biochemical applications of dsc.pdf

7/28/2019 biochemical applications of DSC.pdf

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Ann. Rev. Phys. Chem. 1987. 38:463~88Copyright 1987 by Annual Reviews Inc. All rights reserved

BIOCHEMICAL APPLICATIONSOF DIFFERENTIAL SCANNINGCALORIMETRYJulian M. SturtevantDepartments of Chemistry and of Molecular Biophysics and Biochemistry,Yale University, NewHaven, Connecticut 06511-8118INTRODUCTIONDifferential scanning calorimetry (DSC)and the closely related differentialthermal analysis (DTA)have been widely employedduring the last severaldecades in the thermodynamic study of processes that are initiated byeither an increase or a decrease in temperature. This review focuses onbiochemical applications of DSC.Macromolecular and polymolecular structures stabilized by the coop-eration of numerous weak forces are important to most biochemical pro-cesses. Since such highly cooperative structures undergo conformationalor phase transitions upon being heated, significant information concerningthese structures can be obtained by DSC. Small molecules cannot bestudied by DSC nless they form aggregates showing intermolecular coop-eration, as in crystals. This is illustrated in Table 1. Since the enthalpiesof chemical processes rarely are as large as 20 cal g-l, it is evident thatmolecules having molecular weights, or molecular aggregates havingaggregate weights, in the thousands of daltons are required to give tran-sitions sufficiently sharp for useful DSC bservation.In a scanning calorimeter, one measures he specific heat of a system asa function of the temperature. For a solution, the apparent specific heatof the solute, c2, is given by the expression

1cz = c~+--(c-cl) 1.W2wherec is the specific heat of the solution, c~ is that of the solvent, and wz

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464 STURTEVANTTable 1 Transition widths for a two-statetransition as observed by DSC for variousvalues of the transition enthalpy. Temperatureof half completion = 50C

Transition enthalpy Temperature/Ckcal molt ~ = 0.1 ~ = 0.920 29 7540 39 6260 43 58

extent of conversion.

is the weight fraction of the solute. Since the quantity c--ct is usuallyrelatively small, for example, approximately -0.7% of c t for a 1%aque-ous solution of a protein, it is essential to employ differential schemeofmeasurement n which c- c ~ is directly measured. This is accomplished na differential scanning calorimeter by using two closely matchedcells filledwith equal weights or, more usually, with equal volumes of solution andsolvent. When ne considers that in general a significant, or even major,fraction of the total change in apparent specific enthalpy is due to thesimple heating or cooling of the solvent, it becomes vident that the highestpossible sensitivity and accuracy should be realized.The so-called excess apparent specific heat, cox, is the amountby whichthe apparent specific heat during a transition involving the solute exceedsthe baseline specific heat. A recurring problem in DSC, as in manyothermeasurement echniques, is the determination of the appropriate baselinesince, as is evident, no direct observation of it is possible during thetransition. Figure 1 showsa typical DSC urve observed for the reversiblethermal denaturation of a globular protein. The apparent specific heat ofthe native form of the protein increases with increasing temperature whilethat of the denatured form is independent of temperature. The dashedcurve, obtained by procedures outlined below, is the baseline specific heat,and Cex is as indicated. The integral of Cexover temperature then gives thespecific calorimetric enthalpy, Ah=l, for the transition.In this review, we discuss very briefly the instrumentation for DSC ndthen consider the theoretical aspects of the various applications of DSC;these applications are illustrated with examples aken from the literature.We do not attempt a comprehensive coverage of the rapidly growingliterature in this field.INSTRUMENTATIONIn the opinion of the author, the instruments best suited for work withbiochemical systems are the DASM-1Mescribed by Privalov et al (1), its



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DIFFERENTIAL SCANNING CALORIMETRY 465

Observed ~/~

~mt-"~

-tg-t

ted

m 0.1 col

15 25 55 45TEMPERATURE /CFi#ure I A tracing of the DSC urve observed with a solution of the Arg 96 ~ His mutantof the lysozyme of T4 phage (kindly supplied by Dr. John Schellman of the University ofOregon). Protein concentration 8,29 mgml-~, pH 2.34, 0.02 Mpotassium phosphate buffercontaining 0.025 MKC1.No noise was visible in the original recording. The calculated curvewas obtained as outlined in the text with % = 0.0358+0.00192 t col K-t g-~ and cB ~0.235 col K~ g-~. The calculated curve differs from the observed curve with a standarddeviation of 1%of the maximalapparent specific heat.

successor the DASM-42), and the Microcal 2. The DASM-4s availablefrom V/O Mashpriborintorg, MoscowG-200, USSR, and the Microcal 2from Microcal, Inc., Amherst, Massachusetts, USA.The DASM-4s shown schematically in Figure 2. Two cells composedof platinum or gold capillary tubing are suspended within two adiabaticshields with a 200-junction thermopile between them. The cells have aneffective volumeof 0.5 ml and are filled through vertical extensions of thecapillaries. They are heated by electric heaters in good thermal contactwith them; the power to the heaters is adjusted by means of a controlcircuit, activated by the output of the thermopile between he cells, whichmaintains them at closely equal temperatures. Thermopiles between the

cells and the adiabatic shields activate control circuits, which hold theshield temperatures close to that of the cells. The instrument suppliessignals that show he cell temperature and the differential heating powerto the cells; the signals maybe registered on an X-Y ecorder or maybefed to a computer for subsequent analysis. Each cell is equipped with a



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466 STURTEVANT

Figure 2 Schematic representation of the cells and adiabatic shields of the DASM-4differential scanning microcalorimeter. 1. Capillary inlets; 2. capillary cell; 3. inner shield;4. thermopile between the cells; 5. outer shield. (By permission of Pergamon Press, Ltd.)

second electric heater that is used for calibration purposes. Scan rates of0.125 to 2.0 K min- ~ are available; lower scan rates, whichare occasionallyadvisable, require modification of the heater circuits.The subject of DSC nstrumentation has been reviewed by Privalov (2).

