Geometrical Analysis of Cytochrome c Unfolding

Relaxation of structural constraints during Amicyanin unfolding

We study the thermal unfolding of amicyanin by quantifying the resiliency of the native state to structural perturbations. Three signatures characterizing stages of unfolding are identified. The first signature, lateral extension of the polypeptide chain, is calculated directly from the reported crystallographic data. Two other signatures, the radial displacement of each residue from Cu(II) and the angular spread in the chain as the protein unfolds, are calculated using crystallographic data in concert with a geometrical model we introduced previously (J.J. Kozak, H. B. Gray, R. A. Garza-López, J. Inorg. Biochem. 155(2016) 44-55). Particular attention is paid to the resiliency of the two beta sheets in amicyanin. The resiliency of residues in the near neighborhood of the Cu center to destabilization provides information on the persistence of the entatic state. Similarly, examining the resiliency of residues intercalated between structured regions (beta sheets, the alpha helix) provides a basis for identifying a "hydrophobic core." A principal focus of our study is to compare results obtained using our geometrical model with the experimental results (C. La Rosa, D. Milardi, D. M. Grasso, M. P. Verbeet, G. W. Canters, L. Sportelli, R. Guzzi, Eur. Biophy. J.30(8),(2002) 559-570) on the denaturation of amicyanin, and we show that our results support a classical model proposed by these authors.

Cytochrome unfolding pathways from computational analysis of crystal structures

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 λ̂i of n-residue segments, and by their angular extension 〈βn〉. 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-b562. Our work accords with an earlier experimental report on the presence and persistence of a hydrophobic core in cyt c.

A Euclidean perspective on the unfolding of azurin: chain motion

We present a new approach to visualizing and quantifying the displacement of segments of Pseudomonas aeruginosa azurin in the early stages of denaturation. Our method is based on a geometrical method developed previously by the authors, and elaborated extensively for azurin. In this study, we quantify directional changes in three α-helical regions, two regions having β-strand residues, and three unstructured regions of azurin. Snapshots of these changes as the protein unfolds are displayed and described quantitatively by introducing a scaling diagnostic. In accord with molecular dynamics simulations, we show that the long α-helix in azurin (residues 54-67) is displaced from the polypeptide scaffolding and then pivots first in one direction, and then in the opposite direction as the protein continues to unfold. The two β-strand chains remain essentially intact and, except in the earliest stages, move in tandem. We show that unstructured regions 72-81 and 84-91, hinged by β-strand residues 82-83, pivot oppositely. The region comprising residues 72-91 (40 % hydrophobic and 16 % of the 128 total residues) forms an effectively stationary region that persists as the protein unfolds. This static behavior is a consequence of a dynamic balance between the competing motion of two segments, residues 72-81 and 84-91.

A Euclidean Perspective on the Unfolding of Azurin: Spatial Correlations

We investigate the stability to structural perturbation of Pseudomonas aeruginosa azurin using a previously developed geometric model. Our analysis considers Ru(2,2',6',2″-terpyridine)(1,10-phenanthroline)(His83)-labeled wild-type azurin and five variants with mutations to Cu-ligating residues. We find that in the early stages of unfolding, the β-strands exhibit the most structural stability. The conserved residues comprising the hydrophobic core are dislocated only after nearly complete unfolding of the β-barrel. Attachment of the Ru-complex at His83 does not destabilize the protein fold, despite causing some degree of structural rearrangement. Notably, replacing the Cys112 and/or Met121 Cu ligands does not affect the conformational integrity of the protein. Notably, these results are in accord with experimental evidence, as well as molecular dynamics simulations of the denaturation of azurin.