Article pubs.acs.org/JPCB
Thermodynamics of Downhill Folding: Multi-Probe Analysis of PDD, a Protein that Folds Over a Marginal Free Energy Barrier Athi N. Naganathan*,†,‡ and Victor Muñoz*,†,§ †
Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai 600036, India § Centro Nacional de Biotecnología, Consejo Superior de Investigaciones Científicas, 28049 Madrid, Spain ‡
S Supporting Information *
ABSTRACT: Downhill folding proteins fold in microseconds by crossing a very low or no free energy barrier (1660 cm−1. The 1632 and 1652 cm−1 bands are interpreted as arising from solvent-exposed and buried helical carbonyls, respectively, and include weighted contributions from hydrogen-bonded and non-hydrogen bonded amides in both cases.66,67 However, the FTIR signal of PDD shows only a single band at 1632 cm−1 (inset to Figure 1F), suggesting that the helical carbonyls of PDD are predominantly solvent-exposed. The corresponding unfolding transition is very broad with steep pre- or post-transition baselines (plotted in Figure 1F in units of extinction coefficient). Accordingly, fitting
Table 1. Parameters from the Derivative and Conventional Two-State Analysis of the Unfolding Curves of PDDa S. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
probe DSC fUV CD 222 nm fUV CD 208 nm fUV CD 200 nm fUV CD 193 nm nUV CD 280 nm nUV CD SVD1 nUV CD SVD2 Flu. 320 nm Flu. 340 nm Flu. 360 nm Flu. QY FTIR 1632 cm−1 FTIR SVD1 FTIR SVD2
Tm (K) (derivative)
Tm (K) (twostate)
ΔHm (kJ mol−1) (two-state)
322.2b 315.6
323.4 (0.2) 320.0 (0.1)
113.2 (0.3) 122.2 (1.6)
319.6
319.9 (0.2)
120.5 (2.7)
318.1
320.8 (0.1)
124.0 (1.7)
320.8
319.9 (0.1)
128.3 (1.1)
317.8
321.0 (0.3)
105.1 (2.6)
317.8
320.0 (0.2)
109.4 (2.2)
315.5
321.5 (0.4)
93.8 (3.3)
320.0 322.0 322.9 322.3 318.0
322.6 322.4 321.9 322.1 321.8
(0.2) (0.1) (0.2) (0.1) (2.3)
118.7 (2.7) 114.2 (1.6) 117.1 (2.4) 115.8 (0.6) 64.9 (10.6)
324.7 317.9
326.4 (3.5) 326.1 (4.4)
104.5 (26.3) 53.3 (13.5)
The numbers within brackets are the fitting errors. bObtained from the peak of the DSC thermogram. a
Moreover, the amplitude of the third component shows a peculiar parabolic behavior with the inflection point at ∼315 K, very close to the Tm estimated from the derivative analysis of the 222 nm unfolding curve. These exact same features have been previously observed when investigating the thermal unfolding of short peptides that populate helical conformations by vibrational CD and FTIR, and have been interpreted as diagnostic of helix unfolding by increased fraying.65 Thus, these observations in PDD indicate that its native helices also fray during thermal unfolding (i.e., their average helix length decreases gradually), which incidentally is consistent with the steep changes in the CD signal at 222 nm occurring within the pretransition region. Near-UV CD Experiments. PDD has a lone tyrosine (and no tryptophan) that is placed on an asymmetric helical environment in the native 3D structure. This tyrosine should produce a distinct CD signal in the near-UV region (250−320 nm). Accordingly, the near-UV CD spectra at pH 7.0 display positive ellipticity values with a peak at ∼280 nm (Figure S4). A significant fraction of this positive near-UV CD signal persists even at high temperatures, suggesting that the unfolded ensemble of PDD has residual structure around the tyrosine residue, consistent with the indications provided by far-UV CD. As for previous experiments, the near-UV CD unfolding curve at 280 nm is also sigmoidal, and its fit to a two-state model produces Tm and ΔHm values that are intermediate between those obtained from the DSC and far-UV CD data (Figure 1D and Table 1). The SVD analysis of the near-UV CD spectral set again produces three components, indicating that for this probe there is also an underlying complexity. The second SVD component signals a red shift at high temperatures (peaks of opposite signs at ∼275 and ∼295 nm; Figure S5) that changes with temperature following a sigmoidal curve that has Tm similar to that measured by far-UV CD at 222 nm, but it is 8986
dx.doi.org/10.1021/jp504261g | J. Phys. Chem. B 2014, 118, 8982−8994
The Journal of Physical Chemistry B
Article
equilibrium unfolding of PDD is structurally complex. The next critical question to address is whether it is possible to explain and interpret all the complex features of the PDD equilibrium unfolding using a model that is simple, yet offers sufficient structural richness to permit the accurate calculation of the different spectroscopic properties of the protein as a function of its unfolding. Multiprobe Thermal Unfolding. The details of the statistical mechanical model, specific procedures for calculating the spectroscopic signals for each of the 1 + N*(N + 1)/2 protein microstates, and the fitting parameters, are detailed in the Supporting Information. Briefly, we assign specific spectroscopic signals to each of the 903 partly structured species of the model (all