THEORETICAL CONSIDERATIONSInterpretations of DSC ata are usually based on the equilibrium thermo-dynamic expression(9 In K~ AH, Hwhere K is the equilibrium constant for the process under study, T is theabsolute temperature, and AHvHs the apparent or vant Hoff enthalpy.(Although AHvHs a standard state quantity, the generally small variationof enthalpy with concentration makes it permissible in most cases tocompareAHvr~with the true or calorimetric enthalpy, AHcal.) It is immedi-ately evident that any equilibrium process observed during increase of thetemperature is necessarily endothermic and that any exothermic processso observed must involve rate limitation. For a discussion of the appli-



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DIFFERENTIAL SCANNING CALORIMETRY 467cation of DSC nd DTAo rate-limited processes, the reader is referredto Borchardt & Daniels (3). In the following discussion, it is assumed hatno rate limitation of either chemical or instrumental character is present.That this assumption is valid in any particular case can be demonstratedby showing that the DSCobservations are independent of the scan rateemployed. Reversibility will also be assumed, with consideration of theproblemof irreversibility postponed o a later section.Two-State ProcessesThe vant Hoff equation, Eq. 2, is directly applicable only to two-stateprocesses in which states intermediate between the initial and final statesare not significantly populated at equilibrium. For a process of the simplestpossible form

A ~ B ; AHvn= MAho,~= AHoa~ 3.the indicated equality must hold, with AH~n eing given by the expression

Anvr~ = ART~/2 cexl/2AhcaI"

Here M s the molecular weight, Ahca~ s the calorimetric specific enthalpy,T~/2 = t~/2+273.15; t~/2 is the temperature (C) at which the processhalf completed,C~x,ms the excess specific heat at t~/2, R is the gas con-stant, and the factor A has the value of 4.00. (The expression AH2R~/~T~/~Cox,~/~,whereCex,~/2 is the excess molar heat capacity at t~/2,has been widely employed in the calculation of AHvn. However, it isevident from Eq. 4 that in general, AH n this expression is not a singleenthalpy but is actually the geometrical mean of AH~ nd AHva.)The finding that the equality in Eq. 3 holds within close limits for thethermal denaturation of many globular proteins is the best indicationavailable that protein thermal denaturation can be of all-or-none or two-state character.The value of ll/2, or of tin, the temperature at which Cex reaches itsmaximalvalue c ...... for the two-state process in Eq. 3, should be inde-pendent of concentration. On the other hand, an increase of tm withincrease in concentration is a clear indication of a decrease in the degreeof oligomerization during the reaction, and conversely a decrease ofwith increase of concentration shows that the degree of oligomerizationincreases. If the reacting species is known o be oligomeric at ordinarytemperature, and tm is found to be independent of concentration, it maybe concluded either that the reacting species has becomemonomericby



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468 STURTEVANTthe time the reaction temperature is reached or that no dissociation .orassociation accompanies he reaction.We shall consider two cases involving change in degree of oligo-merization. In the first of these, there is either complete dissociation orcomplete association involving an oligomer in one state and a monomerin the other:

(a) Ao~nB or (b) nA~Bn. 5.If we substitute the appropriate expression for K in terms of ~, the extentof conversion, in Eq. 2 and perform the differentiation, and then use theexpression cex -- Ahcal (d~/dT), we find, since ~ = 0.5 at T,/2, that

AHvH 2(n + 1)RT~/2Cex. 1/2 6.Ahc~tso that the factor A= 2(n + 1). If in place of T,/2 we use Tin, the temperatureat whichCexhas its maximal alue, c ....... in Eq. 4, and c ...... in place ofCex,1/z, A has the values 4.00, 5.83, 7.47, and 9.01 for n --- l, 2, 3, and 4,respectively.The second case involves incomplete dissociation or association to adimer in either the initial or the final state or both:

KIA~BKN ,IT T~, KD 7.

In curve fitting to this model, it seems reasonable to assume that KNandKDdo not vary significantly over the temperature range of the reactioncontrolled by K,. The equilibrium constant for the A to B step is given by

1 -- (1 + 8aK~D(A)0)/2K~K, = 1 - (l + 80 - e)K~(A)0)~/2" K~ 8.

where (A0) is the total concentration expressed in monomer nits. Differ-entiation of In K, gives for the factor A when = 1/2 the value4K~(A) 4K~(A)A = 1 +4KD2(A)0--(1 +4KD2(A)0)/2 + 1 +4K~(A)0-(I +4K~(A)o)/~"

9.Obviously, no simple statement concerning the values of A can be madein this case.It was pointed out above that if association or dissociation accompanies



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DIFFERENTIALCANNINGALORIMETRY 469a process observed by DSC, the value of tm should vary with reactantconcentration. For the case represented by Eq. 5a, when t -- 1/2,

In K~/2 = constant + (n- 1) In (A)0 =- RTI/~2 +constant.10.

Thusa vant Hoff plot of In (A)0 versus 1/T~/2 will have a slopeA/-/vHS- 11.(n- 1)R

A/-/vH evaluated in this way for a two-state process should agree with thevalue given by Eq. 4.For the case represented by Eq. 7, we see from Eq. 8 thatIn KI, ~/z = constant + In [1 -- (1 + 4K~(A)o)/z] _ In [1 - (1 + 4K~(A)o)1/2]

AHvn- + constant. 12.RTI,I/2Simulations in which TL 1/2 is calculated as a function of In (A)0 show hatfor this case, at least with Ks and KD n the range 0.01 to l0 #M1/2 and(A)0 in the range 50 to 1000 #M, and AHvHndependent of temperature,a plot of In (A)0 versus 1/Tl,~/2 is linear. Such simulations also show hefactor by which he slope of the vant Hoff plot must be multiplied to giveAHvH.This factor can vary over a wide range if KNand KDare not verydifferent.The evaluation of AHvH by the means outlined above gives a veryimportant general application of DSC. For a strictly two-state pro-cess, carried out under essentially equilibrium conditions, AHvHAHcal ----- MAhcavf AHvH AH~,I it can be concluded that one or moreintermediate states are of significance in the overall process, whereas ifAHvH AHc,~ ntermolecular cooperation is clearly indicated. DSC s theonly experimental technique that gives such positive indications concerningthese characteristics of a process.Figure 3 showsplots of the excess apparent specific heat, taken arbi-trarily as zero at 0C, versus temperature for two hypothetical reactionsfollowing Eq. 5a, one with n = 1 (curve A) and one with n -- 4 (curveThe parametric values for each reaction are ti/z = 60C and AhcaI =8 cal g-l, with a monomermolecular weight of 12,500. Curve A isnearly but not quite symmetric about tl/~ whereas curve B is markedlyasymmetric. Curve C is the baseline for curve B and is calculated bychanging the initial baseline (CA = 0+0.003 tcal -t g-~) t o t he f inalone (ca = 0.180 + 0.001 tcal K-~ g-~) in proportion to the integrated areaunder the curve as the temperature increases from t = 20C to t = t.



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470 STURTEVANT

1.00

A

025 45 65 85TEMPERATURE, CFigure 3 The calculated variation of excess apparent specific heat with temperature forhypothetical reactions in which 4/2 = 60C, Ahc~ = 8 cal g-, and monomer molecularweight = 12,500 daltons. Curve A, A ~ B; curve B, A4 ~ 4B. Curve C is the calculatedbaseline for curve B with c a = 0-t-0.003 t, CB = 0.180+0.001 tcal K-I g-~.

A process involving association instead of dissociation would haveasymmetry pposite to that of curve B.Eq. 5a maybe extended to include the frequently interesting situationof ligand binding:AnLm nB + rnL. 13.

Here we are assumingcomplete dissociation of ligand from the species B.If the total ligand concentration (L)0, is much arger than (A)0,logarithm of the equilibrium constant in Eq. 13 at half completionmaybewrittenIn K1/2 = constant+ (n-- 1) In (A)0 + rn In (L)0 ZXHv.+ constant.RT1/2 14.



