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Keywords:

  • calorimetry;
  • protein unfolded states

Abstract

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

We have calculated the absolute heat capacities of fragments 1–73 (N fragment) and 74–108 (C fragment) from thioredoxin, their complex and the uncleaved protein, from the concentration dependence of the apparent heat capacities of the solutions determined by differential scanning calorimetry. We find that, while the absolute heat capacities of uncleaved, unfolded thioredoxin and the C fragment are in good agreement with the theoretical values expected for fully solvated chains (calculated as the sum of the contributions of the constituent amino acids), the absolute heat capacities of the N fragment and the unfolded complex are about 2 kJ·K−1·mol−1 lower than the fully solvated-chain values. We attribute this discrepancy to burial of the apolar surface in the N fragment (as burial of the polar area is expected to lead to an increase in heat capacity). Illustrative calculations suggest that burial of about 1000–1600 Å2 of apolar surface takes place in the N fragment (probably accompanied by the burial of a smaller amount of polar surface). In general, this work is supportive of heat capacity measurements on protein fragments being useful as probes of surface burial in studies to characterize protein unfolded states and the high regions of protein folding landscapes.

Abbreviations
ASA

accessible surface area

DSC

differential scanning calorimetry

Trx

oxidized E. coli thioredoxin (the uncleaved protein)

The structural and energetic characterization of protein unfolded states is an essential requisite for the understanding of protein folding processes [1,2]. This characterization is hampered by the fact that, often, protein unfolded states become significantly populated in a comparatively narrow range of experimental conditions. For instance, the (temperature-dependent) heat capacity of proteins may be related to the amounts of polar and apolar areas exposed to the solvent [3–8] and may thus provide useful information about surface burial; however, in the usual differential scanning calorimetry (DSC) experiments the heat capacity of the unfolded state is only available in a small temperature range above the unfolding calorimetric transition. In general, the problem of the experimental accessibility of the unfolded state may be bypassed by working with protein fragments that remain unfolded in a wide range of conditions ([9] and references quoted therein). In this work, we present a DSC study on the complementary fragments 1–73 (N fragment) and 74–108 (C fragment) from oxidized Escherichia coli thioredoxin (Trx), their complex (called the NC complex [1–73][74–108] or cleaved Trx) and the uncleaved protein, in order to determine (and analyze in terms of surface burial) the absolute heat capacities of these species. Previous studies have shown that both fragments are largely disordered and that their spontaneous re-association produces a noncovalent complex that shares the same topology and packing of uncleaved Trx [10,11]. The absolute heat-capacity values reported in this work rely upon the outstanding baseline reproducibility of the VP-DSC microcalorimeter [12] and are calculated from the concentration dependence of the apparent heat-capacity values, a rigorous procedure recently proposed by Kholodenko and Freire [13] that allows for a reliable estimation of the associated errors.

Materials and methods

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

Materials

Wild-type thioredoxin was over-expressed in E. coli JF521 and purified using previously described gel-filtration and ion-exchange chromatographic procedures [14], and reverse-phase chromatography. The protein was proteolytically cleaved in two complementary fragments: (1–73) and (74–108), called the N fragment and the C fragment [15], respectively. These fragments were purified by reverse-phase chromatography and were stored in lyophilized form. Purity of the samples was checked by SDS/PAGE [16], sequencing, amino-acid analysis, and electrospray mass spectroscopy. Protein and peptide concentrations were determined spectrophotometrically using the following molar extinction coefficients: ε280 = 1.41 × 104m−1·cm−1 for the N fragment [17], ε215 = 3.97 × 104m−1·cm−1 for the C fragment [15] and ε280 = 1.4 × 104m−1·cm−1 for Trx [14].

Trx solutions for DSC experiments were prepared by exhaustive dialysis against 10 mm potassium phosphate at the desired pH. The peptide fragments were dissolved in 8 m guanidine, 10 mm potassium phosphate buffer at pH 7 and, subsequently, were extensively dialyzed against phosphate buffer. The NC complex was prepared by mixing stoichiometrically the two fragments at low concentration, followed by dialysis against phosphate buffer, and a concentration step. All samples, isolated fragments, cleaved and uncleaved Trx, were characterized by gel-filtration FPLC to confirm the absence of oligomeric species.

