Classic snake cube1/27/2024 Numbers of exposed surfaces of constituent cubes in the folded conformation are indicated as HP numbers, which will be used in the definition of a new puzzle, the HP puzzle, to be introduced later. Constituent cubes can be of either e-type (at either end), s-type or b-type. Snake cube puzzle in extended (top), arbitrary (bottom left) and folded (bottom right) conformations. A variety of puzzle problems can be produced depending on the sequence of cube types. The aim of the puzzle is to fold the array into a compact 3×3×3 cubic structure. Adjacent cubes in an array can rotate freely about the connecting string, so that the array can assume various three-dimensional conformation. An array is characterized by its specific sequence of cube types. A cube has holes either in opposite faces, so that the string runs straight through ( s-type), or in adjacent faces, so that the string makes a right angled bend through the cube ( b-type). Every cube (except for the one at either end, e-type) has two faces with a hole in the center through which the string runs. The snake cube is a puzzle of a linear array of 27 cubes connected together by a string running through their centers ( Fig. Especially, respective roles of variety of shapes of amino acid residues and hydrophobic interactions in the structure determination are discussed. The result provides a quantitative evidence for the viewpoint of the consistency principle the unique native state structure is realized by various interaction terms working together consistently. Mechanism of sequence determination of protein native state three-dimensional structures is studied by new theoretical models. This is a strong manifestation of the consistency principle: The sequence-specific native structure of protein is realized as a result of consistency of various types of interactions working in protein. However, when this weak cube attribute is compounded to that of the original snake cube puzzle, the power is enhanced very effectively. By comparing the results obtained for the three versions of models, we conclude that the power of the hydrophobic interactions to make the folded structure unique to the sequence is much weaker than the geometrical varieties of constituent cubes as modelled in the original snake cube puzzle. Even among foldable sequences, the structures folded into the compact 3×3×3 cube are found often not uniquely determined from the sequence. In all three versions, out of all possible sequences, only a limited fraction of sequences are found foldable into the compact cube. The aim of the puzzles is to fold the cube array into a compact 3×3×3 cubic structure. Each of the three versions is characterized by the respective set of characteristics attributed to each of its constituent cubes and an array is characterized by its specific sequence of the cube characteristics. The snake cube puzzle made of a linear array of 27 cubes and its modified and extended versions are used as theoretical models to study the mechanism of folding of proteins into their sequence-specific native three-dimensional structures.
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