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DIFFERENTIALCANNINGALORIMETRY 471Thus a plot at constant (A)0 of In (L)0 versus 1/T1/2 should be a straightline with slope S given by

Any.S- 15.mREqs. 6 (or 9), 10 (or 12), and 15 provide three means or estimating AHvH.If the value obtained by Eq. 15 differs from the other two, this maybe dueto incomplete dissociation of the ligand, or even to greater binding of theligand to species B than to A.It may be noted that the dissociation of a tightly bound igand in theabsence of any excess ligand in solution will lead to asymmetry f the DSCcurve in just the same way as does a dissociation involving the ligandbinding species.Two-State Processes with Permanent Changes in SpecificHeatThe preceding treatment must be modified if the process under study isaccompanied by a large permanent change in the apparent specific heat.Anexampleof this situation is shown n Figure 1, which presents a tracingof the DSCcurve observed for the thermal denaturation of T4 lysozymeat pH 2.34 (S. Kitamura and J. M. Sturtevant, unpublished observations).In this case, AHca1 = 31 kcal mol-~ at the start of the transition at 15Cand 108 kcal mol-~at the end of the transition at 45C, so that significanterrors might arise if the data are analyzed on the basis of a temperature-independent enthalpy. In such cases, the best way to evaluate tl/2, Ahcal,and AHvHs by fitting the experimental data to the appropriate theoreticalcurve according to the least squares criterion. Weoutline here the algebrainvolved for a case such as that shown in Figure 3 where the specificheats observed before and after the transition are themselves temperaturedependent.Consider again the process represented by Equation 13 with (L)0assumed o be much arger than (A)0, and with the initial and final specificheats given by the expressions

cA = A+Bt, ca -- C+Dt, t -- C. 16.The enthalpy of denaturation as a function of temperature is then

Ahcal = Aho+(C--A)t+ 1/2(D--B)t 17.where,with Ahl/2 = Ahcal at tl/2,



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472 STURTEVANTAh0= Ah1/2- (C- A) t ~/2- 1/2(D- B) t ~12. 18.

If we set-A = Aho-273.15(C-A)+ 1/2(273.15)2(D-B),

B = (C-A)-273.15(D-B); C 1/2 (D-B), 19.then the integrated form of Eq. 2 can be written

RK"(1T1n~/2~/2 A J ~+Bln T= 1]/2] T~/2 -I-C(T-- T,/2) 20.

where K= K/(L)0, K~/2 is the value of K at 4/2, and the ratiofl = AHvH/Ahcajs assumed to be independent of temperature. The extentof conversion is given by

1 K= 21.n y(1-~); Y=2-~and the excess specific heat, as before, by cCx = Ahcat (d~/dT). The cal-culated baseline for a two-state reaction is

Car = (1 - ~) (A + Bt) + ~(C + 22.so that the total excess specific heat is

Ctot = Cex "[- Cav. 23.The adjustable parameters used in minimizing the standard deviation,[E(ctot- Cob~)2/(--1/2 whee Cob~ arethe ~ observed values, may be t akenin the form 1/2, Ah1/2, and ft. For a simple two-state reaction, fl is expectedto be equal to the molecular weight. K/K~/2, 7, and ~ are calculated fortemperatures corresponding to the observed data points (~ is obtained bysuccessive approximationsfor n > 3) and CCx,C~v, and tot are evaluated.It can be shown by simulation that in cases of modest permanentincreases in specific heat, adequate accuracy can be obtained by drawinga baseline calculated according to Eq. 22, ~ is determined by integrationon the assumption of temperature-independent enthalpy and then by usingdata points relative to this baseline in the equations given earlier, whichassume no permanent change in specific heat.Non-Two-State Processes (AHo~ < An~at)At first sight, it would seem obvious that a large protein molecule with avery complex three-dimensional structure would unfold gradually whenheated, with many tates populated between he initial and final states. Itwas therefore surprising when t became vident, largely as a result of the



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DIFFERENTIAL SCANNING CALORIMETRY 473DSC emonstration, in some cases, of equality of AHca~ nd A//vH, that atleast some proteins unfold in a very nearly all-or-none manner. It is,however, not surprising that in manycases the unfolding is more complexthan two-state. In such cases, as noted above AHvH AH~a~with AHvHcalculated according to Eq. 4 with .4 -- 4.Twodifferent models for processes involving multi-state unfolding areconsidered. The first assumes the existence of several domains in themolecule, each of which unfolds totally independently in a two-statemanner. It is, of course, conceivable, and perhaps probable, that theremay be interactions between domains, but there is no general method bywhich such interactions can be included in our treatment. ~ If we includethe possibility of dissociation at any or all steps, the ith step is of the form

Ai,mi ~- miBi 24.and the parameters o be adjusted for this step are mi, t~/2,i, AhCaLi, ndIt is expected that in most cases, fl,- will be equal to the molecularweightof the entire molecule.A serious problem arises in cases of multi-state transitions for whichthere is a large over-all permanent hange in specific heat, namely hat theexperimental observations give direct information concerning the specificheats of the initial and final states, but none concerning he specific heatsof the intermediate states. Wehave adopted the purely arbitrary procedureof partitioning the over-all change n specific heat between he steps in theprocess at each temperature in proportion to their individual enthalpies atthat temperature. It is then simply a matter of applying the algebradeveloped above to each component ransition, and of summing he indi-vidual ctot.t to evaluate the standard deviation of the data from the theo-retical equation for the assumedmodel.The second non-two-state model to be considered is that of strictlysequential two-state steps. For five sequential steps, the over-all processmaybe represented as

P~ ~ P2 ~ P3 ~ P4 ~ P~ ~ P6 25.where for each step we have Ah~, K~, t~/2,t, and AHvr~,; = fl~Ah~. For apure substance fl~ = f12 ..... molecular weight unless the process is

~ In the ease of a protein containing two domains, any interaction between the domainswould presumably be manifested by changes in t~/2 and/or Ah~for a fraction of either orboth domains when hat fraction of the other domain is denatured. Wehave found that thesimulated DSC urves for such a case with changes in either or both t~/:s of + 10C (originalt~/~s = 50 and 53) and either or both Ahabs of _+0.5 cal g 1 (both original A~s2.5 cal g-l) can still be resolved into two two-state components n the basis of the indepen-dent model with practically as good accuracy as for the unperturbed case, but of coursewith different derived parameters.