Calorimetric experiments

DSC experiments were performed using a VP-DSC microcalorimeter from MicroCal [12] with a scan rate of 1.5 K·min−1 (in most cases) or 0.5 K·min−1. Samples were degassed at room temperature prior to calorimetric experiments. Calorimetric cells (operating volume ≈ 0.5 mL) were kept under an excess pressure of 207 kPa to prevent degassing during the scan. In all measurements, the buffer from the final dialysis step was used in the reference cell of the calorimeter.

Fitting of theoretical models to the DSC transitions

All fittings were done to the absolute molar heat capacity values calculated using subroutines provided by MicroCal. The specific volumes required for the calculation of absolute heat capacities were determined according to Makhatadze et al. [18] and found to be 0.736 mL·g−1 (for the N fragment), 0.770 mL·g−1 (for the C fragment) and 0.750 mL·g−1 (for Trx and the NC complex). It should be noted that, while absolute heat-capacity values calculated from individual DSC thermograms suffice for the fitting purposes described in this section, we describe below a more accurate procedure to calculate absolute heat capacities based on several thermograms corresponding to different protein concentrations.

The equations used in the fitting procedures are based on two-state models and are briefly described below (see also Ibarra-Molero et al.[19]).

For any two-state model the excess enthalpy (taking the native state as reference) is given by:

  • image(1)

where ΔH is the denaturation enthalpy and α stands for the fraction of protein that is denatured. The protein heat capacity can then be written as:

  • image(2)

where ΔCp is the denaturation heat-capacity change.

The two first terms in the right-hand-side of Eqn (2)[inline image + α · ΔCp] describe a sigmoidal-like curve that smoothly connects the heat capacity levels of the native and the denatured states; this curve is usually called the chemical baseline. The third term on the right-hand side is significantly different from zero only when α changes significantly with temperature; that is, within the comparatively narrow temperature range in which the protein denatures. Therefore, the ΔH · (dα/dT) term describes the transition (or ‘peak’) in the thermogram.

The α value at a given temperature is related with the corresponding equilibrium constant for the denaturation process. If denaturation does not involve changes in association state, this relation is:

  • image(3)

which is valid for thioredoxin but not for the NC complex, as, in this latter case, denaturation involves dissociation of the complex into unfolded N and C fragments. Thus, at equilibrium at a given temperature, the concentrations of complex, N fragment and C fragment would be C(1 − α), Cα and Cα, respectively (C being the total protein concentration expressed in moles of complex); hence, the equilibrium constant for NC complex denaturation is:

  • image(4)

Given a value of K, the appropriate equation (Eqn 3 or 4) can be easily solved for α. In addition, expressions allowing the calculation of the temperature dependence of α (required for Cp calculation using Eqn 2) can be easily derived by differentiating in Eqns (3 and 4) solving for dα/dT and using the van’t Hoff equation for the temperature dependence of K. The results are:

  • image(5)

from Eqn (3) (denaturation not coupled to dissociation), and:

  • image(6)

from Eqn (4) (unfolding coupled to dissociation of the NC complex).

Denaturation occurs (i.e. α goes from 0 to 1) in a comparatively narrow temperature range, within which the temperature dependence of the denaturation enthalpy can be neglected. Thus, we will assume that the ΔH value explicitly shown in Eqns (3), (5) and (6) is a temperature-independent value, assign this value to a temperature characteristic of the transition (T1/2, the temperature at which α = 0.5): ΔH(T1/2). Within the same approximation, the temperature dependence of the denaturation equilibrium constant can be written as:

  • image(7)

where K1/2 is the value of K at the temperature T1/2. If denaturation is not coupled to changes in association state, K1/2 = 1. For NC complex denaturation (coupled to fragment dissociation) substitution of α= 0.5 into Eqn (4) gives K1/2 = C/2. It must be noted that neglecting the temperature dependence of K for purposes of α and dα/dT evaluation only causes a very small distortion in the shape of the predicted DSC transitions, distortion which is below the uncertainty caused by chemical baseline definition.

