Evolution based on genome structure: the “diagonal genome universe”

The ratios of amino acid to the total amino acids and those of nucleotides to the total nucleotides in genes or genomes are suitable indexes to compare whole gene or genome characteristics based on the large number of nucleotides rather than their sequences. As these ratios are strictly calculated from nucleotide sequences, the values are independent of experimental errors. In the present mini-review, the following themes are approached according to the ratios of amino acids and nucleotides to their total numbers in the genome: prebiotic evolution, the chronological precedence of protein and codon formations, genome evolution, Chargaff’s second pa- rity rule, and the origins of life. Amino acid formation might have initially occurred during pre- biotic evolution, the “amino acid world”, and amino acid polymerization might chronologically precede codon formation at the end of prebiotic evolution. All nucleotide alterations occurred synchronously over the genome during biolo- gical evolution. After establishing primitive lives, all nucleotide alterations have been governed by linear formulae in nuclear and organelle genomes consisting of the double-stranded DNA. When the four nucleotide contents against each individual nucleotide content in organelles are expressed by four linear regression lines representing the diagonal lines of a 0.5 square – the “Diagonal Genome Universe”, evolution obeys Chargaff’s second parity rule. The fact that linear regression lines intersect at a single point su- ggests that all species originated from a single life source.

Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula

A systematic analysis on experimental data of the half-lives of nuclear double-β decays with two neutrinos(2vββ)is performed based on the analytical formula proposed by Primakoff and Rosen.We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor.This improved formula can closely describe all available experimental half-lives of 2vβ^(-)β^(-)decays,both for ground-state transitions and transitions from ground states of parent nuclei to the first 0+excited states of daughter nuclei.The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an aver-age factor of 2.3.Further predictions are provided for 2vββ-decay candidates with decay energies above 0.5 MeV.We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double-β transitions between the ground state of 48Ca,76 Ge,and 136Xe and the first 0+excited states of their corresponding daughter nuclei,which will be very useful for understanding the underlying mechanisms of double-β decays and for further studying the shell effects on nuclear transition matrix elements.