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474 STURTEVANTcomplicated by dissociation or association at one or more steps. Thefollowing treatment does not include that situation. Using the equations

(P,+1)K,. = (p,~-; (P)0 = (P,)+"" 26.it follows that, with

D = I+K~+K1K2+ "" +K1...K~ 27.(P1)=_I. (P2)_K~. (P3) K1K~. 28.(P)0 O (e)0 O (P)0

Integration of the vant Hoff equation for each step givesIn Ki - R

since Ki = 1 at T1/~.i. Eqs. 2%29 re employed o calculate (P,)/(P)oT+3Tand T-6T, where fit is a small temperature interval. The changein (P3/(P)o in the temperature interval 26T s then

(P~) (at T+~T) -(Pi) (at T--3T). 30.[(P3/(P)o](p)~ (~0This change will lead to a heat absorption due to the ith step ofAq,= A [(P,+ t)/(P)o]" [Ahl + ah2 +.-" + 31.since to arrive at species (i+ 1), Eq. 25 shows hat heats Ahl, Ah2 ... , Ahghave to be absorbed. The excess specific heat at T is then

Cex = (X Aq3/23T. 32.As before, if Aco is large, it seems that the best that can be done is toassume that the fraction of the total specific heat change at each tem-

perature due to step i is proportional to Ah]XAhi, and to use the resultingAc~ o correct the Ahi.Numerical Treatment of DSCDataThe simplest DSC urves readily yield enthalpies by the evaluation of theareas under the curves, for example by means of a planimeter, and vantHoff enthalpies by means of Eq. 4. It was pointed out above that in casesshowing large permanent changes in heat capacity, it is best to obtaincalorimetric and vant Hoff enthalpies by fitting the experimental data toa theoretical curve. In more complex cases, some form of curve fittingseems to be unavoidable.Privalov and his colleagues (4, 5) showed that the complex DSCcurves



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DIFFERENTIAL SCANNING CALORIMETRY 475observed for the melting of transfer RNAs ould be accurately representedas the sums of several two-state curves, which were attributed to theindependent melting of various substructures within the molecules.In an important series of papers published in 1978, Freire & Biltonen(6-8) pointed out that the partition function for a macromolecular ystemcan be calculated by a double integration of the apparent heat capacity asmeasured by DSC. A recursive method was developed to evaluate thethermodynamic parameters of each step in a multistate transition, andsuch quantities as the fractional occupancyof each state were calculatedas functions of the temperature. This analysis was applied in general formto cooperative phenomena7) including the helix-coil transitions of nucleicacids (8) and phase transitions of phospholipid bilayers (9).The Freire-Biltonen procedure is in principle independent of anyassumedmodel, although their treatment for the helix-coil transition ofnucleic acids assumed hat the transition occurs betweena double-strandedand a single-stranded form.Filimonov et al (10) suggested ways to improve the procedure developedby Freire & Biltonen (6). In particular, they demonstrated that incor-poration of feedback into the iterative calculation reduced cumulativeinaccuracies arising from such sources as noise in the DSC ata.Gill et al (11) have recently developeda generalized binding formulationbased on the postulation of multiple allosteric forms of macromolecules.In applying this theory to the melting of a transfer RNA, hey showedthat with the assumption of six allosteric forms they could obtain a rep-resentation of the experimental data that was as accurate as one based onsix independently melting domains. The latter model implies 25= 32energy levels for the molecule while the former model has only 6 energylevels corresponding o the 6 allosteric states.For analyzing a wide range of DSCdata we have employed a procedurethat is based on either of the modelsoutlined earlier involving independentor sequential two-state events, with or without association or dissociation.The parameters defining each step are adjusted to minimize the standarddeviation of points on the calculated sum curve for Ctot from observedpoints. In general, as mentionedearlier, three parameters are required forthe definition of a two-state curve, which maybe taken, as tl/2, Ahead,andAHvH.f Acd 5~ 0, Ahcal, and AHvHre the values at tl/2. In simple cases,where there is no intermolecular cooperation, no dissociation, and noassociation, the ratio AHvH/Ahcalhould be taken equal to the molecularweight of the substance, thus reducing the numberof adjustable parametersto two per step. Even so, the numberof parameters to be determined byfitting to experimental data of limited accuracy is frequently excessive, sothat unique solutions maynot be obtainable. Furthermore, it is frequently



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476 STURTEVANTdifficult or impossible to distinguish betweendifferent models on the basisof the goodnessof the fit finally obtained. This is true, for example,withthe independent and sequential models with transitions close together intemperature.

The minimization of the standard deviation can be accomplished eitherby a "brute force" adjustment of each parameter in succession [Edge et al(12)] or by a nonlinear least squares approach such as supplied by theMarquehardt or.Simplex algorithms (B. G. Barisas, private communi-cation). In the brute force procedure, the numberof successive adjustmentsof each parameter should be limited to four or five in each cycle of thecalculation, and the increments applied should at first be rather large, inorder to minimize the danger of arriving at a local rather than the globalminimum. f shortening the computer time required for the calculation isnot of much importance, the brute force method has some advantage inbeing more readily followed as the computation proceeds.Changet al (13, 14) have developed a similar approach to the analysisof DSCcurves into the sum of simple two-state curves. Their procedureas described does not accommodate a significant permanent change inheat capacity nor the possibility of self association or dissociation.Non-Two-State Processes (AHvH > AHc,t)As noted earlier, when AHvn s calculated by Eq. 4 with a suitable valueof A exceeds AHca1 it may be concluded that the process under studyinvolves intermolecular cooperation. Phase transitions offer the most com-monexample of this situation; since the melting of a perfectly pure crys-talline substance is an isothermal process, AHvHpproaches infinity. Theso-called gel-to-liquid-crystal phase transition of a multilamellar bilayersuspension of carefully purified dipalmitoylphosphatidylcholine in waterwas reported by Albon & Sturtevant (15) to have a ratio of AHvn/AHcalequal to 1400 whenscanned at 0.023 K min-1. It is probable that the ratiowouldhave been still higher at a lower scan rate because of further reliefof instrumental lags. In systems of this sort, the ratio AHvH/AHcaIan betaken as a lower limit for the size in monomermolecules of the average"cooperative unit" for the process. Similarly, in the helix-coil transitionof a polynucleotide of high degree of polymerization, although the reactionis far from all-or-nothing in character so far as the entire molecule isconcerned, the ratio AHvH/AHcal, where AH.I is the enthalpy per mole ofbase pairs, gives a measure of the number of base pairs in the averagecooperative unit.Irreversible ProcessesThe foregoing treatment is strictly valid only for reversible processes thatare subject solely to thermodynamic imitation during their observation



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DIFFERENTIALCANNINGALORIMETRY 477by DSC. Unfortunately, many, if not most, processes of interest in bio-chemistry and otherwise suitable for DSC tudy are, operationally, at leastpartially irreversible as judged by the DSC riterion of the repeatability ofthe DSCscan on rescanning the sample. The thermal denaturations ofmany roteins are found on the basis of this criterion to be irreversible,even in cases where denaturation at lower temperatures by treatment withguanidinium chloride or urea is found to be reversed on dialyzing out thedenaturing agent. The thermal helix-coil transitions of naturally occurringdouble helical polynucleotides are usually incompletely reversible in DSCexperiments, primarily because of the entropic difficulty of achieving exactrealignment of the polynucleotide chains after chain separation.Possible justification for the application of reversible thermodynamicsto apparently irreversible processes has been briefly discussed by Privalov[Ref. (16), pp. 28-29]. Wehave found that reasonable vant Hoff plotsbased, for example, on Eq. 10 are observed even in cases of apparentlyirreversible protein denaturations. Thus, t mfor the denaturation of theregulatory subunits of aspartyl transcarbamoylase in the presence of ATPincreases with increasing ATPconcentration in the manner expected onthe basis of Eq. 14 (12). In other words, the protein during denaturationresponds to the concentration of free ATP n the solution, even at con-centrations of ATPwhere the protein is effectively saturated with theligand. Similarly, tm for the denaturation of the tetrameric core protein ofthe lac repressor of E. coli increases with increasing protein concentrationin accordance with Eq. 14 (17). Furthermore, the highly asymmetric DSCcurve observed with this protein can be accurately fitted to Eq. 5a withn --- 4 and values for tl/2, Ahead,and AHvHgreeing well with the observedvalues. These and other empirical results provide somemeasureof validityto the application of equilibrium thermodynamics to apparently irre-versible processes.

