Figure 1.
Plots of Correlation Matrices Inferred from Superpositions
The upper row (A–D) shows plots in which the true correlation matrix has no correlations (all off-diagonal elements are exactly zero), whereas the lower row (E–H) shows plots where the true correlation matrix has strong, complex, positive, and negative correlations. Positive correlation, zero correlation, and negative correlation are represented by colors ranging from blue to white to red, respectively.
(A, E) The true, assumed correlation matrix used in the simulation.
(B, F) The correlation matrix calculated from a least-squares superposition, including all atoms, of 300 protein structures simulated using the true correlation matrix.
(C, G) The estimated correlation matrix, calculated from a least-squares superposition that omitted residues 1–5, which have the highest variance (most disorder) in the structure.
(D, H) The correlation matrix calculated from a maximum likelihood superposition of the same simulated structures.
Figure 2.
PCA Plots of Least-Squares and ML Superpositions of Simulated Structures
The first principal component (PC) is plotted on the mean structure for various calculations. As in Figure 1, the upper row (A–D) uses a covariance matrix in which all correlations are zero (no correlation), whereas the lower row (E–H) uses a covariance matrix with strong correlations. Red regions are self-correlated, as are blue regions, while blue versus red regions are anti-correlated. White regions indicate no correlation.
(A, E) The true first PC, extracted from the known correlation matrices.
(B, F) The first PC based on the all-atom least-squares superposition.
(C, G) The first PC from a least-squares superposition that excluded residues 1–5 with the largest variance in the simulation.
(D, H) The first PC based on the ML superposition.
Figure 3.
PCA Plot of the 70S Ribosomal Subunit from Haloarcula marismortui
The second principal component is plotted for a superposition of 10 subunits of the large ribosomal subunit bound to different antibiotics. The subunit interface (which binds the small ribosomal subunit) is facing the viewer, with the 5S RNA at the top of the image. The large horizontal swath of “red” correlation co-localizes with the active site cleft that binds the mRNA, tRNAs, and translation factors. The first principal component (not shown) indicates a relatively simple, large-scale hinge-like motion in which the top third of the 70S subunit (in the orientation shown) is positively correlated with the bottom third.
Figure 4.
ML Superposition and PCA Plot of Homologous Telomere Domains
(A) An ML superposition of the first OB-fold from 1otc (blue), 1s40 (magenta), and 1qzg (cyan).
(B) A PCA plot of the first principal component based on the ML superposition in (A), plotted on the mean structure. Two functionally critical loops, shown in blue, are implicated in telomeric ssDNA substrate recognition. These loops are highly correlated, indicating that their conformations have evolved in concert.
Figure 5.
ML Superpositions and PCA Plots Derived from Two NMR Structural Ensembles of Ubiquitin
(A) The first principal component from the correlation matrix is plotted on an ML superposition of the dynamic ensemble refined NMR solution structure of ubiquitin (PDB ID: 1xqq) [22],
Ile30 (in red), and Val5 (in blue) pack together in the hydrophobic core of the protein. In this major mode of correlation, these two residues account for a large fraction of the correlation, and they move, on average, in opposite directions.
(B) The first principal component from the covariance matrix, for the same 1xqq ensemble as in (A). The C-terminal tail (at top and in blue) is disordered largely because of a lack of NOE distance constraints. The low experimental precision of this region contributes to the large variance that dominates the largest principal component of the covariance matrix. The strong covariation in this region (indicated by blue) is thus an artifactual result of experimental uncertainty and dynamics rather than true correlated motion.
(C) The first principal component from the correlation matrix is plotted on an ML superposition of an independent NMR solution structure of ubiquitin (PDB ID: 2nr2) [23].
(D) The first principal component from the covariance matrix, for the same 2nr2 ensemble as in (C). Note that in the disordered C-terminal tail the red versus blue color is arbitrary.