Cytochrome Unfolding Pathways from Computational Analysis of Crystal Structures

Abstract

We have developed a model to study the role of geometrical factors in influencing the early stages of unfolding in three cytochromes: cyt c′, cyt c-b₅₆₂ and cyt c. Each stage in unfolding is quantified by the spatial extension 〈λ̂_i〉 of n-residue segments, and by their angular extension 〈β_n〉. Similarities and differences between and among the three cytochromes in the unfolding of helical and non-helical regions can be determined by analyzing the data for each signature separately. Definite conclusions can be drawn when spatial and angular changes are considered in tandem. To facilitate comparisons, we present graphical portraits of the three cytochromes at the same stage of unfolding, and in relation to their native state structures. We also display specific segments at different stages of unfolding to illustrate differences in stability of defined domains thereby allowing us to make specific predictions on the unfolding of corresponding internal and terminal helices in cyt c′ and cyt c-b_562. Our work accords with an earlier experimental report on the presence and persistence of a hydrophobic core in cyt c.

GRAPHICAL ABSTRACT (SYNOPSIS)

Native (goldenrod) and second extended state for cyt c.

The N-terminal and C-terminal α-helices are in blue, the green loop and the green α-helix are in green, the infrared loop is in magenta, and the red loop in red.

I. Introduction

Both electrostatic and hydrophobic forces play key roles in controlling polypeptide flow up and down a folding funnel [1]. Experimental [2–9] and theoretical [10–13] investigations support the existence of a multiplicity of populations of unfolded configurations, both compact and extended, in denatured ensembles. Funneled energetics of the landscape are believed to be important in influencing unfolded ensembles in the denatured state. But questions remain on whether the folding of small proteins occurs via a hierarchical or non-hierarchical mechanism [14–22], i.e., whether native-like secondary structures form rapidly, interacting with each other to produce intermediates of ever-increasing complexity, or whether folding can be envisioned as a two-state process with no intermediate states.

To provide insight, some workers have focused on early stages in the denaturation, arguing that unfolding is the reverse of folding. Prominent among these efforts are the primarily theoretical and computational studies of Lazaradus and Karplus [23], and Guzzi, Sportelli et al. [24–28], as well as the experimental work of Englander et al. [29] on cytochrome c, and Michel and Bren on cytochrome c-551 [30]. In an early application of our geometrical model, we found substantial agreement between the unfolding behavior of distinct regions in cyt c (foldons) identified in [29] and the predictions of our model, and this will be documented further in the present study.

The stability of a thermodynamic phase can be disrupted not only by changes in such extensive variables as temperature and pressure, but also by local perturbations arising from spontaneous fluctuations. An infinitesimal change in these variables can induce an instability, and may result in transition to a different phase. In our analysis, we take as the starting point the thermodynamically stable state of a protein as defined by its crystallographic structure. Importantly, this is an optimized structure determined by the entire free energy landscape; all inter-residue contacts in the folded protein are encoded (exactly). To visualize early stages in protein denaturation, we have developed a geometrical model to “track” the consequences of perturbing the (already optimized) structure of a protein in its native state.

In formulating our approach, we have been guided by the seminal contributions of Ramachandran [31]. He and his coworkers used crystallographic coordinates to identify two dihedral angles {φ, ψ} flanking each peptide bond, and constructed {φ, ψ} plots for all residues in a given protein. From these plots, theoretically favored regions (conformations of the native state) could be established from geometrical arguments alone. Our “extended Ramachandran” model is similar in spirit, and focuses on the geometrical (steric) factors at play as the native structure of a protein is disrupted and the polypeptide chain begins to unfold.

A fundamental feature of our model is that we keep intact nearest-neighbor repulsive and attractive interactions between residue i and its two nearest-neighbors by introducing a triplet modular unit centered on residue i; crystallographic data are used to specify the geometry of this triplet of residues. Perturbations are then introduced by relaxing incrementally steric constraints (only) between and among non-nearest neighbor residues of the polypeptide chain. We follow quantitatively (via the direct application of classical Euclidian geometry) the consequences of chain unfolding. A series of n = 5 residue, n = 7 residue, …, n = 15 residue “snapshots” are taken of the changing environment of each residue as the polypeptide chain unfolds; as noted above, the geometry of each triplet, a module of n = 3 residues, is conserved and determined by the native state crystallographic data.

