Identifying critical residues of a protein using meaningfully-thresholded Random Geometric Graphs

TL;DR

This paper introduces novel methods using thresholded Random Geometric Graphs to identify critical residues in proteins, validated against experimental data, with potential applications in understanding protein function.

Contribution

It develops three new RGG-based approaches for detecting critical residues, incorporating organic thresholding and dynamic analysis during protein evolution.

Findings

RGG-based methods outperform traditional thresholding techniques

Critical residues identified align well with experimental data

Dynamic analysis reveals residue importance changes over time

Abstract

Identification of critical residues of a protein is actively pursued, since such residues are essential for protein function. We present three ways of recognising critical residues of an example protein, the evolution of which is tracked via molecular dynamical simulations. Our methods are based on learning a Random Geometric Graph (RGG) variable, where the state variable of each of 156 residues, is attached to a node of this graph, with the RGG learnt using the matrix of correlations between state variables of each residue-pair. Given the categorical nature of the state variable, correlation between a residue pair is computed using Cramer's V. We advance an organic thresholding to learn an RGG, and compare results against extant thresholding techniques, when parametrising criticality as the nodal degree in the learnt RGG. Secondly, we develop a criticality measure by ranking the computed differences between the posterior probability of the full graph variable defined on all 156 residues, and that of the graph with all but one residue omitted. A third parametrisation of criticality informs on the dynamical variation of nodal degrees as the protein evolves during the simulation. Finally, we compare results obtained with the three distinct criticality parameters, against experimentally-ascertained critical residues.