doi:10.1016/j.jmb.2011.07.016 J. Mol. Biol. (2011) 413, 297–309

Contents lists available at www.sciencedirect.com

Journal of Molecular Biologyj ourna l homepage: ht tp : / /ees .e lsev ie r.com. jmb

αB-Crystallin Polydispersity Is a Consequence ofUnbiased Quaternary Dynamics

Andrew J. Baldwin 1⁎†, Hadi Lioe 2†, Carol V. Robinson 2,Lewis E. Kay 1⁎ and Justin L. P. Benesch 2⁎1Departments of Molecular Genetics, Biochemistry and Chemistry, The University of Toronto, 1 Kings College Circle,Toronto, Ontario, Canada M5S 1A82Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road,Oxford, Oxfordshire OX1 3QZ, UK

Received 25 April 2011;received in revised form8 July 2011;accepted 11 July 2011Available online3 August 2011

Edited by A. G. Palmer III

Keywords:Polydispersity;mass spectrometry;small heat shock proteins(sHSPs);molecular chaperones;thermodynamics and kinetics

*Corresponding authors. E-mail addajb204@pound.med.utoronto.ca; kay@ca; justin.benesch@chem.ox.ac.uk.

† A.J.B. and H.L. contributed equPresent address: H. Lioe, Bio21 Inst

Chemistry, The University of MelbouAustralia.Abbreviations used: sHSP, small h

MS, mass spectrometry; CID, collisidissociation.

0022-2836/$ - see front matter © 2011 P

The inherent heterogeneity of many protein assemblies complicatescharacterization of their structure and dynamics, as most biophysicaltechniques require homogeneous preparations of isolated components. Forthis reason, quantitative studies of the molecular chaperone αB-crystallin,which populates a range of interconverting oligomeric states, have beendifficult, and the physicochemical basis for its polydispersity has remainedunknown. Here, we perform mass spectrometry experiments to study αB-crystallin and extract detailed information as to its oligomeric distributionand exchange of subunits under a range of conditions. This allows adetermination of the thermodynamic and kinetic parameters that governthe polydisperse ensemble and enables the construction of a simple energyprofile for oligomerization. We find that the quaternary structure anddynamics of the protein can be explained using a simple model with justtwo oligomer-independent interactions (i.e., interactions that are energet-ically identical in all oligomers from 10mers to 40mers) between constituentmonomers. As such, the distribution of oligomers is governed purely by thedynamics of individual monomers. This provides a new means forunderstanding the polydispersity of αB-crystallin and a framework forinterrogating other heterogeneous protein assemblies.

© 2011 Published by Elsevier Ltd.

Introduction

The vast majority of proteins perform their cellularfunctions as multimeric assemblies,1 with interac-tions ranging from the robust to the fleetingly

resses:pound.med.utoronto.

ally to this work.itute, School ofrne, Victoria 3010,

eat shock protein;on-induced

ublished by Elsevier Ltd.

transient.2 The preponderance of these proteinassemblies is currently thought to exist in oneprincipal oligomeric state, reflective of a definedstructure having evolved to perform a particularcellular function.3 Seemingly contrary to this para-digm, however, some proteins instead populate anensemble of stoichiometries at equilibrium.Perhaps the most famous example of such poly-

dispersity is the vertebrate small heat shock protein(sHSP) α-crystallin, which exists in two isoforms(αA and αB) of high sequence similarly.4 The α-crystallins populate all possible oligomers frombetween 10 and 40 subunits,5 a remarkable hetero-geneity that has impeded high-resolution structuralanalysis.6 Nevertheless, structures of α-crystallindimers, generated by removal of approximately

(a) Inter-dimer(‘edge’)

Intra-dimer(‘dimer’)

(b) Fig. 1. The oligomeric organiza-tion of the sHSPs. (a) The proto-meric dimers of αB-crystallin can berepresented as ellipsoids, are stabi-lized by an intra-dimer interface,and assemble into oligomers viainter-dimer interactions. In themodel described in this work,these interfaces are termed dimerand edge interactions, respectively,with their strengths described by

the corresponding free energies ΔGd and ΔGe. (b) These dimers assemble into an ensemble of globular oligomersspanning at least 30 subunits at equilibrium and of unknown structure.

298 Polydispersity of αB-Crystallin

70 N- and 15 C-terminal residues, have beenreported.7–10 These dimers therefore represent thebuilding block of the oligomers11 and assemble intoan ensemble of globular particles.6,12–14 α-Crystallinstructures are therefore stabilized by both intra- andinter-dimer interactions (Fig. 1a).Despite these structural insights, the origins of the

variable stoichiometry of the α-crystallins, vital tothe role of this protein in the eye lens,15,16 are notunderstood. In addition, the oligomers are known tobe very dynamic, with oligomers readily exchangingsubunits17,18 in a process associated with theirprotective function.19,20 αB-crystallin is found inmany tissues,15 where, along with other sHSPs, it iscentral to the maintenance of protein homeostasis.21

Its molecular chaperone function is to bind andmaintain the solubility of unfolded proteins,22,23

thereby preventing their accumulation into poten-tially pathogenic aggregates.24 αB-crystallin mal-function is consequently associated with a range ofprotein deposition diseases, from cataract formationto Alzheimer's disease.25 For an appreciation of themechanism by which αB-crystallin functions as achaperone, a quantitative understanding of theorigins of both the quaternary dynamics andheterogeneity is required.Nanoelectrospray mass spectrometry (MS) is an

emerging structural biology approach, reliablydetermining the stoichiometries of protein assem-blies with unrivalled accuracy.26–28 Furthermore,through benefiting from very high separation effi-ciency, it is particularly valuable in the study ofpolydisperse proteins, allowing the assessment ofthe oligomers they populate.29 Though performed inthe gas phase, such quantification directly reflectsthe distribution observed in solution, but withdramatically improved mass resolution.30–32 Thisapproach has resulted in the quantification of therelative populations of the different oligomerscomprising the polydisperse ensemble of the α-crystallins.5,30,31 Furthermore, the large amount ofdata obtainable by means of MS in real timemakes itwell suited to investigating the quaternary dynamicsof oligomeric proteins, 33 such as the subunitexchange of the α-crystallins.31

