltransferase;SA, solvent-dichroism.ing author:

knots formed by the backbone polypeptide chain,a rather unexpected structural feature.3–10

Knots in proteins are fairly common if the entirecovalent network is considered; disulphide cross-links or metal-atom bridges often create “covalentknots”, which can form either during or afterfolding.11,12 The path of the backbone polypeptidechain alone defines “topological knots”; untilrelatively recently, the only examples of theseinvolved the tucking of a few (ten at most) aminoacid residues through a wide loop in the poly-peptide chain.13,14 These knots are termed shallowtrefoil knots, but remain unconvincing, as they candisappear if the structure is viewed from a differentangle.15,16 A few years ago, a mathematical algor-ithm was developed that allowed the easy identi-fication of knots in proteins.16 The algorithmsmoothes the polypeptide chain repeatedly whilekeeping the termini fixed; if a straight line isobtained the protein is not knotted. If a knot is

d.

1410 Folding Studies on a Knotted Protein

found, the location of the knotted core can bepinpointed; “deep” knots have more than 20 aminoacid residues on either side of the core.17 Thealgorithm led to the identification of an impressivedeep figure-of-eight knot in acetohydroxy acidisomeroreductase (AIR) with over 200 amino acidresidues on one side and 70 on the other. Thus,speculation began on how such a deep andcomplicated knot can form during folding.16,17

A deep topological trefoil knot was first identifiedin the catalytic domain of the hypothetical RNA2 0-O-ribose methyltransferase from Thermus thermo-philus (RrmA), a member of the SpoU family.8 Todate, 12 further protein structures containing deeptrefoil knots have been deposited in the ProteinData Bank, all belonging to the SpoU, TrmD orYbeA families.3–7,9,10 These knotted proteins sharesome common features: structural similarities toother family members as well as functional assign-ment make it likely that all are methyltransferases(MTases), a type of enzyme involved in the transferof the methyl group of S-adenosylmethionine(AdoMet) to carbon, nitrogen or oxygen atoms ofDNA, RNA, proteins and other small molecules.18

All form dimers in solution, with the knot forming alarge part of the dimer interface it is also thought tobe the location of the AdoMet binding site.3–10 Inrecognition of the above similarities betweenMTases with knotted structures, a new class offold has been defined known as the SPOUT (SpoU-TrmD) class MTase fold.3 Features of MTasesbelonging to the SPOUT class include the presenceof a deep trefoil knot that provides the AdoMet co-factor binding site, and dimer formation. Interest-ingly, SpoU, TrmD and YbeA families had beenunified into the SPOUT class on the basis of theirevolutionary origin, and it was predicted that theymight share a similar fold.19

Proteins adopting the SPOUTclass fold representa novel folding problem. It is not obvious how asubstantial length of polypeptide chain manages tothread itself through a loop during the process ofprotein folding. One proposal is that such proteinsfold from a knotted unfolded state,15 althoughtheoretical studies suggest that the chance of adisordered polypeptide chain becoming entangledis small for proteins the size of those consideredhere.20 To understand further the mechanismsinvolved in protein knot formation, we haveundertaken a folding study on YibK, a member ofthe SPOUT class of MTases.6

YibK of Haemophilus influenzae is a 160 amino acidresidue protein sharing significant sequence hom-ology with the SpoU family of MTases. Crystallo-graphy studies indicate that it adopts a structureconsistent with the SPOUT class MTase fold(Figure 1).6 Specifically, a deep trefoil knot is formedat the C terminus by the threading of the last 40residues (residues 121–160) through a knotting loopof approximately 39 residues (residues 81–120)(Figure 1(a)). Like other SPOUT class members,YibK exists as a dimer in solution. The dimerinterface is located at the C-terminal a helix (a5),

and consists of two closely packed monomersarranged in a parallel fashion (Figure 1(b)). YibKis one of the smallest SPOUT MTases identified sofar, and therefore an ideal candidate for a foldingstudy.

Here, we present the first characterisation of thefolding of a protein containing a deep trefoil knot.We have examined the folding of YibK underequilibrium conditions, using probes of bothsecondary and tertiary structure. Conditions arefound under which chemical denaturation by ureais fully reversible, and the equilibrium unfoldingtransition is monitored over a wide range of proteinconcentrations. The data obtained are used to assignan equilibrium-denaturation model in which theYibK dimer unfolds via a monomeric intermediateretaining significant structure.

Results

The homodimeric protein YibK was chosen forstudy as it contains a C-terminal deep trefoil knotin its backbone architecture. Understanding themechanisms involved in the formation of such aknot represents a significant challenge, as in thenative structure a region of polypeptide chain ofabout 40 residues has been threaded through a loop(Figure 1). Current general theories of proteinfolding offer little explanation as to how this typeof structure may fold. Here, we present an initialcharacterisation of the folding of YibK; in particular,a detailed analysis of its unfolding equilibrium.

Determination of the oligomeric state of YibK

The oligomeric state of YibK was examined usinganalytical size-exclusion chromatography (SEC) atvarious concentrations of protein between 0.25 mMand 100 mM. Data throughout this concentrationrange are consistent with a dimeric form of YibK(Figure 2), and no monomer peak is seen. YibKelutes at a volume of 10.6 ml, which corresponds toa KAV of 0.20 and a molecular mass of 36.7 kDa (seethe calibration curve shown as inset (b) in Figure 2).This is close to the calculated molecular mass of36.803 kDa for a YibK dimer.

