Correlation function based Gaussian network models

TL;DR

This paper introduces a unified framework for Gaussian network models (GNMs) based on correlation functions, improving B-factor predictions and connecting GNM with the flexibility-rigidity index (FRI) method.

Contribution

It generalizes GNM using correlation functions, linking it with FRI, and demonstrates improved accuracy in protein flexibility prediction.

Findings

Correlation function based GNMs outperform original GNM in B-factor prediction.

For large scale values, FRI and GNM yield similar predictions.

Unified framework connects GNM and FRI through correlation functions.

Abstract

Gaussian network model (GNM) is one of the most accurate and efficient methods for biomolecular flexibility analysis. However, the systematic generalization of the GNM has been elusive. We show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to correlation function based GNMs, whereas, the direct inverse of the diagonal elements gives rise to FRI method. We illustrate that correlation function based GNMs outperform the original GNM in the B-factor prediction of a set of 364 proteins. We demonstrate that for any given correlation function, FRI and GNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large.