AAindex is a database of numerical indices representing various physicochemical and biochemical properties of amino acids and pairs of amino acids. We have added a collection of protein contact potentials to the AAindex as a new section. Accordingly AAindex consists of three sections now: AAindex1 for the amino acid index of 20 numerical values, AAindex2 for the amino acid substitution matrix and AAindex3 for the statistical protein contact potentials. All data are derived from published literature. The database can be accessed through the DBGET/LinkDB system at GenomeNet (http://www.genome.jp/dbget-bin/www_bfind?aaindex) or downloaded by anonymous FTP (ftp://ftp.genome.jp/pub/db/community/aaindex/).

We have analyzed 29 different published matrices of protein pairwise contact potentials (CPs) between amino acids derived from different sets of proteins, either crystallographic structures taken from the Protein Data Bank (PDB) or computer-generated decoys. Each of the CPs is similar to 1 of the 2 matrices derived in the work of Miyazawa and Jernigan (Proteins 1999;34:49-68). The CP matrices of the first class can be approximated with a correlation of order 0.9 by the formula e ij = h i + h j , 1 ≤ i, j ≤ 20, where the residue-type dependent factor h is highly correlated with the frequency of occurrence of a given amino acid type inside proteins. Electrostatic interactions for the potentials of this class are almost negligible. In the potentials belonging to this class, the major contribution to the potentials is the one-body transfer energy of the amino acid from water to the protein environment. Potentials belonging to the second class can be approximated with a correlation of 0.9 by the formula e ij = c 0 − h i h j + q i q j , where c 0 is a constant, h is highly correlated with the Kyte-Doolittle hydrophobicity scale, and a new, less dominant, residue-type dependent factor q is correlated (~0.9) with amino acid isoelectric points pI. Including electrostatic interactions significantly improves the approximation for this class of potentials. While, the high correlation between potentials of the first class and the hydrophobic transfer energies is well known, the fact that this approximation can work well also for the second class of potentials is a new finding. We interpret potentials of this class as representing energies of contact of amino acid pairs within an average protein environment. Proteins 2005;59:49-57.

We have analyzed 29 published substitution matrices (SMs) and five statistical protein contact potentials (CPs) for comparison. We find that popular, 'classical' SMs obtained mainly from sequence alignments of globular proteins are mostly correlated by at least a value of 0.9. The BLOSUM62 is the central element of this group. A second group includes SMs derived from alignments of remote homologs or transmembrane proteins. These matrices correlate better with classical SMs (0.8) than among themselves (0.7). A third group consists of intermediate links between SMs and CPs - matrices and potentials that exhibit mutual correlations of at least 0.8. Next, we show that SMs can be approximated with a correlation of 0.9 by expressions c(0) + x(i)x(j) + y(i)y(j) + z(i)z(j), 1

We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.