Download - Isothermal titration calorimetry and differential scanning calorimetry

ReviewIsothermal titration calorimetry and differentialscanning calorimetry as complementary tools toinvestigate the energetics of biomolecularrecognition

Ilian Jelesarov* and Hans Rudolf BosshardDepartment of Biochemistry, University of Zurich, CH-8057 Zurich, Switzerland

The principles of isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC) arereviewed together with the basic thermodynamic formalism on which the two techniques are based.Although ITC is particularly suitable to follow the energetics of an association reaction betweenbiomolecules, the combination of ITC and DSC provides a more comprehensive description of thethermodynamics of an associating system. The reason is that the parametersDG,DH, DS,andDCp obtainedfrom ITC are global properties of the system under study. They may be composed to varying degrees ofcontributions from the binding reaction proper, from conformational changes of the component moleculesduring association, and from changes in molecule/solvent interactions and in the state of protonation.Copyright # 1999 John Wiley & Sons, Ltd.

Keywords:isothermal titration calorimetry; differential scanning calorimetry

Received 1 June 1998; accepted 15 June 1998

Introduction

Specific binding is fundamental to the molecular organiza-tion of living matter. Virtually all biological phenomenadepend in one way or another on molecular recognition,which either is intermolecular as in ligand binding to amacromolecule and in the formation of macromolecularcomplexes, orintramolecular as in protein folding. Here wedeal with intermolecular recognition, that is, with bindingreactions. The specificity and precision of binding reactionshas fascinated biologists and chemists from the verybeginning of modern biochemistry, and one of the mostrapidly advancing fields today is the study of molecularrecognition between macromolecules. The quantitativedescription of the forces that govern the formation ofbiomolecular complexes is part of this endeavor. It has greatpractical significance to the knowledge-based developmentof new drugs, vaccines and other medicinal compounds.

The number of high resolution crystal structures ofbiomolecular complexes is growing fast and there is a largedata base describing the complementarity of interactingsurfaces and the precise orientation of interacting groups.From the many detailed, yet static, pictures of biomolecularcomplexes we have learnedhowmolecules interact, but weless well knowwhy they do so. This means we have to find

ways to rationalize structure in terms of energetics, a taskthat still is enormously difficult inspite of some verypromising theoretical developments and of the steadyaccumulation of experimental results. Theoretical conceptshave developed in the tradition of physical-organicchemistry. It is difficult to adapt these concepts in astraightforward way to complex biomacromolecules. Pro-teins and nucleic acids are so large that in solution they maybe regarded as individual macroscopic systems surroundedby solvent (Privalov and Potekhin, 1986). They behavecooperatively and often undergo structural rearrangementsduring binding reactions. The changes range from the subtleadjustments of dihedral angles to the prominent rearrange-ment and even refolding of entire molecular domains(Padlan, 1996). For example, in a DNA binding protein thedomain that binds to the DNA target site can be unstructuredin the free protein and becomes folded only when it is boundto DNA (Patikoglou and Burley, 1997). The energeticconsequence of such binding-induced refolding is far frombeing understood, but the energetic cost is thought to belarge. From this perspective, binding specificity has to beredefined. It is no longer a simple function of spatialcomplementarity and of accumulation of favorable interac-tions between molecules that can be treated as rigid bodies.Binding between large and flexible biomolecules has acomplicated energy profile involving different energeticexpenditures in going from the free components to the finalcomplex. The free energy of complex formation turns out tobe a very small number resulting from a delicate balancebetween large favorable and large unfavorable contribu-tions. Moreover, binding takes place only if thetotal free

JOURNAL OF MOLECULAR RECOGNITIONJ. Mol. Recognit.1999;12:3–18

Copyright# 1999 John Wiley & Sons, Ltd. CCC 0952–3499/99/010003–16 $17.50

* Correspondence to: I. Jelesarov, Department of Biochemistry, University ofZurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.Abbreviations used: DSC, differential scanning calorimetry; ITC, isothermaltitration calorimetry.

energy changedecreases,regardlessof theactualamountoffavorable free energy change accumulated by directmolecular contact between the associating biomolecules.This is to say,solventeffects areasimportantto theenergybalance as are direct noncovalent interactions (Collins,1997;Jelesarovet al., 1998).

BasicThermodynamic RelationshipDescribing Binding Phenomena

The Gibbs free energy change,DG, of an associationreaction is temperaturedependentandis described by

�G�T� � �H�TR� �Z T

TR

�CpdT ÿ T�S�TR�

ÿ TZ T

TR

�Cpd ln T

�1�

DH and DS are the changein enthalpy and entropy,respectively,DCp is the heatcapacity change,andTR is anappropriate reference temperature. If DCp is temperature-independentin the temperature interval of interest, Eq. (1)simplifies to

�G�T� � �H�TR� ÿ T�S�TR��Cp�T ÿ TR ÿ T ln�T=TR��

�2�

Equations (1) and (2) show that the free energy ofassociation hasanenthalpyandanentropycomponent.Thechanges of enthalpy and entropy dependon temperatureaccording to

�Cp � d��H�dT

� Td��S�

dT�3�

To characterizethethermodynamicsof abindingreactionmeansto determine DG, DH andDS at a given referencetemperatureandto obtain DCp to predictthe changeof theabovethreeparameterswith temperature.

Non-calorimetric determination of binding energetics

DG is accessible through many types of binding experi-ments becauseDG is relatedto theassociation constantKA

by DG = -RT ln KA where R is the gasconstant (8.314 JKÿ1molÿ1) and T is the absolute temperature in degreesKelvin. In thesimplestcaseamolecule L reactswith anothermolecule M to thecomplexML.1 TheassociationconstantisKA = [ML]/[M][L] wherethebracketsindicateconcentrationexpressedin units of mol lÿ1 andKA hasunitsof l molÿ1. Totakethelogarithm,KA must beadimensionlessratio.This isachievedby normalizing the molar concentrations to thestandard state concentrationof 1 mol lÿ1. Alternatively, KA

can be expressedas (mol fraction)ÿ1, where 1 mol lÿ1

equals 1.8� 10ÿ2 mol fraction (corresponding to 1/55.56mol H2O per1). Thechoiceof thestandard state is a matterof convention yet is importantwhen comparing valuesofDG andDS.

Therearemanyways to measureKA. Let us beginwiththe simpleequilibrium betweenL, M andML:

L�M ÿ!KA

ÿ ML

Techniqueslike equilibriumdialysis,ultracentrifugation,or radio-ligandbindingassaydirectly yield valuesfor [ML],[M], or [L] to calculate KA. More indirect and mostlyspectroscopicmethodsyield an observable p the changeofwhich is proportional to the degree of saturation, Y,according to:

Y � �pi

�pmax� �ML��M � � �ML� �

KA �L�1� KA �L� �4�

Dpi is a signal change(e.g. a changeof fluorescenceaccompanying the formation of the complex, ML), andDpmax is the maximum signal changeat full saturation(Y= 1). From Y measured at different temperatures,KA(T) and DG(T) are obtained. DH(T) and DS(T) can bederived using the integrated form of the van’t Hoffequation: Z T2

T1

d ln KA �Z T2

T1

�HRT2

dT �5a�

and Z T2

T1

�G� ÿZ T2

T1

�SdT �5b�

Further, taking the second derivative of DG(T) withrespect to temperature,one obtains DCp. The non-calori-metric approach to the thermodynamics of an associationreaction, commonly called a van’t Hoff analysis,hasseveredrawbacks.First, for technical reasons,experimentscanbeperformed only in a limit ed temperature range, andexperimentalerrors propagateinto largeerrorsof DH, DS,and of DCp in particular. Second,KA very often appearstemperature-independent in the experimentally accessibleT-rangebecauseof enthalpy/entropycompensationbetweenlarge and strongly temperature-dependent DH and DS.Therefore,the van’t Hoff analysisof a binding reactionisoftenflawed.

Isothermal Titration Calorimetry

ITC and DSC are the only methods for the directdeterminationof DH. Theprincipleof ITC is now reviewedfirst. It is themostdirectmethodto measure theheatchangeon formation of a complex at constant temperature.Sinceatitrationexperimentis performedin whichL is titratedinto asolution of M (or M into a solution of L), KA and thestoichiometry,n, of the complexarealsoobtained by ITC.Moreover, ITC experiments performed at different tem-peraturesyield DCp definedby Eq. (3).