Each stage in unfolding is quantified by two principal signatures: the spatial extension λ_i of a given residue i in a n-residue segment and the angular extension β_n of this segment relative to a fixed point. The calculation of these signatures using our geometrical approach was described in a recent series of papers on the unfolding of azurin [32–34]; see also references cited therein. In this study, we use these signatures to compare and contrast the early stages of unfolding in Rhodopseudomonas palustris cytochrome c′ (cyt c′) [35], E. coli cytochrome b₅₆₂ (cyt c-b₅₆₂) [36], and yeast iso-1-cytochrome c (cyt c) [37].

II. Methods

We outline below calculation of the extension metric λ_i and the angular extension β_n using a specific example: the second (n = 7) stage of unfolding for residue i in a seven residue segment of cyt c′, a protein with 123 residues [35]. In this example below, residue i is the central residue in the segment spanning residues i = 1 thru i = 7. The local environment of residue i = 4 is then defined by three adjacent triplets, with each triplet’s geometry determined by the native-state crystallographic data. See Fig. (1).

Figure 1.

Specification of the geometrical model for a seven residue segment in cyt c′ (see text).

To apply our method, we must first specify the origin of the coordinate system, a fixed point relative to which the unfolding is calculated. In our previous studies on azurin [32–34], the metal ion Cu(II) was assigned as the invariant site; for the three cytochromes studied here, the natural choice is the metal ion Fe(III).

Referring to Fig. (1), the following distances can be calculated from the crystallographic data (Theorem of Pythagoras):

$$\mathrm{D}(\text{Fe}\text{to}{\mathrm{R}}_{01})=22.25Å;\mathrm{D}(\text{Fe}\text{to}{\mathrm{R}}_{07})=13.11Å;\mathrm{D}({\mathrm{R}}_{01}\text{to}{\mathrm{R}}_{07})=11.72Å.$$

Using the Law of Cosines (Proposition 12 in Euclid’s Geometry) the following angles can be calculated:

$$\beta ={24.83}^0;\alpha ={127.16}^0;\gamma ={28.01}^0.$$

As must be the case, these three angles sum to 180°.

In the fully-extended configuration displayed in Fig. (1), the distance T₀₄ can be determined from the crystallographic data:

$${\mathrm{T}}_{04}={\mathrm{R}}_{01}\text{to}{\mathrm{R}}_{03}+{\mathrm{R}}_{03}\text{to}{\mathrm{R}}_{05}+{\mathrm{R}}_{05}\text{to}{\mathrm{R}}_{07}=19.45Å.$$

Then, using the Law of Sines, we obtain directly the extension metric λ₄ which specifies, for the second stage of unfolding, the change in the radial distance ρ₄′ of residue i = 4 from the Fe atom relative to the distance ρ₄ characterizing the native state; here,

$${{\rho }_4}^{\prime }/{\rho }_4={\lambda }_4\text{with}{\lambda }_4=\mathrm{1.097.}$$

As must be the case, this value can be determined using the Law of Sines and either pair of angles (α, β) or (γ, β).

Again using the crystallographic data and the Law of Cosines, we can determine the angle between residues 1 and 3, residues 3 and 5, and residues 5 and 7:

$$\beta (1to3)={16.14}^0;\beta (3to5)={7.33}^0;\beta (5to7)={24.07}^0.$$

The sum of these three angles, characterizing the angular extension of a fully-extended chain centered on residue 4, is 47.54°, a value that can be compared with the angular extension between residues 1 and 7 in the native state as calculated directly from the crystallographic data, viz., β(1 to 7) = 24.83°. As expected, the angular extension of the extended state (the linear combination of the above three triplets) is greater than that of the native state (in this case, by a factor of ~ 1.9).

Whereas the above calculation was for a segment centered on residue 4, the crystallographic data can also be used to calculate angular signatures for a sequence of residues, for example, valine, isoleucine, alanine and glutamine in Fig. (1). The first sum below is a linear combination of the angles defining n=3 (triplet) segments, and the second is a linear combination of the angles defining n=7 segments, each term centered on one of the residues in the sequence.

$$\begin{array}{l}\sum (n=3)=\beta (3to5)+\beta (4to6)+\beta (5to7)+\beta (6to8)={7.33}^0+{20.93}^0+{24.07}^0+{19.40}^0={71.73}^0\\ \sum (n=7)=\beta (1to7)+\beta (2to8)+\beta (3to9)+\beta (4to10)={24.83}^0+{12.52}^0+{21.55}^0+{40.56}^0={99.46}^0\end{array}$$

Using these sums, we construct the following ratio:

$$\langle {\beta }_4\rangle =\raisebox{1ex}{$\sum (n=7)$}\!\left/ \!\raisebox{-1ex}{$\sum (n=3)$}\right.=1.39$$

This ratio provides one measure of the change in angular constraints as the local neighborhood of each residue is extended. This measure is not unique. Because our modular unit is a triplet, the angular signature introduced leads to register differences for segments with an even number of residues. The difficulty can be removed in the above signature by introducing an additional (but arbitrary) convention, but this can be avoided altogether by calculating the sums Σ(n = 3) and Σ(n = 7) as defined above. The advantage gained is that ratios 〈β_n〉 calculated for segments having either an even or odd number of residues can then be compared unambiguously.

