Comparison between slow anisotropic LE4PD fluctuations and the principal component analysis modes of ubiquitin

Abstract

Proteins' biological function and folding mechanisms are often guided by large-scale, slow motions, which involve crossing high energy barriers. In a simulation trajectory, these slow fluctuations are commonly identified using a principal component analysis (PCA). Despite the popularity of this method, a complete analysis of its predictions based on the physics of protein motion has been so far limited. This study formally connects the PCA to a Langevin model of protein dynamics and analyzes the contributions of energy barriers and hydrodynamic interactions to the slow PCA modes of motion. To do so, we introduce an anisotropic extension of the Langevin Equation for Protein Dynamics, called the LE4PD-XYZ, which formally connects to the PCA 'essential dynamics'. The LE4PD-XYZ is an accurate coarse-grained diffusive method to model protein motion, which describes anisotropic fluctuations in the protein's alpha-carbons. The LE4PD accounts for hydrodynamic effects and mode-dependent free-energy barriers. This study compares large-scale anisotropic fluctuations identified by the LE4PD-XYZ to the mode-dependent PCA's predictions, starting from a microsecond-long alpha-carbon molecular dynamics atomistic trajectory of the protein ubiquitin. We observe that the inclusion of free-energy barriers and hydrodynamic interactions has important effects on the identification and timescales of ubiquitin's slow modes..

Anomalous Dynamics in Macromolecular Liquids

“…The Rouse model provides a simple description of chain dynamics for long polymer chains (the degree of polymerization is assumed to go to infinity), while predicting the scaling exponents of chain dynamics in remarkable agreement with experiments [ 1 , 14 ]. To introduce a more realistic description of the polymer chains, the Rouse model has been modified by adopting intramolecular chain distributions that include local semiflexibility [ 15 ], which accounts for the complex nature of local energy barriers [ 16 , 17 ], and monomer-dependent friction coefficients [ 18 , 19 ]. Furthermore, monomer fluctuations that are harmonic in a body-centered description of the dynamics, are intrinsically anharmonic in the lab reference system of a Rouse-like description due to the coupling of internal fluctuations with the molecular rotational and translational dynamic [ 20 , 21 ].…”