1 In this article the componentsof a complex are designatedL and M,irrespective of their sizeandchemicalnature.Thus,L andM canbe proteins,nucleic acids,low molecularweight metabolites,salt ions, andso on. L oftenis named the ligand and M the receptor. However, this assignmentisarbitrary.

4 I JELESAROVAND H BOSSHARD

Copyright# 1999JohnWiley & Sons,Ltd. J. Mol. Recognit.1999;12:3–18

The IT C experiment

Thebasicprincipleis simple.2 Theexperimentis performedat a constant temperatureby titrating one binding partner(called the ‘titrant’, e.g. L) into a solution containing theother binding partner(called the ‘titrand’, e.g. M) in thesamplecell of thecalorimeter.After eachaddition of asmallaliquotof L, theheatreleasedor absorbedin thesamplecellis measured with respectto a referencecell filled withbuffer.Theheatchangeis expressedastheelectrical power(J sÿ1) required to maintain a constantsmall temperaturedifferencebetweenthe samplecell and the reference cell,whicharebothplacedin anadiabaticjacket.Addition of L isautomatedandoccursfrom a precisionsyringedrivenby a

computer-controlled steppermotor. The contentsof thesample cell are stirred to effect rapid mixing of thereactants. In commercially available instrumentsvolumesof sample cells arein the range0.2–1.4ml. The amountoftitrandrequiredperexperimentdependsonthemagnitudeofthe heatchange;10–100nmol of proteinaretypical.

Figure1A showstherawdataof anITC experiment. Eachpeak corresponds to the heat releasedon addition of analiquot of ligand to the receptor. Integration of thedifferential power signal with respect to time yields theapparentheatchange, Dqi,app, between additions iÿ1 andi:

�qi;app� qi ÿ qiÿ1

Dqi,appcorrespondsto theareaof the ith peakin Fig. 1A.If KA is largeandthemolarratio of L to M at thebeginningof thetitration is low, thenvirtually all theligandis boundtothereceptor andthepeakareasaresimilar. As thefractionalsaturationincreases,Dqi,appgradually decreases.Eventuallyall receptor sites are saturated. Small heat changesregisteredafter full saturation are caused by the heat ofliganddilution, qi,dil, andby other nonspecificeffects,qi,ns.Dqi,appis proportional to thevolumeof thecalorimetriccell,Vcell, to the changein concentration of the bound ligand,D[Li]bound= [Li]bound,ÿ [Li-1]bound, and to the apparentmolar enthalpy of association, DHapp. We write:

�qi;app� �qi ��qi;dil ��qi;ns

� ��Li �bound� Vcell ��Happ�6a�

Dqi,dil � Dqi,ns is obtainedfrom ablanktitration of ligandinto buffer. Vcell is known, andDHapp is constantat fixedpressure,temperatureandsolventconditions.DHappandKA

arecalculated from:

�qi � �qi;appÿ�qi;dil ÿ�qi;ns� n�M �totVcell�Happ� R

�6b�[M]tot is thetotal concentrationof M in thesamplecell of

the calorimeter. Dqi is the effectiveheatchangecausedbytheformation of complex ML at the ith step of thetitration,andR is the root of the quadratic equation:

Y2i ÿ Yi � 1� 1

nKA �M �tot� �Li �tot

n�M �tot

� �� n�Li �tot�M �tot � 0

�7�Yi is the degreeof saturation definedby Yi = D[Li]bound/

[M]tot. [Li]tot is the total concentration of L addeduntilinjection i, andn is thenumberof identical andindependentbindingsitesfor theligandL onthereceptor M. A nonlinearregressionprocedurebasedon Eq (6b) yields n, KA andDHapp from a single titration experiment.

The experimental datacanbeplotted in two ways.In thedifferentialmodethetotalheataccumulatedupto injectioniis normalizedto thetotal ligandconcentrationatstepi andisplotted againstthe total li gandconcentration at step i (oragainsttheratio of thetotal ligandconcentrationat stepi tothe total receptor concentration, [Li]tot/[M]tot). This yieldsthefamiliar sigmoidal titration curveshown in Fig. 1B fromwhich the total calorimetric heat change per mol ofcomplex, DHapp, can be calculated. In the integral mode,the total cumulative heatis plottedagainstthe total ligandconcentration to yield a hyperbolic saturation curve (Fig.

2 Technical details on the constructionof modernmixing calorimeters,theirperformanceand sensitivity, and on the theory of data analysishave beendescribedelsewhere(McKinnon et al., 1984;Wisemanet al., 1989; Freire etal., 1990;Breslaueret al., 1992).

Figure 1. ITC titration data describing the formation of a 16 bpDNA duplex by mixing the complementary strands at 30°C. PanelA shows the differential power signal recorded in the experiment.After integration with respect to time and normalization per molof added ligand (which in this case is single-stranded DNA),DHapp, KA and n can be calculated from Eq. (6) by nonlinear leastsquares analysis, as detailed in the text. The integrated data canbe plotted in two ways: as a sigmoidal plot (panel B) or as ahyperbolic saturation curve (panel C). The DHapp obtained fromthis analysis is a global property of the system corrected fornonspeci®c effects. The solid lines in panels B and C correspondto DHapp = 436 kJ molÿ1, KA=3.1� 106Mÿ1, and n = 1.

ITC AND DSC—REVIEW 5


1C). The same parametersare obtainedfrom either plot.Comparative statistical analysis of the two plots can giveinformation about the accumulation of systematic errors(Bundle and Sigurskjold, 1994). The number of bindingsites, n, and DHapp are strongly correlated, and thesuccessful deconvolution of the binding isotherm oftendepends on additional independentinformation about thenumber of bindingsitesof M.

The casediscussedappliesonly to the binding of L to areceptor M with n identicalandindependent bindingsites.Inthecaseof areceptor with multiplebindingsitesof differentaffinity, statistical thermodynamic treatment of the dataisrequired. The partition function Q givesa general descrip-tion of abindingreaction(WymanandGill, 1990).Q relatesthesumof concentrationsof all speciesto theconcentrationof anarbitrarily chosenreferencespecies, conveniently theunligated form of a receptor:

Q��M � �Pn

j�1�MLj �

�M � � 1�

Pnj�1�MLj �

�M � � 1�Xn

j�1

�j � �L�j

�8�In this equation, [L] and[MLj] arethe concentrationsof

free ligand and ligated receptor, respectively, n is thenumberof bindingsiteson thereceptor, andbj is theoverallbindingconstantrelative to theunligatedreceptor.It canbewritten in terms of the overall step-wise (macroscopic)binding constants, K, as

�j �Yn

j�1

Kj

or in terms of the intrinsic (microscopic) site bindingconstants,k, as

�j � n!

j!�nÿ j�!Yn

j�1

�j

Diff erentbindingmodelscanbediscriminateddependingon the definition of bj. In the caseof a singlebinding site,Eq. (8) reducesto:

Q� 1� KA �L� �8a�where KA is the intrinsic (microscopic) site bindingconstant. If the receptor has one set of j identical andindependentbinding sites:

Q� �1� KA � �L��j �8b�For m sets,eachcontaining j identical and independent

binding sites:

Q�Ym

1

�1� KA;m � �L�� jm �8c�

In the caseof cooperativity between a priori identicalbinding sites, the first ligand binds with KA,1 = KA, thesecond with KA,2 = a� KA, the third with KA,3 = a� b�KA, and so on. The cooperativity factors a, b, … ac-count for the change of intrinsic binding affinity ofthe unoccupied sites when the degree of saturationincreases.

Equation(7) shows that thedeconvolution of thebindingisotherm from anITC experimentrequirescalculationof thechange in the degree of saturation, Yi, with ligandconcentration. In terms of the binding partition function,Yi is expressed by

Yi � @ ln Q@ ln�L� �

Pnj�1

j�j �Li �j

Q�9�

Since [Li]B = [M]tot� Yi, the total heat change aftercompletion of injection i is

�qi � MT � Vcell

Pnj�1

�Happ;i j�j �Li �j

Q�10�

With thehelpof this statistical thermodynamic treatmentit is possible to deconvolute a heat binding isotherm ofa complex system involving non-equivalent and/or inter-acting binding sites. There are instructive examplesdemonstrating the strength of this approach(Eisensteinet al., 1994; Ferrari and Lohman, 1994; Hyre and Spicer,1995; Bruzzeseand Connelly, 1997; Gopal et al., 1997).The deconvolution has a firm thermodynamic foundationand avoids additional assumptions as is necessary inthe analysis of spectroscopic binding data. In practice,however, the success much depends on the quality of theexperimental data and on the number of coupled fittingparameters.

