Non-intertwined binary patterns of hydrophobic/nonhydrophobic amino acids are considerably better markers of regular secondary structures than nonconstrained patterns.

Patterns of hydrophobic and hydrophilic residues (binary patterns) play an important role in protein architecture and can be roughly categorized into two classes regarding their preferential participation in alpha-helices or beta-strands. However, a single binary pattern can be embedded into different longer patterns carrying opposite structural information and thus cannot be as much informative as expected. Here, we consider conditional binary patterns, or hydrophobic clusters, whose existence is conditioned by the presence of a minimum number of nonhydrophobic residues, called the connectivity distance, that separate two hydrophobic amino acids assumed to belong to two distinct patterns. Conditional binary patterns are distinct from simple ones in that they are not intertwined, i.e., they can not include or be included in other conditional patterns and therefore carry a much more differentiated information, in particular being dramatically better correlated with regular secondary structures (especially beta ones). The distribution of these nonintertwined binary patterns in natural proteins was assessed relative to randomness, evidencing the structural bricks that are favored and disfavored by evolutionary selection. Several connectivity distances as well as several hydrophobic alphabets were tested, evidencing the clear superiority of a connectivity distance of 4, which mimics the minimum current length of loops in globular domains, and of the VILFMYW alphabet, selected from structural data (secondary structure propension and Voronoï tesselation), in highlighting fundamental properties of protein folds.