Molecular origins of binding affinity: seeking the Archimedean point

Molecular

origins

of

binding

affinity:

seeking

the

Archimedean

point

Panagiotis

L

Kastritis

and

Alexandre

MJJ

Bonvin

Connectingthreedimensionalstructureandaffinityisanalogous

toseekingthe‘Archimedeanpoint’,avantagepointfromwhere

anyobservercanquantitativelyperceivethesubjectofinquiry.

Herewereviewcurrentknowledgeandchallengesthatlieahead

ofusinthequestforthisArchimedeanpoint.Wearguethat

currentmodelsarelimitedinreproducingmeasureddata

becausemoleculardescriptionofbindingaffinitymustexpand

beyondtheinterfacialcontributionandalsoincorporateeffects

stemmingfromconformationalchanges/dynamicsand

long-rangeinteractions.Fortunately,explicitmodelingofvarious

kineticschemesunderlyingbiomolecularrecognitionand

confinedsystemsthatreflectinvivointeractionsarecoming

withinreach.Thisquestwillhopefullyleadtoanaccurate

biophysicalinterpretationofbindingaffinitythatwouldallow

unprecedentedunderstandingofthemolecularbasisoflife

throughunravelingthewhy’sofinteractionnetworks.

Addresses

Bijvoet Center for Biomolecular Research, Science Faculty –Chemistry, Utrecht University, 3584CH Utrecht, The Netherlands

Correspondingauthor:Bonvin,AlexandreMJJ([email protected])

CurrentOpinioninStructuralBiology2013,23:868–877

This review comes from a themed issue on Protein-protein interac-tions

EditedbyJoe¨lJaninandAlexandreMJJBonvin

For a complete overview see theIssue and theEditorial Available online 19th July 2013

0959-440X #2013TheAuthorsPublishedby ElsevierLtd.

http://dx.doi.org/10.1016/j.sbi.2013.07.001

Introduction

Recognition processes between proteins involve func-tional interactions that underlie the cell’s biology in a precisemanner.Pathologicalconditionsincellphysiology, leading,forexample,tocancerorneurodegenerative dis-eases,alwaysinvolvesomedegreeofprotein miscommu-nication.Despitecurrentadvancesinthebiophysicaland biochemicalmethodsusedfortheelucidationofthe struc-ture andkinetics of biomolecularinteractions,theexact physicochemical basis of macromolecular recognition is

stillamatterofactivediscussion.Foreaseofreference, the relevant physicochemical quantities and constants arelistedinBox1.Foraproperquantitativeformulation ofbiomolecularrecognition,availabilityofbinding affi-nity dataas wellas atomicresolution structuresofthe protein–proteincomplexesandtheirfreecomponentsis deemedcrucial.Inthisreviewweaskthequestion:can we find the ‘Archimedean point’ in our odyssey for definingthebindingaffinitydeterminantsof macromol-ecularrecognition?

Archimedes (c. 287 BC–c. 212 BC), a famous Greek scientist and polymath, suggested during an argument that,givenasufficientlydistantsolidpointawayfromthe Earth(andalongenoughlever),hecouldliftthewhole earth: ‘dv˜& moi pa˜ stv˜ kaı` ta`n ga˜n kina´sv/give me somewheretostandandIwillmovetheearth’.Thepoint wherehewouldstandiscalledthe‘Archimedeanpoint’, aneminent point from where any observer can quanti-tativelycomprehendthesubjectofinquiry,whichinour case, are structure–affinity relationships in protein– proteininteractions.