Infor mational content of ITC data

Free energy changes. As in otherbinding experiments,toobtain reliable binding constants the concentrationsof theinteracting specieshaveto bein a proper rangesothatboththe free ligands and the complex are populated. If theconcentration of binding sites is very much higher than1/KA, all the ligand addedwill be bounduntil saturation,and the binding isotherm as displayed in Fig. 1B has arectangular shapewith a slopeapproachinginfinity. In theopposite casein which the binding site concentration ismuch below 1/KA, thebinding isotherm is very shallowandfull saturationis difficult to approach.For accuratevaluesofKA, theconcentrationof receptor bindingsitesshould notbevery much higher than 1/KA. The dimensionlessnumberobtained by multiplying KA with the total binding siteconcentration is called the c-value(Wiseman et al., 1989).As a rule of thumb,c-valuesbetween 10 and100give goodKA-values.Often,however, optimal concentrations arenotaccessible. For very tight binding reactions, optimalconcentrations are too small to yield measurable heatchanges. It is for this reason that even with the mostsensitive instrumentspresently available, KA higher thanabout109 Mÿ1 (DG� ÿ50 kJ molÿ1 at roomtemperature)cannotbeveryaccurately measured.Very tight bindingcanbe analyzed by DSC to be discussedin the sectionDiff erential ScanningCalorimetry. At the other extremewhen KA is very low, the concentrations required for c-valuesbetween10 and100maybesohigh thataggregationof macromoleculescanobscure the binding reaction.



If DG of binding is temperature dependent, it is some-times possible to chosea temperature at which KA canbemeasured by ITC. Unfortunately, often KA is practicallyindependentof temperature becauseof strong enthalpy/entropy compensation. In this case, the thermodynamiclinkagetheory providesageneral framework for calculatinghigh bindingconstantsfrom anappropriatethermodynamiccycle. For example, KA canchangewith pH andonemaychosea pH whereKA can be obtainedby ITC. If the pKa

valuesof theligatedandtheligand-freeform of thereceptoris known, DG at the tight binding pH conditions can becalculated (Doyle et al., 1995; Baker and Murphy, 1996;Kavanoor and Eftink, 1997). Alternatively, ITC titrationscanbeconductedby titrating a strongly binding ligand intoa solutioncontainingthe receptor alreadysaturatedwith aweakerligand.Freebindingenergiesareobtained from sucha displacement experiment if the strongand weak ligandsexhibit suitabledifferences in bindingenthalpy (Khalifahetal., 1993; Hu andEftink, 1994;Sigurskjold et al., 1994).

Enthalpy changes. Themolar bindingenthalpyDHapp is afitting parameter according to Eqs (6b) and (10) and isobtainedtogether with KA from datacollected in theoptimalconcentrationrange.A betterpracticeis to measureDHappatconcentrations where the binding partners are fullyassociated when the degree of saturation is still low. Insuchexperiments theaccuracyof DHapp is better, yet thec-value is too high for accuratedeterminationof KA. Thus,inpractice KA andDHapp arebestobtainedfrom experimentsperformedat differentconcentrationratios.

The enthalpy change measured by ITC is a globalproperty of thewholesystem.It is the total heatreleasedorabsorbed in the calorimetric cell on eachaddition of theligand. The total heat contains contributions arising fromnonspecific effects. Theseare the heat of dilution of theligand into buffer, heatcausedby the incompletematchofthe temperaturesof the solutions in the cell and at theinjection syringetip, or heateffectsfrom mixing of buffersof slightly differentchemical composition.Thenonspecificheateffectsareaccounted for byDqi,dil andDqi,ns in Eqs(6a)and(6b). But eventhecorrectedheatchangeDqi of Eq.(6b)is itself composedof different contributions. This is thereasonwhy the molar enthalpy change is an apparentquantity (DHapp). It only depends on the initial and finalstateof thebindingreaction,thesolvated freemoleculesandthe final solvatedcomplex.

Contribution of reorganization of solventto DHapp andDG. From the comparison of the calorimetric enthalpychangein H2O and D2O it was concluded that solventreorganization accounts for a large portion of DHapp

(Connelly et al., 1993; Chervenak and Toone, 1994).Indeed, in high-resolution crystal structures, water mole-culescanbeseenat thecomplex interfacewheretheymayimprove the complementarity of the interacting surfaces,andboundwater is sometimesvisible at the emptycontactsurfaceof thefreemolecules(Ladbury, 1996).ExtendedH-bond networks at the complex interface can make theenthalpy changemore favorable,often counterbalancedbyan entropic penalty (Bhat et al., 1994; Holdgate et al.,1997). That addition or removal of interfacial watercontributesto thefreeenergy of bindingwasdirectly shownby lowering the wateractivity throughaddition of glycerol

or another osmolyte (Kornblatt et al., 1993;Robinson andSligar, 1993; Jelesarovand Bosshard, 1994; Goldbaumetal., 1996;Xavier etal., 1997).Complexeswith a low degreeof surface complementarity and with no net changeofhydrationaretolerantto osmoticpressure(Lundback et al.,1998).

Contribution of directnoncovalent bondstoDHapp. Apartfrom thebulk hydrationeffects,directnoncovalent bondsatthe interfacecontributeto DHapp. Thesecontributionsmaybe consideredto representthe binding enthalpy in a strictsense. Yet it is very difficult to sort out the enthalpy offormation of eachspecificnoncovalent interaction. Thenetenthalpy effectof a particular noncovalent bondX–Y at theinterfacecanresult from thebalancebetween theinteractionenthalpy of thebondX–Yin thecomplex andtheenthalpiesfrom bondsbetweenthesolventor solutesandX andY in theisolated molecules. Further, subtle rearrangements of thepacking interactionsat thebindingsitecomparedto thefreemoleculemay addto DHapp.

Mutational approaches have been tried to analyzethecontributions of individual bondsto the enthalpy change.Examplesarealanine scanning mutagenesis(Pearce et al.,1996), removalof a particular H-bond at the binding site(Connellyetal., 1994), or theconstructionof doublemutantcycles(Frischetal., 1997).Calorimetric analysisof mutantssuffersfrom amajorproblem:CanoneattributeachangeofDHapp to the removal of a specific contact? Or is theenthalpic effect of an indirect nature anddecomposition ofDHapp in terms of individual residue-residue contacts oreven atom-atom interactions is not possible? It has beenargued on theoretical grounds that suchdecomposition ofDHapp (aswell asof DG andDS) is not possible (Mark andvan Gunsteren,1994).But others havearguedin favor ofdecompositionof DHapp(BoreschandKarplus,1995;BradyandSharp,1995).

In general,changes of DHapp are not, or only weaklycorrelatedto changesin DG. Recentcarefulanalysisof threeprotein systems indeed suggests the correlationcannot bemade (Ito et al., 1993; Pearce et al., 1996; Frisch et al.,1997). Onereasonfor this unfortunatesituation is enthalpy/entropy compensation. The overall change in bindingenthalpy due to a particular mutation can be partlycompensated by an entropy change. As a result,thereonlyis a small change in the free energy of binding. Thiscommon thermodynamic behavior is thought to reflect amajor role of compensating enthalpy andentropycontribu-tions of waterto thebindingprocess(Lumry andRajender,1970; Dunitz, 1995;van Oss,1997).

