The DSC data analysis for small, single-domain proteins. Application to the SH3 domain

REACTIVE & FUNCTIONAL POLYMERS

ELSEVIER

Reactive

& Functional

Polymers

36 (1998) 221-225

The DSC data analysis for small, single-domain proteins. Application to the SH3 domain J.C. Martinez a, A.R. Viguera b, L. Serrano b, V.V. Filimonov a*1,P.L. Mateo a~* a Department of Physical Chemistry and Institute of Biotechnology, University of Granada, Granada, Spain b EMBL, Heidelberg, Germany Received

15 December

1996; revised version received

13 May 1997; accepted

13 May 1997

Abstract In some cases, small globular domains can maintain their native three-dimensional structure when separated from the rest of the protein. But due to the small size of such domains and low heat effect accompanying their cooperative structure unfolding, this transition occurs in a very broad temperature range. It is shown that for such broad processes an accurate evaluation of the thermodynamic parameters from the DSC data can be done only by a global curve-fitting analysis applied to the multiple DSC curves obtained under various solvent conditions. 0 1998 Elsevier Science B.V. All rights reserved. Keywords:

Protein; Stability; Microcalorimetry; Unfolding; Domain

1. Introduction The most direct information about the stability and thermodynamics of biopolymer structure is obtained by differential scanning calorimetry (DSC). This traditional physico-chemical method has been further developed in biopolymer studies both by designing special microcalorimeters for dilute biopolymer solutions and by creating new methodology for DSC data analysis [14]. It was necessary to develop new instrumentation and methodology since, unlike true phase transitions (crystal melting, for example), temperature induced conformation transitions in biopolymers ’ On leave from the Institute of Protein Research of the Russian Academy of Sciences, Puschino, Moscow Region, 142292 Russia. *Corresponding author. Fax: t34 58 272879; e-mail: [email protected]

1381-5148/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved. PI1 S1381-5148(97)00088-6

are much broader. Another important factor is the need to work with very dilute polymer solutions. The traditional approach to calculating the thermodynamic parameters of protein unfolding from DSC records is reviewed in detail by Privalov [l]. This approach has been applied mostly to relatively large proteins and nucleic acids under conditions when direct and straightforward extrapolation of the partial heat capacity of the native and unfolded states is possible. Recent thermodynamic studies into protein stability, however, have been focused on very small proteins, which exhibit very broad (although cooperative) unfolding transitions accompanied by very small heat effects. This paper deals with the formal approach to the analysis of the DSC records obtained for such very small proteins and their mutants under low structure-stability conditions.

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J.C. Martinez et al. /Reactive & Functional Polymers 36 (1998) 221-225

molecule which can occupy IZ+ 1 macroscopic states (including the reference state, 0) can be expressed as:

80 -

(C,(T))

= ~

=

n -Fi dHi

C

i=a dT

+ ~

Ham

i=o

n

=

c

Cp,iFi + &Cr = CT + SC;

(1)

i=O

300

320

340

360

T VI

Fig. 1. The temperature dependence of the partial molar heat capacity of lysozyme in 25 mM glycine buffer, pH 2.5, at c = 1.07 mglml (solid line). Other lines correspond to the best fitting of the C, to the two-state model: best-fit linear approximations of C,,O (dash-dot line, C,,O = 21.8 + O.l16[T - 293]), C,,U (dashdot-dot line, C,,J = 33.0 + O.OOS[T- 293]), CF (dashed line) and the overall C, (solid dots). The thermodynamic parameters of the two-state transition were AH,,, = 443 f 15 kT/mol at T, = 336.3 + 0.1 K.

2. Results and discussion Fig. 1 shows an example of the DSC record for the ‘classic’ object of protein folding studies, hen-egg lysozyme (M, = 14300) dissolved in water buffer, pH 2.5, at a concentration of about 1 mg/ml. Increasing the solution temperature within the calorimeter results in a breakdown of the native three-dimensional structure of the polypeptide. This is accompanied by a heat absorption spread over a relatively wide temperature range between 320 and 350 K. It has been shown, however, that such a broad peak corresponds to a two-state process, i.e. the structure of this small globular protein unfolds very cooperatively. It was also found that the cooperative domains in globular proteins usually have a molecular weight of about 10000-15000 or smaller and their average enthalpy of unfolding is about 400 kJ/mol at 330 K [ 11. The traditional methods for DSC data analysis are described in detail elsewhere [2-4]. In general the partial heat capacity of the macro-

Here the first term corresponds to the chemical or ‘internal’ heat capacity of the protein in solution (shown in Fig. 1 as the sigmoid dashed line), while the second term reflects the excess heat (absorption peak) of the reaction. To calculate the reaction heat by integration of the &CT one has to approximate the C’F function. This has usually been done by assuming [3-51 that the heat capacities of the states have the same temperature dependence (i.e. that the ACp,i = C,,i - C,,a values are constant) and that