The

complexity

of

molecular

recognition:

the

timescales

of

life

Theextendedrangeofdissociation(koff,s1)and associ-ation(kon,M1s1)rateconstants(andtheirrelated

equi-libriumdissociationconstant (Kd))measured byin vitro assays directly reflects the various types of functional interactions in the cell. For example, protein-inhibitor complexes have a half-life (1/koff) of days, even months—as measured, for example, by Vincent and Lazdunski [1] in the case of the interaction between trypsin and the pancreatic trypsin inhibitor, where the Kdis60fMatT=258CandpH=8.Ontheothersideof thespectrum,electrontransfercomplexesthatcarryout redox reactions within a fraction of a second lead to transient interactions in the mM range. In the case of

phosphorylation,orotherpost-translationalmodifications linkedtometabolismregulation,thecorresponding half-livesoftheformedcomplexesdivergesignificantly,even in simple reactions (whereone protein is the phospho-donor, usually a kinase, and the other the phospho-acceptor): for example, half-lives ranging from seconds for CheYandCheB [2]to several hoursfor OmpR and Spo0F[3]havebeenreported.

Binding affinity (expressed in physicochemical terms as the Kd) may span over 12 orders of magnitude, highlighting cellularfunction.For example, in thecase Open access under CC BY-NC-ND license.

ofreversiblecell–celladhesionprocesses,extremelylow affinitiesarefavored,inthemM[4]tomMrange[5].Thisis

because recognition of cell surface molecules is multi-valentandavidity-driven,andrapidfocaladhesion turn-over must mediate integrin signaling [4]. On the other sideoftheKdspectrum,proteases,RNasesandDNases, ifnotimmediatelyneutralizedandstrictlyregulated,will damagethecellirreversibly.That’swhytheirinhibitors, forexample,cognateinhibitorsofTrypsin,Ribonuclease A, or ColicinE9, bindto their respective partners with Kd’slowerthan6E14M.

An

everlasting

fondness:

buried

surface

area

and

binding

affinity

Modelingbindingaffinityisacomplexproblem,notonly because of thetimescalesinvolved, butalso in termsof understanding how the binding process occurs. Binding cantakeplaceviaasimplelock-and-key(Fischer’s) mech-anism, without any obvious conformational change: for example, the binding of the bovine pancreatic trypsin inhibitor(BPTI)totrypsinwithsubpicomolarKdfollows asimple1:1monovalentandreversibletwo-statebinding reaction. When comparing the crystal structures of the unbound conformers with that of the complex, hardly any changes in the conformation of their interface residues can be observed (root-mean-square-deviation (RMSD)<0.3A˚ ).ManymorecomplexeswithknownKd’s

bindwithonlyminorre-orientationsoftheirside-chains, therefore, in a ‘near-rigid’ manner [6]. Stein et al. [7] recently concluded, that Fischer’s modelholds when it comestoproteinbinding afterstudying>12000domain interactions.Theyalsopointedoutthat,forflexible com-plexes, the bound state is often accessible via intrinsic motionsofthefreestate,whichwouldbeconsistentwitha conformational selection mechanism. For this binding mechanismtooccur,unboundconformationsresembling theboundstatemustpre-exist.

For ‘near-rigid’ complexes, the Buried Surface Area (BSA) hasbeenshownto relatetobindingaffinitywith a Pearson’s correlation coefficient R=0.54 (P -value<0.01) for 70 complexes with various functions [6] (Figure 1a). This simple relation has a sound thermodynamic basis related to the hydrophobic effect for hydrocarbons [8,9]. Some assumptions are however neededtounderstandthiscontributioninprotein–protein complexes (see below). In this model, the dissociation freeenergyDGdiss isapproximatedby

DGdiss¼RTln Kd c0 X iaiBSAi (1)

whereRT0.6kcalmol1at298K,c0istheconcentration of the standard state (1M by convention) and ai is a hydration coefficient, which may be different for each atomtype,andisexpressedinkcalmol1A˚2,similarto the surface tension.The BSA containsbothhydrophilic (BSApol)andhydrophobicsurfacefractions(BSAapol).The