Here, we use MS to obtain oligomeric distribu-tions and subunit exchange kinetics of αB-crystallinover a wide range of pH values and temperatures todescribe fully the thermodynamic and kinetic basisfor its polydispersity. We show that, remarkably,this property can be understood in terms of just twomonomer-level interactions, intra- and inter-dimer,which are independent of oligomer size. Further-more, we demonstrate within the context of thismodel that formation of α-crystallin oligomerdistributions can be explained by the quaternarydynamics associated with single monomers “hop-ping” between oligomers. As such, the seeminglycomplex organization of this protein can be ratio-nalized in terms of very simple physical principles,shedding light on how other polydisperse proteinsmight assemble.

Results

Determining oligomeric distributions anddynamics by means of MS

MS approaches have proven very useful forinterrogating the polydisperse αB-crystallin en-semble.5,30,31,34 A nanoelectrospray mass spectrumof αB-crystallin at pH 7, under conditions optimizedfor the ionization and transmission of intact proteinassemblies, reveals a broad region of signal between8,000 and 14,000 m/z (Fig. 2a), as is typical for thisprotein.5,30,31,34 The extensive overlap of chargestates, stemming from the wide range of co-populated stoichiometries, renders the spectrumessentially uninterpretable. To improve the identifi-cation of the individual species that comprise theoligomeric ensemble, we employed collision-induced dissociation (CID).35,36 In this experiment,all ions are accelerated into an argon-filled cell toeffect their activation. A spectrum obtained at a highacceleration voltage shows a compact series of peaksat low m/z and a multitude of peaks at 16,000 m/zand above (Fig. 2b). These correspond to monomersand complementary “stripped” oligomers, that is,

30

m/z

26283032

342628[αBi-2]i-2+

[αAj-2]j-2+[αAkαBl](k+l)+

[αBi]p+

[αBi-2](p-q-r)+

[αB]r+

[αB]q+

CID

[αBi-2](i-4)+[αBi-2](i-3)+

2224

32

4000 8000 12000 16000 20000 24000 28000

%

0

100

8000 12000

(a)(b) (c)(d)

Fig. 2. Nanoelectrospray MS of αB-crystallin. (a) The mass spectrum of αB-crystallin is typical of what is observed for aheterogeneous protein ensemble, with the peaks corresponding not to individual charge states but, rather, resulting fromthe accumulation of a number of charge states from many different species [αBi]

p+. (b) A mass spectrum as in (a) butobtained under activating conditions in which all ions are submitted to energetic collisions with argon atoms. Peaks areobserved at both low and high m/z corresponding to highly charged monomers, [αB]r+ and [αB]q+, and complementarystripped oligomers, respectively. This is in agreement with the general mechanism of gas-phase protein complexdissociation. The area between ∼18,000 and 25,000 m/z corresponds to αB-crystallin oligomers stripped of twomonomers, [αBi− 2]

(p-q-r)+ and has resolution sufficient to allow the identification and relative quantification of theindividual species (c). Note that even values of i are shown above selected peaks; the peaks corresponding to oligomerswith an odd number of subunits are located between these (black dots). From this, the complete oligomeric distribution ofαB-crystallin can be derived. Spectra are shown for pH 7 (black) and pH 5 (red), with the odd oligomers beingsignificantly more prevalent at pH 5. (d) The peak at∼21,500m/z (black) corresponds to all αB-crystallin doubly strippedoligomers carrying as many charges as subunits [αBi− 2]

(i− 2)+. The equivalent peak for αA-crystallin appears at ∼19,800(red), whereas a fully equilibrated mixture of the two isoforms gives a broader peak between the two, representing thedistribution of hetero-oligomers.31

299Polydispersity of αB-Crystallin

αB-crystallin oligomers having lost one or moremonomers, respectively.5 This sequential removal ofhighly charged monomers leads to an effectivecharge reduction of the parent ions, such thatindividual oligomeric stoichiometries can be identi-fied unambiguously (Fig. 2c).35 In this way, a rangeof oligomeric states of αB-crystallin is observed atpH 7 (Fig. 2c, black), centered on a 28mer. Moreover,from the intensities of the peaks, the relativeabundance of each species can be extracted, provid-ing a basis for the quantification of the thermody-namics of the αB-crystallin ensemble, as describedbelow. It is notable that, at pH 7, oligomers with aneven number of subunits are considerably moreabundant than those with an odd number.30 Anequivalent spectrum obtained at pH 5 shows aremarkable difference (Fig. 2c, red), namely, thispreference for even oligomers is dramatically re-duced, revealing that the strength of the intra-dimerinterface is pH sensitive, as described in detail below.The peak at ∼20,150 m/z (Fig. 2d, black) corre-

sponds to αB-crystallin oligomers stripped of twomonomers, each carrying as many charges as sub-units, and therefore, it contains a contribution fromall oligomers within the ensemble.5 The equivalent

peak, obtained from identical experiments, for αA-crystallin appears at ∼19,800 m/z (Fig. 2d, red), dueto the slightly lower molecular mass at the sequencelevel. Incubation of the two proteins results insubunit exchange, manifested in the mass spectrumby the coalescence of the peaks corresponding to thehomo-oligomers into a broad peak centered on theirmidpoint (purple).31 By obtaining of spectra atdifferent time points, the course of subunit exchangecan be monitored, discussed in detail below, allow-ing a detailed quantitative analysis of the quaternarydynamics of this protein.