Unfolding of YibK monitored by intrinsicfluorescence and far-UV circular dichroism

Intrinsic protein fluorescence provides a con-venient way to monitor loss of tertiary structureduring unfolding, as each YibK monomer containstwo tryptophan residues and five tyrosine residues.Addition of urea to a final concentration of 8 M wasfound to result in an unfolding event, indicated by alarge decrease in fluorescence with a concomitantred shift in the lmax from 328 nm to 347 nm (seeinset (a), Figure 3). The maximum fluorescencechange occurred at 319 nm, and this wavelengthwas used to monitor unfolding in the equilibriumexperiments. To ensure intrinsic fluorescence

Figure 1. Structure of YibK fromHaemophilus influenzae.(a) A ribbon diagram of a monomer subunit (PDB code

Figure 2. Determination of the oligomeric state of YibKby size-exclusion chromatography. Main: Elution profileof YibK at 100 mM (red) and 0.25 mM (blue) protein. Insets:(a) Elution profile of (1) blue dextran 200 (2000 kDa), (2)bovine serum albumin (66.3 kDa), (3) carbonic anhydrase(28.8 kDa) and (4) cytochrome c (12.4 kDa). (b) Calibrationcurve. Conditions: room temperature in 50 mM Tris–HCl(pH 7.5), 200 mM KCl, 10% (v/v) glycerol, 1 mM DTT.

Folding Studies on a Knotted Protein 1411

monitors a global not a local unfolding event, far-UV circular dichroism (far-UV CD) was used as aprobe of secondary structure. The helical signalobserved for native YibK was completely lost onunfolding in 8 M urea, and there is no evidence forsignificant residual structure under the conditionsused (see Figure 3, inset (b)).

Test of reversibility

Both intrinsic protein fluorescence and far-UVCD were used to investigate the reversibility of theYibK unfolding reaction. Unfolded and sub-sequently refolded YibK retains approximately100% of its native fluorescence and far-UV CDsignal (see Figure 3, insets (a) and (b)). Furthermore,refolding fluorescence equilibrium titrations (per-formed by diluting unfolded protein into buffer)superimpose onto unfolding equilibrium titrationsat the same concentration of YibK (Figure 3),confirming that the unfolding of YibK is fullyreversible under the buffer conditions used.

1MXI), showing the deep trefoil knot at the C terminus.The structure is coloured according to definitions givenby Nureki et al.:8 the knotting loop is highlighted in red(residues 81–120), while the knotted chain appears darkblue (residues 121–160). (b) Structure of dimeric YibK,coloured as in (a). YibK dimerises in a parallel fashion,with the knot forming a substantial part of the dimerisa-tion interface. The ribbon diagrams were generated usingRibbons.47 (c) A topological diagram of YibK. Structuralelements that are common to the SPOUT class of MTasesare outlined in red.

Figure 3. Reversibility of the YibK unfolding reaction.Main: YibK fluorescence denaturation (dark blue), fluor-escence renaturation (light blue), and far-UV CD dena-turation (red) profiles at 1 mM protein. Far-UV CD datapoints were not recorded at concentrations of urea below2 M, as there was no change in baseline. Insets: (a)fluorescence and (b) far-UV CD emission spectra of native(black line), denatured (blue line) and renatured from 8 Murea (red circles) YibK at 5 mM protein. Conditions: 25 8Cin 50 mM Tris–HCl (pH 7.5), 200 mM KCl, 10% (v/v)glycerol, 1 mM DTT.

Figure 4. YibK equilibrium denaturation profiles for100 mM (red), 50 mM (yellow), 10 mM (green), 5 mM (lightblue), 2.5 mM (dark blue), 1 mM (purple), 0.5 mM (lilac)and 0.25 mM (dark pink) protein, as measured by (a)fluorescence emission at 319 nm and (b) far-UV CD signalat 225 nm. The data have been normalised for ease ofcomparison, and continuous lines represent the fit to atwo-state dimer denaturation model (equation (7)). Theconditions are as described for Figure 3.

1412 Folding Studies on a Knotted Protein

Equilibrium unfolding experiments: proteinconcentration dependence

YibK equilibrium denaturation curves weremeasured using intrinsic fluorescence and far-UVCD over a 400-fold and a 200-fold range in proteinconcentration, respectively. The results of theseexperiments are shown in Figure 4 (the data havebeen normalised for ease of comparison). Bothsecondary and tertiary structural probes show asingle unfolding transition over the range of proteinconcentrations studied. As expected for a dimer,the denaturation curves are protein concentration-dependent; an increase in the midpoint of theunfolding transition is seen with increasing proteinconcentration. This is a unique characteristic ofoligomeric protein systems, and is due to thecoupled denaturation and dissociation reactionsthat occur during unfolding.21 Loss of secondaryand tertiary structure appears concomitant, asfluorescence and far-UV CD curves superimpose(Figure 3). The concentration-dependence of theYibK unfolding curves can be used to assign thecorrect dimer denaturation model.

Data fitting

Two-state dimer model

Equilibrium unfolding data were first fit to a two-state dimer denaturation model in which nativedimer, N2, is in equilibrium with denatured mono-mer, D (Scheme 1). Fluorescence and far-UV CDdatasets were treated separately, and curves foreach concentration of protein were fit individually

to equation (7). Figure 4 shows the results of thesefits, with the associated thermodynamic parameterscalculated shown in Table 1. While the fits appeargood, there are several indicators that the two-statedimer model is not describing the YibK equilibriumunfolding data adequately. First, Table 1 shows thatfor the fluorescence and far-UV CD data, DGN242D

H2Oincreases with concentration of protein (Pt,measured in terms of monomer). DGN242D

H2Ois the

free energy difference between 1 mol of dimer and2 mol of unfolded monomer in the absence ofdenaturant. If the correct dimer denaturationmodel is being used, DGN242D

H2Oshould remain

constant at all concentrations of protein exam-ined.22,23 Second, the slope of the unfoldingtransition ðmN242DÞ shows an overall increase withprotein concentration, suggesting that at higherconcentrations of YibK unfolding becomes more co-operative. When examined using Student’s t-test,the difference in mN242D of two datasets closest inprotein concentration is not statistically significant.However, themN242D valuesof the lowest andhighestprotein concentration datasets are considered to bevery statistically different, and Student’s t-test givesthe probability of this difference having occurred by