BSA-relatedpartofEqn1hasalsobeensplitintopolarand apolar terms, which yields improved correlations with DGdiss[10].Theexactvaluesofthehydrationcoefficients havebeenamatterofdebateevenforsimplesystems[11]. Arelatedconceptinstructure–affinityrelationshipsisthe bindingefficiency,definedastheinteractionenergyper square a˚ngstro¨m of BSA in the interface. The most efficient complexes (exhibiting high DGdiss and small BSA)generateupto20calmol1A˚2[12], correspond-ing mostly to protein-inhibitor complexes, whereas the least efficientcomplexes canachieve efficiencies<25% ofthemaximalbindingefficiency.Protein-inhibitor com-plexesoftenhavearelativelysmallBSA(1500A˚2)and very low dissociation constants, whereas more ‘flexible’ complexes (flexible being used to denote complexes undergoingconformationalchangesuponbinding),which bury larger surfaces, achieve smaller efficiencies. By considering a standardstate c0=1M,aminimal contact

area for afunctional protein–protein interaction can be derived: Day et al. estimated it approximately 500A˚2 [12],reachingthesameconclusion asapreviousstudy byJaninwhoidentifiedminimalfunctionalinterfacesof

570A˚2fromananalysisofcrystalcontactsizes[13].

Hot-spots

in

protein

–

protein

interfaces:

expanding

the

buried

surface

area

model

Residuesthat,whensubstitutedbyalanine,haveamajor impact on the free energy of dissociation DG_diss (>1.5kcalmol1) are termed hot-spot residues (hot-spots). This was first reported by Clackson and Wells [14]whodiscoveredthat,inthehumangrowth hormone-receptor interface,outof 26mutationswithinthe inter-face,sixincreasedtheKdbyafactorof 30,whereas the others did not have significant effects. Double-mutant cycleexperimentshavealsoshownthatinterfaceresidues dodisplaycooperativity[15].TheSKEMPIdatabase[16] includes binding affinity data from over 700 alanine Box1Terminology

Partitionfunctionof acomplex,Q

Q=qintqtrqrotqvibqconfqsolva

Law of mass actionb

aA + bB !gC, Keq= [C]g/[A]a[B]b

Equilibrium dissociation constant

Kd= c0/Keq= koff/kon

Standardstate(dissociation) freeenthalpy

DG_diss¼RTlnðKd=c0Þ

(Dissociation) free energy, enthalpy, entropyc

DGd= DHdTDSd

Entropy DSd=d(DGd)/dT

Heatcapacity DCp=d(DHd)/dT

Standard state p0_{= 1 bar, c}0_{= 1 mol L}1 Gasconstant R=1.986calmol1K1 a

Contributions:qint,interface;qtr,translational;qrot,rotational;qvib,

vibrational;qconf,conformational;qsolv,solvent.

b _Assuming

a= b= g= 1, [X] and Keqin ML1units. c_{A positive}

scanningexperiments,nextto othertypesofmutations, for62protein–proteincomplexeswith known3D struc-ture.Lookingatthelocationofthesemutationsusingthe Levyclassification[17],hot-spotsarealwaysfoundinthe interfaceanditsdirectperiphery(Figure1b).TheLevy classificationdissectsthesurfaceofprotein–protein com-plexes according to changes in accessible surface area into: first, the interface region; second, the buried and third,exposedperiphery;fourth,thecomplexinteriorand fifth,thecomplexexterior,beyondtheexposed periph-ery.Hot-spots havebeen shownto typically bury more than100A˚2ofsurface.Theyoftencorrespondtoresidues

withlongside-chainssuchasTrp,TyrorArg. Consider-able effects on binding affinity (2-fold changes, DDG_diss>0:4 kcal mol1) have also been observed for sitesdistantfromtheinterface,bothintheproteincore, but more interestingly, on the non-interacting surface (NIS) (Figure 1b). Recent studies by the Kalodimos group[18,19]directlypointtotheroleofconformational entropy in regulating binding affinity, providing a possible explanationfor theeffectof mutations remote fromtheinterface:theseremotemutations,byaffecting theconformationalentropy,areproposedto bepossible on–off switches for theinteraction. These studieshave