In all cases, the experimental temperature range to be fitted was chosen in such a way that the pre- and post-transition baselines were clearly defined, but also that linear temperature dependencies for these baselines could be reasonably assumed. Hence, we used the following equations for inline image and ΔCp in Eqn (2):

  • image(8)
  • image(9)

where a, b and d are constants and ΔCp(T1/2) is the denaturation heat capacity at the temperature T1/2.

 Eqn (2) (together with Eqns 3 or 4, 5 or 6, 7, 8 and 9) was fitted to the experimental heat-capacity data using programs written by us in the mlab environment (Civilized Software Inc.). In each case, the fitting parameters were: T1/2 and ΔH1/2 (which describe the transition) and a, b, d and ΔCp,1/2 (which describe the chemical baseline).

Fitting of the concentration dependence of the denaturation temperature for the NC complex

Denaturation temperature values for the NC complex increase with protein concentration, as is to be expected for a denaturation process coupled to dissociation. Let T0 be the denaturation temperature at unit protein concentration (C = 1) and T1/2 the denaturation temperature at any given concentration, C. Let K0 and K1/2 be the denaturation equilibrium constants at the temperatures T0 and T1/2. Under the assumptions used above, these two equilibrium constants may be related through the following van’t Hoff equation:

  • image(10)

In addition, K1/2 and K0 values can be obtained from Eqn (4) by substituting α= 0.5 and the corresponding protein concentration: K1/2 = C/2 and K0 = 1/2. Substituting these values into Eqn (10) and solving for T1/2 yields:

  • image(11)

This equation was fitted to the experimental T1/2 versus C data for NC complex denaturation using programs written by us in the MLAB environment. Fitting parameters were T0 and ΔH. Clearly, this type of analysis neglects the temperature dependence of ΔH; this however, is again permissible as the experimental T1/2 values usually span a narrow temperature range (about eight degrees for the NC complex).

The calculation of the absolute heat capacities for native and unfolded states from the experimental thermograms

Accurate values for the absolute heat capacities of native and unfolded states were derived from the concentration dependence of the apparent heat-capacity function (ΔCapp), defined as the heat capacity of the protein (or peptide) solution taking the buffer-buffer baseline as reference. It is a well-known fact that ΔCapp may be a negative number, as the amount of water (for which heat capacity is larger than that of a protein or peptide) is lower in the sample cell. Under suitable assumptions, ΔCapp for a solution of a protein or peptide may be expressed as:

  • image(12)

where C is the concentration of peptide (or protein) in mm, V0 is the volume of the calorimetric cell (in mL), Cp, P and Cp, W stand for the heat capacities of the protein and water (buffer), respectively, and Vp and VW are the molar volumes of peptide and water (Vp is easily obtained from the specific volumes calculated using known procedures: see Makhatadze et al.[18]). According to Eqn (12), a plot of ΔCapp versus protein concentration for a given temperature should be linear with zero intercept and with a value for the slope equal to V0 · 10−6 · Cp,P, from which the absolute heat capacity can be easily calculated. Clearly, this procedure requires several thermograms corresponding to different concentrations; however, it shows several important advantages when compared with the usual methods for absolute heat-capacity calculation. These advantages should be evident from the analyses reported under Results but, in any case, they will be summarized at the beginning of the Discussion (see also Kholodenko and Freire [13]).

