Long-range correlation in protein dynamics: Confirmation by structural data and normal mode analysis

Abstract

Proteins in cellular environments are highly susceptible. Local perturbations to any residue can be sensed by other spatially distal residues in the protein molecule, showing long-range correlations in the native dynamics of proteins. The long-range correlations of proteins contribute to many biological processes such as allostery, catalysis, and transportation. Revealing the structural origin of such long-range correlations is of great significance in understanding the design principle of biologically functional proteins. In this work, based on a large set of globular proteins determined by X-ray crystallography, by conducting normal mode analysis with the elastic network models, we demonstrate that such long-range correlations are encoded in the native topology of the proteins. To understand how native topology defines the structure and the dynamics of the proteins, we conduct scaling analysis on the size dependence of the slowest vibration mode, average path length, and modularity. Our results quantitatively describe how native proteins balance between order and disorder, showing both dense packing and fractal topology. It is suggested that the balance between stability and flexibility acts as an evolutionary constraint for proteins at different sizes. Overall, our result not only gives a new perspective bridging the protein structure and its dynamics but also reveals a universal principle in the evolution of proteins at all different sizes.

Functional sensitivity and mutational robustness of proteins

“…[34], Sec. 1.1) and is in line with those of previous studies, demonstrating that the structure of proteins can be described as the packing of amnio-acid residues in a fractal dimension between 2 and 3 [8,59].…”

“…3(f), as the protein size increases, the eigengap |λ −1 1 − λ −1 2 | also increases, showing that slow vibration modes also exhibit a high mutational robustness. It is also understood that large proteins or protein complexes usually have multi-domain structures, which shows the high modularity of their residue contact networks [8]. The enhancement of the molecular flexibility contributes to inter-domain motions, which are usually highly robust.…”

“…For proteins in the solutions, small external perturbations from the milieu can be felt consistently by every other residue within the entire protein. Even weak and transient perturbations can trigger large conformational changes [5][6][7][8]. In this way, proteins can sense external signals ranging from metal ions to other biomolecules, which are functionally beneficial.…”

Functional Sensitivity and Mutational Robustness of Proteins

“…This result is robust for different kinds of weighted GNMs (see SM, Sec. 1.1) and is in line with those of previous studies, demonstrating that the structure of proteins can be described as the packing of amnio-acid residues in a fractal dimension between 2 and 3 [8,58].…”

“…3F, as the protein size increases, the eigengap |λ −1 1 − λ −1 2 | also increases, showing that slow vibration modes also exhibit a high mutational robustness. It is also understood that large proteins or protein complexes usually have multidomain structures, which shows the high modularity of their residue contact networks [8]. The enhancement of the molecular flexibility contributes to inter-domain motions, which are usually highly robust.…”