APoissondistributiondescribes theheterogeneityof αB-crystallin at low pH

MS measurements reveal broad oligomeric distri-butions that are highly pH sensitive (Fig. 2c; Fig. 3a,red). At low pH, the distribution is smooth, while athigher pH, it becomes more uneven, with apreference for oligomers comprising an even num-ber of subunits. By contrast, the distribution doesnot vary appreciably with temperature.37 The factthat both odd and even oligomers are observed in alldistribution profiles means that the exchange must,

pH 5.5

pH 5

pH 6.5

pH 6

pH 7

pH 8 pH 9

0.6

0.8

1.0

1.2

1.4

22 26 30 34i

(b)

[Pi-1

]/[P

i]

(a)

0 10 20 30 40 10 20 30 40 50Number of subunits in oligomer, i

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

10

[Pi]

(μM

)

Fig. 3. Oligomeric distributions of αB-crystallin as afunction of pH. (a) Distributions were obtained for pH 5–9at 37 °C and are normalized to the total proteinconcentration. Experimental data are shown in red, andthe calculated distributions are in blue, where [Pi] is theconcentration of an oligomer consisting of i monomers.Calculated distributions (blue) were obtained using Eqs.(5)–(7.2) to produce ΔGe and ΔGe +d values shown in Fig.4 (see Methods). (b) The ratio [Pi− 1]/[Pi] as a function ofoligomer size at pH 5 (red) and pH 9 (blue). The ratiodepends linearly on i at pH 5 (red line), from which itfollows that the size distribution at this pH obeys Poissonstatistics. The Pearson R2 correlation coefficient for theratio at pH 5 and subunit size is 0.99.

300 Polydispersity of αB-Crystallin

at least in part, be mediated by the movement ofmonomers. In fact, we show immediately below thatthe equilibrium distributions observed can be welldescribed as arising from the exchange of individualsubunits between parent oligomers, an assumptionthat is further validated through NMR studies.38

A simple exchange scheme can be constructedthat can explain the experimental results byconsidering the successive accumulation of mono-mers to form oligomers (monomer exchange),39

P1+P1±kþ2

k −2

P2;P1+P2±kþ3

k −3

P3; N P1+Pi−1±kþi

k −i

Pi

( ),whereP1

is a free subunit in solution, Pi is an oligomer of isubunits, and kj

-/kj+{j ∈ (2,…,i)} are dissociation/

association rate constants. An association equilibrium

constant,KAj =

Pj½ �Pj − 1½ � P1½ �,canbeascribedtoeachbinding

step involving the formation of oligomer j above.Within this scheme, the general rate equations for thetimedependenceof theconcentrationofeacholigomerPi (i≠1) and freemonomer P1 are:

d Pi½ �dt

= − k −i Pi½ � + kþi Pi−1½ � P1½ � − kþi + 1 Pi½ � P1½ �

+ k −i + 1 Pi + 1½ �

ð1Þ

d P1½ �dt

=Xn

2

k −i Pi½ � + k −

2 P2½ � −Xn

2

kþi P1½ � Pi−1½ � −kþ2 P1½ �2

ð2Þ

Both equations are satisfied at equilibrium ifPi½ � = kþi

k −i

P1½ � Pi−1½ �, from which it follows that

KAi = kþi

k −i. Therefore, the concentration of an oligo-

mer at equilibrium can be calculated if the totalprotein concentration and the rates ki

+ and ki- are

known for all sizes of interest using the relation

Pi½ � = P1½ �i Qij=2

kþjk −j

� �, iN1. In the case of αB-crystallin

at pH 5, the ratio Pi − 1½ �Pi½ � was found experimentally to

vary linearly with i such that Pi − 1½ �Pi½ � = i

MA, whereMA is

a constant (Fig. 3b, red points). From the definitionabove of the association equilibrium constant, itfollows that Pi − 1½ �

Pi½ � = k −i

kþi Pi½ �, so that at pH 5

iMA

=k −i

kþi P1½ � ð3Þ

and the ratio of the dissociation and association ratesvaries linearly with increasing oligomer size. It can beshown that, in this case, the oligomer distributionmust follow a discrete Poisson distribution, a specialcase of a Gaussian distribution, where the mean andthe variance are equal,31 Pi½ �~ 1

i! MAð Þi. A conse-quence of the Poisson distribution is that the constantMA is equal to both the mean oligomer size and thevariance of the distribution. In other words, theheterogeneity and the average size of αB-crystallinare intrinsically linked.The simplest kinetic model is obtained by setting

the dissociation rate of a given oligomer to beproportional to the number of component subunitssuch that ki

-= ik -, with the association rate indepen-dent of oligomer size, ki

+=k+. Such a situation ariseswhen (i) the environments of all monomers areessentially the same in all oligomers, as supported

301Polydispersity of αB-Crystallin

by the NMR spectra of αB-crystallin showing asingle cross peak for each probe;11,38 (ii) eachmonomer is equally likely to dissociate from itsparent oligomer at any time; and (iii) there iseffectively a single binding (association) site on theoligomer, independent of its size. Physically, thecondition ki

+=k+ can arise if the rate-limiting step ofassociation reflects the initial binding of a freemonomer to the oligomer, with subsequent internalrearrangements occurring significantlymore rapidly.From Eq. (3) and the assumption ki