To complete the specification of our geometrical model, we recall that one of the diagnostics used to assess the crystallographic data describing a given protein is the α-carbon to α-carbon distance between adjacent residues in the polypeptide chain. For example, averaging over all residues, we calculate this distance to be 3.80 Å for the 123 residues in cyt c′ [35], 3.83 Å for the 106 residues in cyt c-b₅₆₂ [36], and 3.87 Å for the 103 residues in cyt c [37]. In the unfolded states which follow from application of our geometrical model, nearest-neighbor α-carbon to α-carbon distances have a larger dispersion about the theoretical 3.80 Å than the native state. Rather than adjust the individual residue-to-residue distances to the value 3.80 Å, we adopt a statistical constraint: the (overall) average α-carbon to α-carbon distance for (all) nearest-neighbor residues for each segment in the polypeptide chain is adjusted to be 3.80 Å (at each stage of unfolding). The adjusted values of λ_i will be denoted λ̂_i.

Analysis of the crystallographic data for individual cytochromes leads to the identification of distinct regions, e.g., α-helices, β-sheets, (primarily) hydrophobic regions and turning loops. The full data set for our calculations of the average spatial extension (relative to metal ion), and the average angular extension (relative to the native state) for specific regions of each cytochrome in the first six stages of unfolding is given in the Appendix. Tables A1(a–c) give the 〈λ̂_i〉 values for cyt c′, cyt c-b₅₆₂, and cyt c; a similar compilation for the 〈β_n〉 is given in Tables A2(a–c).

III. Results

Before presenting our results on the unfolding of individual segments of each cytochrome, we display in Figs. (2–4) the overall (all-residue) portraits of cyt c′, cyt c-b₅₆₂ and cyt c in the second (n = 7) stage of unfolding. To facilitate later comparisons, the residues defining the helical and non-helical regions in each cytochrome are specified in Table 1. The helix H₁ in the two cytochromes, cyt c′ and cyt c-b₅₆₂, is color coded the same (with a similar convention for the other helices H₂, H₃ and H₄). For cyt c, we use the color convention for the foldon regions identified by Englander et al.; see Table 1 in Ref. (29) for specification of five foldon regions in oxidized cyt c. In Figs (2–4) the iron atom is coded in red, the native state is coded in goldenrod, the N-terminal “end” of the polypeptide chain (or region) is coded in magenta, and the C-terminal “end” in cyan. Panels (4a–4h) in Fig. (4) display individual (foldon) regions in cyt c.

Figure 2.

Figure 2a. Native (goldenrod) and second extended state (n = 7) for cyt c′. The N-terminal helix H₁ is coded in magenta, followed by helix H₂ in red, helix H₃ in blue and the C-terminal helix H₄ in cyan. Iron atom is coded in red. The turning region is in green.

Figure 2b. Spatial extension λ̂_i relative to the native state (horizontal line) versus residue number for cyt c′. The color code is specified in Fig. 2a.

Figure 4.

Figure 4a. Native (goldenrod) and second extended state (n = 7) for cyt c. We use the color convention for the foldon regions introduced in [41]. The N-terminal and C-terminal α-helices are in blue, the green loop and the green α-helix are in green, the infrared loop is in magenta, and the red loop in red. Iron atom is coded in red.

Figure 4b. Spatial extension λ̂_i relative to the native state (horizontal line) versus residue number for cyt c. The color code is specified in Fig. 4a.

Figure 4c. Native (goldenrod), first (n = 5) extended state (black) and second (n = 7) extended state (blue) for the N-terminal blue helix in cyt c. Iron atom is coded in red.

Figure 4d. Native (goldenrod), first (n = 5) extended state (black) and second (n = 7) extended state (green) for the green loop in cyt c. Iron atom is coded in red.

Figure 4e. Native (goldenrod), first (black) and second extended state (magenta) for the the infrared loop in cyt c. Iron atom is coded in red.

Figure 4f. Native (goldenrod), first (black) and second extended state (green) for the green helix in cyt c. Iron atom is coded in red.

Figure 4g. Native (goldenrod), first (black) and second extended state (red) for the red loop in cyt c. Iron atom is coded in red.

