Singular value decomposition for the correlation of atomic fluctuations with arbitrary angle

Abstract

Many proteins exhibit a critical property called allostery, which enables intra-molecular transmission of information between distal sites. Microscopically, allosteric response is closely related to correlated atomic fluctuations. Conventional correlation analysis correlates the atomic fluctuations at two sites by taking the dot product (DP) between the fluctuations, which accounts only for the parallel and antiparallel components. Here, we present a singular value decomposition (SVD) method that analyzes the correlation coefficient of fluctuation dynamics with an arbitrary angle between the correlated directions. In a model allosteric system, the second PDZ domain (PDZ2) in the human PTP1E protein, approximately one third of the strong correlations have near-perpendicular directions, which are underestimated in the conventional method. The discrimination becomes more prominent for residue pairs with larger separation. The results of the proposed SVD method are more consistent with the experimentally determined PDZ2 dynamics than those of conventional method. In addition, the SVD method improved the prediction accuracy of the allosteric sites in a dataset of 23 known allosteric monomer proteins. The proposed method may inspire extended investigation not only into allostery, but also into protein dynamics and drug design.

Allosteric Type and Pathways Are Governed by the Forces of Protein–Ligand Binding

“…During the past decades, vast studies have attempted to elucidate allosteric mechanisms, to detect allosteric binding sites, − to identify allosteric pathways, and to manage allosteric applications (including allosteric materials, − allosteric protein switches, and allosteric network drugs , ). However, what determines and how to up- or down-regulate specific function, another key issue in designing allosteric modulators, remains elusive.…”

Rational design of allosteric modulators: Challenges and successes

“…30,105 Structure-based methods are predominantly based on residue movement cross-correlation within the protein. [106][107][108][109][110] Motional correlations can be obtained from MD simulations or from conformational ensembles produced from MD, [111][112][113][114][115][116] MC simulations, 117,118 using principal component analysis (PCA) or from normal mode analysis (NMA), elastic network models (ENMs) such as the Gaussian network model (GNM), 118,119 the anisotropic network model, 120 or the torsional network model (TNM), 121,122 which uses torsion angles as degrees of freedom. Graph theory has been also employed, which provides a way of representing proteins in a reduced form, identifying allosteric pathways from the dynamic couplings between the residues of the orthosteric and the allosteric sites.…”

“…It must be noted that calculating cross-correlations using the covariance matrix may miss nonlinear correlations and ignore orthogonal vibrations; for this purpose, approaches based on mutual information have been developed, which enable quantifying all correlations, including nonlinear and higher-order correlations [111][112][113]115,116,136,137 or from the singular value decomposition. 120 Additionally, by using the covariance matrix, the time evolution information and dynamic properties of the system are lost. 9,30,60 Another challenge in network-based methodologies using equilibrium sampling is that allosteric conformational changes may occur in time scales inaccessible to plain MD.…”

A comprehensive ensemble model for comparing the allosteric effect of ordered and disordered proteins

“…With the development of structural biology, the description of allostery in terms of structure changes was derived [5], and was used to study allosteric proteins such as lactate dehydrogenase [6]. The structure paradigm also leads to the seeking of specific atomic pathway that connects allosteric sites [7–9]. Nevertheless, the discovery of dynamic structure and multiple conformations of proteins, such as multiple orientations of DNA-binding domains of DNA-binding proteins in the absence of DNA [10] and the intermediate conformation of hemoglobin in solution [11], suggests more possibilities beyond the simple two-state models.…”