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Pressure Perturbation Calorimetry of Unfolded Proteins† Alekos D. Tsamaloukas, Neena K. Pyzocha, and George I. Makhatadze* Department of Biology and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, New York 12180 ReceiVed: July 7, 2010; ReVised Manuscript ReceiVed: August 24, 2010
We report the application of pressure perturbation calorimetry (PPC) to study unfolded proteins. Using PPC we have measured the temperature dependence of the thermal expansion coefficient, R(T), in the unfolded state of apocytochrome C and reduced BPTI. We have shown that R(T) is a nonlinear function and decreases with increasing temperature. The decrease is most significant in the low (2-55 °C) temperature range. We have also tested an empirical additivity approach to predict R(T) of unfolded state from the amino acid sequence using R(T) values for individual amino acids. A comparison of the experimental and calculated functions shows a very good agreement, both in absolute values of R(T) and in its temperature dependence. Such an agreement suggests the applicability of using empirical calculations to predict R(T) of any unfolded protein. Introduction 1
The application of pressure perturbation calorimetry (PPC) to study volumetric properties of (bio)molecules has become increasingly popular within the past decade. Rather than being a measurement of the temperature dependence of the partial specific volume, V(T), itself, PPC measures the first temperature derivative of it, R(T) )(1/V(T)) × ∂TV(T), which is the thermal expansion coefficient. The main virtue of the technique lies in the fact that transitions hardly visible in an integral curve of V(T), as commonly obtained by densitometric techniques, are easily detected in a differential mode that measures R(T) directly. Since the pioneering work of Kujawa and Winnik2 on polymer solutions a considerable variety of other systems has been investigated with this technique. Among these, particularly noteworthy are studies on lipid phase transitions,3-5 micellar shape transitions,6 DNA melting,7,8 and protein unfolding.9-11 A common theme to all these studies is an interest in the sign and magnitude of the relative volume change, ∆V/V, that occurs when the biomacromolecule undergoes a transition between its low- and high-temperature conformations and how this relates to the hydration properties in either state. Until recently, however, the quantification of ∆V/V from PPC remained somewhat arbitrary because no solid thermodynamic framework for its determination was available. A solution to this problem was recently introduced by Schweiker and Makhatadze12 in the form of a stringent, yet mathematically straightforward, two-state thermodynamic formalism that can be applied to any (bio)molecular system that undergoes a transition between two conformations. In this formalism, the temperature dependence of R(T) for both native and unfolded conformation is treated explicitly in the form of third order polynomials that in turn serve to construct a “progress baseline” between the native state RN(T) and the unfolded state RU(T). Values for ∆V/V are then obtained by integrating the excess R(T). Although the methodology appears useful for global fits of experiments conducted under †
Part of the “Robert A. Alberty Festschrift”. * To whom correspondence should be addressed. Phone: (518) 276-4417. Fax: (518) 276-2955. E-mail:
[email protected].
different conditions, for example, a series of different solution pH-values, the introduction of polynomial functions for native and unfolded state baseline has its usual problems. In particular, for nonlinear baselines, it is difficult to find the analytical expression to extrapolate values into the transition region, where neither native nor unfolded state baselines can be measured experimentally. As such, there is always the risk of attempting to extract more fitting parameters out of one curve than it can actually afford (see ref 13 for a recent and very instructive explanation of the concept of “overfitting” experimental data). To overcome this potential pitfall of the methodology described in ref 12, we present experimental data that serve to better define unfolded state baselines. To this end, we have experimentally measured the temperature dependence of R(T) for two fully unfolded proteins, apocytochrome C and the reduced and methylated form of bovine pancreatic trypsin inhibitor (BPTI-RM). Combining this with the previously published data on reduced RNase A, we demonstrate that (i) third order polynomials are indeed a valid description for the unfolded state baseline and (ii) an adequate representation of the unfolded state baseline can be calculated via an additive scheme using the contributions of individual amino acid side chains. Materials and Methods Protein Sample Preparation. Horse heart cytochrome C was obtained from Sigma (St. Louis, MO, USA, cat. No. C-7752, Lot 61H7001). Samples of apocytochrome C were prepared according to the procedure of Stellwagen et al.14 Bovine pancreatic trypsin inhibitor (BPTI) was obtained from United States Biochemical Corp. (Cleveland, OH, USA, cat. No. 11388, Lot 85432). Reduction and methylation of BPTI (henceforth denoted as BPTI-RM) was carried out as previously described.15,16 Purity of the protein samples was checked by SDS PAGE. The molecular masses of the two chemically modified proteins were checked by Maldi-TOF and were found to be 11 744 Da for apocytochrome C, and 6860 Da for BPTI-RM. The value obtained for apocytochrome C is in agreement with the one previously reported by Jankowski and Virelizier.17 On the basis of the molecular