Figure1 5 7 9 11 13 15 17 19 10 15 20 25 30 35 40 45 50 5 7 9 11 13 15 17 19 10 15 20 25 30 35 40 45 50 inner rim outer rim non-interacting surface complex cor e 5 7 9 11 13 15 17 19 5 7 9 11 13 15 17 19 >4 >2 >0.4 <0.4 0 10 20 30 40 50 60 70 80 90 100 interface Δ G o obs (kcal mol -1) Δ G o obs (kcal mol -1) Δ G o obs (kcal mol -1)

ΔGo_calc (kcal mol-1)

ΔΔGo

obs (kcal mol

-1₎ Alanine scanning (% m utants) (a) (b) (c) (d)

NIS polar (%) NIS charged (%)

Current Opinion in Structural Biology

Relationshipsbetweenmolecularpropertiesandmeasuredbindingaffinity.(a)ClassicalBuriedSurfaceAreamodel(DGobs=aBSA+b),relatingthe

binding affinity to changes in the accessible surface area of the complexes; R= 0.54 (P-val < 1E4, N= 70) for ‘near-rigid’ binders (iRMSD1.0 A˚, solid circles); R= 0.16 (P-val = 0.17, N= 72) for ‘flexible’ binders (iRMSD>1.0 A˚, squares (1.0 A˚>iRMSD1.5 A˚) and crosses (iRMSD>1.5 A˚) [6_{]. (b)Alanine}

scanningmutagenesisdatafromSKEMPI[16]revealthatmutationsontheentiresurface,includingthenon-interactingsurface,affectbindingaffinity; theirimpactdecreaseswithincreasingdistancefromtheinterface.(candd)Percentagesofpolar(c)andcharged(d)residuesonthenon-interacting surfaceshowsignificantcorrelationswithbindingaffinityforbothrigid(polar:R=0.42(P-val<2E4,N=72);charged:R=0.46(P-val<1E4, N= 72), respectively) and flexible complexes (polar: R= 0.23 (P-val < 5E2, N= 72); charged: R= 0.23 (P-val < 5E2, N= 72).

provided the experimental proof for the existence of allosterictransitions,whichdonotinvolveconformational changes, ashad beensuggestedinthe1980s[20]. Recently, we have discovered simple relationships be-tween binding affinity and properties of the non-inter-acting surface (Figure 1c, d) for all complexes of the affinity benchmark [6]: for instance, the percentages of polar and charged residues away from the interface showsignificantcorrelationswithprotein–proteinbinding affinity.CombiningthesewiththesimpleBSAmodelfor bindingaffinity(Figure1a)leadstotheformulationofa globalsurfacemodelforbindingaffinity,awhichaccounts forthecontributionofglobalphysicochemicalproperties to theinteraction strength,consistentwithwhatalanine scanningdataarereporting(Figure1b).

The

impact

of

conformational

dynamics

on

binding

affinity

is

substantial

A substantial fraction of protein–protein complexes undergoconformationalrearrangements,fromsmalllocal conformational changes to large disorder-to-order tran-sitions.Someevendisplayanincreaseinflexibilityupon binding, as, for example,the core domain of p53 upon interaction with Hsp90 [21]. Conformational changes seem to be directly relatedto protein evolution:highly coevolving residues are frequently located in flexible regions[22].Thenumberofcomplexesexhibitinglarge conformationalchangesuponbindinghasbeenproposed bytheTeichmanngrouptobemuchlargerthancurrently estimated [23].Theyassociatedrelativeprotein accessi-bility to structural change: Using a simple power-law relationship with molecular weight, already discovered in the1970s[24],they predicted theaccessible surface area of well-folded proteins, proposing that observed deviationsfromitarelinkedtoconformationalchanges. Anotherpotentialreasonfortheunderestimationof con-formationalchangesuponbindingarethecryogenic tem-peraturesregularlyusedin X-raycrystallography, which might introduce a bias toward reduced conformational motions.Room-temperatureconditionsshouldindeedbe preferred, since they might reveal more functional motions[25].Still,conformationalchangesbetweenstatic structures at low temperatures can be observed and motionswithinonestatecouldbedifferentfrom confor-mational changes between two states. The reduced motionsatcryogenictemperaturesmightmainlyimpact the proposed binding mechanisms (i.e. conformational selectionversusinduced fit),but not, perse,the confor-mationalchangesthemselves.