Theoretical estimates for the heat capacities of unfolded and native states

The heat capacity expected for fully solvated, unfolded states of thioredoxin and both fragments was calculated from the amino-acid composition using [20]:

  • image(13)

where N is the number of amino-acid residues, the index i refers to the 20 amino acids, ni is the number of amino acids of type i, Cp, i is the molar heat capacity of the side chain of amino acid i, and Cp, NH-CO,Cp, COOH and Cp, NH2 stand for the heat capacities of the peptide unit, the terminal carboxyl and the terminal amino groups, respectively. Actually, we used for the temperature-dependent Cp, i, Cp, NH-CO,Cp, COOH and Cp, NH2 values the polynomial representations of the Privalov and Makhatadze data [20] given by Freire [21] (see Häckel et al.[22] for a different set of group heat capacity values for use in protein calculations). Theoretical values of the heat capacity of the native proteins were calculated as a function of temperature using the equation given by Freire [21]:

  • image(14)

where Mr is the relative molecular mass of the protein.

Results

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

The absolute heat capacities of the N and C fragments from the ΔCapp analysis

We carried out DSC experiments with solutions of the isolated fragments at pH values 5.7, 7.0 and 8.0 and, for each pH value, at several fragment concentrations within the approximate range 0.1–1.3 mg·mL−1. Several buffer-buffer baselines were obtained before each run with a fragment solution in order to ascertain proper equilibration of the calorimeter, and an additional buffer-buffer baseline was obtained after each fragment solution run to check that no significant changes in instrumental baseline had occurred. Fig. 1 shows a representative example of the raw experimental data; note the outstanding instrumental baseline reproducibility (even with two intervening refilling steps) and that the difference between the heat capacity of the fragment solution and the buffer–buffer baseline is much larger than the experimental scatter of the latter.

image

Figure 1. Original DSC thermograms for a solution of N fragment (concentration 0.2 mg·mL−1) with the corresponding buffer-buffer baselines. The numbers reflect the order in which the thermograms were obtained. Thus, two buffer-buffer baselines (1 and 2) were obtained prior to the experiment with fragment solution (3); a reheating experiment (carried out without removing the N fragment solution from the sample cell) is also shown (4). Finally, the fragment solution was replaced by buffer and an additional buffer-buffer baseline was recorded (5).

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The heat capacity versus temperature profiles for the fragment solutions did not show cooperative transitions in any of the experimental conditions studied and we checked, for representative experimental conditions, that they were reproducible on a reheating run (see Fig. 1). Analysis of these profiles was carried out on the basis of the apparent heat capacity function (ΔCapp), as described in Materials and methods. Thus, for each fragment, and for different temperatures spanning the experimental range, we constructed plots of ΔCapp versus fragment concentration, including data obtained at the different pH values studied (see Fig. 2 for representative examples). These plots were clearly linear with zero intercept, as predicted by Eqn (12). We also found excellent agreement between the ΔCapp data obtained at different pH values (except for the N fragment at temperatures higher than 85 °C; see Fig. 2), which indicates that there is no significant pH dependence of the absolute heat-capacity values for the fragments within the pH range studied. Accordingly, we calculated those absolute values from the slopes of the linear fits to the except for the N fragment at T > 85 °C (separate fittings for the three pH values studied were carried out in this case). The resulting profiles of absolute heat capacity (with associated standard errors) versus temperature for the N fragment the C fragment are shown in Fig. 3. We also include in Fig. 3 the theoretical profiles expected for fully solvated, unfolded state, calculated from the amino-acid composition, as described in Materials and methods. The heat capacity of the C fragment agrees with the theoretical value, but this is not the case, however, with the N fragment, which shows a heat capacity significantly lower than the theoretical prediction (note that the discrepancy is much larger than the standard error associated with the absolute heat capacity values).

image

Figure 2. Plots of apparent heat capacity versus concentration for N fragment (1–73) and C fragment (74–108). (A) Data corresponding to 70 °C. (B) Data corresponding to 100 °C. In both cases, we show the best linear fits (with zero intercept) to the ΔCapp versus C dependencies. The different symbols refer to the pH value: open circles, pH 7.0; closed squares, pH 5.7; closed triangles, pH 8.0. In most cases, we found excellent agreement between the ΔCapp values corresponding to the same fragment and the same temperature, but obtained with solutions of different pH value, as is shown in the illustrative example of panel A (70 °C). (B) (100 °C) is included here to show that at high temperature (above 85 °C) there appears to be a significant pH effect on the heat capacity of the N fragment.