-= ik -, ki+=k+,

it follows directly that MA = kþ P1½ �k − . Thus, within

the framework of our model, monomers exchangebetween oligomers at low pH with microscopicassociation (k+) and dissociation rate constants (k−)that are independent of the size of the exchangingpartners. This model completely reproduces thelow-pH MS data [Fig. 3a and b, red].In a companion paper,38 we show that the

proposed kinetic model can also explain relaxationdispersion NMR data, providing additional supportbut not proof of our kinetic scheme. We haveexplored a range of additional monomer exchangemodels including helical and linear polymerizationschemes,40,41 which cannot explain our experimen-tal data (Fig. S1). Further, more elaborate schemesinvolving the exchange of fragments larger thansingle monomers have also been considered. Withsimilar simplifying assumptions such as ki

-=k-,ki+=k+ and ki

- = ik -, ki+=k+, such models do not

yield equilibrium distributions that resemble theexperimental data (Fig. S1). Finally, it is worthnoting that our model can be contrasted with thecase of the sequential dissociation/association of aligand from a macromolecule containing n equiva-

lent binding sites, PLi−1 + L±kþi

k −i

PLi, where the

oligomeric association and dissociation rates aregiven by ki

- = ik - and ki+=(n-i+1)k+, respectively.42

The dimer interface is strengthened at higher pH

As the pH is increased, the observed size distribu-tions becomeuneven,with a preference for oligomerscomposed of an even number of subunits (Fig. 3a),and thus no longer follow Poisson statistics (Fig. 3b,blue). The model described above must therefore beexpanded slightly to take this into account.A slight preference for αB-crystallin to populate

“even-numbered” stoichiometries indicates thepresence of some dimeric substructure within theoligomers.11,30 This is consistent with atomic-resolution structural data that have revealed thatmonomers of αB-crystallin assemble into dimers bysharing an interface between extended β-strands7,9

and that this interface is very labile (Fig. 1a).8,43 Inorder to assemble into oligomers, these intra-dimerinteractions must be complemented by inter-dimerinteractions (Fig. 1a). In what follows, we refer to

these two classes of contacts as “dimer” (intra-dimer)and “edge” (inter-dimer) interactions, respectively.It is important to stress thatwemake no assumptionsas to the structural origins of these edge interactionsand, in principle, they could involve several contacts.In our model, we assume that all monomers

within an oligomer make the maximum allowednumber of such interactions in order to minimizeeach monomer free energy. Thus, in the case of anoligomer consisting of an even number of mono-mers, all dimer and edge interactions are satisfied,while for an odd-numbered oligomer, a singlemonomer lacks dimer contacts (referred to as anunpaired monomer). When dimer contacts are muchless significant than edge interactions, it is expectedthat the kinetic rates describing the addition/subtraction of a monomer would be essentially thesame, irrespective of whether the binding eventinvolves an even- or odd-numbered oligomer. Thisassumes that the nature of the edge contacts isunchanged in the odd/even cases. Such a situationemerges at low pH, where edge interactionsdominate and where the dissociation kinetics arewell described by a single microscopic rate, k−. Asthe contribution to the stability of the oligomer fromdimer contacts increases, however, it is expectedthat microscopic dissociation rates would not be thesame for unpaired and paired monomers (Fig. 4a).This is because an unpaired monomer would beattached more weakly than all of the other mono-mers so that its dissociating rate, ke

−, would begreater than the corresponding value for removal ofa “paired” monomer from the oligomer ke +d

- . Thus,Eq. (1) is modified according to

P1+Pi−1±kþ

ik −e +d

Pi;d Pi½ �dt

= − ik −e + d Pi½ � + kþ Pi−1½ � P1½ �

− kþ Pi½ � P1½ � + ik −e + d + k −

e

� �� Pi + 1½ �; i = even

ð4:1Þand

P1 + Pi−1�Yp�

kþ

i−1ð Þk −e + d+ k

−e

Pi;d Pi½ �dt

= − i − 1ð Þk −e + d + k −

e

� �Pi½ � + kþ Pi−1½ � P1½ �

− kþ Pi½ � P1½ � + i + 1ð Þk −e + d Pi + 1½ �; i = odd

ð4:2Þ

where explicit use has been made of our assumptionki-= ik -, ki

+=k+ (see above). Note that the factorik −

e +d+ke- preceding [Pi+1] in Eq (4.1) derives from

the fact that, in a particle consisting of i+1monomers (i is even), there are i paired monomersand one that is unpaired. Thus, for each of the i pairedinteractions, dissociation must proceed throughbreaking edge and dimer interactions (ke+d

- ), whilefor the unpaired contact, only the edge interactions

Fig. 4. Thermodynamics of the oligomeric distributionof aB-crystallin. (a) Schematic showing the association anddissociation pathways for a 23mer structure (based on anoctahedron, with dimers placed on each of the edges). Asin Fig. 1, each dimer is represented by a white ellipsoid,with the dimer interface denoted by a red collar, while thesingle monomer is indicated by half an ellipsoid.

302 Polydispersity of αB-Crystallin

must be released (ke−). This situation is illustrated

schematically for the case of a 23mer in Fig. 4a. Itfollows directly from Eqs. (4.1) and (4.2) that theconcentration of each oligomer is given by

Pi½ �even =kþ P1½ �ik −e + d

Pi−1½ � = MA

iPi−1½ � ð5Þ

Pi½ �odd =kþ P1½ �

i − 1ð Þk −e + d + k −

ePi−1½ � = MA

i − 1 + nPi−1½ �

ð6Þwhere ke

-=nk −e+d, n is a multiplier greater than or

equal to 1, and as before MA = kþ P1½ �k −e + d

. In the limitwhere n=1, ke

-=k −e+d=k

- and a Poisson distributionis obtained, as discussed above. The relative free-energy difference between a given oligomer of size iand the corresponding oligomer of size i−1, createdthrough the loss of a monomer from a single, specificsite as depicted in Fig. 4b, is given by