For complexes that undergo ‘large’ conformational changes upon binding (iRMSD>1.0A˚ ), the relation

be-tween BSA and binding affinity is masked by large changesinentropythatcannotbecapturedbythesimple BSA model (Eqn 1, Figure 1a) [6].The latter nearly alwaysoverestimatestheaffinity,withsomeexceptions. Thisisindirectagreementwiththepioneeringreportby Gru¨nberg et al. [26]who showedthat proteinflexibility influences the thermodynamics of binding and may regulate protein–proteinassociation.

Next to conformational changes within the interface,as measuredbytheinterfaceRMSD(iRMSD)betweenfreeand

bound states, disorder-to-order transitionsare also often observed upon binding. In about one-third of the com-plexes of thebinding affinity benchmark[6],even for thosecasesclassifiedasrigid,someresiduesintheinterface aremissingineitherthefreeortheboundform,indicating differencesinflexibilitybetweenthoseformsinthecrystal state. The iRMSD measurealone does notcapture those

(since it can onlybe calculatedonresiduesobservedin boththefreeandboundstates)andthereforeappearstobe aratherloosecriterionforclassifyingflexibilityinprotein– protein interactions. The most flexiblebinders undergo extensivedisorder-to-ordertransitions. For example,the complex between p38 MAPK and MAPK-activated proteinkinase2[27]gains4000A˚2BSAfromloopsthat are onlyobservedin theboundconformation,whilethe iRMSD(measuredonthesegmentscommontothefreeand

boundstates)isonly1.9A˚ .

Recently,variousmethodshavebeenproposedtorelate structural properties to conformational change [23,28]. One of their common features is that the free state’s (intrinsic)flexibilitydirectlyrelatestotheobserved con-formational change.To date, no biophysicalmodel has successfullymodeledthecontributionofconformational changestobindingaffinity,exceptfortheoneproposed bySpolarandRecord[29]whoaccountedfortheentropy offoldingperresidue(5.6calK1):Theycalculatedthe translational and rotational entropy along with a BSA-based hydrophobic contribution for several protein– protein complexes, and subtracted them from the measured DS8ofassociation;iftheresultwasnearzero, thecomplexeswerepredictedas‘near-rigid’binders.The resultingexcessentropywasattributedtoconformational changes.Thismodelcomparedwellwithestimatesbased ontheentropyof foldingperresidueforthoseresidues undergoing‘folding’uponbinding.Consideringthe cur-rentextentofavailableaffinitydata[6,30],are-analysis toquantifyandre-validatetheextentofthecontribution of conformationalentropy tobindingenergy for various complexes shouldbepossible.Explicitmodelingof the energetics associated with conformational change has been estimated todecrease theerrorinbinding affinity prediction [31]. The conformational entropy has been proposedtohavealargecontributiontothefreeenergyof binding,reachingup to7kcalmol1[32].

a

Describedin:KastritisPL:Propertiesofthenon-interactingsurface modulatethebindingaffinityofprotein–proteininteractions.InOnthe binding affinityof macromolecular complexes.Daring to ask whyproteins interact.PhD thesis,Utrecht University;2012:161–208.ISBN: 978-9-03-935871-9.