Simulations show that results similar to those outlined above can beobtained for a modelwhere an equilibrium dissociative process is followedby a rate-limited irreversible step, with selection of a rate constant, k 1, andan activation energy, Ea, which lead to as muchas 75%conversion to theirreversible species when he A to B conversion is 95%complete.APPLICATIONSThe Thermal Denaturation of ProteinsPerhaps the most important applications of DSC n biochemistry areconcerned with the thermal unfolding of proteins, since the calorimetricanalysis can give information concerning the fundamental nature of thisprocess and the forces involved in the stabilization of the native structures



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478 STURTEVANTof proteins. A very recent and complete listing of changes in free energy,enthalpy, and heat capacity accompanying he unfolding of proteins hasbeen published by Pfeil (18). This listing includes the numerousvaluesobtained by methods other than DSC.

We irst consider relatively simple two-state denaturations and thenmore complex multistate denaturations.TWO-STATEENATURATIONScomprehensive review of the literature (upto 1979) on the thermal denaturations of small globular proteins, most ofwhich are of very nearly all-or-none or two-state character, has beenpublished by Privalov (19). In this section, we consider a few more recentexamples of two-state denaturations that illustrate important possibilitiesof the DSCmethod.Two-state denaturations with self-dissociation or association The firstprotein shownby DSC o undergo dissociative unfolding was Streptomycessubtilisin inhibitor (SSI). This protein was known o be dimeric at ordinarytemperatures. Its denaturational DSCcurves were found to be slightlyasymmetric, and the values of t mincreased with increasing protein con-centration. Quantitative analysis of the DSC urves showed clearly thatthe denaturation follows the schemeA2 ~- 2B (20). Thus the native proteinremains dimeric up to temperatures in the vicinity of 80C.

The so-called core protein obtained by limited proteolysis from the lacrepressor of E. eoli is tetrameric at ordinary temperatures. It is interestingthat the DSC ata for the thermal denaturation of this protein, which isan operationally irreversible process, yield three different estimates forAHvHhat are in reasonable agreement: (a) Curve fitting of the data to themodel A4 ~-4B as outlined in an earlier section gave AHvr~= 525+30 kcal mol-~; (b) calculation according to Eq. 4 with A = 10 gaveAHvH 585 + 31 kcal mol 1; (c) the slope of a vant Hoff plot of In (L)0(L0 = total protein concentration) versus I/T~/2, with n = 4 in Eq. 11, gaveAHvH = 498 _ 24. These can be compared with AH~al = 594 +32 kcal mol-~. This agreement, modest though it is, gives further supportto the unorthodox procedure of applying equilibrium thermodynamics toirreversible processes.Two-state denaturations with ligand dissociation The first application ofDSC o protein/ligand association reactions involved the binding of L-arabinose and D-galactose to the arabinose binding protein (ABP) ofcoli (21). The thermal denaturation of A BP s reversible both in the absenceand presence of the ligands. The ratio AH~H/AHca~ is 1.26 in the absenceof ligands, indicating somedegree of association, and 0.91 in the presenceof ligands, indicating approximately two-state behavior. It was found that



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DIFFERENTIALCANNINGALORIMETRY 479the tm for the denaturation increased with increasing ligand concentration,and that a vant Hoff plot of In (L0) versus 1/Tmwas a slightly curved line(ACd> 0) the slope of which gave (taking rn = 1 in Eq. 15) AHvn=kcal mo1-1 at 58C and 161 at 65C kcal mol-l for both ligands. Thesevalues are considerably smaller than the values (183 kcal tool-~ for arabi-nose and 174 kcal mol-l for galactose) calculated from the DSCcurvesby means of Eq. 4 (A = 4), perhaps because of some nonspecific bindingby the native protein or more residual binding by the unfolded protein. Itis interesting that the data involvedin this vant Hoff plot, with tm increas-ing from 58.4C to 65.1C, are for protein ranging from 97.7 to 99.98%saturated by ligands, and that still higher concentrations of ligands wouldlead to further increases in t m. It is thus quite clear that this continu-ing increase in tm is not due to ligand-induced structural changes in theproteins.The value for AHcal n the presenceof glucose at 59C s 200.7___1.8 kcaltool- ~ while that in the absenceof glucose at 59C s 169.2 _ 1.1 kcal mol- 1.The difference between hese figures, 31.5 kcal mol-1, agrees very well withthe value 30.1 kcal mol-1, calculated from the equation

AHdisso~= 15.26_+0.47+(0.436+_0.047) (t-25 ) kcal m01-1 33.which expresses the results of isothermal calorimetric measurementsonthis system (21). We hus see that the excess enthalpy of denaturationthe presence of the ligands is simply the enthalpy of the dissociation of theligand that accompanies the denaturation.

The binding ofisopropyl fl-D-thiogalactoside (IPTG) to the core proteinof lac repressor has effects on the apparently irreversible denaturation ofthe protein similar to those of arabinose on the denaturation of ABP sindicated by the fact that a plot of In (L)0 versus 1/Tm s a straight line theslope of which gives a value for AHvHn reasonable agreement with theAHo,Ifor the denaturation plus ligand dissociation. It thus appears thatthe protein during denaturation is influenced by the concentration ofunbound igand free in solution, which could hardly be the case if thedenaturation were an absolutely irreversible process.Two-state denaturations with large permanent specific heat changes Thedenaturation of a mutant of T4 lysozyme shown in Figure 2 is a goodsample of a denaturation with a large change in specific heat (S. Kitamuraand J. M. Sturtevant, unpublished observations). The thermodynamicproperties of this transition were evaluated by curve fitting to a two-statemodel including a temperature-dependent ACd.The denaturation of the iso- 1 form of yeast cytochromec in which thesingle thiol group has been blocked by treatment with methyl methane