ACp,i

2 const AHi which, in general, is incorrect. Nevertheless, the errors which might be introduced into calculation of the ,CF by such an oversimplification should be small when: (a) the amplitude of the heat absorption peak is much larger than the overall change in the heat capacity, AC,,,, and (b) the temperature dependencies of the C,,, and C,,a might be adequately extrapolated over the whole temperature range of the transition. Both of these conditions hold good for the lysozyme curve shown in Fig. 1 since the amplitude of its peak (-55 kJ/Kmol) is 8 times larger than AC, (-6.5 kJ/Kmol) and the heat capacities of the initial and final states were recorded over relatively large temperature ranges. Usually only two states are populated at equilibrium during single-domain protein unfolding

N&J

(3) and the two terms of the heat capacity function 1 can be presented as K Fu = l+K

(4)

J.C. Martinez et al. /Reactive

& Functional Polymers 36 (1998) 221-225

223

.8 -

sty=-

K

AH;

RT2 (l+

GCT(T,)=

K)2

(6)

% .s r! & B

.6 .4.2 -

s

(7) In

(The enthalpy increment, A Hm = AH (T,) is also equal to the integral of SC? over temperature, where T, is the transition midpoint defined as K(T,)= 1). Unfortunately, very small globular proteins (with iV& of 60004000) have lower unfolding heat effects than those of lysozyme and, as seen from Eq. 7, their C, peaks should have much lower amplitudes. In addition, since protein unfolding heats strongly depend on temperature, the DSC peaks get even broader when Tm decreases to room temperatures. Fig. 2 shows microcalorimetric records obtained for SH3 domain (Mr = 7000) in diluted solutions with pH values between 2 and 3.5. As in the case of lysozyme the thermal unfolding of the SH3 fragment is almost 100% reversible despite the fact that the DSC records were obtained at relatively high protein concentrations (up to 5 mg/ml). It can be seen that even under the conditions of maximum stability of SH3 (pH 3.5) the peak amplitude is close to the CF increment. When stability decreases the peaks get so much smaller and wider that linear extrapolations of the initial and final heat capacity becomes very uncertain, as occurs for example at pH 2.0. The most adequate approach to the analysis of DSC data presented in Fig. 2 is based on the following observations. Firstly, a two-state approximation still holds for proteins smaller than lysozyme. Secondly, an analysis of the heat capacities of the native and unfolded states of globular proteins has shown that they follow a linear dependence of temperature with a reasonable accuracy. The slopes of these dependencies are, however, different for the two conformations, it being always higher for the native state. Thus, for

280

300

320

340

360

T WI Fig. 2. The temperature dependencies of the partial molar heat capacity for the spectrin SH3 domain (pH 2.25 and 3.5) and of its circular permutation m6b [7] (pH 2.0) (lower part, solid lines). Other lines show the best fits of each curve to the two-state model: CF and C, are shown by the dashed lines and solid dots, respectively. Common best fit approximations of the C,,c (dash-dot line) and C,J (dash-dot-dot line) were C,,a(T) = 10.6+0.05(T-293) and Q(T) = 14.8+0.012(T-293). The thermodynamic parameters for each individual curve are plotted in Fig. 3. The upper graph shows the populations of the two states for each curve, FN (dash-dot line) and FU (dash-dot-dot line). The vertical dotted bars correspond to the T, values. (It can be seen that the wider the transition, the higher the difference between the T,, value and observed peak maximum).

each DSC curve in Fig. 2, we can write C,,o = ao + boT

(8)

C,,u = au + buT

(9)

AC,,u = (au -ad

+ (bU - bo)T

(10)

=AafAbT In addition T

AH,

=

AC, dT = AH, s &I

+ Ab(T2 2

T;)

+ Aa(T -

TId (11)

224

A&J =

J.C. Martinez et al. /Reactive & Functional Polymers 36 (1998) 221-225

s

T ACP

-dT=T, T

A& T, -

Td

(12)

where Tm is the transition midpoint as defined above. Then AGU = AHu - TASu

(13)