Table 1. Thermodynamic parameters for the fit of YibK equilibrium unfolding data to a two-state dimer denaturationmodel

Fluorescence Far-UV CD

Pt (mM)[D]50%(M urea)

mN242D

(kcal molK1 MK1)

DGN242DH2O

(kcal molK1)[D]50%(M urea)

mN242D

(kcal molK1 MK1)

DGN242DH2O

(kcal molK1)

0.25 4.68G0.01 3.81G0.09 26.8G0.6 – – –0.5 4.79G0.01 4.19G0.07 28.7G0.5 4.82G0.02 3.90G0.25 27.4G1.71 4.88G0.01 4.12G0.11 28.3G0.8 4.86G0.01 4.04G0.25 27.8G1.72.5 4.97G0.01 4.28G0.07 28.9G0.5 5.01G0.01 4.10G0.20 28.2G1.45 5.06G0.01 4.26G0.10 28.8G0.7 5.04G0.01 4.24G0.15 28.6G1.010 5.13G0.01 4.39G0.08 29.3G0.5 5.11G0.01 4.46G0.18 29.6G1.250 5.34G0.01 4.61G0.06 30.5G0.4 5.29G0.01 4.40G0.12 29.1G0.8100 5.46G0.01 4.66G0.05 30.9G0.3 5.40G0.01 4.52G0.17 29.9G1.1

Fluorescence was monitored at 319 nm and far-UV CD at 225 nm. The parameters are quoted with their standard errors. Urea-

denaturation profiles were fitted singularly to equation (7) using Prism, version 4, and DGN242DH2O

was calculated using equation (4).

Folding Studies on a Knotted Protein 1413

chance to be less than 1%. This observation is notexpected for a simple two-state denaturation mech-anism, and indicates that a more complex scheme isnecessary to describe the system fully.24,25 In particu-lar, the variation in m-value with protein concen-tration implies that an equilibrium intermediate stateis populated under equilibrium conditions.26,27

Figure 5. Global fit of (a) fluorescence and (b) far-UVCD YibK equilibrium denaturation data to a three-statedimer model with a monomeric intermediate (equation(16)). Protein concentrations are indicated by colour as inFigure 4, and the continuous lines represent the fit to themodel.

Three-state dimer models

Three-state dimer models involving either adimeric (Scheme 2) or a monomeric (Scheme 3)intermediate were applied to the YibK equilibriumunfolding data. For both, the complexity of thesystem results in a large number of variableparameters (see equations (12) and (16)), and it isnot possible to fit an individual dataset with anydegree of accuracy. However, the models can beapplied globally with thermodynamic parametersshared throughout all datasets. Denaturation pro-files for all concentrations of protein were fitglobally to both models in this manner; fluorescenceand far-UV CD datasets were considered separ-ately. The best fit to the data was achieved using athree-state dimer denaturation model with a mono-meric intermediate, and the results of this fit alongwith the thermodynamic parameters obtained areshown in Figure 5 and Table 2, respectively.DGN242D

H2O, the free energy change corresponding to

complete unfolding of dimer to two unfoldedmonomers in the absence of denaturant for astandard state of 1 mol of dimer, is calculated tobe 31.9 kcal molK1 and 33.7 kcal molK1, usingfluorescence and far-UV CD data sets, respectively.The free energy difference between dimer andmono-meric intermediate, DGN242I

H2O, is 18.9 kcal molK1 and

19.1 kcal molK1 for fluorescence and far-UV CDdatasets, respectively. The monomeric intermediatehas a stability of 6.5 kcal molK1 and 7.3 kcal molK1

relative to denatured monomer, for fluorescence andfar-UV CD datasets, respectively. The equilibriumunfolding data do not agree well with a three-statedimer model involving a dimeric intermediate, andthe thermodynamic parameters could not be deter-mined with any precision (data not shown).

Relating m-values and the change in solvent-accessible surface area

The change in solvent-accessible surface area(DSASA) upon unfolding is strongly correlated withthe m-value of a protein.28 The crystal structure ofYibK was used to calculate the SASA of both anative dimer and a fully folded monomeric subunit,allowing the DSASA upon dissociation to bedetermined (Table 3). The m-value associated withdissociation from native dimer to fully foldedmonomers (N242N) is 0.4 kcal molK1 MK1,

Table 2. Thermodynamic parameters for the fit of YibK equilibrium unfolding data to a three-state dimer denaturationmodel with a monomeric intermediate

YI

DGN242IH2O

(kcal molK1)mN242I (kcalmolK1 MK1)

DGI4DH2O

(kcal molK1)mI4D (kcalmolK1 MK1)

DGN242DH2O

(kcal molK1)amN242D (kcalmolK1 MK1)b

Fluorescence 0.61G0.04 18.9G0.4 1.80G0.09 6.5G0.2 1.53G0.05 31.9G1.2 4.86G0.29Far-UV CD 0.39G0.05 19.1G0.1 2.03G0.01 7.3G0.1 1.60G0.02 33.7G0.5 5.23G0.07

Fluorescence and far-UV CD datasets were analysed separately. Global analysis was performedwith the non-linear, least-squares fittingprogram Prism, version 4. Errors quoted are the standard errors calculated by the fitting program.

a DGN242DH2O

ZDGN242IH2O

C2DGI4DH2O

.b mN242DZmN242IC2mI4D.

1414 Folding Studies on a Knotted Protein

estimated using equation (17). EvaluatingDSASA forcomplete unfolding involves an estimate of SASA ofeach residue in the denatured state. Two alternativemethods are used here: one based on tripeptidemodel compound studies,29 the other on a model oftheunfoldedpolypeptide chain generated fromhard-sphere simulations.30,31 The values calculated forYibKare shown inTable 3, alongwith the correspond-ing DSASA for unfolding and the associatedm-valueestimated using equation (17). The m-value corre-sponding to complete unfolding of dimeric YibK intotwo denatured monomers is estimated to be 4.4–5.5 kcal molK1 MK1, depending on the method usedto model the denatured state SASA. This is in goodagreement with the mN242D values shown in Table 2of 4.86 kcal molK1 MK1and 5.23 kcal molK1 MK1

using fluorescence and far-UV CD data, respectively.