DGe+d = Gi;e+d−Gi−1;e+d = − RTlnP1½ �kþk −e+d

= − RTln MAð Þð7:1Þ

ΔG (

kJm

ol-1

)

pH

(c)

-10

-8

-6

-4

-2

0

4 5 6 7 8 9 10

ΔGe +d

i) ΔGe ii) ΔGe +d(b)

[Pi][Pi-1] [Pi+1]

ke

k+[P1] k+[P1]

ke +d- -

ΔGe

ΔGd

ke (unpaired)-

ke +d (paired)-

Dissociation, i=23 Association, i=23

k+[P1]

(a)

DGe = Gi;e − Gi−1;e = − RTlnP1½ �kþk −e

= − RTlnMA

n

� �ð7:2Þ

depending on whether i is even (ΔGe+d, addedmonomer is paired) or odd (ΔGe, added monomer isunpaired). It follows that the stability of the dimerinterface is given by

DGd = DGe + d − DGe = − RTlnn ð7:3ÞNote that all three quantities ΔGe +d, ΔGe, and

ΔGd are independent of i, the number of subunitswithin the oligomer. This model therefore allowsfitting of the experimental size distributionsobtained fromMS at all pH values and temperatureswith ΔGe and ΔGd as free parameters. The fitsreproduce the experimental data extremely well(Fig. 3a and Fig. S2), demonstrating that our model

Dissociation may take place through the loss of a pairedmonomer with rate ke+d

- (yellow arrow) or an unpairedmonomer with rate ke

- (blue arrow). In the case of the23mer, the rate of loss through dissociation is 22ke+d

- +ke-

(contributions from 22 paired monomers and 1 unpairedmonomer). Each of the 22 paired monomers is equallylikely to dissociate in any given time period. Associationof a monomer with a 23mer to form a 24mer isindependent of the number of oligomers and occurswith a rate of k+[P1][P23]. In the limit where the dimerinterface is relatively strong (ke

- Nke +d- ), unpaired mono-

mers are easily lost and even oligomers are favored, asobserved at high pH. In the limit where the dimer interfaceis relatively weak (ke

-≈ke+d- ), the equilibrium profile is

well approximated by a smooth Poisson distribution, asobserved at low pH. (b) Schematic showing the physicalorigin of the two free-energy parameters required to fit theMS distribution data. The sphere represents an oligomer,with interactions between groups of dimers within theoligomer indicated. (i) Free-energy change on adding asingle “unpaired” monomer, ΔGe, to an even-numberedoligomer where only the edge interactions are formed,along with the microscopic rate constants describing ratesof association with and dissociation from a specific site.The dissociation rate of the unpaired monomer is fasterthan that of a paired monomer (ke

- Nke+d- ). (ii) Free-energy

change on adding a single “paired” monomer to an oddoligomer, ΔGe+d=ΔGe +ΔGd. Note that the dissociationrate from each site is ke +d

- so that the net rate of monomerrelease for an oligomer with i paired monomers is ike +d

- .Values of ΔGe +d, ΔGe, ke

- and ke +d- are independent of

oligomer size. (c) Variation in ΔGe +d, ΔGd, and ΔGe as afunction of pH, 37 °C, demonstrates that the dimericinterface is weakened at low pH, while the inter-dimeredge interaction is strengthened.

303Polydispersity of αB-Crystallin

provides a good description of the oligomerizationof αB-crystallin (Fig. 3a, blue) and allowing anestimation of the strength of the inter- and intra-dimer interactions. The variation of ΔG with pHestablishes that, at low pH, the edge interactionsdominate those at the dimer interface (Fig. 4c). Bycontrast, at high pH, the importance of thesecontributions is reversed, leading to a preponder-ance of even-numbered oligomers. Notably, thefree-energy ΔGe +d, which dictates the averageoligomer size, varies little with pH. It is worthnoting that, even for pH values≥6, where thedistribution clearly favors even-numbered oligo-mers, the profiles are well explained by a model thatassumes monomer exchange exclusively. In thecompanion paper to this article, it is shown, further,that the timescale for dimer exchange is inconsistentwith the rate of subunit exchange measured byMS38

(see below).It is interesting to note that oligomer size

distributions are observed to be independent oftotal protein concentration over 3 orders of magni-tude, implying that [P1] is invariant (buffered) overthis range.4 Such behavior is anticipated by ourmodel, and it is possible to show that d P1½ �

d PTotal½ �c0 inthe experimentally accessible concentration regime.

when analyzing two-dimensional data of the type shown in (bpH 5 (continuous lines) and pH 9 (dotted lines). Only these tthermodynamics of oligomer formation and size distribution.

This is similar to what is found at equilibrium inlinear and helical polymerization assemblymodels.41,44

The quaternary dynamics vary in a markedfashion with both pH and temperature

The thermodynamic parameters obtained byfitting equilibrium population distributions do notprovide unique rates of oligomer assembly anddissociation. To obtain complementary kinetic in-formation, we have performed time-resolved MSexperiments to monitor the exchange of subunitsbetween oligomers of αB- and αA-crystallins (Fig.5a). The m/z range monitored represents alloligomeric species within the ensemble, with αA-and αB-crystallin homo-oligomers giving rise topeaks at ∼19,800 and ∼21,500 m/z, respectively(Fig. 2d). Initially, these two distinct populations areobserved, but upon incubation, they coalesce toproduce an equilibrium distribution of hetero-oligomers containing both isoforms (Fig. 5a).31 At37 °C, pH 5, this process is complete within 1 min,whereas, at the same temperature but at pH 9, fullexchange is only reached after approximately 5 h,consistent with previous studies.18 In order to