10.1021/jp106294p 2010 American Chemical Society Published on Web 09/13/2010
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mass of native BPTI (6511 Da), the attachment of 6CH3CONH2 in samples of the reduced and methylated form of the protein results in the value given above. UV-vis absorption spectra of the proteins were recorded on a Hitachi U-2900 dual beam spectrometer (Hitachi High Technologies Corp., Tokyo, Japan) in 5 mm path length quartz cuvettes. Spectra were baseline corrected by the results obtained in scans with buffer in both cuvettes. Correction of the spectra for light scattering artifacts was carried out according to the empirical formalism of Winder and Gent.18 The following extinction coefficients were used to spectrophotometrically determine protein concentration: ε277 nm) 0.92 mL/ (mg cm) for apocytochrome C14 and ε280 nm) 0.78 mL/ (mg cm) BPTIRM.16 Partial specific volumes, Vpr, used for analysis of the PPC data of 0.740 mL/g for apocytochrome C and 0.730 mL/g for BPTI-RM were determined from the amino acid sequence as described.20 Both extinction coefficient and partial specific volume were assumed to be independent of pH. Protein samples were dialyzed extensively (3-4 changes of beakers containing 1 L buffer) against the following buffers prior to the PPC experiments: pH 2.5-3 (20 mM glycine/HCl), pH 4.5 (20 mM sodium acetate/acetic acid), and pH 7 (20 mM cacodylic acid/sodium hydroxide). Dialysis was carried out at 4 °C using Spectrapor3 dialysis membranes with a molecular mass cutoff of 3500 Da. Circular Dichroism (CD) Experiments. Far-UV CD spectra (λ ) 200-260 nm) were recorded at 5 °C on a Jasco-710 spectropolarimeter (Jasco Corp., Tsukuba, Japan) in a 1 mm path length quartz cuvette. Spectra for both apocytochrome C and BPTI-RM were obtained at pH 2.5 (20 mM Glycine/HCl buffer), and pH 7 (20 mM cacodylic acid/NaOH buffer). Protein samples were extensively dialyzed prior to recording the CD spectra. Concentrations for both proteins were between 0.3-0.4 mg/mL. Data are reported as mean residue ellipticity, [θ] (in deg cm2/dmol), obtained from the ellipticity values, Θ (in mdeg), recorded by the instrument according to the relation
[θ] )
Θ · ΜR l·C
(1)
where C denotes protein concentration (in mg/mL), l is the optical path length (in cm), and MR is the mean molecular mass of each amino acid in the protein, that is, for apocytochrome C MR ) (11 744/104) Da, and for BPTI-RM MR ) (6860/58) Da, respectively. Pressure Perturbation Calorimetry (PPC) Experiments. PPC experiments were performed on a MicroCal VP-DSC instrument with a PPC accessory (MicroCal, LLC, Northampton, MA, USA). Initial data processing was carried out using Origin 7 with custom add-on for PPC data analysis supplied with the instrument (OriginLab Corp., Northampton, MA, USA): Experiments were conducted according to standard procedures as previously described.1,12 Briefly, at each pH value a series of three blank experiments consisting of a water/water-, buffer/ water-, and buffer/buffer-scan, respectively, were carried out. These were run in duplicate with temperature increments of 4 °C between 2 and 110 °C. Scans were averaged and fitted to fourth-order polynomials. Polynomial coefficients were saved and used for data analysis as described.21 Scans of protein against buffer were conducted in duplicate with temperature increments of 3 °C from 2 to 110 °C. Values of R for protein at each temperature were averaged from pressure increase and release and also from duplicate experiments (see Supporting Information for details). Prior to the full temperature scan, proper
filling of the calorimeter cells was assessed by a test jump at 23 °C. When heat values obtained upon pressure increase and decrease agreed to within 0.5 µcal (or better), a full sequence of pressure jumps was started. Otherwise, the cells were reloaded due to the presence of air bubbles. Concentrations used in the buffer/protein scans were between 1 and 2 mg/mL for both proteins. These relatively dilute protein solutions were previously shown to be particularly useful to obtain reliable PPC data.12 The thermal expansion coefficient of a protein, R, at a given temperature, T, is related to the thermal expansion of the water, RH2O, and the change in the heat of the calorimetric cell during a water/buffer scan (∆QH2O/buf) and a buffer/protein scan (∆Qbuf/pr) due to a change in the pressure (∆P) of the system as:
R ) RH2O -
∆QH2O/buf T∆PVcell
-
∆Qbuf/pr T∆PVcellcprVpr
(2)