Discussion

YibK is a member of the SPOUT class ofmethyltransferases, a group of homodimeric

Table 3. Changes in SASA for YibK upon dimer dissociation

A. Dissociation

Native dimer (N2) SASAa (A2)Fully folded monomer sub-unit (N) SASAa (A2)

14,461 8806

B. Unfolding

SASA forfolded pro-teina (A2)

SASA estimate for unfoldedprotein (A2) D

Tripeptidemethode

Upperboundarymethodf

Tm

Native dimer(N2)

14,461 53,814 45,740 3

Fully foldedmonomer (N)

8806 26,907 22,870 1

a Calculated using the web-based program GETAREA, version 1.1b DSASA upon dissociationZ2(SASA of monomer subunit)–(SAS

dissociation assumes no unfolding of the monomer subunits.c Estimated using equation (17), a correlation equation given by Md DSASA for unfoldingZ(SASA unfolded protein)–(SASA foldede Calculated using values from tripeptide studies.29f Calculated using data given by Creamer et al.31

proteins that contain deep trefoil knots in theirbackbone topology. The knot structure forms anintegral part of the dimer interface, and consists of asegment of polypeptide chain, approximately40 residues in length, threaded through a loop(Figure 1). YibK is one of the smallest SPOUTMTases identified so far, making it an idealcandidate for studies aimed at understanding howthis class of knotted protein folds. Here, we reportthe results of experiments on the equilibriumdenaturation of YibK, and propose a model for theequilibrium unfolding reaction.

Dimeric YibK

YibK and other SPOUT MTases are known to bedimers in the crystalline form.3–10 Size-exclusionchromatography (SEC) was used to confirm theoligomeric state of YibK over the range of proteinconcentrations used in these experiments. All datawere consistent with a dimeric structure, confirm-ing that YibK is a stable dimer down to sub-micromolar concentrations (Figure 2). From these

and unfolding, along with estimated m-values

DSASA for dissociationN242Nb (A2)

m-value estimate fordissociation N242Nc

(kcal molK1 MK1)

3151 0.4G0.1

SASA for unfoldingd (A2)m-value estimate for unfol-dingc (kcal molK1 MK1)

ripeptideethod

Upperboundarymethod

Tripeptidemethod

Upperboundarymethod

9,353 31,279 5.5G0.4 4.4G0.3

8,101 14,064 2.5G0.2 2.0G0.1

.46

A of dimer). The value calculated for the DSASA upon dimer

yers et al.28 The errors were estimated also using this equation.protein).

Folding Studies on a Knotted Protein 1415

data, an upper limit of 1 nM can be estimated for Kd,the equilibrium dissociation constant for monomer–dimer interconversion (N242N), and the absenceof monomers even at low concentrations of proteinindicates that dimer association is strong under theconditions used.

Equilibrium unfolding of YibK occurs via amonomeric intermediate

The equilibrium denaturation of YibK wasstudied using both intrinsic protein fluorescenceand far-UV CD over a large range of proteinconcentrations. Within this range, the unfoldingtransition was shown to be fully reversible, mono-phasic and protein concentration-dependent. Theprotein concentration-dependence of equilibriumunfolding curves in dimer systems is expected, andcan be rationalised from the way the equilibriumconstant KU is defined: KUZ[D]2/[N2]. At a givenconcentration of denaturant, KU and DG remain thesame for all concentrations of protein; only thefraction of each equilibrium species presentchanges with Pt. In a dimeric two-state system,[D]50% is defined as the concentration of denaturantwhere the fraction of unfolded monomers is equalto the fraction of monomers present as dimers. Thisis also where KUZPt (see the section on dataanalysis for more details); therefore, the concen-tration of denaturant where [D]50% occurs willdepend on Pt, and a change in [D]50% with totalprotein concentration is expected. DGN242D

H2Oremains

constant with changing Pt and [D]50% (equation (4)).The m-value of a protein is related to DSASA.26,32 Itis, therefore, a constant for each protein, and shouldnot be affected by protein concentration. Fluor-escence and far-UV CD YibK unfolding data weretreated separately and fit to both a two-state modeland three-state models with either a dimeric or amonomeric intermediate. If the denaturation mech-anism were two-state, the mN242D and DGN242D

H2Ovalues determined should remain the same for allconcentrations of protein examined.22,23 However,when YibK unfolding data were analysed accordingto a two-state denaturation model, an increase inmN242D and DGN242D

H2Ovalues with increasing protein

concentration was observed (Table 1). Thus, a two-state model does not describe the experimentalresults adequately. Global fitting of the YibKdenaturation curves to both three-state modelsshowed that a denaturation mechanism involvinga monomeric intermediate best described the data(Figure 5 and Table 2). A three-state model with adimeric intermediate was ruled out, as there werevery large errors associated with the thermodyn-amic parameters obtained from the global fit of thedata to this model (data not shown).