Changesinconformationaldynamicscanbemeasuredin vitrousingNMR.ProteindynamicsasmeasuredbyNMR T1,T2andHET-NOErelaxationmeasurementscanbe interpreted in termsof conformationalentropy [33–35]. Results on carbohydrate-protein interactions show that theconformational entropycontribution to DGdiss could be comparable in magnitude to that of the binding enthalpy [33]. Its quantification from NMR relaxation datais,however,nottrivialandhasbeenrestrictedsofar tofewbiomolecularsystems(e.g.[18,36,37]).Todate, more than 30structural ensembles of complexes deter-mined by NMR, with known unbound structures and measured Kd’s, are available in the Protein Data Bank (Table S1). Unfortunately, except for ubiquitin-related interactiondata,noneofthesehavebeencharacterizedin termsof conformationalentropyalbeit NMR relaxation datadoexistforafew.Anexampleofrigorous physico-chemicalmodelingisavailablefor theengineered com-plexbetweentheZ(Taq)affibodyanditsbindingpartner (anti-Z(Taq) affibody) whose structure and that of its unbound constituents have both been solved by NMR [38]: the conclusion of this work is that the favorable hydrophobicsurfacedesolvationuponcomplexformation is compensatedby losses in translational and rotational entropy as well as unfavorable conformational entropy changes [38]. Such an analysis, however, requires data fromIsothermalTitrationCalorimetry(ITC)reportingon enthalpy,entropy,andheatcapacitychanges, aswellas knowledge of the conformational changes and folding transitionsfromstructuraldata.

Crowding

effects

on

conformational

dynamics

and

binding

affinity

remain

elusive

Next to the classical conformational/flexibility changes anddisorder-to-ordertransitionsmentionedabove,novel paradigmsofcomplexesthatformwithincreasedoraltered dynamicscomparedtotheirboundstructureshavebeen described(e.g.[21,37])andextensivelyreviewedthelast twoyears[39–41].Inaddition,manyinteractingproteins arethoughttofunctionthroughmoleculardisorder (hav-ingnoparticularsecondarystructure),theso-called intrin-sicallydisorderedsystems[42,43].

Thebindingaffinityofveryflexiblebindersisrelatedto kon[44],inlinewiththeproposed‘fly-casting’recognition mechanismfor flexiblecomplexes[45],wherekonisnot diffusion-limitedanddisplaysaninversedependenceon solventviscosity [46]. A controversy hasbeenraised to whetherdisorderhasanactualmolecularexplanationin thecellularcontext[42,47]anditisnotjustflexibilityat its extreme, erroneously considered to be functional disorder [47]. Accumulated data suggest that disorder couldbeexaggeratedinvitrointheabsenceofcrowding conditions(e.g. [48]).Incontrast,anotherstudyshowed thattheaccessibleconformationalspaceofthedisordered polypeptide chain linked to functional recognition is mildlyaffectedbycrowdingagents[49].Theimpact of

macromolecularcrowdingconditionsonbindingaffinity isalso controversial.Itseffectmightnotbeassevereas suggestedfromtheory[50].Forexample,theassociation rateofab-lactamasetoitsproteininhibitoris25%lower in vivo than values reported from in vitro studies [51]. Highly electrostatic complexes are expected to show lowerkonincrowdedconditions.To date,noconclusive evidence on the effectof macromolecular crowding on bindingaffinity(orconformationaldynamics)isavailable sincemethodsforinvivobindingaffinitymeasurements arestillin theirinfancy[52].

Current

models

for

binding

affinity

prediction

must

include

properties

beyond

the

interface

Severalmodelshavebeendevelopedinthelastyearsto modelthebindingaffinityofmacromolecularinteractions (reviewedin[53]).Allconsideronly thebound confor-mationoftheprotein–proteincomplex,therefore ignor-ing the energetic contribution of the free state. These modelsonlyqualitativelycorrelatewithbindingaffinity, atbest [54]. They are all relatively cheap in terms of computationalcosts compared to analytical calculations using molecular dynamics simulations in combination with PBSA calculations for instance [55]. MM-PBSA calculationshaveshowninafewspecificcasesto reason-ablyreproducebindingaffinities,forexample,inthecase of the interaction between RAD51 and BRC peptides [56]andtheH-Ras/C-Raf1complex[57].Sofar,noneof the proposed models has achieved a better prediction than thesimple model proposed byHorton and Lewis morethan20yearsago[10].However,eventhissimple modeloftenoverestimatesthebindingaffinity,in particu-larfor flexiblebinders [6].Thelatter, typicallyin the mM–mMKdrange,oftenexhibithighBSAdueto confor-mationalchanges.SimpleBSA-basedmodelsconsidering only the bound form clearly overestimate the binding affinitybycompletelyneglectingthelossof entropyfor suchsystems. Currentalgorithmsfor affinityprediction relyheavilyoninterfaceinteractions[53,58].Theyhave been successful in specific cases [59], but, due to their complexity (e.g. large number of descriptors, support vector machine-based or neural network-based, etc.) (e.g. [60]), can often not fully explain the biophysical factorsgoverningbindingaffinity.Besidesthat,theyalso unanimously neglect the role of the remainder of the surface,thenon-interactingsurface,whoseglobal physi-cochemicalpropertiesarealsorelatedtobindingaffinity (Figure1c, d)[6].Thenon-negligibleroleofthe non-interacting surface is supported by experimental muta-genesis studiesthathave unanimously shownthatboth proteininteriorandthenon-interactingsurfacedoaffect thefreeenergy ofbinding(Figure1b).

