High-Order Correlations in Internal Protein Motions and Energetics

Abstract

Background: Despite originating as a linear sequence of amino acids, folded proteins display a remarkable diversity and specificity of motions, or dynamics, which constitute the building blocks of cellular metabolism. A growing body of evidence also suggests that these motions are hierarchical, involving a multitude of spatial and temporal scales. A key task in biology is thus to elucidate the relationship between hierarchical nature of protein dynamics and function. Characterizing these spatial/ temporal fluctuations in molecular dynamics (MD) simulations is critical to understanding enzyme catalysis, ligand binding, and allosteric signaling - all therapeutically exploitable processes.Results: Using 0.5us simulation for ubiquitin, a 76 residue protein that labels other proteins for degradation, we show that positional deviations exhibit non-Gaussian behavior (kurtosis >> 3), at functionally important regions of the protein. To analyze the spatial deviations we propose a general and statistically rigorous method Quasi Anharmonic Analysis (QAA) that meaningfully captures non-Gaussian behaviors overlooked with established methods. QAA, which is an extension of independent component analysis (ICA) techniques, is a more realistic encoding of protein fluctuations and atomic coupling since its basis vectors capture, in addition to variance, higher-order spatial statistics. QAA benefits from relaxing the constraint of orthogonality in basis vectors (e.g., PCA) or assumptions of Gaussian deviations. This coupling between the basis vectors from QAA allows one to elucidate how ‘fast’ and ‘slow’ motions in ubiquitin allow it to bind to different substrates with high specificity.Conclusions: QAA is a novel approach to organize and visualize conformational landscape spanned by a protein. QAA naturally characterizes long-tailed distributions and separates conformational clusters with exceptional clarity when projected onto the novel representation space. The transitions we observe in ubiquitin signal biologically important structural shifts and highlight meaningful energetic barriers in the underlying energy landscape.