Kiryu hexose and pentose matrix: A comprehensive model of epimers, structures, and C-1/C-6 inversion products for hexoses and pentoses.

Various methods have been proposed to memorize the structures of hexoses and pentoses, but none have been widely accepted. Hexoses are classified into four types based on two factors: (1) the combination of hydroxyl group orientations at positions C-2 and C-5, and (2) the symmetry of hydroxyl group orientations from C-2 to C-5. These four types were visualized in a four-part matrix referred to as the "Kiryu Hexose Matrix." This matrix enables the easy and comprehensive identification of the epimeric relationships among aldohexoses and ketohexoses. Furthermore, the matrix can identify hexoses with multiple epimerized hydroxyl groups. This matrix facilitates the derivation of all aldohexose structures based on differences from d- and l-allose, whose C-2 to C-5 hydroxyl groups face right or left, respectively. Ketohexose structures can also be derived. Aldose derivatives with identical functional groups at both ends, such as sugar alcohols, form a synonym pair, which can also be systematically identified using the matrix. Similarly, a corresponding matrix, the "Kiryu Pentose Matrix," can be constructed. By combining Izumoring, a comprehensive diagram of hexose transformations, with the hexose matrix, we were able to incorporate an epimerization-induced model. This model is called the "Izumori-Kiryu matrix." Additionally, we propose a new representation for saccharides using matrices, called the δ/λ-representation. The method easily represents complex saccharide structures with multiple synonyms and comprehensively identifies all synonyms without omission.