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image

Figure 3. Absolute heat capacity versus temperature profiles for the N fragment (1–73) and the C fragment (74–108). The absolute heat-capacity values were obtained from the slopes of plots of ΔCapp versus concentrations (such as those shown in Fig. 2) and the associated standard errors derived from the linear fits to the ΔCapp/C dependencies are shown here. In most cases, all the data obtained at different pH values (5.7, 7.0 and 8.0) were used in the calculation of the absolute Cp values (open circles). However, a pH effect on ΔCapp was apparent in the case of the N fragment at temperatures above 85 °C and, in this case, ΔCapp data at different pH values were analyzed separately; the resulting absolute heat-capacity values at pH 5.7, 7.0 and 8.0 are shown in this figure with closed circles. We also show in this figure with continuous lines the theoretical predictions for fully solvated, unfolded N and C fragment (see Materials and methods for details on this calculation).

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Thermal denaturation of thioredoxin and absolute heat capacities of the native and unfolded states from the ΔCapp analysis

We carried out DSC experiments with thioredoxin solutions of pH values 5.7, 7.0, 7.5, 8.0 and 8.5 and several protein concentrations for each pH value. Reproducibility of the buffer-buffer baseline before and after the run with the protein solution was ascertained as described above for the experiments with fragment solutions. In all cases a cooperative transition was observed in the thermograms and we checked in several representative experimental conditions that the unfolding process was highly reversible (reproducibility of the transition in the reheating run; results not shown). Good fits of the two-state equilibrium model to the data were obtained in all cases (see, for instance, Fig. 4) and the transition temperatures derived from the fittings did not appear to change significantly with protein concentration. The values of the fitting parameters are collected in Table 1.

image

Figure 4. Heat capacity versus temperature profile for thioredoxin, obtained from a DSC experiment carried out at pH 7.0 and a protein concentration of 1.0 mg·mL−1. The empty circles are the experimental data and the continuous line is the best fit of the two-state equilibrium model.

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Table 1.  Transition temperatures (T1/2), and values of the unfolding enthalpy and the unfolding heat capacity derived from the two-state fittings to DSC profiles for uncleaved thioredoxin. The uncertainty associated with the ΔH values is estimated to be about 10 kJ·mol−1 or less from the scatter of the values corresponding to the same pH and (approximately) the same T1/2. The average of all ΔCp values for thioredoxin unfolding is 5.8 kJ·K−1·mol−1 with an associated standard error of ± 0.8 kJ·K−1·mol−1. This value is in good agreement with the absolute heat capacities given in Fig. 5. Thus, at 86 °C the difference between the heat capacities of unfolded Trx (as given by the line labeled U in the figure) and native Trx (as given by the dashed line in the figure) is 6.4 kJ·K−1·mol−1.
pH C (mg·mL−1) T 1/2 (°C)ΔH(T1/2) (kJ·mol−1)ΔCp(T1/2) (kJ·K−1·mol−1)
5.71.9088.44385.1
5.73.0087.64326.0
7.00.5086.74786.5
7.00.9786.54776.6
7.01.0086.64756.0
7.01.4086.54705.5
7.01.1086.44715.9
7.51.5186.04694.6
7.51.5186.14664.3
8.00.7485.54616.4
8.01.2285.54697.0
8.51.2184.24605.3

We used the ΔCapp procedure to calculate the absolute heat capacities of native and unfolded thioredoxin. That is, from the pre- and post-transition baselines of the DSC thermograms for thioredoxin unfolding and the instrumental baselines we obtained ΔCapp values that we subsequently plotted against protein concentration. These ΔCapp versus C plots were linear (results not shown) and there was excellent agreement between the ΔCapp data corresponding to different pH values. The absolute heat capacities for native thioredoxin were calculated from the slopes of the plots corresponding to temperatures ≤ 70 °C, while the plots corresponding to T ≥ 90 °C were used to obtain values for the absolute heat capacity of unfolded thioredoxin (clearly, the transition temperature range, 70 °C < T < 90 °C was not used in the ΔCapp analysis). As shown in Fig. 5, the absolute heat capacities for native and unfolded Trx were in good agreement with the theoretical predictions (see Materials and methods for details) for the heat capacity of the native state and the heat capacity of a fully solvated unfolded state.