The feasibility of a particular three-state modelcan be thought about intuitively by considering theslope of the unfolding curves (i.e. the apparent m-value calculated in the two-state analysis, shown inTable 1). In a dimer system, the presence of anintermediate is obvious if the equilibrium unfolding

transition is biphasic33–37 and each transition can beconsidered separately. If the transition appearsmonophasic, however, an intermediate cannot beobserved directly, but canmanifest itself in a proteinconcentration-dependent slope change.24 Withmany monomeric proteins a decrease in apparentm-value upon mutation is due to the population ofan intermediate state.27,38 This decrease is depen-dent on the spectral properties of the intermediateand its concentration; a significant population of theintermediate will result in an underestimation ofthe m-value for an N4D process.26,27 With dimericproteins, the concentration of any intermediatedepends on the values of K1 and K2, and the totalconcentration of protein. At a particular concen-tration of denaturant, K1 and K2 remain constantand do not change with Pt. They are defined,respectively, in terms of the concentrations ofspecies present as:

K1 Z½I2�

½N2�and K2 Z

½D2�

½I2�

for a three-state model with a dimeric intermediate,and as:

K1 Z½I�2

½N2�and K2 Z

½D�

½I�

for a three-state model with a monomeric inter-mediate. If a dimeric intermediate is involved, theratio of [I2] to [N2] remains the same for all proteinconcentrations. However, the definition of K2 meansthat as [I2] increases with the total protein concen-tration, [D] will increase only in proportion to thesquare-root of [I2]. Overall, this will lead to anincrease in the fraction of I2 present. Therefore, in adimer three-state system with a dimeric intermedi-ate, the slope of the transition would be expected todecrease as the total protein concentrationincreases, due to an increased population of theintermediate state. Table 1 shows that this is not thecase for YibK, making a dimeric intermediateunlikely. The same argument can be applied to athree-state model involving a monomeric inter-mediate. In this case, for a particular value of K2, theratio of [I] to [D] will remain constant at all Pt.Conversely, the definition of K1 means that as Pt

increases, [I] increases with only the square-root of[N2]. This will lead to an overall decrease in thefraction of I present with increasing proteinconcentration. Reflecting this, the slope of theequilibrium unfolding transition in a dimericsystem with a monomeric intermediate is expectedto increase as Pt increases. Table 1 shows that this isindeed what happens with YibK, and, as expected,the best fit of the data is to a three-state dimerdenaturation model involving a monomeric inter-mediate (Figure 5 and Table 2).A recent study by Gunasekaran and co-workers

revealed a distinct correlation between dimerscomposed of stable monomeric subunits and theratio of the dimer interface area to the total surface

1416 Folding Studies on a Knotted Protein

area.39 This ratio for YibK is comparable to that ofcomplexes consisting of stable monomers.

The thermodynamic parameters obtained fromthe fit to a three-state dimer denaturation modelwith a monomeric intermediate gave the freeenergy of unfolding from native dimer todenatured monomers, DGN242D

H2O, as 32–34 kcal molK1

(Table 2). This is comparable to values reported forother dimer systems.21 Here, however, it is import-ant to bear in mind that experiments were done in abuffer containing glycerol, an additive known tostabilise the native states of proteins.40 This wasnecessary to maintain 100% protein solubilityduring experiments at higher concentrations ofYibK, which were required for an accurate globalanalysis. Experiments carried out in the absenceof glycerol suggest that its addition stabilises YibKby some 5 kcal molK1 (data not shown). Theassociated m-value for complete unfolding, mN242D,was calculated to be 4.9–5.2 kcal molK1 MK1,in good agreement with the m-value of 4.4–5.5 kcal molK1 MK1 estimated from the DSASA ofunfolding (Table 3), therefore giving confidence inthe parameters obtained from this model.

Figure 6.Modelling the fraction of native (N2, dark bluediamonds), monomeric intermediate (I, red circles) anddenatured (D, light blue triangles) species present as afunction of the concentration of urea for (a) 100 mM YibKand (b) 0.25 mM YibK. Fractions are calculated using thethermodynamic parameters obtained from the global fitof YibK fluorescence unfolding data to a three-statedenaturation model involving a monomeric intermediate(equation (16)).

The monomeric intermediate

The thermodynamic parameters shown in Table 2provide information about the monomeric inter-mediate state. The free energy of the intermediaterelative to the denatured monomer, DGI4D

H2O, is

6.5–7.3 kcal molK1, and within the range found formany small globular proteins.41 This stabilitysuggests that the intermediate state has significantstructure. The experimentally determined m-values,mN242I andmI4D (Table 2), can be comparedto m-values estimated from the SASA changesinvolved in dissociation and unfolding (Table 3).The m-value predicted for dissociation of aYibK dimer into two native-like monomers is0.4 kcal molK1 MK1. This is substantially less thanthe experimental mN242I value measured of 1.8–2.0 kcal molK1 MK1, and indicates that each mono-mer has partially unfolded on dissociation to formthe intermediate state. Likewise, the m-value pre-dicted for the unfolding of a native-like monomer is2.0–2.5 kcal molK1 MK1 (Table 3), which is higherthan the experimental m-value for the I4Dtransition of 1.5–1.6 kcal molK1 MK1. Again, thisindicates a loss of structure in the intermediate statecompared to the monomeric unit in the crystalstructure. The experimentally determined spectralsignal for the intermediate (YI) is given in Table 3,relative to a signal of 0 for a native monomericsubunit in a dimer and 1 for a denatured monomer.The global fit to far-UV CD data yields a value of YI

of 0.39, suggesting that the monomeric intermediateretains significant helical structure. Fluorescencedata give a YI value of 0.61. This indicates thatchanges in quaternary and tertiary structure onformation of the intermediate state lead to anincreased exposure of tyrosine and tryptophanresidues to solvent. The thermodynamic

parameters, therefore, are consistent with a mono-meric intermediate that has undergone partialunfolding, involving some loss of both secondaryand tertiary structure.