Calorimteri c and van’t Hoff enthalpy changes. Thevan’tHoff enthalpy change (DHvH) is calculated from thetemperaturedependenceof KA obtained either by ITC orcalculatedfrom spectroscopicor otherdata[Eq. (5)]. Hence,DHvH reflectsthe enthalpy intimately associated with thebindingeventthatcausesthesignalchange, for example thequenching of thefluorescenceof a tryptophanresiduein thecomplex ML. Therefore, DHvH equalsDHcal only if thebinding reactionfollows a two-statetransitionbetween freeand bound molecules and if the signal changeused tocalculateKA reflects theentirepopulationof freeandboundmolecules. Otherwise, DHcal and DHvH are different.Indeed, systematic discrepanciesbetween DHcal andDHvH



havebeenreported(Gilli et al., 1994;Naghibiet al., 1995)andtherehavebeenattempts to rationalize the differences(Dunitz, 1995;Chaires,1997;vanOss,1997).On theotherhand,aratioof DHcal/DHvH = 1 canbetakento indicate thata bindingeventconformsto a two-statetransitionfrom freemolecules to the complex with no detectableintermediatesand with at most very minor contributions from waterreorganization,conformational rearrangements, or changesin the stateof protonation.3

Protonation effects. Among the many possible contribu-tionsto DHapp, theeffectof changes in theprotonation stateis worth considering in moredetail becausethe number ofprotons, nH�, taken up or releasedduring the bindingprocesscanbemeasuredby titrationcalorimetry (Murphyetal., 1993;JelesarovandBosshard, 1994;GomezandFreire,1995;Kresheck etal., 1995). If bindinginvolvesachangeinthe protonationstateof L and/orM, protonsareexchangedwith the buffered medium. Therefore, the calorimetricallyobservedenthalpy change, DHapp, depends on the enthalpyof ionization of the buffer, DHbuffer. Repeating theexperiment at the samepH in buffersof differentDHbuffer

allows oneto calculate thebinding enthalpy, DHbind, from:

�Happ� �Hbind� nH� ��Hbuffer �11�Values of DHbuffer have beentabulated (Christensenet

al., 1976) or can be measured by ITC (JelesarovandBosshard, 1994).DHbind can be partitioned further into atermthat is independent of theprotonation change, DH'bind,and a term describing the enthalpic contribution of theprotonation reaction,DHH�:

�Hbind � �H 0bind� nH��HH� �11a�Combining Eqs(11) and(11a):

�Happ� �H 0bind� nH� �HH� ��Hbuffer� � �11b�If a pH can be found wherebinding is pH-independent

(nH� = 0),DHapp= DH'bind follows from Eq.(11b). Figure2shows an example in which binding of two proteins isaccompaniedby theuptake of a single proton.This systemwas particularly revealingsinceDH'bind was 26kJ molÿ1,very muchhigherthanDHapp becauseDH'bind andDHbuffer

almostcanceled at pH 7. In practice,it is recommended toalwaysrepeattheITC experimentat thesamepH in abufferthat hasa differentheatof ionization. If the sameDHapp isfoundin bothbuffers, there is nochangein protonationof Land/or M whenthecomplex forms.Conversely, variationofDHapp with buffer is a clear sign of a protonation eventduring the association reaction. Occasionally, one mayobtain a hint from DHH� (deducedwith thehelpof Eq. 11)about the nature of the group(s) undergoing protonation/deprotonation(Jelesarov and Bosshard, 1994; GomezandFreire,1995;BakerandMurphy, 1997).

Heat capacity changes.Modern ITC instrumentsallow to

precisely measure DHapp between about5 and 70°C, andDCp canbecalculatedfrom aplot of DHappversusT (Eq.3).In manycasessuchplotsarelinearwithin theexperimentalerror in a narrow temperature range, suggesting that DCp

itself doesnot dependon temperature.What is theorigin ofthechangein heatcapacitywhen acomplex is formed?DCp

is almost always negative if the complex is taken as thereferencestate. This meansthat the complex hasa smallerheatcapacity thanthesumof its free components.This andother observations as well as theoretical considerationsindicatethatDCp originatesfrom changes in the degree ofsurfacehydrationin the freeandthecomplexedmolecules,and to a lesser extent also from changes in molecularvibrations (Sturtevant, 1977; Murphy and Freire, 1992;Spolar et al., 1992; Gomezet al., 1995; Makhatadze andPrivalov, 1995).The often seentemperature-independenceof DCp infersthatneithertheareaof contactsurfacenor thedifferenceof the vibrational content between the complexandits componentschangewithin theobservedtemperaturerange.

Calculated and measured DCp. The association of twoproteinsto a complex canbe compared to the folding of asingle protein. In both reactionsa substantial fraction ofpolar and nonpolar surface is buried and the degree ofsurface hydration is likely to change. There are semi-empirical methodsto calculateDCp from thechangeof thewater-accessible polar andnonpolar surfaceareain proteinfoldingandin proteinassociation(MurphyandFreire,1992;Spolar et al., 1992; Makhatadze and Privalov, 1995).Several communications report good agreement betweentheexperimentally determinedDCp andthatcalculatedfromthemolecular surfaceburiedin thecomplex (Connelly andThomson,1992;Murphy et al., 1993;Baker andMurphy,1997; McNemaret al., 1997).However, a goodcorrelationseems to hold only for thoseinteractions that conform to alock-and-keyor rigid-body binding model.Very often this

3 For DHcal/DHvH = 1 in a system in which there is considerablewaterreorganization, conformationalrearrangementor changein protonationstates,the observablepi of Eq. (4) has to mirror all the above phenomena.Thisseemsnot very likely in casethe observableis, for example,a fluorescencechangeof a singlechromophore.

Figure 2. Apparent enthalpy change, DHapp, for the binding offerredoxin to ferredoxin:NADP� oxidoreductase at 27°C as afunction of the ionization enthalpy of the buffer. ITC experimentswere performed at pH 7.5 in Tris (square), Mops (triangle),phosphate (circle), and cacodylate buffer (diamond). Dashed line:linear least squares ®t to Eq. (11). Slope = 0.96� 0.03; intercept atzero buffer ionization enthalpy = 1.03� 1.46 kJ molÿ1. (Adaptedfrom Jelesarov and Bosshard, 1994.)



model is inadequate. Significant discrepancies betweencalculatedandmeasuredDCp werereportedfor small ligandbinding(Faergemanet al., 1996;Holdgateet al., 1997),forprotein-protein complexes(Bhat et al., 1994;Pearce et al.,1996),andmost notably for protein-DNA complexes(Jinetal., 1993;Ladburyet al., 1994;Ayala et al., 1995;MerabetandAckers, 1995;Bergeretal., 1996;Odaetal., 1998).It isaccepted that a lack of correlation between measuredandcalculated values of DCp is a consequence of foldingtransitions coupled to the association event (Spolar andRecord, 1994),andalsoto significant dynamicrestriction ofvibrational modesat thecomplex interface(Botuyanet al.,1993; Ladbury et al., 1994; Berglund et al., 1997).Interestingly, weaker complexes tend to show larger DCp

valuesperunit of surfaceareaof contact.The likely reasonis enhancedenthalpic andentropic fluctuationat a lesstightcomplex interface (Tidor and Karplus, 1994). Largeconformational rearrangements during binding and thepreexistence of temperature-dependent conformationalequilibria can causedeviationsfrom linearity in the plotsof DHapp against T, that is, temperature-dependent DCp

(Ferrari andLohman,1994;BruzzeseandConnelly, 1997).No doubt, the methods to calculate DCp from theparametrization of structuraldataneedmuchimprovementbefore becoming reliable predictors of heat capacitychanges. In the meantime onehasto rely on experiments.Here, a very careful examination of the conformationalstatesof themoleculesin isolation andof thecomplextheyform is required to account for theobservedenergeticvaluesin structural terms (Pearceet al., 1996; Wintrode andPrivalov, 1997;Odaet al., 1998).This information canbeobtained by DSC.

Entropy changes. The entropy of association can becalculated from measured values of DG, DH and DCp

according to the laws of thermodynamics. The changeinentropyof a complex relativeto theunligatedmoleculesislargely caused by hydrationeffectsbecausethe entropyofhydration of polar and apolargroupsis large and thereissignificant reductionof wateraccessiblesurfaceonbinding.Therefore, when a complex is formed the overall entropychange is often large and often positive. Occasionally,however,ordering of waterat thecomplex interfaceoccurs,which contributes unfavorably to DS and favorably to DH(Holdgate et al., 1997). Another important, unfavorablecontribution to the entropy change originates from thereduction of side chain mobility at the binding site.Furthermore, a statistical term has to be added to theentropychangeto accountfor thereduction in thenumberofparticles and their degrees of freedom in the complex.Diff erent estimates of the mixing entropy have beendiscussed, yet it appearsthatthe‘cratic’ correction accountsadequately for the loss of translationand rotation (Kauz-mann, 1959; Murphy et al., 1994; Tamura and Privalov,1997). Obviously, a negative entropy changecan havedifferent reasonsand,most importantly, doesnot necessa-rily indicate that hydration of the interface remainsunchanged or increases with respectto the free complexpartners. On the other hand, a positive DS is a strongundication that water molecules havebeenexpelledfromthe complex interface.

