We investigate the supersecondary structure of a large group of proteins, the so-called sandwich proteins. The analysis of a large number of such proteins has led us to propose a set of rules that can be used to predict the possible arrangements of strands in the two -sheets forming a given sandwich structure. These rules imply the existence of certain invariant supersecondary substructures common to all sandwich proteins. Furthermore, they dramatically restrict the number of permissible arrangements. For example, whereas for proteins consisting of three strands in each -sheet 180 possible strand arrangements exist a priori, our rules imply that only 15 of them are permissible. Five of these predicted arrangements describe all currently known sandwich proteins with six strands.protein secondary structure ͉ supersecondary structure ͉ structure prediction P roteins that do not appear to have sequence similarity may have similar folds (1-4). This fact implies that structure is better conserved than sequence. One of the possible explanations for the limited number of protein folds is that certain rules exist that constrain the folding of a polypeptide chain. It has been suggested that such rules can be divided into two types: rules that allow one, starting from a given sequence, to predict the secondary structure elements (strands and helices), and rules that govern the assembling of strands and helices into a tertiary structure (5-9). Both of these problems are actively investigated by computational structural biologists.Much progress has occurred with respect to the first problem. Indeed, several efficient programs (most of them based on the neural network approach) that allow one to determine strands and helices in a given amino acid sequence (10-13) exist.Researchers investigating the second problem are trying to find rules that constrain the packing of strands and helices into the limited canonical structures found in nature. For  proteins, this problem can be formulated as follows: Starting from a given consecutive set of strands, the goal is to find the possible arrangement of these strands in the -sheets. The pioneering research of this kind is the famous work of Richardson (14), who discovered the so-called Greek key topology: it has been shown that this structural motif occurs in Ϸ70% of  proteins. Another interesting approach to this problem is based on the analysis of the folding mechanism of  proteins (5): it has been shown that the number of permissible topologies depends on the number of -strands and on the folding pathway. Furthermore, a number of regularities for -sheet motifs, such as the nonexistence of knots in the chain, has been discovered (15-20). It has also been shown that loops do not cross (14,21).In this article, we focus on a large group of  proteins, the so-called sandwich-like proteins. This type of architecture unites a number of very different protein superfamilies, which have no detectable sequence homology. The aim of our research is to find rules that govern the structura...