The inevitability of biological molecules connected by covalent and hydrogen bonds

A statistic fluid-dynamical model derived based on a quasi-stability concept and the indeterminacy principle extended from our previous reports (Naitoh, JJIAM, 2001, Artificial Life Robotics, 2010) reveals the magic numbers observed in various molecules connected by covalent and hydrogen bonds, although our previous model explains only those connected by hydrogen bonds. First, this model explains the reason why particles such as biological cells and nitrogenous bases have bimodal size ratios of 1:1 and about 2:3 between the golden and silver ratios. Next, a higher order of analysis also clarifies other asymmetric ratios, i.e., the super-magic number of about 1:3.5, 1:2.5, 1:2.1, 1:1.78, 1:1.35, and 1:1.27 in various systems including chromosomes, amino acids, and proteins.