image

Figure 5. Absolute heat-capacity values for native and unfolded states of uncleaved thioredoxin and the NC complex. The absolute heat-capacity values were obtained from the slopes of plots of ΔCapp versus concentrations and the associated standard errors derived from the linear fits to the ΔCapp/C dependencies are shown. The dashed line is the theoretical prediction for the absolute heat capacity of the native state (see Materials and methods for details. The data labeled N + C is the sum of the heat capacities of the N fragment and the C fragment (shown in Fig. 3); the absolute heat-capacity values derived from experimental data for the unfolded complex are also shown (open triangles: values obtained using ΔCapp data at pH values 5.7, 7.0 and 8.0; closed squares: values obtained using ΔCapp data at pH values 7.0 and 8.0; closed triangles: values obtained using ΔCapp data at pH 5.7). The continuous line labeled U is the theoretical prediction for the fully solvated unfolded state (see Materials and methods for details).

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Thermal denaturation of the NC complex and absolute heat capacities of the native and unfolded states from the ΔCapp analysis

DSC experiments with the NC complex were carried out with solutions of pH values 5.7, 7.0, 7.5, 8.0 and 8.5 and, for each pH value, at several complex concentrations within the approximate range 0.05–3 mg·mL−1. In all cases a cooperative transition was observed, which was found to be highly reversible, as shown by reproducibility on reheating runs carried out for representative conditions (results not shown). These transitions were asymmetrical and concentration dependent, as is to be expected for an unfolding process coupled with dissociation. Good fits of the two-state model with dissociation were obtained in all cases (the values obtained for the fitting parameters are collected in Table 2); however, small systematic deviations between the experimental values and the best-fit predictions were often observed. The T1/2 values derived from these fittings increased with protein concentration (Table 2), as is to be expected for a denaturation process coupled to dissociation. The nonlinear, least squares fits of Eqn (11) (based on the two-state model: see Materials and methods) to the experimental T1/2 versus C data were excellent (results not shown); however, the unfolding enthalpy values derived from the fittings (452 kJ·mol−1 and 418 kJ·mol−1, from the data at pH 7.0 corresponding to 1.5 and 0.5 K·min−1, respectively) were somewhat larger than the values (335–390 kJ·mol−1) determined from the analysis of the DSC transitions (we obtained similar discrepancies for pH 5.7 and pH 8.0). We believe that this disagreement, as well as the above-mentioned small deviations in the two-state fitting, could be due, at least in part, to a slow-equilibrium distortion of the DSC transition [23], as, in this system, comparatively slow association-dissociation rates are expected in the transition region within the concentration range employed [15]; this interpretation is supported by the fact that the discrepancy between the ΔH values obtained from the T1/2 versus C dependence and those determined from the analysis of the DSC transitions is smaller for the lower scan rate.

Table 2.  Transition temperatures (T1/2), and values of the unfolding enthalpy and the unfolding heat capacity derived from the two-state fittings to DSC profiles for the NC complex (cleaved thioredoxin). All values were determined from the analysis of DSC experiments carried out at 1.5 K·min−1 except those indicated. The uncertainty associated with the ΔH values is estimated to be about 10 kJ·mol−1 from the scatter observed in plots of ΔH versus T for the same pH. The average of all ΔCp values for NC complex unfolding is 5.8 kJ·K−1·mol−1 with an associated standard error of ± 0.9 kJ·K−1·mol−1. This value is in good agreement with the absolute heat capacities given in Fig. 5. Thus, at 62 °C the difference between the heat capacities of the unfolded complex (as given by the sum of the heat capacities of the N fragment and the C fragment: line labeled N + C in the figure) and native complex (as given by the dashed line in the figure) is 6.1 kJ·K−1·mol−1.
pH C (mg·mL−1) T 1/2 (°C)ΔH(T1/2) (kJ·mol−1)ΔCp(T1/2) (kJ·K−1·mol−1)
  1. a   DSC experiments carried out at a scan rate of 0.5 K·min −1.