(14) and Fu, CT and C.7 are defined by Eqs. 4-6. Using the above definitions, heat capacity peaks can be fitted to Eq. 1 using any nonlinear, least-square fitting algorithm by adjusting some of the parameters. If the quality of fitting to the two-state model (which is formally defined as the sum of the residual squares) is good enough and not worse than the fitting to any multistate unfolding scheme, it may be concluded that the process is really a two-state one. As can be seen from Fig. 1 this is exactly the case for lysozyme, the melting curve of which fits well to the twostate process with the parameters specified in the figure legend. The combination of CP,a and C,,JJ gives the value of 6.5 kJ/Kmol for AC,,,. Thus, all three parameters characterizing the transition under given solvent conditions, AH,, T, and AC,,, agree quite well with those found by traditional DSC analysis methods [l]. As mentioned above, the case of lysozyme at pH 2.5 is relatively simple and can therefore be solved equally well either by traditional methods or by the curve fitting procedure. The case of the SH3 domain, however, is much more complicated since the traditional approach is not feasible here and thermodynamic parameters can only be obtained by curve fitting on the assumptions discussed above. The result of such an individual curve fitting is also shown in Fig. 2. As expected, each of the curves fits the two-state equations very well but, naturally, with its own characteristic AHm and T, values. Since the heat capacities after the unfolding transitions apparently merge

together, it is not surprising that the fitting procedure gives the same temperature dependence of C,,J for all three curves. Interestingly enough the fitting procedure also gives very similar C,,a functions for all three curves, despite the fact that the initial C, values differ substantially. The explanation for this may come from a consideration of the state populations, calculated by Eqs. 4 and 5 and shown in the upper part of Fig. 2. It can be seen that at pH 2.25 and 2 the population of the initial state never reaches lOO%, whereas the final state with a higher partial heat capacity is from 10 to 20% populated, even at very low temperatures, thus giving rise to the overall heat capacity of the protein. Therefore, unlike the transition parameters, AHIII and Tm, which are dependent upon solvent conditions and/or mutations, the intrinsic heat capacities and AC,,, are much less so. In fact, as was shown by the structural analysis of thermodynamic data, the heat capacities of polypeptides in water depend mostly on the hydrophilic and hydrophobic surfaces exposed to the solvent in each state. Since two curves correspond to the same polypeptide and the third to its circular permutation, which has an amino acid composition and tbree-dimensional structure similar to those of the wild-type protein, the coincidence of the C,,O and C,,u for all the curves shown in Fig. 2 is not surprising. This observation allows us a further improvement in the DSC data analysis in that a global or simultaneous fitting of all three curves may be made with a fewer adjustable parameters, i.e. with a single set of ai and bi values. This simultaneous analysis of several melting curves also leads to a decrease in the fitting uncertainties and to the creation of a coherent thermodynamic model of protein unfolding under various solvent conditions. Changing the pH in the acidic range usually impinges only on the entropic factor of the Gibbs energy, but not on the entbalpic one. Therefore, the C, values found from the curve fitting must be equal or similar to the slope of the AH, vs. Tm plot. Fig. 3 presents the correlation found for the wild-type spectrin SH3 [6] by DSC data analysis in the pH range 2-4. The

J. C. Martinez et al. /Reactive

& Functional

Polymers 36 (1998) 221-225

225

by the curve fitting is virtually the same. The conclusion is that the mutation causes some conformational changes which result in a decrease in the T, of the process and an increase in the AH, at any given temperature, but scarcely unchanging heat capacities. This observation awaits an adequate structural interpretation.

Acknowledgements

300

310

320

330

340

350

Tm (K)

Fig. 3. The dependence of the unfolding enthalpy, AH,,,, on T,,, for the spectrin SH3 domain. Solid line, the quadratic regression through the experimental data taken from [6]; filled circles, the data for spectrin SH3 corresponding to pH 2.25 and 3.5 curves of Fig. 2; open circles, the data for the circular permutation mutant of spectrin SH3 corresponding to the curve of pH 2.0 from Fig. 2. The bar shows 10% error.

correlation is not linear, as might be expected for a temperature-dependent AC,. It is also seen that the data obtained here for the circular permutation mutant at pH 2.0 does not belong to this correlation, although the AC, value obtained

This work has been supported by PB93-1163 and INTAS-93-7 grants. V.F. also acknowledges the financial support from the Sabbatical Program of the Spanish Government. We also thank Dr. John Trout for revising the English text.

References 111 P.L. Privalov, Adv. Prot. Chem. 33 (1979) 167. 121E. Freire, R.L. Biltonen, Biopolymers 17 (1978) 463. [31 V.V. Fiiimonov, S.A. Potekhin, S.V. Matveyev, P.L. Privalov, Mol. Biol. (USSR) 16 (1982) 435. 141 P.L. Privalov, S.A. Potekhin, Meth. Enzymol. 114 (1986) 4. 151 K. Takahashi, J.M. Sturtevant, Biochemistry 20 (1981) 6185. [61 A.R. Viguera, J.C. Martinez, V.V. Filimonov, P.L. Mateo, L. Serrano, Biochemistry 33 (1994) 2142. 171 A.R. Viguera, F.J. Blanco, L. Serrano, J. Mol. Biol. 247 (1995) 670.