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480 STURTEVANTthiol sulfonate has been found to have both a large change in specific heatand an increase in dimerization accompanying denaturation as shown bya decrease in tl/2 upon increase of protein concentration (B. T. Nail andJ. M. Sturtevant, unpublished results). Data for this denaturation overconcentration range of 63 to 630/~Mwere well fitted by the model of Eq.7, with no significant dimerization of the native form of the enzyme, butwith the extent of dimerization of the denatured protein ranging from 0.79to 0.93 over the concentration range covered.MULTI-STATEENATURATIONSrivalov and his colleagues have appliedtheir curve resolution method o the DSC ata obtained for a large numberof complex protein denaturations, including those of pepsin and pepsin-ogen, various calcium-binding proteins, plasminogen, immunoglobulins,histones H1 and H5, fibrinogen, tropomyosin, paramyosin, and others.This work, together with reports by others in this field up to 1982, hasbeen reviewed in detail by Privalov (16). Some of these proteins, forexample plasminogen(22), have been the subjects of detailed reports sincethe publication of Privalovs review.The thermal denaturation of taka-amylase A gives a DSCcurve with asingle asymmetric peak, and with AHvH/AHcal bout 0.17, indicating amulti-state transition (H. Fukada, K. Takahashi, J. M. Sturtevant, sub-mitted for publication). This protein contains a single tightly boundCa+,and in the absence of any added Ca2+ its denaturation curves can beaccurately resolved into the sumof three, independent two-state transitionsincluding the dissociation of the Ca2+ during the last step. As expected,the dissociation of a tightly bound ligand in the absence of added excessligand has the same effect on the DSC urve as would he self-dissociationof a dimer. In the presence of added Ca2+, the temperature of denaturationincreases with increasing Ca2+ concentration, further confirming that thetightly boundCa2 dissociates during the unfolding. This indication of theexistence of three domains n the molecule is consistent with the structureof the molecule as revealed by X-ray crystallography, which shows a cleftdividing the molecule into a smaller and a larger part. The suggestionbased on the DSC esult is that the larger part is composed f two domainsand the smaller part of one.Aspartyl transcarbamoylase is a complex protein composed of six so-called catalytic polypeptide chains and six regulatory chains per moleculeof 310,000 daltons. The c6r6 molecule can be separated into two catalyticsubunits, c3, and three regulatory subunits, r2. DSC tudy (12) showsthat the denaturational curve of c3 can be resolved into three two-statecomponents, that of r2 into two components, and that of c6r6, composedof two separate peaks, into five two-state components. The values of tm



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DIFFERENTIAL SCANNING CALORIMETRY 481for the denaturations of c3 and r2 are independent of concentration, indi-cating that the polypeptide chains do not separate on denaturation, whilethose for the denaturation of c6r6 increase with increasing concentration,showing hat dissociation, presumably nto ca and r2 subunits, accompaniesthe denaturation. The effects of the ligands ATP,CTP, and the bisubstrateanalog N-(phosphonoacetyl)-L-aspartate (PALA)on the DSCcurves ofand r2 are consistent with the view that the former two bind to r2 and aredissociated on denaturation, while PALA inds more strongly todenatured r2 than to the native protein; PALAinds to c3 and is dissociatedon denaturation, whereas the two nucleotides are more strongly bound todenatured than to native c3, As might be expected, the effects of these threeligands on the DSC urve for err6 are quite complicated, but qualitativelyconsistent with their various effects on the curves for c3 and r2.DENATURATIONOF MUTANTFORMS OF PROTEINS With the development oftechniques for accomplishing single amino acid replacements in proteins,and for achieving high yield biosynthesis of these altered proteins, muchinterest attaches to determination of the thermodynamic ffects of such"synthetic mutations." Perhaps at present the protein most carefully stud-ied from this point of view is the Arg 96 --, His mutant of the lysozymeofT4 bacteriophage (23). DSCmeasurements n the pH range 2.2 to 2.84 (S.Kitamura and J. M. Sturtevant, unpublished observations) showed theunfolding of this protein to be reversible and gave the results summarizedas follows:

Wild type: AHca~= 5o97+2.33t kcal mo1-1 34.(standard deviation __+4,20)

tl/2 = 2.11 + 17.29t C(standard deviation ___ 0.58)

Arg 96--, His: maca 1 -~- -8.58+2.66t kcal molt 35.(standard deviation _+ 4.48)

tl/2 = - 19.84+21.31t C(standard deviation _ 0.51)

From hese data, since the free energy of unfolding, AGo,equals zero att 1/2, one can calculate by meansof the Gibbs-Helmholtz quation the AGo-temperature profiles at various pH values within the experimental range.Taking the free energy of stabilization as the value of AGu or the mutantform less that for the wild type at fixed pHand temperature, values of theorder of --3.5 kcal mol-l, i.e. an apparent destabilization, are obtained,



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482 STURTEVANTa quantity surprisingly large for a replacement of one charged group byanother. Of course, as mentionedearlier, it cannot be decided on the basisof the DSC ata alone whether the mutation caused destabilization of theactive form or stabilization of the unfolded form, although the formercertainly seems more likely. In any case for which ACd#- 0 for either forboth wild type or mutant forms, the free energy of stabilization mayundergo a change of sign of dGu/dT within the temperature range ofinterest. Unless stated otherwise, free energies of stabilization quotedbelowwill be the values at the tl/2 of the wild type protein.An early study of the effects of single aminoacid replacements involvedthe replacement of Gly 211 of the a-subunit of tryptophan synthase byeither arginine or glutamic acid (24). The arginine replacement hadbarely perceptible effect on tn, but caused an increase in enthalpy of 17kcal mol- ~, while the glutamic acid substitution increased t~ by 1.8C andenthalpy by 10 kcal mol-l (enthalpies calculated to the tm for the wild typeusing the observed values for ACd). Thus very small effects on the freeenergy were accompaniedby relatively large effects on the enthalpy.A more elaborate DSC tudy of glutamine and serine replacements ofGlu 49 in this protein (25) showed decreases in t,, of 3.0 and 1.9Crespectively at pH7.0, and increases of 8.1 and 4.3C respectively at pH9.3. In terms of free energy changes at the tm of the wild type, 54.3, thesechanges correspond to apparent stabilizations of 2.8 and 1.4 kcal mol-1respectively. Within experimental uncertainty, all three proteins have thesame enthalpy of denaturation, varying from 81 kcal tool -I at 45C to124 kcal mol-~ at 60.The denaturational DSCcurve for the 2 repressor of E. coli showstwo clearly separated peaks: The one at lower temperature is due todenaturation of the N-terminal portion of the molecule and the other athigher temperature to the denaturation of the C-terminal portion (26).Fourteen single amino acid replacements and one double replacement, allin the N-terminal portion of the molecule, have been subjected to DSCstudy (27 29). Within experimental uncertainty, none of these replace-ments affected the peak that results from the denaturation of the C-terminal portion, which indicated that the two domains do indeed unfoldapproximately independently. A maximalapparent stabilization of 1.3 kcalmol- l (Gin 33 -~ Tyr) and destabilization of 2.8 kcal mol- ~ (Ala 66 -~ Thr)were observed. In the five cases of replacements of glycine (a poorhelix former) in an a-helix by another residue, stabilization was observed.In most cases, the enthalpy change (maximal decrease 22 kcal tool -~) waslarger in magnitude than the free energy change, indicating enthalpy-entropy compensation.Seven mutant forms of the tail spike protein of phage P22 have been