possible single stretches of native structure) and the global unfolded state. The observed signal at each temperature is directly calculated as the sum of the probability weighted signals for all the species in the model. The free parameters of the model are then obtained by globally fitting the DSC thermogram, the far- and near-UV CD spectra as a function of temperature, the QY of NALA and the IR change at 1632 cm−1. The total number of floating parameters is only 11, including three thermodynamic parameters (changes in enthalpy, entropy, and heat capacity per residue), two defining the temperature dependent heat capacity of the unfolded state for DSC, two defining the near-UV CD signal (the width and intensity of the tyrosine band), two for reproducing the QY of NALA (the temperature dependence of the QY in the fully unfolded state and a quenching factor for microstates with native structure) and two for the IR signal (the intensity and temperature dependence of the non-hydrogen bonded carbonyl’s extinction coefficient). Other spectroscopic parameters, including the calculation of the far-UV CD spectrum of the fully unfolded and native microstates, are predefined according to suited reference measurements and thus fixed during the fitting procedure (see Supporting Information). Remarkably, the model is able to quantitatively reproduce all the experimental data accurately using reasonable assumptions (Figure 3). Moreover, the thermodynamic parameters produced by the fit are physically plausible. As an example, the entropic cost of fixing PDD residues in their native conformation estimated from the fit is −17.8 J mol−1 K−1 per residue at the reference temperature of 385 K, which is very similar to the average change in entropy at the same temperature obtained from the empirical analysis of DSC experiments on a large collection of two-state proteins68 (−16.5 J mol−1 K−1 per residue). The quality of the global fit is remarkable given the intrinsic heterogeneity of the data, the simplicity of the model, and the highly constrained set of parameters employed in this exercise. The fitted model, for instance, reproduces extremely well the broadness of the DSC thermogram and its steep pretransition region (Figure 3A). Moreover, it explains the steep temperature dependence of the DSC pretransition region as a direct manifestation of redistributions in the probabilities of microstates within the native ensemble (conformations with long native stretches), consistently with the empirical interpretation discussed in the previous section. The temperature dependence of the heat capacity (assumed to be identical for all the microstates in the model including the fully unfolded and native states) that is obtained from the fit is 25.3 J mol−1 K−2, which is in good agreement with the expectation from the Freire equation based on the molecular weight of the protein (i.e., 31.1 J mol−1 K−2 for PDD). On the other hand, the resulting
the FTIR unfolding curve to a two-state model produces a change in enthalpy upon unfolding of only 65 kJ mol−1 that, in spite of the larger fitting errors of these data, is significantly smaller than the enthalpy change obtained for all other probes (Table 1). The Tm from this fit (∼318 K) is, however, similar to the Tm from far-UV CD and lower than those from DSC and NALA fluorescence. A distinctive character of the FTIR thermal unfolding experiments of proteins is the presence of a strong intrinsic temperature dependence of the absorptivity of carbonyls. This change in absorptivity depends on the degree of alignment between adjacent amide dipoles, and thus on the length of the helix, as well as on the coupling with solvent vibrational modes. SVD analysis offers a simple procedure to dissociate the two contributions to the amide I′ band as a function of temperature (Figure S7). The first component from the SVD of the FTIR data produces a sigmoidal curve with a very high Tm (i.e., 326.4 K) that is consistently obtained from both fitting to a two-state model and the derivative analysis. On the other hand, the second SVD component, which contains the intrinsic temperature dependence of the amide I′ band absorptivity, produces an unfolding curve with steep pre- and post-transition baselines that is similar to the curve measured at 1632 cm−1 and which accordingly renders very similar thermodynamic parameters when analyzed with the two-state model (Table 1). The amplitude of the fourth SVD component (the third component is noise) displays a parabolic trend that is similar to those observed by far-UV and near-UC CD. Summarizing, the derivative analysis of the multiprobe unfolding curves results in a significant dispersion in Tm values, which range from 316 K (far UV CD at 222 nm) to 325 K (SVD of first FTIR component). The spread in Tm is somewhat smaller when the unfolding curves are individually fitted to a two-state model (Figure 2), but still highly significant (∼6 K).