Modelling the equilibrium unfolding of YibK

The thermodynamic parameters in Table 2 can beused to model the equilibrium unfolding of YibK atdifferent concentrations of protein. Figure 6(a) and(b) shows the fraction of native dimer, monomericintermediate and denatured protein present as afunction of urea concentration for YibK concen-trations of 100 mM and 0.25 mM, respectively.Figure 6 shows that at 100 mM YibK the intermedi-ate state is hardly populated, while at 0.25 mM YibKit is present at fractions up to 0.14 at concentrationsof urea close to the midpoint of the unfoldingtransition. The YibK denaturation profiles aremonophasic within the protein concentrationrange used in this study, where the two unfoldingtransitions N242I and I4D remain closelycoupled. Figure 7 illustrates how the equilibriumunfolding curves are predicted to vary over a largerrange of YibK concentrations. A biphasic profilebecomes apparent at sub-nanomolar concentrationsof protein; here, the protein concentration-

Figure 7. The theoretical YibK denaturation profiles for0.1 pM (lilac triangles), 1 pM (pink circles), 10 pM (purpletriangles), 0.1 nM (purple circles), 1 nM (dark bluetriangles), 10 nM (dark blue circles), 0.1 mM (light bluetriangles), 1 mM (light blue circles), 10 mM (green tri-angles), 0.1 mM (green circles), 1 mM (yellow triangles),10 mM (yellow circles), 0.1 M (red triangles) and 1 M (redcircles) protein modelled using the thermodynamicparameters obtained from the best fit of (a) fluorescenceand (b) far-UV CD unfolding data to a three-state modelwith a monomeric intermediate (equation (16)).

Folding Studies on a Knotted Protein 1417

dependent N242I transition occurs at lowerconcentrations of denaturant than the proteinconcentration-independent I4D transition. Thevalue of YI dictates the relative height of eachtransition, and so fluorescence and far-UV CDunfolding profiles no longer superimpose where abiphasic transition is seen (Figure 7).

Conclusions

Proteins belonging to the SPOUT class of knottedMTases represent an intriguing protein-foldingproblem; during the course of folding, a consider-able segment of polypeptide chain has to threadthrough a loop. Here, we have established con-ditions under which YibK, a homodimeric SPOUTclass member, can be unfolded reversibly using thechemical denaturant urea, thus demonstrating thatmolecular chaperones are not required for theefficient folding of this protein. A series of equili-brium unfolding experiments using secondary andtertiary structural probes demonstrate that the

protein unfolds through a monomeric intermediatestate. Using global fitting analysis, we have shownthat this intermediate state is quite stable withrespect to the denatured state, with a free energy ofunfolding of 6.5–7.3 kcal molK1, comparable tomany small monomeric proteins. The thermodyn-amic parameters obtained suggest that, in additionto the dissociation of the dimer, there has been apartial loss of secondary and tertiary structure ofthe monomer subunit on formation of the inter-mediate state. Whether the topological knot con-tinues to exist in the intermediate state remains tobe shown. The growing number of knotted struc-tures deposited in the Protein Data Bank impliesthat knots in proteins may be more common thenpreviously thought. Moreover, the results of thisstudy show that, despite the presence of a deeptrefoil knot, YibK undergoes equilibrium denatura-tion in the samemanner as many unknotted dimers.Therefore, it appears that Nature has not onlyevolved mechanisms to successfully fold polypep-tide chains, but in some cases, to knot them as well.

Materials and Methods

Materials

A plasmid containing the YibK gene inserted into apET-17b vector was a kind gift from Dr Osnat Herzberg(University of Maryland Biotechnology Institute, MD).Chromatography columns andmedia were obtained fromAmersham Biosciences, and molecular biology gradeurea was purchased from BDH Laboratory Supplies. Allother chemicals and reagents were of analytical grade andwere purchased from Sigma or Melford Laboratories.Millipore-filtered, double-deionised water was usedthroughout.

YibK expression and purification

C41 (DE3) cells containing the YibK plasmid weregrown at 37 8C in 2!YT medium containing 100 mg mlK1

ampicillin until they reached mid-log phase. Expressionwas induced with IPTG to a final concentration of0.1 mM, followed by continued incubation at 37 8C forfour hours. Cells were harvested by centrifugation,resuspended in 20 mM Tris–HCl (pH 7.5), 200 mM KCl,10% (v/v) glycerol, 1 mM DTT, and lysed by sonication.The cell debris was removed by centrifugation, and thesupernatant applied to a Q-Sepharose anion-exchangecolumn. This was used to bind contaminants, while YibKappeared in the flow-through. The fractions enrichedwith YibK (as assessed by SDS-PAGE) were pooled,dialysed into 50 mM sodium acetate (pH 5.8), 125 mMKCl, 5% glycerol, 1 mM DTT and applied to an SP-Sepharose cation-exchange column. The column waseluted with a linear gradient of 0–0.5 M NaCl over 20column volumes; YibK eluted at approximately 0.1 MNaCl. Fractions containing purified protein (as assessedby SDS-PAGE) were pooled and dialysed against 50 mMTris–HCl (pH 7.5), 200 mMKCl, 10% glycerol, 1 mMDTT.Protein yield was approximately 70 mg lK1. Purity wasassessed by SDS-PAGE and analytical size-exclusionchromatography. Protein was flash-frozen and stored atK80 8C until required. YibK concentration, in monomer

1418 Folding Studies on a Knotted Protein

units, was verified spectrophotometrically using anextinction coefficient at 280 nm of 18,700 MK1 cmK1,determined using the method of Gill & von Hippel.42

Since oxidised DTTabsorbs at 280 nm,43 care was taken toensure reference and sample buffers were identical.

Size-exclusion chromatography

SEC was performed on an AKTA FPLC system using aSuperdex 75 10/300 GL analytical gel-filtration columnequilibrated at 25 8C in 50 mMTris–HCl (pH 7.5), 200 mMKCl, 10% glycerol, 1 mM DTT. Pre-equilibrated samplesof YibK (three hours) at concentrations between 0.25 mMand 100 mMwere injected (100 ml), and the relative elutionvolume was compared to that of molecular mass (M)standards. The relative elution volume was calculated as:

KAV ZVe KVo

Vg KVo

(1)

where Ve is the elution volume, Vo is the void volumedetermined by the elution of blue dextran 2000(2000 kDa), and Vg is the geometric column volume. Astandard curve was plotted of KAV versus log (M).Molecular mass standards were bovine serum albumin(66.3 kDa), carbonic anhydrase (28.8 kDa) and cyto-chrome c (12.4 kDa).

