Ideal amino acid exchange forms for approximating substitution matrices

The Ancient Operational Code is Embedded in the Amino Acid Substitution Matrix and aaRS Phylogenies

The underlying structure of the canonical amino acid substitution matrix (aaSM) is examined by considering stepwise improvements in the differential recognition of amino acids according to their chemical properties during the branching history of the two aminoacyl-tRNA synthetase (aaRS) superfamilies. The evolutionary expansion of the genetic code is described by a simple parameterization of the aaSM, in which (i) the number of distinguishable amino acid types, (ii) the matrix dimension and (iii) the number of parameters, each increases by one for each bifurcation in an aaRS phylogeny. Parameterized matrices corresponding to trees in which the size of an amino acid sidechain is the only discernible property behind its categorization as a substrate, exclusively for a Class I or II aaRS, provide a significantly better fit to empirically determined aaSM than trees with random bifurcation patterns. A second split between polar and nonpolar amino acids in each Class effects a vastly greater further improvement. The earliest Class-separated epochs in the phylogenies of the aaRS reflect these enzymes' capability to distinguish tRNAs through the recognition of acceptor stem identity elements via the minor (Class I) and major (Class II) helical grooves, which is how the ancient operational code functioned. The advent of tRNA recognition using the anticodon loop supports the evolution of the optimal map of amino acid chemistry found in the later genetic code, an essentially digital categorization, in which polarity is the major functional property, compensating for the unrefined, haphazard differentiation of amino acids achieved by the operational code.

Amino acid properties conserved in molecular evolution

That amino acid properties are responsible for the way protein molecules evolve is natural and is also reasonably well supported both by the structure of the genetic code and, to a large extent, by the experimental measures of the amino acid similarity. Nevertheless, there remains a significant gap between observed similarity matrices and their reconstructions from amino acid properties. Therefore, we introduce a simple theoretical model of amino acid similarity matrices, which allows splitting the matrix into two parts – one that depends only on mutabilities of amino acids and another that depends on pairwise similarities between them. Then the new synthetic amino acid properties are derived from the pairwise similarities and used to reconstruct similarity matrices covering a wide range of information entropies. Our model allows us to explain up to 94% of the variability in the BLOSUM family of the amino acids similarity matrices in terms of amino acid properties. The new properties derived from amino acid similarity matrices correlate highly with properties known to be important for molecular evolution such as hydrophobicity, size, shape and charge of amino acids. This result closes the gap in our understanding of the influence of amino acids on evolution at the molecular level. The methods were applied to the single family of similarity matrices used often in general sequence homology searches, but it is general and can be used also for more specific matrices. The new synthetic properties can be used in analyzes of protein sequences in various biological applications.

Derivation of an amino acid similarity matrix for peptide: MHC binding and its application as a Bayesian prior

BACKGROUND

Experts in peptide:MHC binding studies are often able to estimate the impact of a single residue substitution based on a heuristic understanding of amino acid similarity in an experimental context. Our aim is to quantify this measure of similarity to improve peptide:MHC binding prediction methods. This should help compensate for holes and bias in the sequence space coverage of existing peptide binding datasets.

RESULTS

Here, a novel amino acid similarity matrix (PMBEC) is directly derived from the binding affinity data of combinatorial peptide mixtures. Like BLOSUM62, this matrix captures well-known physicochemical properties of amino acid residues. However, PMBEC differs markedly from existing matrices in cases where residue substitution involves a reversal of electrostatic charge. To demonstrate its usefulness, we have developed a new peptide:MHC class I binding prediction method, using the matrix as a Bayesian prior. We show that the new method can compensate for missing information on specific residues in the training data. We also carried out a large-scale benchmark, and its results indicate that prediction performance of the new method is comparable to that of the best neural network based approaches for peptide:MHC class I binding.

CONCLUSION

A novel amino acid similarity matrix has been derived for peptide:MHC binding interactions. One prominent feature of the matrix is that it disfavors substitution of residues with opposite charges. Given that the matrix was derived from experimentally determined peptide:MHC binding affinity measurements, this feature is likely shared by all peptide:protein interactions. In addition, we have demonstrated the usefulness of the matrix as a Bayesian prior in an improved scoring-matrix based peptide:MHC class I prediction method. A software implementation of the method is available at: http://www.mhc-pathway.net/smmpmbec.

Analysis of the impact of solvent on contacts prediction in proteins

Background

The correlated mutations concept is based on the assumption that interacting protein residues coevolve, so that a mutation in one of the interacting counterparts is compensated by a mutation in the other. Approaches based on this concept have been widely used for protein contacts prediction since the 90s. Previously, we have shown that water-mediated interactions play an important role in protein interfaces. We have observed that current "dry" correlated mutations approaches might not properly predict certain interactions in protein interfaces due to the fact that they are water-mediated.