Other environment effects on protein–protein binding affinitythathavenotbeen includedsofarinanymodel arebufferconditions,Temperature,pHandsalt concen-tration.Somemodelshaveincludedthedependence of

kon on the salt concentration using Debye–Hu¨ckel-like approximations, but not in the context of Kd modeling [61,62].Especially,changesinpHcouldchangetheKdby two orders of magnitude (2.8kcalmol1). Models to explicitlyaccountforprotonation/deprotonationeventsin protein–protein interactions are under active develop-ment[63,64],buthavenotyetbeenintegratedinbinding affinity models. Finally, as discussed above, crowding

effects and molecular flexibilityare not yetunderstood andbothexperimentalistsandtheoreticianswill haveto work together to understand their impact on binding affinity.

Conclusions

and

perspectives

WheretheArchimedeanpoint liesforunderstanding contribu-torstoprotein–proteinbindingaffinityandifitactuallyexists

Figure2 cytochrome bc1 complex (complex III) (a) (b) (c) colicin Ia Ia receptor colicin E3

mitochondrial membrane complex interacting with cytochrome c

Kd~ μM outer membrane proteins

with colicin ligands K_d~ nM

cytochrome c (isoform 1) vitamin B12 receptor

Current Opinion in Structural Biology

IllustrationofthreemembranecomplexeswithboundandunboundstructuresandexperimentallymeasuredbindingaffinitypresentintheProteinData Bank. Black arrows indicate the approximate location of conformational changes that occur upon binding. (a)Complex between colicin Ia (PDB ID: 2HDI, chain B) and its membrane receptor (PDB ID: 2HDF) (Kd1E10 M): domain rearrangements required for opening of the receptor are observed intheextracellularside,toallowtheinsertionofthecolicinmolecule.(b)ComplexofcolicinE3(PDBID:1UJW,chainB)tothevitaminB12receptor (PDBID:2GUF):Thebindinginducesconformationalchangesthatincludeloopreorientationsaswellassecondarystructurerearrangementsallover theinterfaceintheextracellularside;theinteractionisstrong,inthenMrange(Kd9E10M).(c)bc1Complex(complexIII)oftherespiratorychain (PDB ID: 1KB9) in complex with cytochrome c oxidase (PDB ID: 1YCC): The interaction (PDB ID: 3CX5) may induce an allosteric change in the structure; the equilibrium dissociation constant is in the mMrange.

arestill open questions.What wedoknow, however,is that,for‘near-rigid’complexes,changesintheaccessible surfaceareaarerelated to thebindingaffinityin anear quantitativemanner.Further,foralltypesofcomplexes, thatis,includingflexibleones,globalsurfaceproperties mustplayaroleinbindingaffinityaswell—buthowis stillanopenquestion.Hot-spotsareusuallynotobserved outsidetheinterface and itsclose periphery.Still, resi-dues can contribute significantly to the binding free energy,evenatdistalsitesonthenon-interactingsurface. The impact of conformational changes or changes in molecularflexibilityisnowappreciatedtobesubstantial

but lacksa proper quantification. Pioneering structure– functionstudiesofthecomplementsystem,animmune defense mechanism present in both vertebrates and invertebrates point to the fact that cellular signaling is basedonaplethoraofcomplexregulatorymechanismsfor protein–protein interactions, mediated by domain re-arrangements (up to 100A˚ ), allosteric auto-activation controls, substrate-product binding and flexibility changes [65]. Available and forthcoming crystallo-graphic and NMR data, in combination with kinetic/ thermodynamicmeasurements,shouldprovidemore pre-cise information on the role of conformational changes andmolecularflexibilityonbindingaffinity.

