The parametric description of residue environments through solvent accessibility, backbone conformation, or pairwise residue-residue distances is the key to the comparison between amino acid types at protein sequence positions and residue locations in structural templates (condition of protein sequence-structure match). For the first time, the research results presented in this study clarify and allow to quantify, on a rigorous statistical basis, to what extent the amino acid type-specific distributions of commonly used environment parameters are discriminative with respect to the 20 amino acid types. Relying on the Bahadur theory, we estimate the probability of error in a single-sequence-structure alignment based on weak or absent discriminative power in a learning database of protein structure. We present the results for many residue environment variables and demonstrate that each fold description parameter is sensitive with respect to only a few amino acid types while indifferent to most of the other amino acid types. Even complex structural characteristics combining solvent-accessible surface area, backbone conformation, and pairwise distances distinguish only some amino acid types, whereas the others remain nondiscriminated. We find that the knowledge-based potentials currently in use treat especially Ala, Asp, Gln, His, Ser, Thr, and Tyr as essentially "average" amino acids. Thus, highly discriminative amino acid types define the alignment register in gapless sequence-structure alignments. The introduction of gaps leads to alignment ambiguities at sequence positions occupied by nondiscriminated amino acid types. Therefore, local sequence-structure alignments produced by techniques with gaps cannot be reliable. Conceptionally new and more sensitive environment parameters must be invented.

The success rates reported for secondary structural class prediction with different methods are contradictory. On one side, the problem of recognizing the secondary structural class of a protein knowing only its amino acid composition appears completely solved by simply applying jury decision with an elliptically scaled distance function. Chou and coworkers repeatedly (see Crit. Rev. Biochem. Mol. Biol. 30:275-349, 1995) published prediction accuracies near 100%. On the other hand, traditional secondary structure prediction techniques achieve success rates of about 70% for the secondary structural state per residue and about 75% for structural class only with extensive input information (full sequence of the query protein, its amino acid composition and length, multiple alignments with homologous sequences). In this article, we resolve the paradox and consider (1) the question of the secondary structural class definition, (2) the role of the representativity of the test set of protein tertiary structure for the current state of the Protein Data Bank (PDB); and (3) we estimate the real impact of amino acid composition on secondary structural class. We formulate three objective criteria for a reasonable definition of secondary structural classes and show that only the criterion of Nakashima et al. (J. Biochem. 99:153-162, 1986) complies with all of them. Only this definition matches the distribution of secondary structural content in representative PDB subsets, whereas other criteria leave many proteins (up to 65% of all PDB entries) simply unassigned. We review critically specialized secondary-structural class prediction methods, especially those of Chou and coworkers, which claim almost 100% accuracy using only amino acid composition, and resolve the paradox that these prediction accuracies are better than those from secondary structure predictions from multiple alignments. We show (i) that these techniques rely on a preselection of test sets which removes irregular proteins and other proteins without any class assignment (about 35% of all PDB entries); and (ii) that even for preselected representative test sets, the success rate drops to 60% and lower for a 4-type classification (alpha, beta, alpha + beta, alpha/beta). The prediction accuracies fall to about 50% if the secondary structural class definition of Nakashima et al. is applied and only few irregular proteins are preselected and removed from automatically generated, representative subsets of the PDB. We have applied two new vector decomposition methods for secondary structural content prediction from amino acid composition alone, with and without consideration of amino acid compositional coupling in the learning set of tertiary structures respectively, to the problem of class prediction and achieve about 60% correct assignment among four classes (alpha, beta, mixed, irregular) as well as single sequence-based secondary structure prediction methods like GORIII and COMBI. Our results demonstrate that 60% correctness is the upper limit for a 4-type class prediction from amino acid composition alone for an unknown query protein and that consideration of compositional coupling does not improve the prediction success. The prediction program SSCP offering secondary structural class assignment for query compositions and sequences has been made available as a World Wide Web and E-mail service.

The predictive limits of the amino acid composition for the secondary structural content (percentage of residues in the secondary structural states helix, sheet, and coil) in proteins are assessed quantitatively. For the first time, techniques for prediction of secondary structural content are presented which rely on the amino acid composition as the only information on the query protein. In our first method, the amino acid composition of an unknown protein is represented by the best (in a least square sense) linear combination of the characteristic amino acid compositions of the three secondary structural types computed from a learning set of tertiary structures. The second technique is a generalization of the first one and takes into account also possible compositional couplings between any two sorts of amino acids. Its mathematical formulation results in an eigenvalue/eigenvector problem of the second moment matrix describing the amino acid compositional fluctuations of secondary structural types in various proteins of a learning set. Possible correlations of the principal directions of the eigenspaces with physical properties of the amino acids were also checked. For example, the first two eigenvectors of the helical eigenspace correlate with the size and hydrophobicity of the residue types respectively. As learning and test sets of tertiary structures, we utilized representative, automatically generated subsets of Protein Data Bank (PDB) consisting of non-homologous protein structures at the resolution thresholds < or = 1.8A, < or = 2.0A, < or = 2.5A, and < or = 3.0 A. We show that the consideration of compositional couplings improves prediction accuracy, albeit not dramatically. Whereas in the self-consistency test (learning with the protein to be predicted), a clear decrease of prediction accuracy with worsening resolution is observed, the jackknife test (leave the predicted protein out) yielded best results for the largest dataset (< or = 3.0A, almost no difference to the self-consistency test!), i.e., only this set, with more than 400 proteins, is sufficient for stable computation of the parameters in the prediction function of the second method. The average absolute error in predicting the fraction of helix, sheet, and coil from amino acid composition of the query protein are 13.7, 12.6, and 11.4%, respectively with r.m.s. deviations in the range of 8.6 divided by 11.8% for the 3.0 A dataset in a jackknife test. The absolute precision of the average absolute errors is in the range of 1 divided by 3% as measured for other representative subsets of the PDB. Secondary structural content prediction methods found in the literature have been clustered in accordance with their prediction accuracies. To our surprise, much more complex secondary structure prediction methods utilized for the same purpose of secondary structural content prediction achieve prediction accuracies very similar to those of the present analytic techniques, implying that all the information beyond the amino acid composition is, in fact, mainly utilized for positioning the secondary structural state in the sequence but not for determination of the overall number of residues in a secondary structural type. This result implies that higher prediction accuracies cannot be achieved relying solely on the amino acid composition of an unknown query protein as prediction input. Our prediction program SSCP has been made available as a World Wide Web and E-mail service.