Discrete breathers in protein structures

Abstract

Recently, using a numerical surface cooling approach, we have shown that highly energetic discrete breathers (DBs) can form in the stiffest parts of nonlinear network models of large protein structures. In the present study, using an analytical approach, we extend our previous results to low-energy discrete breathers as well as to smaller proteins. We confirm and further scrutinize the striking site selectiveness of energy localization in the presence of spatial disorder. In particular, we find that, as a sheer consequence of disorder, a non-zero energy gap for exciting a DB at a given site either exists or not. Remarkably, in the former case, the gaps arise as a result of the impossibility of exciting small-amplitude modes in the first place. In contrast, in the latter case, a small subset of linear edge modes acts as accumulation points, whereby DBs can be continued to arbitrary small energies, while unavoidably approaching one of such normal modes. In particular, the case of the edge mode seems peculiar, its dispersion relation being simple and little system dependent. Concerning the structure-dynamics relationship, we find that the regions of protein structures where DBs form easily (zero or small gaps) are unfailingly the most highly connected ones, also characterized by weak local clustering. Remarkably, a systematic analysis on a large database of enzyme structures reveals that amino-acid residues involved in catalysis tend to be located in such regions. This finding reinforces the idea that localized modes of nonlinear origin may play an important biological role, e.g., by providing a ready channel for energy storage and/or contributing to lower energy barriers of chemical reactions.

Correlated motions are a fundamental property of β-sheets

“…2). An analysis of the low-frequency modes (3)(4)(5)(6)(7)(8)(9)(10) shows that the correlations were mostly consistent with the non-homologous b-sheet ensemble; however, there are regions where there is disagreement (Supplementary Figs 3 and 4) due to contributions of overtones of the fundamental mode frequencies. Despite the disagreement in some regions of the b-sheet, regions of agreement were found in many of the first 10 normal modes, as identified by the alternating checkerboard pattern of positive and negative dihedral correlations.…”

“…The existence of channels of correlated motions is implicitly required as the inter-atomic interactions that govern them decay rapidly with distance 2 . While the mechanisms that cause these behaviours are still largely unknown, recent progress has been made in the study of the allostery of enzymes that contain a central b-sheet, where weakly correlated motions link interaction sites 3,4 and store energy for preparation for binding and catalysis 5 .…”

“…While for energy storage within localized modes of nonlinear origin, known as discrete breathers, there is a requirement for weak coupling between adjacent peptide planes 5,7 . Given the importance of these phenomena, much work has been directed to determining the degree of correlation between the motions of distal sites in the conformational dynamics of proteins 8 .…”

Long-range energy transfer in proteins

“…More precisely, we have shown that spatially localized bandedge normal modes (NM) can be continued from low energies to DB solutions centered at the same sites as the corresponding NMs (the NM sites). Note that the latter lie, as a rule, within the stiffest regions of a protein [33,39]. More generally, however, DBs display a gap in their excitation spectrum.…”

Quantitative theory of hydrophobic effect as a driving force of protein structure

“…This process is accompanied by large structural rearrangements if there is an energy exchange between protein regions with "discrete breathers" (localized excitations). [28][29][30][31] The conformational selection paradigm implies that "discrete breathers" should be located close to ligand-binding sites. Although at first sight, the conformational selection paradigm and the approach that we used in this study look different, the similarity between them becomes clear if we make an analogy between "discrete breathers" and the eigenmodes of the burial mode model energy function 12 -in both descriptions, ligand-binding suppresses one mode and stimulates another, coupling large scale motions to the transduction of small forces.…”