Results

The goal of this study has been to analyze the impact of including solvent into the concept of correlated mutations. For this purpose we use linear combinations of the predictions obtained by the application of two different similarity matrices: a standard "dry" similarity matrix (DRY) and a "wet" similarity matrix (WET) derived from all water-mediated protein interfacial interactions in the PDB. We analyze two datasets containing 50 domains and 10 domain pairs from PFAM and compare the results obtained by using a combination of both matrices. We find that for both intra- and interdomain contacts predictions the introduction of a combination of a "wet" and a "dry" similarity matrix improves the predictions in comparison to the "dry" one alone.

Conclusion

Our analysis, despite the complexity of its possible general applicability, opens up that the consideration of water may have an impact on the improvement of the contact predictions obtained by correlated mutations approaches.

Distance matrix-based approach to protein structure prediction

Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r(ij)(2)] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r (ij) is greater or less than a cutoff value r (cutoff). We have performed spectral decomposition of the distance matrices D = sigma lambda(k)V(k)V(kT), in terms of eigenvalues lambda kappa and the corresponding eigenvectors v kappa and found that it contains at most five nonzero terms. A dominant eigenvector is proportional to r (2)--the square distance of points from the center of mass, with the next three being the principal components of the system of points. By predicting r (2) from the sequence we can approximate a distance matrix of a protein with an expected RMSD value of about 7.3 A, and by combining it with the prediction of the first principal component we can improve this approximation to 4.0 A. We can also explain the role of hydrophobic interactions for the protein structure, because r is highly correlated with the hydrophobic profile of the sequence. Moreover, r is highly correlated with several sequence profiles which are useful in protein structure prediction, such as contact number, the residue-wise contact order (RWCO) or mean square fluctuations (i.e. crystallographic temperature factors). We have also shown that the next three components are related to spatial directionality of the secondary structure elements, and they may be also predicted from the sequence, improving overall structure prediction. We have also shown that the large number of available HIV-1 protease structures provides a remarkable sampling of conformations, which can be viewed as direct structural information about the dynamics. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM) that is based on the contact matrix C (related to D), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to atomic molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide a similar sampling of conformations. Finally, we use distance constraints from databases of known protein structures for structure refinement. We use the distributions of distances of various types in known protein structures to obtain the most probable ranges or the mean-force potentials for the distances. We then impose these constraints on structures to be refined or include the mean-force potentials directly in the energy minimization so that more plausible structural models can be built. This approach has been successfully used by us in 2006 in the CASPR structure refinement (http://predictioncenter.org/caspR).

Inconsistent distances in substitution matrices can be avoided by properly handling hydrophobic residues

The adequacy of substitution matrices to model evolutionary relationships between amino acid sequences can be numerically evaluated by checking the mathematical property of triangle inequality for all triplets of residues. By converting substitution scores into distances, one can verify that a direct path between two amino acids is shorter than a path passing through a third amino acid in the amino acid space modeled by the matrix. If the triangle inequality is not verified, the intuition is that the evolutionary signal is not well modeled by the matrix, that the space is locally inconsistent and that the matrix construction was probably based on insufficient biological data. Previous analysis on several substitution matrices revealed that the number of triplets violating the triangle inequality increases with sequence divergence. Here, we compare matrices which are dedicated to the alignment of highly divergent proteins. The triangle inequality is tested on several classical substitution matrices as well as in a pair of "complementary" substitution matrices recording the evolutionary pressures inside and outside hydrophobic blocks in protein sequences. The analysis proves the crucial role of hydrophobic residues in substitution matrices dedicated to the alignment of distantly related proteins.

Nature of protein family signatures: insights from singular value analysis of position-specific scoring matrices

Position-specific scoring matrices (PSSMs) are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left singular vectors. The first right singular vectors were correlated with various amino acid indices including relative mutability, amino acid composition in protein interior, hydropathy, or turn propensity, depending on proteins. A significant correlation between the first left singular vector and a measure of site conservation was observed. It is shown that the contribution of the first singular component to the PSSMs act to disfavor potentially but falsely functionally important residues at conserved sites. The second right singular vectors were highly correlated with hydrophobicity scales, and the corresponding left singular vectors with contact numbers of protein structures. It is suggested that sequence alignment with a PSSM is essentially equivalent to threading supplemented with functional information. In addition, singular vectors may be useful for analyzing and annotating the characteristics of conserved sites in protein families.

AAindex: amino acid index database, progress report 2008

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/).