Time- and ensemble-average statistical mechanics of the Gaussian Network Model

TL;DR

This paper provides analytical expressions for time- and ensemble-averaged physical observables in a generalized Gaussian Network Model, useful for studying internal motions in proteins and mechanical structures.

Contribution

It introduces a generalized GNM with analytical results and provides a C++ code implementation for these calculations.

Findings

Analytical formulas for physical observables derived

Applicable to protein internal motions and mechanical frames

Code implementation available for researchers

Abstract

We present analytical results (up to a numerical diagonalization of a real symmetric matrix) for a set of time- and ensemble-average physical observables in the non-Hookean Gaussian Network Model (GNM) - a generalization of the Rouse model to elastic networks with links with a certain degree of extensional and rotational stiffness. We focus on a set of coarse-grained observables that may be of interest in the analysis of GNM in the context of internal motions in proteins and mechanical frames in contact with a heat bath. A C++ computer code is made available that implements all analytical results.