where Vcell is the volume of the calorimetric cell; cpr is the concentration of protein in the calorimetric cell, and Vpr is the partial specific volume of protein. Precise knowledge of protein concentrations is mandatory for a reliable analysis of PPC data (see eq 2). Simulations show that relative error in concentration almost directly propagated into the values of R at low temperature (2 °C). For example, a 5% overestimate in the concentration leads to a 5% reduction in the values of R and vice versa. This effect is temperature dependent and almost vanishes at high temperatures (>70 °C). This means that the measurements of R(T) values will have smaller errors at high temperatures. To minimize concentration errors we have proceeded as follows for all PPC data presented in this work: To account for small residual volumes, which always remain in the calorimeter cells (and filling syringe), protein solutions were loaded into the sample cell, removed from there again, and were then transferred into the UV cuvette for concentration measurement. After the UV-vis spectra were obtained, protein samples were loaded into the sample cell and the experiments were started. Results and Discussion Spectroscopic Characterization of the Protein Samples. The goal of this work is to characterize the temperature dependence of the thermal expansion coefficient R(T) for the unfolded state of proteins. Thus, we first characterized the conformation of protein samples using far-UV CD spectroscopy. Far-UV CD spectra have been shown to provide information concerning the conformation of the polypeptide backbone. Figure 1 compares far-UV circular dichroism (CD) spectra for apocytochrome C and BPTI-RM at pH 7 and pH 2.5. The featureless CD spectra illustrate that both proteins are largely unfolded irrespective of the pH of the solution. Such spectral properties are usually attributed to unfolded proteins.22,23 For BPTI-RM, the spectra shown in Figure 1 are similar to those reported previously24 and are in agreement with later studies on the effects of mutations on the hydrodynamic properties of this protein.25 For apocytochrome C, similar spectra have also been previously reported.23,26 Importantly, the spectra of BPTIRM at the two pH values overlay almost perfectly. The spectrum of apocytochrome C at pH 2.5 is also very similar to those of BTPI-RM. There is, however, a small but detectable difference of the far-UV CD spectrum of apocytochrome C at pH 7. According to Hamada et al.,27 apocytochrome C at neutral pH exists in a compact collapsed state that does not have an
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Figure 1. Far-UV circular dichroism spectra of apocytochrome C (O, b) and BPTI-RM (9, 0) at 5 °C. Open symbols are for pH 2.5, solid symbols are for pH 7.0. Only every tenth experimental point is shown for clarity. Solid lines are drawn to guide the eye.
appreciable amount of secondary structure as measured by farUV CD, but has overall dimensions 30% smaller than the fully unfolded state. As will be discussed later, this difference in the compactness of apocytochrome C at pH 2.5 and pH 7 can be detected by a difference in the thermal expansion coefficient. Overall, within the experimental accuracy of our measurements, a good agreement between spectrum at low (BPTI-RM and apocytochrome C) and neutral pH (BPTI-RM) is observed, suggesting that under these conditions these two proteins exist in the unfolded state. Temperature Dependence of the Thermal Expansion Coefficient of Unfolded States. Figure 2 shows experimentally measured temperature dependencies of expansion coefficient R(T) for apocytochrome C and BPTI-RM in solution with various pH values. In addition, we plotted the previously reported1,28 R(T) values for reduced and methylated RNAase A, RNAase-RM (also known to be unfolded23,29). Several interesting properties are apparent from a close inspection of Figure 1. First, the dependence of R(T) on temperature is nonlinear. It decreases steeply up until ∼55 °C, and then continues decreasing with a much shallower slope afterward. Second, the values of R(T) are independent of pH for BPTI-RM. For apocytochrome C, the R(T) function is similar at all pH values except pH 7.0. As we discussed above, Hamada et al27 have shown that apocytochrome C exists in the unfolded state at acidic pH and adopts a compact state at neutral pH. We propose that the difference in R(T) between low and high pH values for this protein is a direct manifestation of this, that is, the collapsed state of apocytochrome C at pH 7.0 has fewer hydrophobic side chains exposed to solvent and thus larger values of R(T). This is a very interesting observation and more experiments addressing this issue are currently in progress. Third, the dependence of R(T) on temperature can be accurately approximated by a third order polynomial. As can be seen from Figure 2, a four-parameter fit describes the R(T) function for all three proteins very well. Having the temperature dependence of R(T) for these three unfolded proteins, we can ask whether it is possible to predict these functions using empirical rules. For example, in an unfolded polypeptide chain all residues are solvent exposed. Therefore, the effects of individual amino acid residues should
Figure 2. Experimental values of thermal expansion coefficient as a function of temperature as measured by PPC. Panel A: apocytochrome C measured at pH 2.5 (O), 2.6 (]), 3 (3), 4.5 (0), and 7 (2). Panel B: BPTI-RM measured at pH 2.5 (O), 4.5 (0), and 7 (3). Panel C: RNaseRM data at pH 5.5 (O, ref 1) (0, ref 28). The solid lines correspond to a third-order polynomial fit of all experimental data points (except pH 7.0 for apocytochrome C). Dashed lines show 95% confidence interval of the fit.