Figure 4h. Native (goldenrod), first (black) and second extended state (blue) for the C-terminal blue helix in cyt c. Iron atom is coded in red.

Table 1.

Helical and Turning Regions (K) in Cytochrome c′, Cytochrome c-b₅₆₂ and Cytochrome c¹

Cytochrome c′		Cytochrome c-b562		Cytochrome c
Segment	Region	Segment	Region	Segment	Region
3–26	Helix 1	3–19	Helix 1	3–14	Blue Helix 1
33–60	Helix 2	24–40	Helix 2	19–36	Green Loop
61–67	K	41–55	K	40–57	Infrared Loop
68–96	Helix 3	56–80	Helix 3	62–70	Green Helix
100–121	Helix 4	85–104	Helix 4	71–85	Red Loop
				87–101	Blue Helix 2

¹The PDB ID’s of the three cytochromes above are: cytochrome c′ (PDB ID: 1MQV); cytochrome c-b₅₆₂ (PDB ID: 2BC5); cytochrome c (PDB ID: 1YCC)

The portraits, Figs. (2–4), were developed after adjusting the spatial metric λ_i (to λ̂_i) to ensure that the average α-carbon to α-carbon distance of (all) adjacent residues in the polypeptide chain is 3.80 Å; at this stage of unfolding (and most others), the overall scaling factor is the same for all three cytochromes. The scaling factor for individual segments can be different from that for the protein as a whole; in Tables A1 (a,b,c) we include the scaling factor for distinct helical and non-helical regions in the three cytochromes.

Accompanying each portrait is a bar graph which shows the extension λ̂_i as a function of residue number for each cytochrome. Similar diagrams were developed in our earlier studies of these cytochromes [38–40], but these were based on calculated values of the (unadjusted) metric λ_i. An advantage of enforcing the constraint on adjacent α-carbon distances is that the resulting data set {λ̂_i} for residues in a well-defined segment (helical or turning region) is more regular (less punctuated by outliers) than is the case for the original data set {λ_i}.

A. Cytochrome c′

We report first results on averages of the spatial and angular signatures for individual segments in cyt c′; see Tables A1(a) and A2(a). In the first stage of unfolding, n=5, the first residue for which calculations can be carried out using our geometrical model is i = 3, the center residue in the 5-residue segment, residues 1 to 5. In the second stage, n=7, the first residue that can be considered is i = 4 [see Fig. (1) and the example in the previous section], …, and for n=15, it is residue i = 8. A similar situation pertains when considering residues at the C-terminal end of the polypeptide chain. This attenuation is accompanied by a decrease in angle between terminal residues in the (truncated) segments H₁ and H₄ as the protein unfolds [see Tables A2 (a,b,c)]. Consequently, in following the unfolding, stage by stage, the data set for the terminal helices H₁ and H₄ in cyt c′ is less complete than for the two interior helices, H₂ and H₃. Trends reported for interior helices H₂ and H₃ are more reliable than those for the terminal helices H₁ and H₄.

Conclusions drawn from calculations of regional averages for the spatial and angular signatures are more reliable the longer the segment. In cyt c′, the helical region H₁ has 23 residues, H₂ has 27 residues, H₃ has 28 residues, and H₄ has 21 residues. However, the non-helical region K, which is bracketed by the two interior helices, H₂ and H₃, has only 7 residues, so the trends reported for the latter stages of unfolding of this region are less reliable.

Mindful of the above caveats, our calculations show that in the earliest stage of unfolding, n =5, the spatial extension of three of the four helices [H₁, H₃, H₄] is greater than that of both helix H₂ and the non-helical, turning region K. However, in the most extended states, there is a reversal of behavior. The data show that the non-helical region is more extended than either of the two interior helical regions, H₂ and H₃, and for the terminal helices as well.

Turning next to the angular signature of segments [H₁, H₂, K, H₃, H₄] in cyt c′, we report the ratios 〈β_n〉 in Table A2(a); also included, for comparison, is the angle between the terminal residues of each segment in the native state. In the earliest stage of unfolding, the non-helical segment is more extended than any of the helices. As the protein continues to unfold, the 〈β_n〉 for all four helices increases, whereas the ratio 〈β_n〉 for non-helical region remains relatively constant. In the last stage of unfolding (considered in this study), the 〈β_n〉 ratios suggest that the non-helical, primarily hydrophobic, segment is relatively more compact than the four helical regions.

B. Cytochrome c-b₅₆₂

We next report results on the spatial and angular signatures of segments in cyt c-b₅₆₂; see Tables A1(b) and A2(b). Here, helical region H₁ has 16 residues, H₂ has 16 residues, H₃ has 24 residues, and H₄ has 19 residues; the non-helical, turning region in cyt c-b₅₆₂ has 14 residues, a factor of two larger than for cyt c′.

