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.