Curvature and Torsion of Protein Main Chain as Local Order Parameters of Protein Unfolding

Abstract

Thermal protein unfolding resembles a global (two-state) phase transition. At the local scale, protein unfolding is, however, heterogeneous and probe dependent. Here, we consider local order parameters defined by the local curvature and torsion of the protein main chain. Because chemical shifts (CS's) measured by NMR spectroscopy are extremely sensitive to the local atomic environment, CS has served as a local probe of thermal unfolding of proteins by varying the position of the atomic isotope along the amino acid sequence. The variation of the CS of each C α atom along the sequence as a function of the temperature defines a local heat-induced denaturation curve. We demonstrate that these local heatinduced denaturation curves mirror the local protein nativeness defined by the free energy landscape of the local curvature and torsion of the protein main chain described by the C α −C α virtual bonds. Comparison between molecular dynamics simulations and CS data of the gpW protein demonstrates that some local native states defined by the local curvature and torsion of the main chain, mainly located in secondary structures, are coupled to each other whereas others, mainly located in flexible protein segments, are not. Consequently, CS's of some residues are faithful reporters of global protein unfolding, with heat-induced denaturation curves similar to the average global one, whereas other residues remain silent about the protein unfolded state. For the latter, the local deformation of the protein main chain, characterized by its local curvature and torsion, is not cooperatively coupled to global unfolding.

Anatomy of unfolding: The site-specific fold stability of Yfh1 measured by 2D NMR

“…We described in detail how the unfolding of Yfh1 is a much more complex process than a two-step global unfolding both at high and low temperature. Our data clearly show how, as recently advocated by Grassein et al, 14 local nativeness is probe dependent and, as such, needs to be studied at the individual residue level.…”

“…Cold denaturation of Yfh1 has also been independently confirmed by five independent techniques. [14][15][16]…”

“…13 Using the approach previously developed, 13 we systematically analysed in the current work the heat and cold denaturation of Yfh1 at residue detail but we reversed the perspective and wondered what information, if any, would be carried by residues far from the hydrophobic core and how they reflect the process of unfolding. This subject has increasingly attracted attention: as put in the words of a recent study by Grassein et al 14 : "For most of the proteins, this global heat-induced denaturation curve can be formally described by a simple two-state (folded/unfolded) statistical model. Agreement with a two-state model does not imply, however, that the macromolecule does not unfold through a number of intermediate states….…”

Missense Mutations Modify the Conformational Ensemble of the α-Synuclein Monomer Which Exhibits a Two-Phase Characteristic

“…Assuming a constant virtual bond length between C α atoms of successive residues, a chain of N amino acids is fully characterized by N − 3 torsion angles γ n , built from the positions of C α n −1 , C α n , C α n +1 , and C α n +2 with n = 2 to N − 2; and N − 2 bond angles θ n , built from C α n −1 , C α n , and C α n +1 , with n = 2 to N − 1. These angles have clear geometrical meanings: they are respectively the discrete version of the local curvature ( θ n ) and the local torsion ( γ n ) of the chain formed by the successive C α − C α virtual bonds ( Grassein et al, 2020 ). From a mathematical point of view, the local curvature and torsion fully describe the structure of a string and form a complete set of local order parameters for protein folding ( Grassein et al, 2020 ).…”

“…Application of DSSP to coarse-grained structures simulated by UNRES requires to build a compatible all-atom structure from the C α coordinates of the UNRES model using reconstruction programs ( Feig et al, 2004 ; Rotkiewicz and Skolnick, 2008 ). To avoid the high computational cost of all-atom reconstructions from coarse-grained coordinates, we developed here an algorithm which assigns an α -helix or a β -sheet secondary structure to each residue based on the C α - C α distances and on the coarse-grained angles formed by C α - C α pseudobonds, which correspond to the local curvature and torsion of the protein main chain ( Grassein et al, 2020 ). The accuracy of the present algorithm, named CUTABI (CUrvature and Torsion based of Alpha helix and Beta-sheet Identification), to quantify the β -sheet content of proteins is improved compared to an existing algorithm based on C α coordinates [P-SEA ( Labesse et al, 1997 )] and is comparable to the accuracy of DSSP (see the Material and Methods section).…”