In contrast to the behavior exhibited by cyt c′, no significant differences in spatial extension are found among the four helices in the first stage of unfolding. Also in contrast to the behavior noted for cyt c′, the spatial extensions of all four helices {H₁, H₂, H₃, H₄} are smaller than that of the non-helical region, K. However, in the last stage of unfolding, the behavior of the two cytochromes, cyt c′ and cyt c-b₅₆₂, is similar; the non-helical region is more extended than the four helical regions.

With respect to the angular signature, the data in Table A2(b) show that in the first stage of unfolding, the 〈β_n〉 for helix H₄ and the non-helical region are comparable and larger than for helices H₁, H₂, and H₃. Significantly, the ratios 〈β_n〉 for the non-helical region increase more gradually in intermediate stages of unfolding than for the helical segments. In the most extended stage, both the terminal helical regions, H₁ and H₄, and the non-helical region, are more compact than the interior helices, H₂ and H₃.

C. Cytochrome c

For the articulated protein cyt c, data on the spatial metric in Table A1(c) and the angular ratio in Table A2(c) are displayed for the foldon regions identified by Englander et al. [Refs. (21, 29, 41)]. We have obtained results for the N-terminal blue α-helix, the green loop (residues 19–36), the green α-helix (residues 62–70), the infrared loop (residues 40–57), the red loop (residues 71–85) and the C-terminal blue α-helix. Calculations were not done for the yellow β-sheet (the two anti-parallel β-strands, residues 37–39 and 58–61) since application of our geometrical model requires a minimum of n=5 residues.

From their experimental studies on hydrogen exchange of marker residues, Englander et al. deduce that cyt c unfolds sequentially as follows:

$$\text{IRYGB}(\text{Native})\leftrightarrow \begin{array}{c}\text{iRYGB}\\ \\ \text{IrYGB}\end{array}\leftrightarrow \text{irYBG}\leftrightarrow \text{iryGB}\leftrightarrow \text{irygB}\leftrightarrow \text{irygb}$$

(in their notation, I represents the infrared loop, R the red loop, Y the anti-parallel β-strand, G the green α-helix, and B the N- and C-terminal α–helices; native state is upper case, unfolded state is lower case). In broad outline, Englander et al. determined that the three helical regions lagged behind the green, red and infrared loops as the protein denatured.

Examining the spatial signatures in Table A3(c), in the first stage of unfolding the results are mixed. The C-terminal blue helix lags behind the green α-helix and the N-terminal blue helix. Values of 〈λ̂_i〉 for the green, infrared and red loops are intermediate between those calculated for the two terminal helices. In the most extended stage of unfolding considered in this study (n = 15), the spatial extensions of the helical and non-helical regions follow the order reported by Englander et al. except that the order of the infrared loop and the red loop are reversed. The infrared loop is bracketed by the two β-strands; in our model the influence of the β-strands cannot be decoupled from the behavior of adjacent residues in the infrared loop. This limitation may account for the reversal.

From the angular signatures 〈β_n〉 reported in Table A2(c), we find that in the first stage of unfolding, the three helical regions are more compact than the three non-helical loops. In the most unfolded stage (n = 15), the green loop and the red loop are more compact than the N-terminal blue helix, the green helix and the C-terminal blue helix. As noted above, values calculated for 〈β_n〉 for the infrared loop (may) reflect the fact that this region is bracketed by the two β-strands.

IV. Discussion

The principal conclusion that can be drawn from our study is that although the first stages of unfolding of cyt c′, cyt c-b₅₆₂ and cyt c have some features in common, data on the spatial and angular signatures of specific regions reveal quantitative, and sometimes qualitative, differences in behavior. We have drawn attention to factors that may limit the reliability of our analysis. Apart from these, no further approximations are introduced in calculating values of the spatial and angular signatures. The only functions required to elaborate our geometrical model are sines and cosines, and the trigonometric relations that these functions satisfy. Since our geometrical model is strictly deterministic and based on well-defined functions, no technical restrictions (e.g., software limitations or compilation times) arise in carrying out calculations. The task then becomes one of analyzing what these data are telling us.

