An edge-based formulation of elastic network models

TL;DR

This paper introduces an edge-based framework for elastic network models that characterizes edge fluctuations and mechanical susceptibility, linking to network rigidity and applicable to protein systems at multiple scales.

Contribution

It presents a novel edge-centric formulation for elastic network models, incorporating complex forces and relating to network rigidity, with applications to protein structures.

Findings

Edge mechanical embeddedness quantifies force response on edges.

The formulation relates to infinitesimal rigidity of networks.

Applicable to protein systems at residue and atomistic levels.

Abstract

We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterise edge fluctuations of geometric networks defined in d- dimensional space and define the edge mechanical embeddedness, an edge mechanical susceptibility measuring the force felt on each edge given a force applied on the whole system. We further show that this formulation can be directly related to the infinitesimal rigidity of the network, which additionally permits three- and four-centre forces to be included in the network description. We exemplify the approach in protein systems, at both the residue and atomistic levels of description.