The inevitability of the bio-molecules: Five nitrogenous bases and twenty amino acids

Living beings meta-stable between unstable and neutral-stable conditions use only five types of nitrogenous bases and twenty amino acids selected naturally. The unified momentum theory derived at the triple point of the deterministic Boltzmann equation, the stochastic Langevin equation, and the indeterminacy principle [K. naitoh, Artificial Life Robotics, 2010] reveals the reason why the molecular weights of the twenty types of amino acids show a threefold variation between 240 of cysteine as the maximum and 75 of glycine as the minimum, whereas that of purines and pyrimidines among nitrogenous bases varies by only about 1.5 times, although the variation principle for the energy conservation law cannot do so. Let us take a higher order of the Taylor series for the unified momentum equation describing the deformation motions of biological molecules. Even-numbered terms such as the second and fourth ones show no other quasi-stable size ratios. However, odd-numbered terms result in other quasi-stable ratios. The threefold variation of amino acids will come from the third term of the Taylor series.