Concluding remarks on ITC

Thebeautyof titrationcalorimetry is in its simplicity, whichallowsto obtaintheentiresetof thermodynamic parametersfrom performing only a few experiments at a seriesofdifferent temperatures.The difficulty, however, lies in thefact that the observedheatchange, which is the immediateoutcomeof ITC, is a global property. Only in those caseswhere thebinding reaction follows a lock-and-keyor rigid-body mechanism that can be described by a two-statetransition betweenfree and complexed molecules, and inwhich thereis nochangein theprotonation stateof L and/orM nor in thehydration stateof theinterface, DHapp is equalto the ‘true’ binding enthalpy attributable to noncovalentbondsin thecomplex. A goodindicator– though noproof–for this simple mechanismis theequality DHcal = DHvH. Inthe majority of casesDHapp has different origins, whichoftenaredifficult to distinguish.Thecontributionsto DHapp

sometimes can be separated. For example, a positiveentropy changeis a good indication for the extrusion ofwaterfrom the complex interface.A changeof DHapp withthe chemical nature of the buffer points to a protonation/deprotonation eventconcurrent with the binding reaction,andcarefulanalysisof DHappwith bufferandpH canrevealthe number and sometime eventhe nature of the group(s)whose ionization statechanges.Finally, calculationof DCp

from theareaof thesurfaceburiedin thecomplex (possibleonly if the necessary three-dimensional structures areavailable) and comparisonwith DCp obtained by ITC cangive a clue as to changes in conformational states andvibrational contents between the complex and its freecomponents.Theselatter changescanbeanalyzedin moredetail with the help of DSCto bediscussednow.

Differential ScanningCalorimetry

DSCis themost directexperimental techniqueto resolve theenergetics of conformational transitions of biologicalmacromolecules.By measuring thetemperaturedependenceof the partial heat capacity, a basic thermodynamicproperty, DSC gives immediateaccessto the thermody-namic mechanism that governsa conformational equili-brium, for examplebetween the folded and the unfoldedforms of a protein,or between singleanddouble strandedDNA. The theory of DSC and the thermodynamicinterpretation of theexperimentaldatahavebeenthesubjectof excellentreviews(Privalov andPotekhin, 1986;Sturte-vant, 1987; Freire, 1995). The combination of DSC withITC to characterize the energy profile of an interactingsystem in a broad temperatureinterval and at varyingsolvent conditionshasbeenbrought up before (Connelly,1994; Plum andBreslauer, 1995).Herewe wish to give abasic description of the informational content of DSCmeasurements with special emphasis on the potential ofDSC to analyzethe energeticsof macromolecular associa-tion reactions.

The DSC experiment

DSC measures the heat capacity of a solution of the



molecule understudy asa functionof temperature.Modernscanning calorimeters are equipped with twin cells andoperate in a differentialmode. The solutioncontaining thesolute– in thepresentcontextabiologicalmacromolecule–is placedin thesamplecell andanequalvolumeof solvent(buffer) in the reference cell. The system is heated (orcooled)quasi-adiabatically at a constantrate,typically 0.5–1.5K minÿ1. 4 Sincetheheatcapacitiesof thesolution in thesamplecell and the solvent in the referencecell differ, acertainamount of electrical power is requiredto zero thetemperaturedifferencebetween the two cells. The powerdifference(J sÿ1), after normalization by the scanning rate(K sÿ1), is a direct measure of the heatcapacity differencebetween thesolution andthesolvent:DCp

sol-solv= Cpsol- Cp

solv

(in units of J Kÿ1).Obviously, oneis interestedin Cp(T), thepartial specific

heatcapacity (J Kÿ1 gÿ1) of thesoluteM To obtain Cp(T),the partial specificheatcapacity of the solvent, Cp,solv(T),has to be subtracted. This correction requires preciseknowledge of the massesof the macromolecule and thesolvent, of the mass of the solvent displaced by themacromolecule,and of the partial specificvolumesof themacromolecule and the solvent. These quantities aretemperature dependent and the coefficients of thermalexpansion of the chemical species as well as of thecalorimetric cell must be known. It canbe shownthat thepartial specificheatcapacity of the soluteM (in units of JKÿ1 gÿ1) is given by:

Cp�T� � Csolvp

vM

vS��Csolÿsolv

p

mM�12�

mM and vM are, respectively, the mass and the partialspecificvolumeof M, andvs is thepartial specificvolumeofthe solvent.

Because the measuredpower difference, �Csolÿsolvp , is

small and the volumesof the calorimetric cells are 0.3–1.5ml, milligram amounts of biomacromolecules arenecessary for DSC measurements. In some cases, themacromolecule concentrations may be so high that thesolutions are far from the ideal condition to which thethermodynamic models apply.This difficulty hasto bekeptin mind when performing DSC measurementsandonehasto checkfor nonspecific aggregation of macromoleculesinthecalorimetercell, oftenrevealedby afaint turbidity whenthe solution is removedfrom the cell after the experiment.

Infor mational content of DSC data

The first result obtained from a DSC experimentis thepartial specific heatcapacity,Cp(T). This quantity containsimportant information aboutthe conformational stateof aprotein in the temperature interval of the experiment. Forsmall globular proteins, the absolute value of Cp at 25°Cvariesin therange1.2–2.3J Kÿ1 gÿ1 andincreaseslinearlywith temperaturewith a slopeof (6–8)� 10ÿ3 J Kÿ2 gÿ1.Deviationsfrom thesevaluesmayindicate loose packingoftheproteinor structural fluctuations(PrivalovandPotekhin,

1986; Gomezetal., 1995).Thepartial specific heatcapacityof the nativeprotein is significantly lower than that of thedenatured protein. Cp of a fully unfolded protein can beapproximatedfrom theaminoacidsequenceby summingupthe heat capacities of the amino acid residues and thecontributions of the peptidebonds(Privalov and Makha-tadze, 1990; Makhatadze and Privalov, 1995). If theexperimentally measuredCp after completion of unfoldingis lower thanCp calculatedfrom the aminoacid sequence,this may indicate that the denaturedprotein has someresidual structureand is not a fully solvated polypeptidechain.5

When a protein solution is heatedup, Cp(T) follows apeak-shaped curveif proteindenaturationis cooperative andreversible.Figure3 showsa typical DSCtrace,alsocalled athermogram or a thermal transition curve. The proteindenatures in the temperature interval T1 to T2 with atransition midpoint Tm.

4 A constantpressureis applied to the two cells. Depending on this pressure,the uppertemperaturelimit canbe ashigh as150°C for aqueoussolutions.

Figure 3. Partial molar heat capacity of a protein undergoingreversible thermal denaturation in the temperature interval T1ÿT2

and with a transition midpoint at Tm. The heat capacity of thenative state, hCp,Ni, shows a linear temperature dependence(dashed line). The heat capacity of the denatured state, hCp,Di, isapproximated by a quadratic function (dashed-dotted line). Thefunctions hCp,N(T)i and hCp,D(T)i can be extrapolated into thetransition zone between T1 and T2 in proportion to the progress oftransition (dotted line). The difference between hCp,Di and hCp,Niis the heat capacity increment of protein denaturation, DCp

den. Itis positive because the denatured protein has a larger heatcapacity than the native protein. The excess partial heat capacity,hDCpi, is de®ned as hDCpi = hCpi ÿhCp,Ni. hDCpi is composed of theintrinsic excess heat capacity, hdCp

inti, which accounts for all themolecular species that become populated in the progress of thetransition from the native to the denatured state, and from thetransition excess heat capacity, hdCp

trsi, originating from theincreased ¯uctuation of the system when the protein changesbetween different enthalpic states in the course of thermaldenaturation. The relative magnitudes of hdCp

inti and hdCptrsi at

temperature Tx are indicated.

5 The term ‘denatured’refers to the ensembleof conformational stateswhenthermal transitionis complete. In practice,this is at a temperaturewell abovethe transition temperature Tm. The denaturedprotein is not necessarilyequivalent to the completely unfolded protein, which is an idealized statereferring to the polypeptidechain in its fully solvatedconformation.Hereweprefer the term ‘denatured’to indicatethis difference.



