Figure 1.
Squares of correlation coefficients between eigenvectors obtained from Bx matrix with the eigenvectors obtained from the B100 matrix.
Figure 2.
Squares of correlation coefficients between the of-diagonal elements of Bx matrices and their reconstructions.
The i-th model of each matrix is reconstructed using i eigenvectors. The reconstruction with i = 0 is limited to G-matrix, the remaining models use eigenvectors EVi (i = 1…6). The left panel displays entire range of r2, the right panel is a close-up for r2 larger than 0.8.
Table 1.
Eigenvectors of BLOSUM100 matrix.
Table 2.
The variance explained by the eigenvectors in reconstructed BLOSUM matrices.
Figure 3.
The relative quality of the reconstructed matrices.
The value on Y-axis is a fraction of best possible reconstruction achieved by the model. It is estimated as a fraction of r2 achieved in reconstruction with eigenvectors derived from B100 and r2 obtained in reconstruction with its own eigenvectors. The left panel displays entire range of Y, the right panel is a close-up for Y larger than 0.9.
Figure 4.
The optimal number of eigenvectors for reconstruction of the BLOSUM matrices.
The optimal number of eigenvectors was obtained with the help of the Bayesian Information Criterion.
Table 3.
Optimised coefficients for matrix reconstruction for final models.
Figure 5.
The differences between original BLOSUM62 matrix and its reconstruction.
The matrix was reconstructed using G-matrix and 5 eigenvectors derived from BLOSUM100 matrix. The triangle above diagonal displays differences between matrices scaled to half bit units and rounded, the diagonal and triangle below displays differences between matrices scaled to half bit units and not rounded. The shades of gray correspond to the differences.
Figure 6.
Amino acids in the eigenvector space.
Six panels display projections of amino acids on all combinations space spanned on four eigenvectors: EV2, EV3, EV4 and EV5.
Table 4.
The amino acid properties that highly correlate with the eigenvectors of the BLOSUM100 matrix.