Information-theoretical measures identify accurate low-resolution representations of protein configurational space

Abstract

A steadily growing computational power is employed to perform molecular dynamics simulations of biological macromolecules, which represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data are produced, from which useful, synthetic, and intelligible information has to be extracted to make the crucial step from knowing to understanding. Here we tackled the problem of coarsening the conformational space sampled by proteins in the course of molecular dynamics simulations. We applied different schemes to cluster the frames of a dataset of protein simulations; we then employed an information-theoretical framework, based on the notion of resolution and relevance, to gauge how well the various clustering methods accomplish this simplification of the configurational space. Our approach allowed us to identify the level of resolution that optimally balances simplicity and informativeness; furthermore, we found that the most physically accurate clustering procedures are those that induce an ultrametric structure of the low-resolution space, consistently with the hypothesis that the protein conformational landscape has a self-similar organisation. The proposed strategy is general and its applicability extends beyond that of computational biophysics, making it a valuable tool to extract useful information from large datasets. RESOLUTIONRELEVANCE high-resolution reference average linkage random linkageTable-of-contents entry. Higher values of relevance are associated to clustering methods producing structurally accurate coarse representations of a protein's conformational space.

In Search of a Dynamical Vocabulary: A Pipeline to Construct a Basis of Shared Traits in Large-Scale Motions of Proteins

“…Distance in dynamics After all the pairwise alignments between the elements of the dataset are performed, a distance matrix that expresses differences in the large-scale dynamics is obtained (Figure 1c); then, the dataset undergoes hierarchical clustering [52] based on this distance matrix, in order to identify groups of dynamics-related proteins (Figure 1d). The optimal number of clusters is identified from the interplay between resolution and relevance [53][54][55][56][57]. These two quantities are entropies that are related to each other and depend on the clusterization procedure adopted.…”

In search of a dynamical vocabulary: a pipeline to construct a basis of shared traits in large-scale motions of proteins

“…After all the pairwise alignments between the elements of the dataset are performed, a distance matrix that expresses differences in the large-scale dynamics is obtained; then the dataset undergoes hierarchical clustering [46] based on this distance matrix, in order to identify groups of dynamics-related proteins. The optimal number of clusters is identified from the interplay between resolution and relevance [47][48][49][50][51]. These two quantities, which are defined in more detail in the Methods section, are entropies that are related to each other and depend on the clusterization procedure adopted.…”