For a meaningful comparisonof the thermal transitioncurves of different substancesthe specificheatcapacityisinadequate because it is normalized to the mass ofsubstance. The appropriate quantity is the partial molarheat capacity, hCpi, which has units of J Kÿ1 molÿ1.It is obtained by multiplying Cp (J Kÿ1 gÿ1) by themolecular weight (g molÿ1). The angular brackets, h i,designate the ensemble-averagedpopulationof all mole-cular statesthat becomepopulated during the transitionfrom thenativeto thedenaturedform. It is very importanttorecognizethatduringthetransitionthepartialheatcapacityfunction can no longer be ascribed to a single structuralstate.

The partial molar heat capacity of the native protein,hCp,Ni, can be approximated by a linear function (dashedline in Fig. 3), andthatof thedenaturedprotein, hCp,Di, by aquadratic function (dash-dottedline in Fig. 3) (Griko et al.,1994b; Viguera et al., 1994; Xie et al., 1994). The heatcapacity increment accompanying protein denaturation, orheat capacity of denaturation for short, is defined asDCp

den= hCp,D(T)i ÿ hCp,N(T)i. It is positive because thedenatured proteinhasa largerheatcapacity thanthenativeprotein. The absolute specificDCp

den is similar for manyglobular proteins,typically 0.3 to 0.7J Kÿ1 gÿ1. A positiveDCp

den is mainly a consequence of hydration effectsdominated by the positive heat capacity of hydration ofapolar groups, which becomeexposed to the solventwaterafterdisruption of thecompactfoldedconformation. Semi-empirical methodshavebeendevelopedcorrelatingDCp

den

with the increase of solvent accessible surface upondenaturation (Murphy and Freire, 1992; Spolar et al.,1992;MakhatadzeandPrivalov, 1995).6

Excess heat capacity, excess enthalpy and excessentropy. If the native state is taken as a reference,anexcesspartial molar heatcapacity canbe definedas

h�Cpi � hCpi ÿ hCp;NiThe excess heat capacity can be divided in two

components.The first componentaccounts for the sumof the molecular speciesthat becomepopulated in theprogressof the transitionfrom the native to the denaturedstate.7 This componentis often referred to as the intrinsicexcess heatcapacity, hdCp

inti. The second contribution tohDCpi originates from the increased fluctuation of thesystem when the protein changes between differententhalpic statesin the courseof thermal denaturation. Thiscomponent is called transition excess heat capacity,hdCp

trsi, and is usually much larger than hdCpinti as

indicated in Fig. 3. The excess molar heat capacity cannow be written as:

h�Cpi � h�Cintp i � h�Ctrs

p i �13�

To calculate hdCpinti, the functions hCp,N(T)i and

hCp,D(T)i haveto be extrapolated into the transitionzonebetween T1 andT2 in proportion to theprogressof transition(Sturtevant, 1987). This extrapolation is indicatedby thedotted line in Fig. 3. The excess enthalpy of the thermaldenaturation,DHden, is definedby:

�Hden�Z T2

T1

h�Ctrsp idT �14�

DHden corresponds to the area of the peak above thedotted line in Fig. 3. The excessentropyof denaturation isdefinedby:

�Sden�Z T2

T1

h�Ctrsp i

TdT �15�

DHden represents the ‘true’ calorimetric estimate of thedenaturationenthalpyandis amodel-independent value,i.e.it does not dependon the shapeof the transition curvebetween T1 andT2.

The integral of dCptrs [Eq. (14)] can also be analyzed

according to the van’t Hoff equation to obtain DHdenvH,

sometimes called the ‘effective’ enthalpy of transition.DHden

vH is model-dependent.Thereason is thatdetermina-tion of DHden

vH assumesan equilibrium between only twoforms, native and denatured protein, to calculate anequilibrium constant K(T) from which DHden

vH followsaccording to Eq. (5a). DHden

vH now canbe comparedwiththe calorimetric, model-independent enthalpy change,DHden

cal, described by Eq. (14) (the superscriptcal is addedonly to distinguish the calorimetrically measuredquantityfrom thecalculatedvan’t Hoff enthalpy change).If DHden

vH

/ DHdencal = 1, denaturation is thought to obeya two-state,

cooperative unfolding reaction. A ratio >1 may indicatesignificantly populated intermediate states. Values aboveunity also result if thedefinition of thecooperatively foldingunit is not the same in the calorimetric and in the van’tHoff analysis. This is the caseif the excessheatcapacityfunction does not display a symmetric curve and hidestransitionsbetween morethantwo states.8 A ratio<1 pointsto an irreversible process. The approach to compareDHden

vH with DHdencal, both calculatedfrom DSC data as

outlined above,may be in error when hdCpinti is not much

smaller than hdCptrsi and, more generally, if the system

deviatesfrom thetwo-statebehavior (Privalov andPotekhir,1986).

Statistical thermodynamic treatment of the heat capa-city function. At this point it is important to discuss thehigh informative potential of a statistical-mechanicaltreatment of DSC data.The strength of the DSC methodis that it provides direct access to the system partitionfunction without invoking ad hoc assumptions about thethermodynamic mechanism of conformational transition

6 The vibrational contentof the polypeptidechain increasesupon unfolding,which also contributesto the positivevalueof DCp

den. The magnitudeof thiseffect is small in comparisonto the hydration effect. Parametrisation ofDCp

den in terms of the change in solvent-accessiblesurfacearea has beenbasedon thermodynamicdata for the dissolutionof model compounds.Theparametrisationpartly accountsfor vibrationalcontributions.7 In the caseof a simple two-state transition it is only the native and thedenaturedstate.

8 hdCptrs(T)i is a symmetric bell-shaped curve only for monomolecular

transitions. In the case dissociation of a complex and unfolding of itscomponentsare coupled reactions,the heat capacity trace is skewedat thehigh-temperatureshoulder.The maximum of the heat absorptionpeak,Tm, ishigher than the temperatureat which the transition is half-complete(Fi =0.5,see the section ‘Statistical thermodynamictreatment of the heat capacityfunction’.



(Freire and Biltonen, 1978a,b; Freire, 1994). For anarbitrary systemcontaining N different states(N = 2 for atwo-state transition), the system partition function isdefinedas:

Q�XN

i�1

Ki �XN

i�1

exp ÿ�Gi

RT

� ��16�

The expressionunderthe summation sign represents thestatistical factors of eachstate.DGi is definedby Eq. (1).Theexcessenthalpyof thesystemwith respectto thenativestateis:

h�Hi �XN

i�1

�HiFi �17�

where DHi is the enthalpy of statei relative to the nativereferencestate,andFi is thepopulationof statei in termsofthe system partition function Q:

Fi �exp ÿ�Gi

RT

ÿ �Q

�18�

Sincetheexcessheatcapacity is thefirst derivativeof theexcess enthalpywith respect to the temperature,hDCpi canbe expressed as:

h�Cpi � h�HidT

�PNi�1��HiFi�

dT

�XN

i�1

�Cdenp Fi �

XN

i�1

�HidFi

dT

�19a�

andafter differentiation of dFi/dT:

h�Cpi � h�HidT

�XN

i�1

�Cdenp Fi � h�H2i ÿ h�Hi2

RT2

�XN

i�1

h�Cintp;i i �

XN

i�1

h�Ctrsp;ii

�19b�The statistical-mechanical treatment does not include

arbitrary assumptionsaboutthenumber of statespopulatedin thetransitionprocessandaboutthemutualinteraction ofthese states.The data can be rigorously tested againstdifferent thermodynamic models by variation of thedefinition of the partition function. Well-establishedstatis-tical optimization procedures areusedto find a model thatbest describes the experimental data. This approachhasbeen successfullyexploited to study complex unfoldingprocesses(Montgomery et al., 1993; Griko et al., 1994a;Haynie andFreire, 1994;Johnson et al., 1995).

