Prediction of the structural motifs of sandwich proteins

Secondary and Supersecondary Structure of Proteins in Light of the Structure of Hydrophobic Cores

The traditional classification of protein structures (with regard to their supersecondary and tertiary conformation) is based on an assessment of conformational similarities between various polypeptide chains and particularly on the presence of specific secondary structural motifs. Mutual relations between secondary folds determine the overall shape of the protein and may be used to assign proteins to specific families (such as the immunoglobulin-like family). An alternative means of conducting structural assessment focuses on the structure of the protein's hydrophobic core. In this case, the protein is treated as a quasi-micelle, which exposes hydrophilic residues on its surface while internalizing hydrophobic residues. The accordance between the actual distribution of hydrophobicity in a protein and its corresponding theoretical ("idealized") distribution can be determined quantitatively, which, in turn, enables comparative analysis of structures regarded as geometrically similar (as well as geometrically divergent structures which are nevertheless regarded as similar in the sense of the fuzzy oil drop model). In this scope, the protein may be compared to an "intelligent micelle," where local disorder is often intentional and related to biological function-unlike traditional surfactant micelles which remain highly symmetrical throughout and do not carry any encoded information.

Compact Structure Patterns in Proteins

Globular proteins typically fold into tightly packed arrays of regular secondary structures. We developed a model to approximate the compact parallel and antiparallel arrangement of α-helices and β-strands, enumerated all possible topologies formed by up to five secondary structural elements (SSEs), searched for their occurrence in spatial structures of proteins, and documented their frequencies of occurrence in the PDB. The enumeration model grows larger super-secondary structure patterns (SSPs) by combining pairs of smaller patterns, a process that approximates a potential path of protein fold evolution. The most prevalent SSPs are typically present in superfolds such as the Rossmann-like fold, the ferredoxin-like fold, and the Greek key motif, whereas the less frequent SSPs often possess uncommon structure features such as split β-sheets, left-handed connections, and crossing loops. This complete SSP enumeration model, for the first time, allows us to investigate which theoretically possible SSPs are not observed in available protein structures. All SSPs with up to four SSEs occurred in proteins. However, among the SSPs with five SSEs, approximately 20% (218) are absent from existing folds. Of these unobserved SSPs, 80% contain two or more uncommon structure features. To facilitate future efforts in protein structure classification, engineering, and design, we provide the resulting patterns and their frequency of occurrence in proteins at: http://prodata.swmed.edu/ssps/.

Systematic construction and prediction of the arrangement of the strands of sandwich proteins

The problem of predicting the three-dimensional structure of a protein starting from its amino acid sequence is regarded as one of the most important open problems in biology. Here, we solve aspects of this problem for the so-called sandwich proteins that constitute a large class of proteins consisting of only beta-strands arranged in two sheets. A breakthrough for this class of proteins was announced in Kister et al. (Kister et al. 2002 Proc. Natl Acad. Sci. USA 99, 14 137-14 141), in which it was shown that sandwich proteins contain a certain invariant substructure called interlock. It was later noted that approximately 90% of the observed sandwich proteins are canonical, namely they are generated by certain geometrical structures. Here, employing a topological investigation, we prove that interlocks and geometrical structures are the direct consequence of certain biologically motivated fundamental principles. Furthermore, we construct all possible canonical motifs involving 6-10 strands. This construction limits dramatically the number of possible motifs. For example, for sandwich proteins with nine strands, the a priori number of possible canonical motifs exceeds 360000, whereas our construction yields only 49 geometrical structures and 625 canonical motifs.

Fold classification based on secondary structure--how much is gained by including loop topology?

Background

It has been proposed that secondary structure information can be used to classify (to some extend) protein folds. Since this method utilizes very limited information about the protein structure, it is not surprising that it has a higher error rate than the approaches that use full 3D fold description. On the other hand, the comparing of 3D protein structures is computing intensive. This raises the question to what extend the error rate can be decreased with each new source of information, especially if the new information can still be used with simple alignment algorithms.

We consider the question whether the information about closed loops can improve the accuracy of this approach. While the answer appears to be obvious, we had to overcome two challenges. First, how to code and to compare topological information in such a way that local alignment of strings will properly identify similar structures. Second, how to properly measure the effect of new information in a large data sample.

We investigate alternative ways of computing and presenting this information.

Results

We used the set of beta proteins with at most 30% pairwise identity to test the approach; local alignment scores were used to build a tree of clusters which was evaluated using a new log-odd cluster scoring function. In particular, we derive a closed formula for the probability of obtaining a given score by chance.Parameters of local alignment function were optimized using a genetic algorithm.

Of 81 folds that had more than one representative in our data set, log-odds scores registered significantly better clustering in 27 cases and significantly worse in 6 cases, and small differences in the remaining cases. Various notions of the significant change or average change were considered and tried, and the results were all pointing in the same direction.

Conclusion

We found that, on average, properly presented information about the loop topology improves noticeably the accuracy of the method but the benefits vary between fold families as measured by log-odds cluster score.

Strict rules determine arrangements of strands in sandwich proteins

From a computer analysis of the spatial organization of the secondary structures of beta-sandwich proteins, we find certain sets of consecutive strands that are connected by hydrogen bonds, which we call "strandons." The analysis of the arrangements of strandons in 491 protein structures that come from 69 different superfamilies reveals strict regularities in the arrangements of strandons and the formation of what we call "canonical supermotifs." Six such supermotifs account for approximately 90% of all observed structures. Simple geometric rules are described that dictate the formation of these supermotifs.

A geometric construction determines all permissible strand arrangements of sandwich proteins

For a large class of proteins called sandwich-like proteins (SPs), the secondary structures consist of two beta-sheets packed face-to-face, with each beta-sheet consisting typically of three to five beta-strands. An important step in the prediction of the three-dimensional structure of a SP is the prediction of its supersecondary structure, namely the prediction of the arrangement of the beta-strands in the two beta-sheets. Recently, significant progress in this direction was made, where it was shown that 91% of observed SPs form what we here call "canonical motifs." Here, we show that all canonical motifs can be constructed in a simple manner that is based on thermodynamic considerations and uses certain geometric structures. The number of these structures is much smaller than the number of possible strand arrangements. For instance, whereas for SPs consisting of six strands there exist a priori 900 possible strand arrangements, there exist only five geometric structures. Furthermore, the few motifs that are noncanonial can be constructed from canonical motifs by a simple procedure.