Fig. 5. Kinetics of α-crystallinsubunit exchange. (a) Subunit ex-change time course at 37 °C, pH 5(upper) and pH 9 (lower), moni-tored by using MS, c.f. Fig. 2d,shows the coalescence of the twohomo-oligomer peaks into a singlepeak representing the distributionof hetero-oligomers. This m/z rangecorresponds to doubly strippedoligomers carrying the same numberof charges as subunits [αBi− 2]

(i− 2)+,meaning that, in this range, m/z isequivalent to the average mass ofthe subunits comprising the oligo-mer in question. (b) Alternative“top-down” view of the data (left),compared to the simulated timecourses that best fit the experiment(right). (c) One-dimensional “slices”of (b), demonstrating the loss ofhomo-oligomers (red) and the gainof hetero-oligomers (black) alongwith the simulation that bestmatches the experiment at pH 5(continuous lines) and pH 9 (dottedlines). The high precision of theexperimentally determined rateconstants (Fig. S2b) arises from theaccuracy with which the point ofcoalescence can be determined

). (d) Variation in ke-, ke+d

- , and k+[P1] with temperature athree parameters are necessary to explain the kinetics and

304 Polydispersity of αB-Crystallin

quantify the time dependence of this mixing processin terms of the pseudo-first-order association ratek+[P1] and dissociation rate constants for paired(ke +d

- ) and unpaired (ke-) monomers, we performed

simulations to reproduce the experimental data (Fig.5b and c). Best-fit values of k+[P1], ke +d

- , and ke- were

therefore obtained as a function of temperature, inthe range 24–50 °C, at both pH 5 and pH 9. Underthe conditions examined, rate constants were deter-mined to a precision of ±5% on average (Fig. S2) andvary by 4 orders of magnitude, with rates increasingat higher temperature and lower pH (Fig. 5d). Thedata were found to show Arrhenius behavior,allowing activation parameters ΔH⁎ and ΔS⁎ to becalculated (Table S1), following transition statetheory (see Methods).Under all conditions, the concentration of free

monomer (and oligomer concentrations for sizes lessthan approximately 10 monomers, Fig. 3a) was toosmall to detect, and hence, the first-order rateconstant k+ could not be obtained (only thepseudo-first-order rate, k+[P1]). Nonetheless, limitscan be placed on the free monomer concentrationand, hence, on the association rate k+. First, anestimate for the upper limit of [P1] can be made byconsidering the noise level in measured MS datasets. The lower limit of monomer detection is ca10 nM (upper bound for [P1]), 3 orders of magnitudelower than the concentration of the 24mer (40 μMtotal sample concentration). With such an estimate,the microscopic association rate constant k+ variesbetween ≈105 M−1 s−1 (pH 5, 30 °C; pH 9, 40 °C)and ≈107 M−1 s−1 (pH 5, 40 °C; pH 9, 50 °C). Notethat association rates on the order of 107 M−1 s−1 areclose to the diffusion limit,45 indicating that associ-ation is rapid. A lower limit for [P1] can be obtainedby assuming that the association rate is at thediffusion limit (≈107 M−1 s−1). Under this assump-tion, [P1] varies between≈0.1 nM (pH 5, 30 °C; pH 9,40 °C) and ≈10 nM (pH 5, 40 °C; pH 9, 50 °C). Thus,an approximate concentration range for free mono-mer in solution is 0.1 nM≤ [P1]≤10 nM under theexperimental conditions employed.

Discussion

The distribution and subunit exchange experi-ments we have described here have provided adetailed picture of αB-crystallin quaternary dynam-ics and organization in terms of the thermodynamicand kinetic properties that relate to the associationand dissociation of individual monomers. We haveshown that the complex polydisperse ensemble andthe underlying quaternary dynamics can beexplained purely by the movement of monomers(see also our companion paper38) and in terms ofthree oligomer-size-independent parameters, k+[P1],ke-, and ke +d

- . The stability increase accompanying

binding of monomer to a growing oligomer favorsparticles of increasing size. This tendency, in turn, isbalanced by a net dissociation rate that growslinearly with oligomer stoichiometry, leading natu-rally to a maximum in the distribution profile, asobserved in the MS data. The kinetic parametersextracted here depend strongly on pH and temper-ature, with the unimolecular process of subunit lossrate limiting. As such, we have presented a meansfor understanding the underlying physical basis bywhich αB-crystallin populates a polydisperse en-semble at equilibrium.Our data show a clear pH dependence to the

strength of both the intra- and the inter-dimerinteractions. At low pH, the dimer interface isweakened considerably, in agreement with studiesperformed on a stabilized α-crystallin dimer,43 andcan be understood in terms of the network of chargedinteractions at the interface.46 The pH variation inΔGd is compensated by that of ΔGe, with the edgeinterface becoming stronger with decreasing pH(Fig. 4c). This remarkable self-compensatory behav-ior ensures that, in essence, the sum of the two freeenergies, a quantity that is directly related to both theaverage oligomer size and polydispersity [Eq. (7.1)],is conserved. It therefore appears that αB-crystallinhas evolved to maintain a constant average oligo-meric size that is resistant to variations over anexceedingly broad range of pH (5–9) and tempera-ture (20–50 °C). This can be understood in terms ofthe role of α-crystallin in maintaining eye lenstransparency while avoiding crystallization.16 En-tropy and enthalpy compensation is a well-knownphenomenon in biophysics47 and underlies theworkings of many allosteric protein machineries.48