Figure3

∏

A + B C

B

A

C

A

+ B

C

A

+ B

C

C

C

C

B

B

B

A +

n

B C

=

=

=

k₁ k₀

A

+ B

C

+ B

C

+ B

A

+ B

C

+ B

C

C

+ B

C

C

C

Current Opinion in Structural Biology

Illustration of kinetic models linked to various binding processes. Proteins A and B are represented in blue and gray spheres, respectively. Different (allosteric)statesofproteinAareindicatedbyvariousblueshades.AmodulatorproteinZisindicatedingreen.(a)1:1bindingmodel.(b)Concerted binding.(c)Sequentialbinding.(dande)Allostericmodelswith(d)singlebindingsiteandallostericchangeand(e)multipleallostericchanges, including a modulator protein and sequential complexation. In the kinetic schemes, [A], [B], [C], [Z] denote the concentrations of protein A, protein B, their derived complex C and a modulating protein Z, respectively. The K(d,i,a...z,1...n)’s denotes various equilibrium constants and k(0n)the equilibrium constant for interconversion between states in the allosteric models d and e.

Therearefurthermanyopenchallengestobeaddressed and opportunitiesto betaken to bring us closer to the Archimedean point. Modelingproteinhydration, proto-nationandpolarizabilityshouldleadtoamorethorough understandingofinteractionphenomena.Studying mem-branesystemswithknownboundandunboundstructures (Figure 2) andmodelingtheiraffinities,forexample,as theHoniggroupdidforcadherinclustering[66],should highlight theimpactof theconformationalconfinement in the lipid environment. It is indeed expected that membrane anchoring is more frequentthan anticipated insignalingcascades[67]andthatthelipidenvironment hasaroleinregulatingprotein–lipidandprotein–protein interactions[68].Furthermore,inordertotackle com-plex multi-component systems, we will have to reach beyond the 1:1 protein–protein interaction model for two-state kineticsfor whichmostcomputationalmodels have been developed so far, as more kinetic schemes currentlyproposedformacromolecularrecognitionawait experimentaldataformodeling(Figure3).Despitethat, for multi-component assemblies, the thermodynamic dataalmostalwaysconcernbinarysubassemblies; obtain-ingreliablethermodynamicquantitiesforsuchsystemsis currentlyunrealistic,exceptinfewspecificcasesmay-be. Finally, technological advances in binding affinity measurements are required to push the limits forward. Weexpect thatmethodsto measureconcentrations and rate constantsinvivowillbecomemoreprevalent,even measuringin-cellpHchangesinrealtime[69],thereby hopefullyimprovingbothmodelingandexperimentation. For example, a wealth of data are available for actin polymerization invitro [70], but modelsdeveloped for this exact phenomenon do not yet include effects of hundredsofproteinmodulatorsregulatingthe polymer-izationprocess.Thiscomplexityinprotein–protein inter-actionswillrequiremodelerstothinkoutsidetheboxand unifyavailable,accumulatedandfutureknowledgefrom diverseresearch fields.

Acknowledgement

ThisworkwassupportedbytheDutchFoundationforScientificResearch (NWO)throughaVICIgrant(no.700.56.442)toA.M.J.J.B.

Appendix

A.

Supplementary

data

Supplementary material related to this article can be found, in the online version, at http://dx.doi.org/ 10.1016/j.sbi.2013.07.001.

References

and

recommended

reading

Papersofparticularinterest,publishedwithintheperiodofreview, have been highlighted as:

ofspecialinterest ofoutstandinginterest

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