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.
Highlights
Elastic network models (ENMs) are ubiquitous in physics and have been applied to describe properties of a wide variety of structures including glasses [1,2], biological tissue [3], supercooled liquids [4], and, recently, the design of allosteric materials [5]
The principal assumption of ENMs is that we may approximate the bottom of the potential energy well of a structure by a quadratic function, by taking the Taylor series of the potential energy with respect to node displacements about the minimum r0
While real potential energy surfaces of proteins are complex, highly nonlinear, and containing many minima [7], elastic models have been surprisingly effective for the analysis of slow equilibrium motions of proteins [8,9]
Summary
Elastic network models (ENMs) are ubiquitous in physics and have been applied to describe properties of a wide variety of structures including glasses [1,2], biological tissue [3], supercooled liquids [4], and, recently, the design of allosteric materials [5]. While real potential energy surfaces of proteins are complex, highly nonlinear, and containing many minima [7], elastic models have been surprisingly effective for the analysis of slow equilibrium motions of proteins [8,9] Another common use of ENMs is for the calculation of node fluctuations, which have shown good agreement with crystallographic B factors [10,11]. The Born-Huang model [17] has often formed the basis for the study of lattice structures but its weakness in handling disordered materials like glasses has been highlighted in the context of rigidity percolation [18] and more recently by Zaccone and Scossa-Romano [19], who extended the Born model to include nonaffine responses to external stresses In many systems such as proteins, function is often driven by changes in structure, but crucially it is the relative change in node positions that is of interest.
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