Recent studies of αB-crystallin dimers provide aninteresting clue as to the structural origins of thiscompensation, namely, changes in the curvature ofand loop orientations within the dimeric buildingblocks as a function of either pH or mutation ofinterface residues.8,11 Such changes in conformationof the dimer would be expected to relax or strain theinter-dimer interactions.In the case of a homogeneous, monodisperse

oligomeric assembly, specific interactions lead toone oligomeric form becoming overwhelminglydominant within the ensemble,49 as is the case forthe crystallized sHSP oligomers.50,51 However, forαB-crystallin, the specificity of these interactions isrelaxed, as the polydispersity stems from relativelypromiscuous quaternary dynamics that allow amonomer to recombine with any sized oligomer.The question arises as to the functional role of thispolydispersity. It has been postulated that, throughhampering of crystallization despite the extremelyhigh protein concentrations, polydispersity is im-portant for maintaining transparency of the eyelens.16 However, it is important to consider thatαB-crystallin is still polydisperse at the lower

305Polydispersity of αB-Crystallin

concentrations in which it is found in other tissues,4

as indeed are other human sHSPs such as HSP27.52

Furthermore, we have recently shown that a plantsHSP undergoes a monodisperse-to-polydispersetransition upon activation, leading to formation ofa broad range of stoichiometries between the sHSPand the client protein.53 Taken together, thissuggests that the polydispersity and quaternarydynamics play an important role in cellular sHSPchaperone function.Our results also have implications for the molec-

ular mechanism by which αB-crystallin preventsaggregation of target proteins. It has been postulat-ed that activity results from the encounter betweensub-oligomeric forms of the sHSP with unfoldingprotein, with oligomer dissociation amounting to anactivation of the chaperone.19,20,54 Interestingly,however, αB-crystallin is able to curtail the precip-itation of insulin at 25 °C, pH 7, on a timescale ofapproximately 1 h.55 Under these conditions, therate of monomer dissociation is 5.3×10−6 s−1,equivalent to a subunit exchange timescale of over50 h . At least in this case, it is likely that the primaryevent for chaperone activity is not the encounterbetween target protein and free αB-crystallin mono-mer but, rather, with an oligomeric form of thechaperone. This is consistent with a cross-linkingstudy on α-crystallin,56 previous work on thedynamics of αA-crystallin,18 and our investigationof a truncated form of the same protein thatdisplayed a reduced subunit exchange rate but nodecrease in suppression of aggregation in vitro.31

Through comparative kinetic measurements, thequantitative approach we have developed hereprovides a means for addressing this aspect ofsHSP chaperone action in future studies.An alternative activation mechanism, based upon

changes in oligomerization from single stoichiome-try to polydisperse ensemble, has been observed forHSP18.1 from pea.53 Such a scenario may berelevant here. As we observe no change in theoligomeric distribution of αB-crystallin with tem-perature, it would appear that the ensemble ofoligomeric states that have been characterized in thepresent study represents the active chaperone stateof αB-crystallin. The dramatic differences in inter-face strengths and kinetics we observe as a functionof pH might act to regulate the chaperone activity ofthis protein. Indeed, differences in chaperoneactivity have been noted in vitro as a function ofpH.57–59 This is pertinent to two tissues where αB-crystallin is known to perform a protective chaper-one role: the eye lens and cardiac muscle. In theformer, there is a pH gradient across the lens, withthe center of the lens, populated by the oldest, mostposttranslationally modified, and hence aggrega-tion-prone lens proteins, being considerably moreacidic than the periphery.60,61 Similarly, during anischemic episode, the pH of the cardiac cell cytosol is

known to drop.62 Both of these circumstancesprovide clear examples where pH regulation ofαB-crystallin activity would act to protect the cellfrom the deleterious consequences of protein aggre-gation and deposition.Previous studies have shown that mimicking

phosphorylation results in a loss of a preferencefor αB-crystallin oligomers with an even number ofsubunits.30,63 Interpreted in the context of the modeldescribed here, this observation implies a weaken-ing of the dimeric interface, similar to what we haveshown here with wild-type protein upon acidifica-tion. Applying the quantitative approach describedin the present work has enabled us to extract thethermodynamic consequences of this phospho-mimicking (Fig. S3). Consistent with our previousstudy,30 we find that, at 37 °C and pH 7, themutation S19D gives a distribution identical to thatof the wild-type protein and the double mutantS19/45D results in a dramatic increase in ΔGd (from−7.7 to −4.3 kJ/mol) with a compensatory decreaseinΔGe (from −1.5 to −3.9 kJ/mol). The triple mutantS19/45/59D results in a further destabilisation ofthe dimer interface, with a change in ΔGd to−0.79 kJ/mol and a compensatory effect on ΔGe(−7.43 kJ/mol). Strikingly, the double mutant istherefore approximately equivalent to making theprotein behave at pH 7 as the wild-type does atpH 6, and the triple mutant makes the proteinbehave at pH 7 as the wild type does at pH 5. Whilethe specifics of how these variations in interfacestrengths control chaperone activity in vivo remainto be elucidated, this provides evidence for differentregulatory mechanisms for αB-crystallin operatingvia a common pathway.Thiswork has shown the inherent link between the

movement of single αB-crystallin subunits betweendifferent oligomeric forms and the resultant largeparticle size distributions. The ability to adopt arange of oligomeric forms and to do so on thetimescale of minutes likely underpins the promiscu-ous and versatile interactions that this protein canmake. Furthermore, our demonstration that thecomplex oligomerization behavior of αB-crystallincan be explained in terms of two monomer-levelinteractions provides a template for similar under-standing of other polydisperse proteins.