Equilibrium unfolding and refolding experiments

All experiments were performed in a thermostaticallycontrolled cuvette at 25 8C in 50 mM Tris–HCl (pH 7.5),200 mM KCl, 10% glycerol, 1 mM DTT. Aggregation ofthe native state prevents fully reversible unfolding at thispH without salt and glycerol as stabilising agents. Forurea equilibrium denaturation curves, a stock solution ofurea (approximately 9 M) in buffer was prepared in avolumetric flask and stored at K20 8C. The concentrationof this stock was determined from its refractive index,44

measured using an Atago 1T refractometer (Abbe). Thestock urea solution was diluted with buffer using aHamilton Microlab apparatus to give 800 ml aliquots ofurea at various concentrations between 0 M and 9 M. Fordenaturation profiles, YibK stock solution (100 ml) atvarious concentrations of protein was added to eachaliquot to give final concentrations of urea from 0 M to8 M, and final concentrations of YibK from 0.25 mM to100 mM (measured in monomer units). For renaturationprofiles, YibK at various concentrations was left to unfoldin 7.2 M urea. At this concentration of urea, unfolding iscomplete after 90 minutes. Unfolded protein (100 ml) wasadded to each aliquot to give final concentrations of ureafrom 0.8 M to 8.7 M. Samples were left for at least ninehours to equilibrate, after which no further change inspectroscopic signal was seen.

Spectroscopic measurements

Fluorescence measurements were taken with a SLM-Amico Bowman series 2 luminescence spectrometer usinga 1 cm path-length cuvette. The excitation wavelengthwas 280 nm with a band pass of 4 nm for both excitationand emission. Emission spectra were taken between300 nm and 355 nm at a scan rate of 1 nm sK1. The largestdifference in fluorescence between native and denaturedYibK was observed at 319 nm, and emission at thiswavelength was used in subsequent analysis. Denatura-tion profiles were measured for various YibK

concentrations between 0.25 mM and 100 mM, with atleast two curves recorded in all cases.Far-UV CD spectra were acquired using a Jasco J-720

spectropolarimeter with an emission band pass of 2 nm.Scans were taken between 210 nm and 250 nm at a scanrate of 1 nm sK1. The largest difference in signal betweennative and denatured YibK was observed at 225 nm, andthis wavelength was used to monitor unfolding. Dena-turation profiles were measured for YibK concentrationsof 0.5–2.5 mM using a 1 cm cell, 5–10 mM using a 0.3 cmcell and 50–100 mM using a 0.1 cm cell, with at least twocurves recorded in all cases.

Data analysis

Two-state dimer denaturation model

Equilibrium unfolding data were fit to a two-statedimer model, with native dimer (N2) in equilibrium withunfolded monomer (D):

N24KU

2D Scheme 1

The equilibrium constant for concerted unfolding, KU, isdefined as KUZ[D]2/[N2], and the total protein concen-tration in terms of monomer, Pt, is PtZ2½N2�C ½D�. Thefraction of monomers involved in native dimers, FN, isgiven as FNZ1KFD, where FD is the fraction of unfoldedmonomers, and can be written as FDZ[D]/Pt. Theseequations can be combined to give FD in terms of KU

and Pt:

FD Z

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK2U C8KUPt

qKKU

4Pt

(2)

KU can be defined according to the linear free energymodel, which states that the free energy of unfoldingvaries linearly with concentration of denaturant:26,32

DGU ZKRT lnðKUÞZDGH2O Km½denaturant� (3)

DGH2O is the free energy of unfolding in the absence ofdenaturant, andm is a constant of proportionality relatingto the solvent exposure difference between native anddenatured states.In a two-state dimer system, [D]50% is defined as the

concentration of denaturant where the fraction ofunfolded monomers equals the fraction of monomersinvolved in native dimers (FNZFDZ0.5). At this concen-tration of denaturant:

½D�Z 0:5Pt and 2½N2�Z 0:5Pt

Thus, at [D]50%:

KU Z½D�2

½N2�Z

0:25P2t

0:25Pt

ZPt

This can be compared to monomeric two-state systemswhere at [D]50%, KUZ[D]/[N]Z1. Substituting this intoequation (3) gives:

DGH2O ZKRT lnðPtÞCm½D�50% (4)

KU now becomes:

KU Z expRT lnðPtÞKmð½D�50% K ½denaturant�Þ

RT

� �(5)

For ease of comparison, denaturation data are normalisedto give the relative spectral signal, Yrel:

Yrel ZðY0 KYNÞ

ðYD KYNÞ(6)

Folding Studies on a Knotted Protein 1419

where Y0 is the spectroscopic signal at a given concen-tration of urea, and YN and YD are the spectroscopicsignals for native and denatured YibK monomericsubunits at a concentration of Pt, respectively. The termsYN and YD vary linearly with urea concentration;45

therefore, YNZaNCbN[denaturant] and YDZaDCbD[denaturant] where aN and aD are the intercepts, and bNand bD are the gradients of the native and denaturedbaselines, respectively. In the case of a two-state dimersystem, Yrel is equal to FD, therefore:

Y0 ZYNð1KFDÞCYDFD (7)

Fluorescence and far-UV CD datasets for each concen-tration of YibK were fit individually to equation (7), withFD and KU defined as in equations (2) and (5), respectively.Fits were performed using Prism, version 4 (GraphPadSoftware) to give thermodynamic parameters mN242D,[D]50%; DG

N242DH2O

was calculated from equation (4). Thevalues obtained for YN and YD were then used tonormalise the data according to equation (6).