5.70.0661.23418.5
5.70.1162.23224.8
5.70.2064.13335.1
5.70.6266.73484.8
5.71.1067.83626.3
5.72.3068.93796.8
7.00.0657.93405.6
7.00.1159.23356.8
7.00.2060.53356.3
7.00.3861.73465.6
7.00.3861.0a354a6.4a
7.00.7563.23585.6
7.01.1464.13666.0
7.01.3063.5a358a5.2a
7.01.6164.83585.3
7.02.9065.7a391a5.1a
7.50.7261.63464.4
8.00.1055.03065.2
8.00.1556.03215.7
8.00.2757.03086.8
8.00.3757.93125.9
8.00.6058.93065.9
8.00.9860.23194.7
8.01.8961.73255.5

As with thioredoxin above, we used the ΔCapp procedure to calculate the absolute heat capacities of native and unfolded NC complex; thus, from the pre- and post-transition baselines of the DSC thermograms for the NC complex and the instrumental baselines we obtained ΔCapp values that we subsequently plotted against protein concentration. Again, these ΔCapp versus C plots were linear (results not shown) and there was excellent agreement between the ΔCapp data corresponding to different pH values, except for temperatures close to 100 °C, at which the data for pH = 5.7 appeared significantly different. The absolute heat capacities for the native complex were calculated from the slopes of the plots corresponding to temperatures ≤ 40 °C, while the plots corresponding to T ≥ 80 °C were used to obtain values for the absolute heat capacity of unfolded thioredoxin (the transition temperature range, 40 °C < T < 80 °C, was not used in the ΔCapp analysis). The absolute heat capacity versus T profiles are given in Fig. 5.

Discussion

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

Absolute heat capacity values reported in this work have been obtained from the concentration dependence of the apparent heat capacity [13]. This ‘ΔCapp analysis’ shows several advantages.

(a) Each absolute heat capacity value (at a given temperature) is calculated from several experiments carried out at different protein or peptide concentrations. This decreases the error associated with the heat-capacity value and allows for a reliable estimation of this error. Also, as different experiments (with different instrumental buffer-buffer baselines) are used to construct each given ΔCapp versus C plot, the error associated to the instrumental baseline is effectively randomized and taken into account in the analysis; note, nevertheless, that the uncertainty associated with the buffer-buffer baseline (about 15 µJ·K−1; see Fig. 1) is smaller than the size of the symbols in Fig. 2.

(b) ΔCapp data derived from experiments carried out at different pH values (or at different values of some other experimental condition, such as scan rate) can be included in the same ΔCapp versus concentration plot. This permits a straightforward assessment of the pH effect on ΔCapp and, in the case that no significant effect is found (as in most instances described in this work), allows us to use data at different pH values to calculate absolute heat capacity values, thus further decreasing the associated error.

Absolute heat-capacity values obtained in this work are summarized in Figs 3 and 5. The heat capacity of the C fragment shows a good agreement with the theoretical prediction for a fully solvated, unfolded state, while that for the N fragment is significantly lower (about 2 kJ·K−1·mol−1) than the theoretical prediction (Fig. 3). This ‘anomalous’ behavior of the N fragment is also reflected in the fact (Fig. 5) that the heat capacity of unfolded thioredoxin (which agrees with the theoretical prediction for a fully solvated, unfolded state) is about 2 kJ·K−1·mol−1 higher than the heat capacity of the unfolded complex (which agrees with that calculated as sum of the heat capacities for the N and C fragments); note that the result that the absolute heat capacity is larger for unfolded thioredoxin than for the unfolded complex (N fragment plus C fragment) is independent of any theoretical model for the heat capacity of fully solvated, unfolded proteins. Note also that the discrepancy is only observed for the unfolded states and that there is good agreement between the heat capacities of native thioredoxin and native complex (a fact that strongly disfavors that the found discrepancies are due to errors in the extinction coefficients used).