Appl ication of DSC to association reactions

How canwe derive the energetic parametersof biologicalassociation reactionswith thehelpof DSCdata? If a ligandL bindsto thenativestate of a protein M with high affinity,the heatcapacity of the resulting complex LM will differfrom that of M and L alone. As a consequence,the DSC

profilesof L, M andML will havedistinct shapes.Dramaticdeformationsof the thermogramsof proteinsin the ligatedstate have been reported (Takahashi and Fukada,1985;ShrakeandRoss,1990;Lin et al., 1994;Conejero-LaraandMateo, 1996). The influence of ligand binding on thestability of a whole protein, or a protein domain,can belarge evenif the ligand is a small organic compound.Thesituation is evenmorecomplicatedwhen theliganditself isa macromolecule undergoing conformational transition(s)with temperature.Furthermore,becausethebindingaffinityand the stability of the complexpartners and the complexitself aresensitiveto pH, to ionic strengthandto thenatureof cosolutes, the excessheatcapacity function, hDCp(T)i,canbedistortedwhen thesolventconditionsvary (Ramsayand Freire, 1990; Carra and Privalov, 1997). A carefuldeconvolution of theobservedthermogramsgivesinsightinthethermodynamic forcesthatdrivetheassociationreactionand can provide structural and mechanistic informationaboutthe interacting molecular species(Daviset al., 1995;Lit vinovich and Ingham, 1995; Filimonov and Rogov,1996).

Whenthemutualstabilizationof thecomplex partners inML is high, the dissociation of the complex is tightlycoupledto thedenaturationof its components.Theresultisa single peak in the heat capacity trace at a temperatureabovethedenaturationtemperaturesof L andM in isolation.Figure 4 showsan idealized example. In such a case, asimplified procedurecanbe appliedto extractthe enthalpyof complex formation. It involves extrapolation of theenthalpiesof denaturation of thecomponents to themeltingtemperatureof the complex (Fukada et al., 1985;Makarov

Figure 4. Simulated excess heat capacity pro®les of ligand L,protein M and complex ML. In this idealized example, thermaltransitions of L (Tm = 320 K) and M (Tm = 340 K) are well separatedand lower than the thermal transition of the complex LM. Strongassociation leads to mutual stabilization of the complex partnersin LM. The dissociation of the complex is tightly coupled to thedenaturation of its components and a single peak appears in theheat capacity trace with Tm = 343 K, above the denaturationtemperatures of L and M in isolation. The curves were calculatedwith the help of Eq. (22) for the conditions given in Fig. 5 withDHc(298 K) =ÿ20 kJ molÿ1 and Kc(298 K) = 1010 Mÿ1.



et al., 1994; Yakovlev et al., 1995). The energetics ofcomplex formation canbestudied alsoby investigating thedependenceof DHm and Tm on the saturation level of thesystem(Bhushanand McNamee,1990; Shrakeand Ross,1990; Anteneodo et al., 1994; Horvath et al., 1994).However, in the majority of systems studied so far, theDSC trace has a complicated shapeand exhibits severaloverlapping transitions.Moreover, evenif the dissociationand the denaturationtake place in a narrow temperaturerange, there is no a priori information about a possibleredistribution of sub-statesin the melting zone.

Deconvolution of DSC traces.Thethermodynamic theoryof deconvolution of coupled equilibria in macromolecularsystems hasbeendevelopedalreadywith the first appear-anceof sensitivemicrocalorimeters.An extensive thermo-dynamic framework for extracting the free energy andenthalpy of binding from DSC datawasfirst developedbyRobert et al. (1989)andby BrandtsandLin (1990). Morerecently, the statistical-mechanicalaspects of the deconvo-lution techniquehavebeenformulatedby other investiga-tors in the light of a global linkage analysis of two-dimensional heat capacity surfaces (by variation oftemperatureand ligand concentration; Ramsay andFreire,1990;Straume andFreire, 1992;Straume, 1994;Baroneetal., 1995).The idea is to redefine the partition function ofthe system to account for the interaction between themolecules and then to use the standard expression ofstatistical thermodynamics, which is analogousto Eq. (5a),to calculatethe excess enthalpy:

� ln Q�T� h�Hi

RT2�20�

Therelevant equationscanbeexplicitly solvedfor only afew simple models, but numerical methodsof non-linearoptimization can help to adapta particular model to theexperimental data.To illustrate a strategyof how to dealwith heatcapacity traces, weagain considerthesimplecaseof interaction between L and M to the 1:1 complex ML,which we call C. The total concentrationsare kept equal,[L]tot = [M]tot. The overall process is described by thefollowing scheme:

LN � MN ÿ!KC

ÿ C

KL "# "# KM

LD MD

L and M exist in the native and the denatured form(subscriptsN andD, respectively). The freecomponents aredescribedby thefollowing setof parameters(X denotesL orM): free energies of denaturation, DGX; equilibriumdenaturation constants,KX; melting temperatures, TmX;denaturation enthalpies, DHmX; and heat capacity incre-ments of denaturation, DCp,X

den. The parameters for thecomplex C are: free energy of binding, DGC; bindingconstant, KC; arbitrarily chosenreferencetemperature,TR,C;enthalpy of complex formation, DHC; and heat capacitychangeof binding,DCp,C. In whatfollows,two assumptionsaremade. Only LN andMN interactto form thecomplex C,andTmC is alwayshigher thanTmX asshown in theidealizedexample of Fig. 4. If this second condition is not fulfi lled,

the denaturation of L and/or M are/is not coupledto thebinding equilibrium.

Thepartitionfunction of thesystemdescribestherelativepopulationof thenativeanddenatured statesof L, M andthepopulation of C. Formally,we canwrite separatefunctionsfor L andM:

QL � 1� KL � KC�MN�QM � 1� KM � KC�LN�

The two functionsarecoupledandthe concentrationsofLN, MN andC are:

�LN� � �L�tot

QL

�MN� � �M �tot

QM

�C� � KC�LN��MN�The concentrations of the free components, [LN] and

[MN], canbe solvedsimultaneouslyin termsof the knowntotal concentrationsand the equilibrium constantsKL, KM

and KC, which are temperature dependent parametersaccording to (subscriptX denotesL, M or C and subscriptR a referencetemperature):

KX�T� � KX�TR;X� exp ÿ�HR;X

R1Tÿ 1

TR;X

� ��Cp;X

Rln

TTR;X

� TR;X

Tÿ 1

� �� 21�

The excess enthalpy of the system, relative to thecomplex C as the reference state, for the given totalconcentrations[L]tot and[M]tot, canbewritten in analogytoEq. (17) as:

h�Hi �X

X�L;M

KX

QX�HX � KX

QX�Cp;X

� �ÿ �C��L�tot

�HC ÿ �C��L�tot�Cp;C

�22�

The last two termsin theaboveequation arecorrectonlyif [L]tot = [M]tot.

9 The combination of Eqs (21) and (22)describes the excessenthalpy function, hDH(T)i, of anassociating system. From the combined equations, theexcess heat capacity function, hDCp(T)i, is calculated byeitherexplicit or by numericaldifferentiation.

A setof simulationsaccordingto thisgeneralprocedureisshown in Fig. 5. Panel A shows how the DSC trace isinfluencedby thestabilityof thecomplex(variation of KC atfixedKM andKL). If the complex is weak,the thermogramshows the denaturation of free L and free M as two wellseparatedthermal transitions.Whenthecomplexdominates,a singlesharppeakat high temperature is seenbecausethedissociation of C and the denaturation of L and M arestrongly coupled.For casesin between, thetraceenvelopesthe dissociation of thecomplex andthedenaturation of thefreecomponents.PanelB showshow theDSCtracechanges

9 If [L]tot ≠ [M]tot, the binding polynomial has to be used to calculate thefraction of complexat eachtemperature.



with the magnitudeof the enthalpy of complex formation,DHC. From Eq. (21), it follows that KC hasa maximumatthetemperaturewhereDHC = 0, thatis, whereDHC changessign. PanelC demonstrateshowtheDSCtracechangeswiththe molar ratio of [L]tot/[M]tot.

In practice,modelscanbetestedagainsttheexperimentaldata by statistical methods. The statistical analysis issimpler if theunfoldingenthalpies, unfolding heatcapacityincrementsand unfolding free energies of eachcomplexpartner in isolation are known from separate DSC scans.Here, thestatistical analysis of theDSCtracesasshown inFig. 5 can be limit ed to the parameters of the associationreaction, keeping the parameters pertaining to the freecomponentsfixed.In principle, it is also possible to performa global statistical analysis without a priori knowledgeofsome of the thermodynamic parameters. However, suchrigorousstatistical analysis by non-linearfitting procedurescanbe flawed becauseof the multi-minima problemwhenthenumberof parametersis largeandsomeparametersarestrongly interdependent.

