H2rs: deducing evolutionary and functionally important residue positions by means of an entropy and similarity based analysis of multiple sequence alignments

Abstract

Background: The identification of functionally important residue positions is an important task of computational biology. Methods of correlation analysis allow for the identification of pairs of residue positions, whose occupancy is mutually dependent due to constraints imposed by protein structure or function. A common measure assessing these dependencies is the mutual information, which is based on Shannon's information theory that utilizes probabilities only. Consequently, such approaches do not consider the similarity of residue pairs, which may degrade the algorithm's performance. One typical algorithm is H2r, which characterizes each individual residue position k by the conn(k)-value, which is the number of significantly correlated pairs it belongs to.

Results: To improve specificity of H2r, we developed a revised algorithm, named H2rs, which is based on the von Neumann entropy (vNE). To compute the corresponding mutual information, a matrix A is required, which assesses the similarity of residue pairs. We determined A by deducing substitution frequencies from contacting residue pairs observed in the homologs of 35 809 proteins, whose structure is known. In analogy to H2r, the enhanced algorithm computes a normalized conn(k)-value. Within the framework of H2rs, only statistically significant vNE values were considered. To decide on significance, the algorithm calculates a p-value by performing a randomization test for each individual pair of residue positions. The analysis of a large in silico testbed demonstrated that specificity and precision were higher for H2rs than for H2r and two other methods of correlation analysis. The gain in prediction quality is further confirmed by a detailed assessment of five well-studied enzymes. The outcome of H2rs and of a method that predicts contacting residue positions (PSICOV) overlapped only marginally. H2rs can be downloaded from http://www-bioinf.uni-regensburg.de.

Conclusions: Considering substitution frequencies for residue pairs by means of the von Neumann entropy and a p-value improved the success rate in identifying important residue positions. The integration of proven statistical concepts and normalization allows for an easier comparison of results obtained with different proteins. Comparing the outcome of the local method H2rs and of the global method PSICOV indicates that such methods supplement each other and have different scopes of application.

Figure 1

Computation of a pairwise similarity matrix A. (A) For each residue (k, blue) of our dataset, all neighbors with a distance of at most 5 Å measured between the centers of heavy atoms were determined. Here, it is one residue l marked red. (B) Residue positions k, l were linked with the corresponding columns of the MSA and transition frequencies were deduced from a comparison of the residue pairs. (C) In this illustrative example, we observe one transition from AA to AC, two transitions from AA to CA and one transition from AA to CC. Transition frequencies were used to construct the 400 × 400 matrix A of substitution frequencies for residue pairs.

Figure 2

Distribution of U_vNE() values for one pair of residue positions. The histogram (blue) shows the distribution of the U_vNE(k*, l*) values of the first two residue positions of ssTrpC resulting from shuffling the content of columns k and l of the MSA. A normality test on this distribution failed (P = 0.991), which indicates that the distribution is not Gaussian. The corresponding cumulative distribution is shown in black. The cumulative Gumbel distribution with parameters μ and β deduced from 25 randomization tests is shown in green. The red line depicts the actual U_vNE value of this pair of residue positions. The orange line shows the U_vNE value this pair would need to surpass a p-value of 0.01.

Figure 3

Residues of the stTrpA/stTrpB complex possessing highest conz(k)-values. For stTrpA (light blue) and stTrpB (gold), residues with conz(k)-values ≥ 2.0 and p-values ≤ 10^-11 are plotted in red as sticks. H2rs predicted for stTrpA 2, and for stTrpB 13 important residue positions. Ligands indole-3-glycerol phosphate and pyridoxal phosphate are plotted as green sticks. The sodium ion is shown as a green ball.

Figure 4

Residues of ssTrpC with highest conz(k)-values. For ssTrpC, H2rs identified 7 residues with conz(k)-values ≥ 2.0 and p-values ≤ 10^-11, which are shown as red sticks. The ligand indole-3-glycerol phosphate is shown as green sticks.

Figure 5

ecDHFR residues with highest conz(k)-values. For ecDHFR, H2rs predicted 6 residues with conz(k)-values ≥ 2.0 and p-values ≤ 10^-11, which are shown as red sticks. The ligands folic acid and NADP are shown as green sticks.

Figure 6

smHK residues with highest conz(k)-values. For smHK, H2rs predicted 10 residues with conz(k)-values ≥ 2.0 and p-values ≤ 10^-11, which are shown as red sticks. The ligand GLC is shown as green sticks and the SO₄ ion in the catalytic cleft as green balls.