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DIFFERENTIAL SCANNING CALORIMETRY 483studied by DSC M.-H. Yu, J. King, J. M. Sturtevant, unpublished obser-vations). In this case, a maximaldestabilization of + 17 kcal mol- ~ (Arg283 -~ Ser) was determined, the largest destabilization so far observed fora single amino acid replacement. An interesting point is that all theseproteins were elaborated at 30C by temperature-sensitive mutants thatare unable to form mature protein at 40C. All the proteins have valuesfor tm between 83 and 88C. Thus the temperature sensitivity is not asimple matter of thermodynamics nd must involve some kinetic effects.Preliminary DSCwork with eleven mutant forms of staphylococcalnuclease has shown mall destabilizations (maximalvalue 0.4 kcal tool-1)and stabilizations (maximal value 1.4 kcal mol-~) (J. Gerlt, D. Shortle,and J. Sturtevant, unpublished observations).The Asp 27-o Asn and Asp 27-~ Ser mutant forms of dihydrofolatereductase have been prepared and studied (E. Howell, J. Kraut, and J.Sturtevant, unpublished observations). In each case, tm is raised (3.8and 5.2C respectively) and there is thus apparent stabilization (1.3 and1.0 kcal mol-~respectively). It is interesting that in the former case thedenaturational enthalpy is increased by 15 kcal tool-~ and in the lattercase it is decreased by 7 kcal mol~.Conformational Transitions of NucleotidesThe helix-coil transitions of oligo- and polynucleotides have been exten-sively studied by means of DSC. As a rough generalization, the enthalpyincrease accompanying his transition maybe taken to be 8-10 kcal (moleof base pairs) ~. If allowance is made or "fraying" at each end of a doublehelix of nucleotides, it appears that a transition of useful amplitude andsharpness requires an oligonucleotide containing at least 6 base pairs.The early literature in this field was summarizedby Privalov in 1974(30). A recent systematic DSC tudy of 19 deoxy oligonucleotides anddeoxy polynucleotides by Breslauer and his colleagues has enabled themto compile a consistent set of nearest neighbor base-stacking enthalpies,which has been shown o be successful in predicting helix-coil enthalpiesin DNAsof known sequence. This work has recently been summarized(31).The first DSC tudy of the unfolding of a tRNAwas made by Bode etal (32). Privalov et al have employedDSC o study the melting of severaltRNAs. It was in the course of this work that the first resolutions ofcomplex DSCcurves into two-state component curves were introduced.These and other research are well summarized by Privalov & Filimonov(5).DSChas been applied to the study of DNA-ligand nteractions in muchthe same way as to protein-ligand interactions. Particularly important



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484 STURTEVANThas been its application to the study of binding of antitumor drugs toDNA 33).In recent years there has been much nterest in the left-handed doublehelical form of DNAknown as Z DNA. The thermodynamics of thetransition from the more usual right-handed helical B form to the Z formhas recently been determined by DSCboth for poly (dG-mSdC) (34)and for poly (dGdC)-poly (dGdC) (J. B. Chaires and J. M. Sturtevant,unpublished observations). The B-helix-to-coil and Z-helix-to-coil tran-sitions of these polynucleotides, which occur at temperatures as high as125C depending on experimental conditions, were also observed. Thiswork illustrates an important feature of the DASM-4alorimeter, namelythat an excess pressure of N2of approximately 2 atm is applied above theliquids in the cells, thus permitting scanning of aqueous solutions up to130C.Phase Transitions of Phospholipids and PhospholipidMixturesPhospholipid bilayers have been extensively studied during the last twodecades both because they serve as simple models for complex biologicalmembranes 35) and because they are intrinsically interesting as quasi-twodimensional systems. Muchhas been learned about model and biologicalmembranes from studies of their thermotropic properties, and DSC sin most cases the method of choice for such studies, especially whenthermodynamic data are of importance. McElhaney n 1982 (36) publishedan extensive review of this application of DSC. Here we shall brieflyconsider certain general points and some recent developments.EXPERIMENTALONSIDERATIONShospholipids in bilayer suspensions inaqueous media undergo several different phase transitions. Of these, theso-called main, or gel-to-liquid crystal, transition of phosphatidylcholines(PCs) has been shown o be a first order phase transition (15). In principlethis means hat for a highly purified PC the transition should be close toisothermal, and this in turn means hat very low scan rates, of 0.1 K min-1or less, should be employed to minimize instrumental broadening of thetransition. Since the size of a DSC ignal decreases with a decrease inthe time rate of heat flow into the sample, low scan rates require highinstrumental sensitivity.Phospholipid phase transitions have in some eases been shown to pro-duce two or more closely spaced DSC peaks (37, 38), sometimes forunknown auses. The existence of such transitions is another reason forusing low scan rates, at least with single componentipid systems.It has been found that there are kinetic limitations in the formation of



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DIFFERENTIAL SCANNING CALORIMETRY 485certain phospholipid phases (39, 40). These phenomenaseem to occurmore often in the formation of phases during lowering rather than raisingof the temperature, but in any case they emphasize the need for morecareful experimentation than was formerly thought to be necessary.EFFECTSOF ADDEDOLUTESt has frequently been observed that theaddition of any one of a wide variety of substances to a phospholipidbilayer lowers the phase transition temperature and broadens thetransition. The cooperativity of a transition of a pure lipid is manifestedin its sharpness and maybe expressed in terms of the size in lipid moleculesof the cooperative unit given by the ratio AHvH/AHcaI where AH~ s theenthalpy of the transition in cal per mole of lipid and AHvns estimatedfrom the transition curve as outlined in an earlier section. Although t hasusually been assumed hat solute broadeningof a transition curve indicatesa decrease in cooperativity, it has been shown ecently, on the basis ofideal solution theory, that such broadeningdoes not necessarily reflect lossof cooperativity and, conversely, that there maybe a loss of cooperativityin cases where the transition breadth is not decreased or is even increasedby addition of a foreign substance to the lipid (41, 42). Suchconsiderationsare considerably complicated if an added solute causes a change from thegel phase to the recently discovered interdigitated phase (43).Recent work has demonstrated the value of fitting DSCdata obtainedat modest added solute concentrations to theoretical curves based on idealsolution theory, including independently determined aqueous phase-lipidphase distribution coefficients (44) in the case of solutes showing ignificantwater solubility (45).PHASE TRANSITION PROPERTIES OF COMPLEXLIPIDS As an illustration ofthe application of DSC o the study of the thermotropic behavior of lipids,which are somewhat more complicated than PCs, we may cite the recentwork of Maggioet al (46-48). Twenty chemically related glycosphingo-lipids were studied, and also mixtures of certain of these with dipalmitoyl-phosphatidylcholine and/or myelin basic protein.Conformational Transitions of PolysaccharidesAlthough DSC as not as yet been extensively applied to the thermally-induced transitions that occur in certain polysaccharides, it has recentlybeen shown o be potentially as useful in this field as in those involvingother biopolymers such as proteins and nucleic acids.One of the most extensively investigated processes involving poly-saccharides is the double helix-coil transition of iota- and kappa-carra-geenan (49, 50). The observed enthalpy for these systems can be inter-preted in terms of the Manningheory (5 l, 52), since these polysaccharides,



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486 STURTEVANTwhich carry charged sulfonate groups, can be regarded as linear poly-electrolytes.