Figure 2. Unfolding probabilities (pN) as a function of temperature for PDD as obtained from the fits to a two-state model of the various probes employed in this work.
The two-state fits also produce a large spread in unfolding enthalpy that goes from 50 to 130 kJ mol−1. It is important to emphasize that the differences in unfolding behavior are found not only between data from various experiments but also in wavelength data from the same experiment, or from the amplitudes of the various components obtained from SVD analysis of a given experiment (Table 1). The unfolding curves of PDD are broad and have clear signs of gradual structural disorder taking place at low temperatures. Statistical Modeling of the PDD Equilibrium Unfolding Process. All of the above observations reveal that the 8987
dx.doi.org/10.1021/jp504261g | J. Phys. Chem. B 2014, 118, 8982−8994
The Journal of Physical Chemistry B
Article
Figure 3. Global fit of the statistical mechanical model to the spectroscopic unfolding curves of PDD. In all panels, circles and red curves represent experimental data and fits, respectively. (A) DSC profile shown together with the native and unfolded baselines represented as green continuous and dashed lines, respectively. The black line is the Freire baseline. (B) Far-UV CD spectra as a function of temperature in MRE units. Inset: The absolute mean difference between data and fit as a function of temperature. (C) Far-UV CD unfolding curves at 208 and 222 nm (left axis), and at 193 nm (right axis). (D) Amplitudes of the first and second near-UV CD components from the SVD analysis. (E and F) Fits to the unfolding curves monitored from the quantum yield of NALA (QYNALA) and the IR extinction coefficient at 1632 cm−1.
change in heat capacity upon folding is only 8.6 J mol−1 K−1 per residue, which is much smaller than the average value obtained for larger two-state proteins (50−58 J mol−1 K−1 per residue68) and even smaller than that obtained previously for the structural/functional homologue BBL (i.e., 30 J mol−1 K−1 per residue28). Such a small change in heat capacity upon folding indicates that the unfolding free energy as a function of temperature for PDD is minimally curved and thus that this protein should have very little propensity to cold denature. This prediction from the model is fully consistent with the results from the double perturbation equilibrium experiments monitored by far-UV CD at 222 nm, which show no rollover of the native baseline at any conditions of temperature and urea concentration (see ref 49 and Figure 4). The theoretical analysis of the far- and near-UV CD data for PDD (Figure 3B−D) deserves a more detailed explanation. We computed the far-UV CD spectrum for each microstate in the model by simply determining its helical composition from the PDB file (fraction of each helix present in any given microstate or native stretch) and employing the spectroscopic parameters from Chen and co-workers that define the basis CD spectrum and length dependence of the α helix.69 This calculation does not include phenomenological changes in CD signal with temperature (temperature-independent signals). Therefore, any observed sloping of the pre- and post-transition baselines for the unfolding curves at different wavelengths is entirely accounted for by the helix fraying that is concomitant to the probability redistribution of the microstates in the model. It is thus quite remarkable that despite the highly constrained spectroscopic treatment of the far-UV CD signal, the obtained fit is of rather good quality (Figure 3B) since it produces mean absolute differences between experimental and theoretical spectra that are