The simplest explanation for the above discrepancies is that significant burial of the apolar surface takes place in the N fragment. Thus, changes in heat capacity can be related to changes in accessible surface area (ASA) through [7]:

  • image(15)

where the changes in accessible surface area are in Å and the change in heat capacity is in J·K−1·mol−1. (The values of the coefficients of ΔASAap and ΔASApol given in the above equation are those corresponding to 25 °C; actually these coefficients change somewhat with temperature, although we will not need to use this temperature dependence in the qualitative analysis that follows.) According to Eqn (15), an absolute heat-capacity value lower (by about 2 kJ·K−1·mol−1) than that expected for a fully solvated chain must be explained in terms of apolar surface burial, as burial of polar surface would lead to an increase in heat capacity (note the signs of the coefficients of ΔASAap and ΔASApol in Eqn 15). If we assume that no burial of polar surface takes place, Eqn (15) indicates that burial of about 1000 Å2 of apolar surface are required to explain the 2 kJ·K−1·mol−1 discrepancy in heat capacity. Of course, it appears unlikely that the apolar area could be buried without the concomitant burial of some polar area; if we assume that both types of ASA are buried in the ratio found in native proteins (ΔASApol/ΔASAap= 0.59 [24]), the Eqn (15) indicates that about 1600 Å2 are buried in the N fragment (together with some 950 Å2 of polar surface). In any case, this analysis suggests that protein-unfolded states showing significant burial of apolar area may become populated under the usual conditions of the folding-unfolding experiments in vitro. This conclusion appears to be consistent with a number of experimental studies (often based on NMR), which suggest the existence of interactions between apolar residues in unfolded proteins or unfolded protein fragments and, in particular, the formation of hydrophobic clusters [25–34].

It remains now to make some suggestions regarding the origin of the anomalous behavior of the N fragment as compared with that of unfolded thioredoxin. Thus, we could conjecture that surface burial in the N fragment is brought about by association of this fragment; this would be an interesting possibility, as transient protein aggregation has been shown to occur in several refolding processes in vitro ([35], and references quoted therein); however, we found no evidence of aggregation in gel-filtration experiments carried out as part of this work and, in addition, previous sedimentation analysis studies, carried out under the same experimental conditions employed here, indicated only the presence of monomeric species [15]. It appears likely therefore that, in this case, surface burial occurs in an intramolecular manner, although a specific structural model is lacking at this stage; we note, nevertheless, that local structure prediction based on the I-sites library [36,37] suggests that residues 7–27, which complete a hydrophobic core in the crystal structure of thioredoxin, could form a stable structure in the N fragment (Chris Bystroff, personal communication). The fact that surface burial appears to occur in the N fragment and not in unfolded thioredoxin (which shows a ‘normal’ heat-capacity behavior, at least within the narrow temperature in which its heat capacity is available; Fig. 5) could be due to the electrostatic effect of the extra ionizable group created upon cleavage; this hypothesis is clearly speculative, but it is supported by the fact that a pH effect on the absolute heat-capacity value can be detected at high temperature for the N fragment and the unfolded complex, but not for unfolded thioredoxin (Figs 3 and 5).

Finally, we would like to point out that, the above uncertainties notwithstanding, our results clearly support that heat capacity measurements on protein fragments may be useful as probes of surface burial in studies addressed to characterize protein unfolded states and the high-energy regions of protein folding landscapes.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

This research was supported by the Spanish Ministry of Education and Culture (Grant PB96-1439 from the DGES to J. M. S.-R.), the ‘Fundacion Ramon Areces’ (Grant to J. M. S.-R.), the RCMI Grant from NIH to CCNY, NIH Grant GM53808 to M. L. T. and Grant MCB-9507255 from NSF to M. L. T., who is an NSF career awardee. We thank C. Bystroff for carrying out local structure predictions based on the I-sites library. M. M. G.-M. is a recipient of a predoctoral fellowship from the ‘Junta de Andalucia’.

References

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References