Current examples of this are the studies by Paoletti et al (53) andKitamura et al (54) of the order-disorder transition of xanthan poly-electrolyte, which is composed f a cellulosic backbonewith trisaccharideside chains carrying carboxyl groups, some of which are on pyruvateresidues condensed at the carbonyl group. Significant differences in thetransition properties of native and partially depyruvated xanthans wereobserved, which according to the Manning heory suggest that the nativeform has a mixed structure with single and double helical regions whilethe depyruvated form is entirely double helical.Itou et al (55) reported that the triple helical polysaccharide sch-izophillan undergoes a sharp transition at about 6C. Recently this poly-saccharide has been studied in water-dimethyl sulfoxide mixtures (S. Kita-mura, T. Kuge, J. M. Sturtevant, unpublished results), and it has beenfound that two transitions are observed over most of the range of solventcompositions. The transition at higher temperature may be due to a triplehelix-single coil change in conformation.In DSC tudies ofpolysaccl~arides, as in those involving polynucleotides,polydispersity must be taken into account. The ratio ofvant Hoffenthalpyto calorimetric enthalpy maybe employed, as outlined earlier, to obtainan estimate of the size of the cooperative unit for the process under study.

APPLICATIONS TO COMPLEX SYSTEMSThe first attempt to apply DSC o a complex system was probably thework of Steim et al (56) on the plasma membrane f Aeholeplasma aidlawiiB. Two endotherms were observed: The one at lower temperature wasfully reversible and appeared to be due to the phase transition of gel phaselipids while the irreversible transition at higher temperature was pr.obablydue to denaturation of membrane roteins.Brandts and his co-workers have made very effective use of DSC nstudying the humanerythrocyte membrane 57). Four well-defined tran-sitions were observed, of which two have been demonstrated to be due torelatively simple unfolding transitions of proteins (58).

Loike et al (59) employed DSC o study the heat produced by sus-pensions of murine macrophages. The total heat that was evolved in theinterval 10-37C, during scanning at 1 K rain -~, ranged from 300 to2500x 10-12 cal per cell, dependingon cell density, glucose concentration,and the presence or absence of various drugs. Approximately 24%of theheat liberated was due to conversion of glucose to lactic acid, and an



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DIFFERENTIAL SCANNING CALORIMETRY 487additional 14-~1%was due to hydrolysis of ATP, depending on whetherthe final product was ADP r AMP.Thompson t al (60) found that the complex DSCcurve observedheating a suspension of photosystem I in the temperaturerange 30-70Ccould be resolved into 5 two-state curves. An earlier study (61) with a lesssensitive instrument had given similar results. A partial assignment ofthese peaks to the componentsof the system has been made, includingassignment of a peak at 48.2C to the functional denaturation of theoxygen-evolving complex. This peak, which accounts for only 2%of thetotal enthalpy absorbed, is extremely sharp WithAHvn/AhcaI = 3 106.The cause of this unusual effect is unknown.DSCgives a convenient method for following the thermally inducedreversible polymerization f the coat protein of tobacco mosaicvirus (62).ACKNOWLEDGMENTSThedifferential scanningcalorimetric work n the authors laboratory hasbeen supported by grants from the National Institute of Health (GM-04725) and the National Science Foundation (PCM-8117341and DMB-8421173). Comments, uggestions, and corrections by Drs. S. Kitamuraand A. Tanakawere very helpful.Literature Cited1. Privalov, P. L., Plotnikov, V. V., Fili-monov, V. V. 1975. J. Chem. Thermoodyn, 7:41-472. Privalov, P. L. 1980. Pure Appl. Chem.52:479-973. Borchardt, H. J., Daniels, F. 1951. J.Am. Chem. Soc. 79:41-464. Filimonov, V. V., Privalov, P. L., Hinz,H.-J., vonderHaar, F., Cramer, F. 1976.Eur. J. Biochem. 70:25-315. Privalov, P. L., Filimonov, V. V. 1978.J. Mol. Biol. 122:447-646. Freire, E., Biltonen, R. L. 1978. Bio-polymers 17:463-797. Freire, E., Biltonen, R. L. 1978. Bio-polymers 17:481-968. Freire, E., Biltonen, R. L. 1978. Bio-polymers 17:4925109. Freire, E., Biltonen, R. L. 1978.Biochim.Biophys. Acta 514:54~8I0. Filimonov, V. V., Potekhin, S. A., Mat-veev, S. V., Privalov, P. L. 1982. Mol.Biol. 16:551~52

11. Gill, S. J., Richey, B,, Bishop, G.,Wyman, . 1985. Biophys. Chem. 21: 1-1412. Edge, V., Allewell, N. M., Sturtevant, J.M. 1985. Biochemistry 24:5899-5906

13. Chang, L.-H., Li, S.-J., Ricca, T. L.,Marshall, A. G. 1984. Anal Chem. 56:1502-714. Chang, L.-H., Marshall, A. G. 1986.Biopolymers 25:1299-131315. Albon, N., Sturtevant, J. M. 1978. Proc.Natl. Acad. Sci. USA75:22584016. Privalov, P. L. 1982. Adv. Protein Chem.35:1-10417. Manly, S. P., Matthews, K. S., Stur-tevant, J. M. 1985. Biochemistry 24:3842-4618. Pfeil, W. 1986. In ThermodynamicDatafor Biochemistry and Biotechnology, ed.H.-J. Hinz, pp. 349 76. Berlin/Heidel-berg: Springer-Verlag19. Privalov, P. L. 1979. Adv. Protein Chem.33:167-24120. Takahashi, K., Sturtevant, J. M. 1981.Biochemistry 21: 6185-9021. Fukada, H., Sturtevant, J. M,, Quiocho,F. A. 1983. J. Biol. Chem. 258: 13193-98

22. Novokhatny, V. V., Stanizlav, A. K.,Privalov, P. L. 1984. J. MoLBiol. 179:215-3223. Grutter, M., Matthews, B. 1982. J. Mol.Biol. 154:525-35



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488 STURTEVANT24.Matthews, . R., Crisanti, . M.,Gcpncr, . ., clicclebi,., turtc-vant, J. M. 1980. Biochemistry 19: 1290-9325. Yutani, K., Khechinashvili, N. N., Lap-shina, E. A., Privalov, P. L., Sugino, Y.

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