Fractal Structure of Shortest Interaction Paths in Native Proteins and Determination of Residues on a Given Shortest Path

TL;DR

This study reveals the fractal nature of shortest interaction paths in proteins, showing their self-similarity and multifractality depending on interaction cutoff distances, and introduces an algorithm to identify key residues involved in information transport.

Contribution

It uncovers the fractal properties of shortest paths in proteins and presents a novel algorithm to determine residues on these paths, linking path properties to protein entropy landscapes.

Findings

Shortest paths are self-similar with fractal dimension 1.12 beyond 6.8 Å.

Paths become multifractal below 6.8 Å cutoff.

Residues on shortest paths are highly visited during signal transport.

Abstract

Fractal structure of shortest paths depends strongly on interresidue interaction cutoff distance. The dimensionality of shortest paths is calculated as a function of interaction cutoff distance. Shortest paths are self similar with a fractal dimension of 1.12 when calculated with step lengths larger than 6.8 {\AA}. Paths are multifractal below 6.8 {\AA}. The number of steps to traverse a shortest path is a discontinuous function of cutoff size at short cutoff values, showing abrupt decreases to smaller values as cutoff distance increases. As information progresses along the direction of a shortest path a large set of residues are affected because they are interacting neighbors to the residues of the shortest path. Thus, several residues are involved diffusively in information transport which may be identified with the present model. An algorithm is introduced to determine the residues of a given shortest path. The shortest path residues are the highly visited residues during information transport. These paths are shown to lie on the high entropy landscape of the protein where entropy is taken to increase with abundance of visits to nodes during signal transport.