Discrete breathers in protein structures

TL;DR

This paper investigates the formation and properties of discrete breathers in protein structures, revealing their site selectiveness, energy gaps, and potential biological roles in enzyme activity through analytical and numerical methods.

Contribution

It extends previous numerical results to analytical analysis of low-energy breathers and explores their biological significance in enzyme structures.

Findings

Discrete breathers can form in specific protein regions with high connectivity.

Energy gaps for breather excitation depend on spatial disorder and normal mode structure.

Enzymatic residues are often located in regions conducive to breather formation.

Abstract

Recently, using a numerical surface cooling approach, we have shown that highly energetic discrete breathers (DB) 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 localisation 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 result of the impossibility of exciting small-amplitude modes in the first place. On the contrary, in the latter case, a small subset of linear edge modes act 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 enzymatic activity tend to be located in such regions. This finding reinforces the idea that localised 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.