contribute additively to the overall property of the chain. An analogous approach has been previously used for calculation of the partial molar heat capacity of unfolded proteins.30,31 Additive Scheme for the Contribution of Amino Acid Side Chains to the Measured r(T). To model the experimentally determined R(T)-curves for both apocytochrome C and BPTIRM, we use an additive scheme previously described by this laboratory.12 It is based on the assumption (justified by a number of empirical calculations20,32,33) that the partial molar volume of proteins is an additive function of the partial molar volumes of individual amino acid residues. Briefly, for any unfolded protein state Rcalc(T) can be calculated as a weighted sum of the contributions of individual amino acid side chains:12
Rcalc(T) )
∑ Vi(T)Ri(T) i
∑ Vi(T)
(3)
i
where Vi(T) and Ri(T) are the partial molar volume and coefficient of thermal expansion of side chain i, respectively. Lin et al.1 have presented an extensive set of third-order polynomial coefficients {ai, bi, ci, di} that describe the Ri(T)curves for 16 out of the 20 naturally occurring amino acid side chains and the peptide unit. Using these values, it can be shown
Pressure Perturbation Calorimetry of Unfolded Proteins
J. Phys. Chem. B, Vol. 114, No. 49, 2010 16169 groups (6 × CH3CONH2) in samples of BPTI-RM and RNaseRM were modeled by six side chains of Asn in our calculation. Using the known amino acid sequences for BPTI-RM (a total of 58 amino acids), apocytochrome C (a total of 104 amino acids for horse heart apocytochrome C), and RNase-RM (a total of 124 amino acid residues) we calculated the Rcalc(T) function using eqs 3-5. The results of the calculation are compared to the experimental values in Figure 2. We observed a very good agreement between Rcalc(T) and Rexp(T) for all three proteins; the sum of squared deviations between calculated and experimental values is on the order of ∼10-8 to 10-9 K-2. This suggests that eq 3 can be used to predict R(T) function for any protein in the unfolded state from its primary sequence. Conclusions Using experimentally measured values of the thermal expansion coefficient of three different unfolded proteins, we have established the temperature dependence of this parameter. R(T) for the unfolded state is a nonlinear function of temperature and can be well approximated by a third order polynomial. We tested an additivity approach to calculate R(T) from the amino acid sequence of proteins and found that this empirical approach can well predict both absolute values and temperature dependence of R for unfolded proteins. We also found that the R(T) parameter is sensitive to the global conformation of the polypeptide chain. This can be potentially used to probe hydration of different collapsed states of denatured, or even intrinsically disordered, proteins.
Figure 3. Comparison of experimental and calculated functions of R(T). Panel A - apocytochrome C; Panel B - BPTI-RM; Panel C RNase-RM. Solid lines are the Rcalc(T) functions, calculated according to eq 3. Symbols are for fit of the experimental points to a third-order polynomial with the size of the symbols chosen to represent error at 95% confidence (see Figure 2).
that the partial molar volume of side chain i can be calculated as:
(
Vi(T) ) Vi(T0) exp Ci + aiT +
)
(
bi 2 ci di T + T3 + T4 2 3 4
bi 2 ci di T0 + T30 + T40 2 3 4
)
Supporting Information Available: The results of pressure perturbation calorimetry experiments with apocytochrome C illustrate the reproducibility and error analysis. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
(4)
where T is the temperature in °C, Vi(T0) is the partial molar volume of side chain i at temperature T0 ) 25 °C, and the constant Ci is given by
Ci ) - aiT0 +
Acknowledgment. We would like to thank Lucas Wafer for the helpful comments on the manuscript.
(5)
To avoid confusion, we note that in order to get the temperature dependence of the partial molar volume of, for example, the side chain of alanine according to eq 4 using Lin’s data,1 one should proceed as follows: use the partial specific volume for Ala ) 1.22 mL/g), Ala at 25 °C given in Table 1 of ref 1 (VSC multiply this number by the difference in molar mass between alanine and glycine: MAla - MGly ) 14 Da to obtain the partial molar volume for the side chain of alanine, VAla(T0) ) 17 mL/ mol, and finally use eqs 4 and 5 to get the complete VAla(T). To account for the polynomial coefficients of the four missing side chains in the data of Lin et al.,1 we have made the assumption that these can be best described as: Gly ) peptide unit, Lys ) Arg, Tyr ) Phe, and Asp ) Glu. The additional functional
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