Displaying calculated values of λ̂_i and β_n may be viewed as projections of the underlying crystallographic data set on different screens to illuminate facets of the protein’s structure as it unfolds. For example, as noted in the previous section, in the earliest stage of unfolding, the spatial signature of the internal helix H₂ in cyt c-b₅₆₂ suggests that this helix (with 16 residues, 4 turns of α-helix) is only slightly displaced from its native state configuration, whereas H₂ in cyt c′ (27 residues and 7 turns) shows a more pronounced departure. This is somewhat counterintuitive; but, since H₂ is an internal helix in both cytochromes, and both helices have at least 4 turns, neither of the caveats mentioned previously apply. We can be reasonably confident that there are real differences in the unfolding behavior of H₂ in the two cytochromes.

This conclusion is based on examining data on both the spatial signature and angular signature, but independently. In fact, as the protein unfolds, both spatial and angular extensions of the polypeptide chain occur synchronously. Hence, it is desirable to visualize the unfolding when both diagnostics are at play, concurrently. The conformational changes in helix H₂ in the first two stages (n = 5, 7) of unfolding are displayed graphically in Fig. 5 for cyt c-b₅₆₂ and in Fig. 6 for cyt c′. These graphics substantiate the conclusion reached above: in early stages of unfolding, the behavior of the internal helix H₂ is qualitatively different in the two cytochromes, with the helix H₂ in cyt c′ being more labile.

Figure 5.

Native (goldenrod), first (n = 5) extended state (black) and second (n = 7) extended state (red) for helix H₂ in cyt c-b₅₆₂. Iron atom is coded in red.

Figure 6.

Native (goldenrod), first (n = 5) extended state (black) and second (n = 7) extended state (red) for helix H₂ in cyt c′. Iron atom is coded in red.

As noted in the Introduction, the present study has been guided by Ramachandran’s recognition of the importance of geometrical (steric) constraints in delimiting regions of the (φ, ψ) phase portrait. In Figs. (7,8) we display the Ramachandran plot for cyt c′ and cyt c-b₅₆₂, respectively, color coded so that the residue coordinates for helix H₂ can be distinguished. The phase portrait for cyt c-b₅₆₂ is relatively localized, whereas the distribution of H₂ residues in cyt c′ is (much) more delocalized. Importantly, we see that the different lability of the H₂ helices in the two cytochromes is already forecast in the (φ, ψ) phase portrait of the native state of each. This correspondence may be an isolated, accidental correlation, but if the correlation can be shown to be more general, then it opens up a new pathway for using native state, (φ, ψ) phase portraits in concert with our geometrical approach to identify regions of a given protein that are more likely to destabilize as the polypeptide begins to denature.

Figure 7.

Phi vs psi for cytochrome cyt c-b₅₆₂ where blue diamonds → H₁, red diamonds → H₂, green diamonds → H₃, orange diamonds → H₄ and crosses represent non-helical regions including K.

Figure 8.

Phi vs psi for cytochrome c′ where blue diamonds → H₁, red diamonds → H₂, green diamonds → H₃, orange diamonds → H₄ and crosses represent non-helical regions including K.

The angular signatures for the two internal helices H₂ and H₃ of cyt c′ and cyt c-b₅₆₂, show a significant change from the early to the latter stages of unfolding. The non-helical region region in cyt c′ (residues 61 to 67) is probably too small to draw meaningful conclusions from the data. This is not the case for cyt c-b₅₆₂ for which the non-helical region spans 14 residues, a length which is comparable to the adjacent internal helices, H₂ and H₃. The data for this segment show that the angular signature remains effectively constant as the protein unfolds, i.e., the turning region remains relatively intact. This suggests that the region contains a “hydrophobic core” which is conserved in the early stages of denaturation.

Lastly, we consider the results for cyt c. This protein provides an “acid test” for the usefulness of the geometrical model described here because, in contrast to cyt c′ and cyt c-b₅₆₂, there are two lines of experimental evidence on the site-specific or regional behavior of cyt c as this protein unfolds. In addition to the experimental studies of Englander et al. (21,29,41) on hydrogen exchange of marker residues in horse heart cyt c, we have for yeast iso-1 cytochrome c the results of a study [9] of the time-resolved fluorescence energy transfer (trFET) from a dansyl fluorophore (Dns) to Fe (III). The derivatized residues examined in the trFET experiments [9] are in correspondence with residue “markers” used in (21,29) for hydrogen exchange studies.

The trFET study revealed large populations of compact structures in the unfolded Dns(C50), Dns(C39) and Dns(C66) proteins. Interestingly, Pletneva et al. [9] suggested that the associated compact structures play a role in forming a hydrophobic core during the folding process. Whereas residue 39 is adjacent to one of the β-strands, and residue 85 is adjacent to the C-terminal blue helix, residue 50 is in the middle of the infrared loop, a segment with 17 residues, and hence a region where we can expect our geometrical model to yield reliable predictions.