Appl ications of the deconvolution analysis. Deconvolu-tion analysis of DSC traceswas successfully applied tostudy the energeticsof small ligand binding like ferric ionbinding to transferrins(Lin et al., 1994),sulfate binding toyeastphosphoglycerate kinase(Hu and Sturtevant,1989),and biotin binding to streptavidin(Gonzalez et al., 1997).Otherexamplesareinhibitor bindingto barnase(Martinezetal., 1994), to ribonuclease(Barone et al., 1995), and tothymidylate synthase(Chenet al., 1996),or monosacchar-ide bindingto proteins(Schwarz etal., 1993).In mostcasesgood agreement was observedbetweenthe binding freeenergies determined by DSC and other equilibriummethods, and the superiority of DSC to measure bindingaffinities not accessibleby othertechniqueswasdocumen-ted.Indeed, DSCallows to measurevery tight binding,andthis is amajorassetof thetechniquecomparedto ITC andtonon-calorimetric equilibrium techniques.The high resolu-tion potentialof thedeconvolution of complexheatcapacitytraceswasdocumentedin studiesof proteinsystemslike theS-protein–S-peptidecomplex (Graziano et al., 1996), thebarnase–barstar complex (Martinez et al., 1995), and theheparin/antithrombin complex (DeLauder et al., 1992).Conformational transitions were found to accompany thedimerizationof a thermolysin fragment (Conejero-Lara andMateo, 1996), and the association of an unfoldingintermediate of the Cro repressor from bacteriophage lwasidentified (Filimonov andRogov, 1996).

The statistical mechanical approach to DSC data wassuccessfully applied to study the domain structure anddomain-domain interactions in some very complicatedmolecular systemslike the Escherchia coli DNA gyrase(Blandamer et al., 1994), the multimeric molecularchaperon DnaK (Montgomery et al., 1993), and theheparin-binding fragment of fibronectin (Novokhatny etal., 1992). Recent work on protein binding to single-stranded DNA andto DNA-duplexes illustratedthe powerof the combined ITC and DSC approach. Protein–DNAassociation is characterized by low discrimination betweenspecific and nonspecific binding and by large structuralrearrangementsaccompanying the binding reaction. Thethermodynamic analysis of thesecomplex systems could

Figure 5. Simulated excess heat capacity pro®les for theinteracting system L�M → C. The curves were simulated withthe help of Eq. (22). The following parameters were ®xed for allsimulations: Tm,L = 320 K, Tm,M = 340 K, DHL(Tm) = 350 kJ molÿ1,DHM(Tm) = 450 kJ molÿ1, DCp,L = 5.5 kJ Kÿ1 molÿ1, DCp,M = 4.5 kJKÿ1 molÿ1, and DCp,C =ÿ1 kJ Kÿ1 molÿ1. The traces drawn in thickline are for identical conditions in all three panels. Panel A:variation of the DSC trace with variation of Kc. The curves fromleft to right were calculated for Kc = 1, 105, 106, 107, 108, 109, and1010 Mÿ1 at 298 K. The leftmost curve has two well-separatedpeaks centered at 320 and 340 K, respectively. The peakscorrespond to the denaturation of free L and free M, respectively.The rightmost curve has a single peak centered at 343 K. Itcorresponds to the coupled dissociation and denaturation of thecomplex and its components, undisturbed by the presence of freeL and M. The curves in between are composed to variabledegrees of the transitions of the free and the complexed species.DHR,C was ®xed at ÿ20 kJ molÿ1 and 298 K. Panel B: variation ofthe DSC trace with variation of the excess enthalpy of thecomplex at the reference temperature 298 K. The curves from leftto right were calculated for DHR,C = 20, 0, ÿ20, ÿ40, and ÿ80 kJmolÿ1 at 298 K. It is seen how the temperature in¯uences KC

according to eqn (21). Hence, the overall trace of a DSCexperiment changes with DHR,C. The leftmost trace calculatedfor DHR,C =�20 kJ molÿ1 clearly has two peaks. The reason is thatKC decreases with increasing temperature if DHR,C is positive, asfollows from Eq. (21). Conversely, KC increases with temperatureif DHR,C < 0 and, therefore, the rightmost curve essentially hasonly a single peak, albeit with a broad shoulder. KC was ®xed at107 Mÿ1 at 298 K. Panel C: Variation of the DSC trace withvariation of the ratio [L]tot/[M]tot. The curves from left to right werecalculated for [L]tot/[M]tot = 0.5, 0.67, 1, 1.5, 2, and 4. DHC(298 K)was ®xed at ÿ20 kJ molÿ1 and KC(298 K) at 107 Mÿ1.



profit from the synergism of the ITC-DSC combination(Cooper et al., 1994; Davis et al., 1995; Merabet andAckers,1995;CarraandPrivalov, 1997;Odaet al., 1998).

ConclusionsWe have tried to give an overview of the calorimetrictechniques and to summarize some recent representativeapplications aimed at dissecting the energetics of macro-molecular recognition. In view of the high sensitivity ofcommercially availableinstruments andof the capacityofmolecular biology techniquesandsolid phasesynthesis toproduce large amountsof pure proteins andnucleic acids,thecomprehensivethermodynamicdescription of agrowingnumber of associating systems will becomepossible in thenearfuture. Figure6 illustrateshow the powerof ITC andDSCcanbe combined andlinked with structural data.Thecentralaim is to obtainanenergyprofileof thecomplexandto formulate a plausible mechanism of the associationreaction.To knowtheenergy profilemeansto knowtheheatcapacity changeof the association reactionand to predictthefreeenergy, enthalpy, andentropychangeof associationover as broad a temperature range as possible and forvarying conditions of solvent,pH, cosolutes,etc. To knowthemechanismof theassociation reaction meansto describethetransitionfrom thefreecomponentsto thefinal complexin terms of all intermediate states populated underequilibrium conditions, and to reveal their mutual inter-dependence.

ITC is clearly the methodof choiceto measurethe freeenergy, enthalpy, heat capacity and stoichiometry of abinding reactionof modest affinity. Very weak and very

tight binding constantsarenot directly accessibleby ITC.Datacollectedby non-calorimetric methodsareusedto getvan’t Hoff enthalpies, which when comparedwith calori-metric enthalpiescanhelp to clarify a binding mechanism.The quality of DH and DCp from ITC is high when theassociationcanbeapproximatedby arigid-bodyinteraction.However,thelock-and-key concept is anoversimplificationfor many protein–protein complexesand is almostalwaysinappropriate when applied to protein–DNA interactions.The resolution of ITC datacan be improved substantiallywhen the structure of the complex and of its freecomponents is known (or a reasonable model can beproposed). In this case, semi-empirical, structure-basedcalculationscan complement the experimental data. Still,these computational methodscannot(yet) replaceexperi-mental data.Here, the DSC techniquecomes to help. Bydeconvolution of the excess heatcapacities of the interact-ing moleculesoneis in a position to ascribeat leastpartofthe enthalpy andheatcapacity measuredby ITC to foldingevent(s) induced by the binding reaction. DSC data areinvaluablein theestimationof entropicfactors of a bindingequilibrium and in measuring extremely high bindingaffinities. Statistical-mechanical analysis of two-dimen-sional excessheat capacity surfaces can provide furtherinformationonthenatureof acomplexandon theenergeticfactors driving its formation. DSC is the only methodtoaccess the system partition function to calculate thepopulation of free and bound molecular species as afunction of temperatureandconcentration.

Even the best and the most comprehensive set ofthermodynamic datacan be flawed, and we have tried tolay bare possible difficulties and inconsistencies of dataanalysis. Indeed, thermodynamic studies always need

Figure 6. Scheme depicting the combined experimental and theoretical approach to theanalysis of complex binding energetics. ITC provides the global thermodynamicparameters of the binding reaction (top left). Semi-empirical, structure-based calculationscomplement ITC data (lower left). DSC on the complex and on its free components (righthand side) can help to decompose the global parameters from ITC into contributions fromconformational changes, folding of molecular domains, etc. Data from non-calorimetricmethods complement the picture (bottom and lower right hand side). The energy pro®le ofthe binding reaction is the ®nal result of the combined ITC-DSC approach (center) and acorner stone in the elucidation of structure±function relationships (bottom).



companyof additional studiesbasedon other biochemical,structural and biophysical methods. As stated in theIntroduction, weknowmuchabouthowbiomacromolecules

associateandwish to betterunderstandwhy theydo so,butthe howandwhy arestrongly interdependent.

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