Correlation-Based Feature Selection to Identify Functional Dynamics in Proteins

Abstract

To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the time scale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances. As typically only a small subset of those coordinates is involved in a specific biomolecular process, it is important to discard the remaining uncorrelated motions or weakly correlated noise coordinates. This is because they may exhibit large amplitudes or long time scales and therefore will be erroneously considered important by PCA and TICA, respectively. To discriminate collective motions underlying functional dynamics from uncorrelated motions, the correlation matrix of the input coordinates is block-diagonalized by a clustering method. This strategy avoids possible bias due to presumed functional observables and conformational states or variation principles that maximize variance or time scales. Considering several linear and nonlinear correlation measures and various clustering algorithms, it is shown that the combination of linear correlation and the Leiden community detection algorithm yields excellent results for all considered model systems. These include the functional motion of T4 lysozyme to demonstrate the successful identification of collective motion, as well as the folding of the villin headpiece to highlight the physical interpretation of the correlated motions in terms of a functional mechanism.

Nonequilibrium Modeling of the Elementary Step in PDZ3 Allosteric Communication

“…To identify the intramolecular interactions mediating the allosteric transition in PDZ3, we have employed a recently proposed correlation analysis of interresidue contact distances. 47 It reveals a network of highly correlated α 3 -protein contacts (Fig. 3b) that mediate a cooperative contact rearrangement in PDZ3 (Fig.…”

“…To discriminate collective motions underlying functional dynamics from uncorrelated motion, we calculated (the modulus of) the linear correlation matrix of these coordinates and rearranged this matrix in an approximately block-diagonal form. Following Diez et al, 47 this is achieved via a community detection technique called Leiden clustering, 48 employing the Python package MoSAIC 47 and a Leiden resolution parameter γ = 0.5.…”

Nonequilibrium Modeling of the Elementary Step in PDZ3 Allosteric Communication

“…To discriminate collective motions underlying functional dynamics from uncorrelated motion, we calculated (the modulus of) the linear correlation matrix of these coordinates and rearranged this matrix in an approximately block-diagonal form. Following Diez et al, 47 this is achieved via a community detection technique called Leiden clustering, 48 employing the Python package MoSAIC 47 and a Leiden resolution parameter γ = 0.5.…”

“…To identify the intramolecular interactions mediating the allosteric transition in PDZ3, we have employed a recently proposed correlation analysis of interresidue contact distances. 47 It reveals a network of highly correlated α 3 -protein contacts (Figure 3b) that mediate a cooperative contact rearrangement in PDZ3 (Figure 5). Involving only a one-step contact changing process, the cooperative transition can be considered as a minimal solution to transduce the information on the state of the α 3 -helix to the ligand and represents therefore the elementary step in the allosteric communication in PDZ3.…”

“…To identify the intramolecular interactions mediating the allosteric transition in PDZ3, we have employed a recently proposed correlation analysis of interresidue contact distances . It reveals a network of highly correlated α 3 -protein contacts (Figure b) that mediate a cooperative contact rearrangement in PDZ3 (Figure ).…”