As with the helices, while the individual spatial and angular signatures are of value in analyzing the behavior of the infrared loop on unfolding, a composite portrait when both factors are at play is more instructive. Displayed in Fig. 9a is the behavior of this non-helical region in the first stage of unfolding (n = 5), and in Fig. 9b an intermediate stage (n = 9) and the last stage considered in this study (n=15). Focusing on the interior of the region, in the vicinity of residue 50, proximity to the native state configuration is displayed in both stages of unfolding. This strongly suggests the presence and persistence of a hydrophobic core, in agreement with the analysis in [9].

Figure 9.

Figure 9a. Native (goldenrod) and first extended state (n = 5) of the infrared (foldon) loop (magenta) in cyt c. Iron atom is coded in red.

Figure 9b. Native (goldenrod), third extended state (n= 9) (black), and sixth extended state (n = 15) of the infrared (foldon) loop (magenta) in cyt c. Iron atom is coded in red.

V. Conclusions

The signatures {λ̂_i, β_n} describe the unfolding of cyt c′, cyt c-b₅₆₂, and cyt c. From these results as well as from those obtained in our recent study of several azurins [32–34], the importance of geometrical factors in influencing the early stages of denaturation has been established. Whereas the summative portraits presented in Tables A1(a,b,c) and Tables A2(a,b,c) present quantitative evidence on the separate, spatial and angular behavior of specific regions, the graphical representations in the figures present an integrated picture of the unfolding and allow more definite predictions to be made.

We note that in the azurin studies [32–34] a third signature was introduced, one that allowed conclusions to be drawn on segmental chain motion. A systematic study of this signature for cyt c′, cyt c-b₅₆₂, and cyt c will be presented in a separate contribution, and will be accompanied by molecular dynamics evidence.

Importantly, we have identified regions in the protein where structures are perturbed from ones they would adopt if they were not embedded in a globally minimized framework. The beauty of our model is its simplicity: as in Ramachanran’s use of crystallographic coordinates to identify the dihedral angles {φ, ψ}, all you need in our geometrical approach to predict unfolding propensities are the atom coordinates of a good crystal structure.

Figure 3.

Figure 3a. Native (goldenrod) and second extended state (n = 7) for cyt c-b₅₆₂. The N-terminal helix H₁ is coded in magenta, followed by helix H₂ in red, helix H₃ in blue and the C-terminal helix H₄ in cyan. Iron atom is coded in red. The turning region is in green.

Figure 3b. Spatial extension λ̂_i relative to the native state (horizontal line) versus residue number for cyt c-b₅₆₂. The color code is specified in Fig. 3a.

HIGHLIGHTS.

• We probed the geometrical factors that influence early unfolding in cytochromes.

• Cytochromes c, c′ and c-b562 were our models.

• This permits prediction of unfolding propensities from known structures.

Appendices

Table A1(a).

Unfolding of cyt c′ described by averages 〈λ̂_i〉 for stages n=5 to n=15. In the parenthesis below each entry is the factor which scales the λ_i such that all α-carbon to α-carbon distances between adjacent residues in that segment is 3.80 Å.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15	Turns
3–26	H-1	1.22 (0.94)	1.18 (0.99)	1.21 (0.97)	1.27 (0.89)	1.20 (0.95)	1.16 (0.96)	6
33–60	H-2	1.15 (0.85)	1.03 (0.97)	1.03 (0.97)	1.10 (0.91)	1.05 (0.92)	1.09 (0.88)	7
61–67	K	1.17 (0.83)	1.22 (0.78)	1.33 (0.67)	1.09 (0.91)	1.39 (0.61)	1.22 (0.78)
68–96	H3	1.26 (0.74)	1.02 (0.98)	1.05 (0.95)	1.24 (0.76)	1.16 (0.94)	1.07 (0.93)	7
100–121	H4	1.22 (0.78)	1.01 (1.00)	1.07 (0.93)	1.21 (0.75)	1.09 (0.91)	1.10 (0.90)	5

Table A1(b).

Unfolding of cyt c-b₅₆₂ described by averages 〈λ̂_i〉 for stages n=5 to n=15. In the parenthesis below each entry is the factor which scales the λ_i such that all α-carbon to α-carbon distances between adjacent residues in that segment is 3.80 Å.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15	Turns
3–19	H-1	1.02 (1.00)	0.97 (1.05)	1.08 (0.95)	1.01 (0.92)	1.36 (0.72)	1.15 (0.85)	4
24–40	H-2	1.03 (0.97)	1.00 (1.00)	1.04 (0.96)	1.14 (0.86)	1.15 (0.85)	1.18 (0.82)	4
41–55	K	1.17 (0.83)	1.22 (0.78)	1.33 (0.67)	1.09 (0.91)	1.39 (0.61)	1.22 (0.78)
56–80	H3	1.02 (0.98)	1.06 (0.94)	1.03 (1.03)	1.09 (0.91)	1.19 (0.81)	1.14 (0.86)	6
85–104	H4	1.08 (0.93)	1.00 (1.00)	0.97 (1.04)	1.06 (0.94)	1.21 (0.79)	1.12 (0.88)	5

Table A1(c).