Three-state dimer denaturation models

There are two possible three-state denaturation models,in which native dimer (N2) is in equilibrium with either adimeric (I2) or monomeric (I) intermediate and unfoldedmonomer (2D):

N24K1

I24K2

2D Scheme 2

N24K1

2I4K2

2D Scheme 3

For a three-state model involving a dimeric intermediate(Scheme 2), the equilibrium constants for the first (K1)and second (K2) transitions can be defined, respectively,as K1Z[I2]/[N2] and K2Z[D]2/[I2]. The total proteinconcentration, in terms of monomer, is PtZ2½N2�C2½I2�C ½D�, and the sum of the fractions of individualspecies is equal to 1: FNCFICFDZ1, where FI representsthe fraction of monomeric subunits involved in theintermediate state. Combining these relationships gives:

K1 ZFIFN

(8)

and

K2 Z2PtF

2D

FI(9)

By defining FI and FN solely in terms of FD, K1, K2 and Pt,FD can be expressed as a function of K1, K2 and Pt:

FD ZKK1K2 C

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðK1K2Þ

2 C8ð1CK1ÞðK1K2ÞPt

p4Ptð1CK1Þ

(10)

In a three-state model the relative spectroscopic signal,obtained by normalising the data using equation (6)becomes:

Yrel ZYNFN CYIFI CYDFD (11)

YI is the spectroscopic signal of the intermediate.Substituting equations (8) and (9) into equation (11)gives the final fitting equation:

Yrel ZYN

2PtF2D

K1K2

� �CYI

2PtF2D

K2

� �CYDðFDÞ (12)

For a three-state model involving a monomeric inter-mediate (Scheme 3), the equilibrium constants K1 and K2

are defined, respectively, as K1Z[I]2/[N2] and K2Z[D]/

[I]. The total protein concentration in terms of monomer isPtZ2½N2�C ½I�C ½D�, and again FNCFICFDZ1. Combin-ing these relationships results in:

K1 Z2PtF

2I

FN(13)

K2 ZFDFI

(14)

FN and FD can now be defined solely in terms of FI, K1, K2

and Pt, and therefore FI in terms of K1, K2 and Pt:

FI ZKK1ð1CK2ÞC

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK21ð1CK2Þ

2 C8PtK1

q4Pt

(15)

The fitting equation is obtained by substituting equations(13) and (14) into equation (11):

Yrel ZYN2PtF

2I

K1

� �CYIðFIÞCYDðK2FIÞ (16)

Global fitting to three-state dimer denaturation models

For both three-state models, the number of variablesinvolved means that global analysis involving fitting theunfolding data for all YibK concentrations to the modelsimultaneously is necessary to achieve accurate thermo-dynamic parameters. Analysis was carried out using thenon-linear, least-squares fitting programme Prism, ver-sion 4, and fluorescence and far-UV CD datasets wereconsidered separately. For both three-statemodels, K1 andK2 are defined from equation (3) as:

K1 Z expKDG1

H2OCm1½denaturant�

RT

!

K2 Z expKDG2

H2OCm2½denaturant�

RT

!

For a three-state model involving a dimeric intermediate,normalised data were globally fit to equation (12), with FDdefined as in equation (10), and K1 and K2 defined asabove. For a three-state model involving a monomericintermediate, normalised data were globally fit toequation (16), with FI defined as in equation (15), andagain K1 and K2 defined as above. For both models, thethermodynamic parameters DG1

H2O, DG2

H2O(stabilities of

the first and second unfolding transitions, respectively),m1, m2 (the m-values for the first and second unfoldingtransitions, respectively) and YI (the spectral signal of theintermediate) were obtained; YI was assumed not to varywith denaturant concentration to minimise the number ofparameters needed. To reduce any baseline artefacts, thebaselines were constrained to zero slope, with YN and YD

defined as zero and 1, respectively. To ensure theparameters calculated by the fitting programme repre-sented a global minimum in the fitting procedure, initialestimates were varied individually by approximatelyG15%. A global minimum in the non-linear, least-squaresfit was assumed if the parameters calculated remained thesame, despite the change of initial estimates.

Data modelling

The three-state denaturation mechanism of YibKinvolving a monomeric intermediate was modelled

1420 Folding Studies on a Knotted Protein

using the equations described above and DGN242IH2O

, DGI4DH2O

,mN242I, mI4D and YI values determined from globalanalysis (Table 2). Denaturation profiles were modelledfor various values of Pt usingMicrosoft Excel 2000, as wasthe change in the fraction of species present withdenaturant concentration.

Solvent-accessible surface area and m-valuecalculations

The SASA of native dimeric YibK was calculated fromthe coordinates of its X-ray crystal structure,6 using theweb-based program GETAREA version 1.1.46 The SASAwas also calculated for a fully folded YibK monomersubunit. The SASA of an unfolded monomer wasestimated using values for individual residues obtainedfrom tripeptide studies.29 These studies used Gly-X-Glytripeptides as model compounds for the SASA of side-chains in the unfolded state. However, tripeptide modelsare thought to often overestimate the SASA of theunfolded state; therefore, the SASA of an unfolded YibKmonomer was estimated using values obtained fromhard-sphere simulations, termed the Upper BoundModel.30,31

It has been shown that them-value of a protein is highlycorrelated to the DSASA between native and denaturedstates,28 and the following relationship has been observedfor proteins without crosslinks:

Urea m-valueZDSASAð0:14G0:01Þ (17)

This relationship, along with the DSASA calculated forthe YibK unfolding transition, was used to estimatethe m-value associated with complete YibK unfoldingfrom native dimer to two unfolded monomers. Thetheoretical m-value associated with dimer dissociationto fully folded monomer subunits was also estimatedusing this method; the DSASA upon dissociation is thedifference in SASA between native dimer and two fullyfolded monomers.

Acknowledgements

A.L.M. holds an MRC PhD studentship. Wethank Alexei Murzin for introducing us to knottedproteins, Dr Osnat Herzberg for donation of theYibK expression vector, and Andrew Brown andother members of the Jackson group for helpfuldiscussions. We thank Professor Sir Alan Fersht,and Professor Chris Dobson for access to biophysicalequipment. The work was funded, in part, by TheWelton Foundation.

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Edited by F. Schmid

(Received 4 November 2004; received in revised form 20 December 2004; accepted 23 December 2004)