Methods

Obtaining oligomeric distributions

αB- and αA-crystallins were expressed in Escherichia coliand purified using standard approaches.64 To investigatethe distribution of oligomeric stoichiometries populatedby αB-crystallin, we employed nanoelectrospray MSunder solution and instrument conditions optimized forthe preservation of non-covalent interactions.65 No

306 Polydispersity of αB-Crystallin

monomers or oligomers containing fewer than 10 subunitsare observed in the spectra, demonstrating that there is nodissociation of the oligomers during transfer into the gasphase. Solutions of αB-crystallin were prepared at amonomeric concentration of 50 μM in 200mM ammoniumacetate, at the specified pH. Samples were analyzed on aQ-ToF 2 mass spectrometer (Waters UK Ltd.), modifiedfor the study of large protein assemblies,66 usingpreviously described instrument settings.5

CID was performed by accelerating all species, withoutselection in the quadrupole analyzer, into a collision cellpressurized with 35 μbar of argon.5 The resulting doublystripped oligomers, those derived from the removal of twosuccessive highly charged monomers, are spread over awide m/z range and can thereby be identified unambig-uously and, due to charge conservation, can be relateddirectly to their parent oligomer.5,35 Moreover, as no otherdissociation pathways are operative, during either ioni-zation or activation, the relative abundances can bequantified from the intensity of the peaks correspondingto the all charge states observed for each of the doublystripped oligomers, as described previously5 and asillustrated in Fig. 2. It is important to note that thereproducibility of these experiments is very high, with therelative abundances of oligomers varying by less than±5% between replicate experiments,53 a value comparableto the uncertainties in the quantities back calculated usingthe model (Fig. S2).Optimum values of MA and n and hence values of

ΔGe+d,ΔGe, andΔGd [see Eqs. (7.1)–(7.3) in the text] wereobtained as follows. The total concentration of monomers

in the system is given by P½ �Total =PNi=1

i Pi½ �, with the

concentration of a given oligomer expressed as

Pi½ � = P1½ �iYij=2

kþjk −j

!; i N 1 ð8Þ

Rearranging Eq. (8) so that

Pi½ � = P1½ �Yij=2

P1½ �kþjk −j

; i N 1 ð9Þ

it follows that

P½ �Total = P1½ � + P1½ �XNi=2

iYij=2

P1½ �kþjk −j

ð10Þ

where from Eqs. (5) and (6) of the text

kþj P1½ �k −j

=kþ P1½ �jk −

e + d=

MA

j; even j

kþj P1½ �k −j

=kþ P1½ �

j − 1ð Þk −e + d + k −

e=

MA

j − 1 + nð Þ ; odd j

ð11Þ

The total monomer concentration was determined bymeasuring the absorbance of the solution at 280 nm usingan extinction coefficient of 13,980 M−1 cm−1. Our limit ofdetection is determined from the signal-to-noise ratio inthe spectrum, taking into account the m/z dependence ofmultichannel plate sensitivity.67 For a given choice of MAand n, Eq. (10) is solved for [P1] fromwhich [Pi] is obtained

via Eq. (9). Consequently, each oligomer concentrationdepends only on [P]Total, MA, and n. Values of MA and nare, in turn, obtained via minimization of the χ2 target

functionPNi=1

Pi½ �exp− Pi½ �calc� 2

.

Quantifying the kinetics of subunit exchange

We probed the quaternary dynamics of αB-crystallinby mixing it with its lighter isoform, αA-crystallin. Therate of subunit exchange is known to be isoformindependent68 and is very low at reduced temperature.18

After incubation of the reaction mixture for varioustimes, quenching of a given aliquot was achieved bychilling on ice, allowing off-line analysis by means ofnanoelectrospray MS as described above. Mass spectrawere obtained under CID conditions, with the doublystripped oligomer region examined for quantitativeanalysis. By monitoring the peaks corresponding tothose doubly stripped oligomers carrying as manycharges as subunits, we obtained the time dependenceof the disappearance of homo-oligomers and the con-comitant appearance of hetero-oligomers, as describedpreviously.31,32The time courses are then analyzed in detail by fitting

the experimental data to the general rate equationsdescribing the time evolution of the concentration of anoligomer containing i and j monomers of type I (αB) andtype II (αA) during an equilibration period,

d Pi;j �dt

=−ik −

e+d Pi;j �

+kþ Pi−1;j �

P1;0 �

−kþ Pi;j �

P1;0 �

+ ik −e+d+k

−e

� �Pi+1;j �

−jk −e+d Pi;j �

+kþ Pi;j−1 �

P0;1 �

−kþ Pi;j �

P0;1 �

+ jk −e+d+k

−e

� �Pi;j+1 �

ð12Þ

where (i,j) are even. Similar equations can be written forthe remaining three cases corresponding to (i odd, jodd), (i even, j odd), and (i odd, j even). The timedependence of monomer exchange was simulated usingEq. (12), keeping ΔGe and ΔGd fixed to the valuesobtained from fits of αB-crystallin size distributions,under the assumption that, at t=0, the only nonzerooligomer concentrations are those of Pi,0 and P0,j. Thesevalues, in turn, can be obtained from distributionsgenerated from MS data, as described above. The bestfit of the experimental data to the time course predictedby Eq. (12) subject to the constraints of the sizedistribution equilibrium data gives k+[P1], ke +d

- , ke-that

are reported in the text.

Acknowledgements

We thank Gillian Hilton, Nelson Barrera, Chris-tine Slingsby and Sarah Meehan for stimulatingdiscussions. This work was supported by grantsfrom the Canadian Institutes of Health Research andthe Natural Sciences and Engineering ResearchCouncil of Canada (L.E.K.). A.J.B. holds a Canadian

307Polydispersity of αB-Crystallin

Institutes of Health Research postdoctoral fellow-ship, H.L. was a European Molecular BiologyOrganization fellow, C.V.R. is a Royal SocietyProfessor, L.E.K. holds a Canadian Research Chairin Biochemistry, and J.L.P.B. is a Royal SocietyUniversity Research Fellow.

Supplementary Data

Supplementary data associated with this articlecan be found, in the online version, at doi:10.1016/j.jmb.2011.07.016

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