Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Abstract

Gaussian network model(GNM) and anisotropic network model(ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM(gGNM) and ANM methods and 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 gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method.With this connection,we further introduce two multiscale elastic network models, namely, multiscale GNM(mGNM) and multiscale ANM(mANM), which are able to incorporate different scales into the generalized Kirchkoff matrices or generalized Hessian matrices.We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins.We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large.More importantly,we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate benefit of our mGNM in the B-factor predictions on many proteins that fail the original GNM method. We show that the present mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the simulation of protein collective motions.

21 pages,16 figures

References in corpus (2)

• Persistent homology analysis of protein structure, flexibility and folding
• Fast and Anisotropic Flexibility-Rigidity Index

Cited by in corpus (6)

• A review of mathematical representations of biomolecules
• Persistent Dirac for molecular representation
• Generalized flexibility-rigidity index
• Dissecting the roles of local packing density and longer-range effects in protein sequence evolution
• Multiscale virtual particle based elastic network model (MVP-ENM) for biomolecular normal mode analysis
• Sequence-based Multiscale Model (SeqMM) for High-throughput chromosome conformation capture (Hi-C) data analysis