Unfolding of cyt c described by averages 〈λ̂_i〉 for stages n=5 to n=15. In the parenthesis below each entry is the factor which scales the λ_i such that all α-carbon to α-carbon distances between adjacent residues in that segment is 3.80 Å.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15
3–14	Blue Helix 1	1.43 (0.81)	1.27 (0.99)	1.28 (1.01)	1.24 (1.07)	1.31 (0.98)	1.17 (1.06)
19–36	Green Loop	1.33 (0.67)	1.27 (0.73)	1.30 (0.70)	1.26 (0.74)	1.27 (0.73)	1.22 (0.78)
40–57	Infrared Loop	1.19 (0.85)	1.23 (0.77)	1.21 (0.79)	1.05 (0.95)	1.20 (0.65)	1.04 (0.89)
62–70	Green Helix	1.33 (0.67)	1.02 (0.98)	1.14 (0.86)	1.26 (0.73)	1.23 (0.77)	0.96 (1.04)
71–85	Red Loop	1.20 (0.80)	1.09 (0.91)	1.10 (0.90)	1.18 (0.83)	1.25 (0.75)	1.34 (0.66)
87–101	Blue Helix 2	1.13 (0.87)	1.09 (0.78)	1.04 (0.96)	1.21 (0.80)	0.88 (1.12)	0.98 (1.02)

Table A2(a).

Unfolding of cyt c′ described by angular averages 〈β_n〉 for unfolding stages n=5 to n=15. In parenthesis below each entry is the angle between terminal residues in the native state.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15
3–26	H-1	1.22 (140.50)	1.80 (142.90)	2.26 (145.50)	2.72 (129.60)	3.36 (124.90)	3.60 (129.70)
33–60	H-2	1.41 (157.20)	2.17	2.82	3.50	4.17	4.76
61–67	K	1.66 (12.50)	1.91	2.03	2.07	2.03	2.25
68–96	H3	1.38 (151.80)	2.12	2.73	3.37	3.96	4.47
100–121	H4	1.23 (136.50)	1.89 (124.60)	2.37 (107.40)	2.96 (96.20)	3.26 (98.10)	3.70 (84.10)

Table A2(b).

Unfolding of cyt c-b₅₆₂ described by angular averages 〈β_n〉 for unfolding stages n=5 to n=15. In parenthesis below each entry is the angle between terminal residues in the native state.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15
3–19	H-1	1.10 (112.90)	1.66 (99.30)	2.08 (82.30)	2.56 (78.10)	2.76 (66.00)	3.16 (54.10)
24–40	H-2	1.17 (77.10)	1.92	2.42	3.11	3.84	4.47
41–55	K	1.51 (44.80)	2.01	2.46	2.70	2.94	3.12
56–80	H3	1.16 (105.70)	1.84	2.31	2.87	3.47	4.01
85–104	H4	1.51 (119.30)	2.01 (108.30)	2.46 (111.30)	2.70 (97.70)	2.94 (81.40)	3.12 (69.40)

Table A2(c).

Unfolding of cyt c described by angular averages 〈β_n〉 for unfolding stages n=5 to n=15. In parenthesis below each entry is the angle between terminal residues in the native state.

Segment	Region	n=5	n=7	n=9	n=11	n=13	n=15
3–14	Blue Helix 1	1.08 (45.60)	1.82 (34.80)	2.28 (32.90)	2.78 (38.10)	2.87 (29.70)	3.19 (17.70)
19–36	Green Loop	1.63 (72.40)	2.14	2.30	2.31	2.32	2.65
40–57	Infrared Loop	1.70 (20.30)	2.26	2.73	3.01	3.32	3.47
62–70	Green Helix	1.38 (56.60)	2.03	2.41	2.89	3.24	3.34
71–85	Red Loop	1.70 (50.00)	2.28	2.62	2.77	2.81	2.72
87–101	Blue Helix 2	1.38 (80.50)	2.17 (71.80)	2.96 (67.00)	3.65 (64.90)	4.67 (57.70)	5.74 (49.60)