Conflict between Translation Initiation and Elongation in Vertebrate Mitochondrial Genomes

The strand-biased mutation spectrum in vertebrate mitochondrial genomes results in an AC-rich L-strand and a GT-rich H-strand. Because the L-strand is the sense strand of 12 protein-coding genes out of the 13, the third codon position is overall strongly AC-biased. The wobble site of the anticodon of the 22 mitochondrial tRNAs is either U or G to pair with the most abundant synonymous codon, with only one exception. The wobble site of Met-tRNA is C instead of U, forming the Watson-Crick match with AUG instead of AUA, the latter being much more frequent than the former. This has been attributed to a compromise between translation initiation and elongation; i.e., AUG is not only a methionine codon, but also an initiation codon, and an anticodon matching AUG will increase the initiation rate. However, such an anticodon would impose selection against the use of AUA codons because AUA needs to be wobble-translated. According to this translation conflict hypothesis, AUA should be used relatively less frequently compared to UUA in the UUR codon family. A comprehensive analysis of mitochondrial genomes from a variety of vertebrate species revealed a general deficiency of AUA codons relative to UUA codons. In contrast, urochordate mitochondrial genomes with two tRNA(Met) genes with CAU and UAU anticodons exhibit increased AUA codon usage. Furthermore, six bivalve mitochondrial genomes with both of their tRNA-Met genes with a CAU anticodon have reduced AUA usage relative to three other bivalve mitochondrial genomes with one of their two tRNA-Met genes having a CAU anticodon and the other having a UAU anticodon. We conclude that the translation conflict hypothesis is empirically supported, and our results highlight the fine details of selection in shaping molecular evolution

Caputo fractional approximation using positive sublinear operators

Here we consider the approximation of functions by sublinear positive operators with applications to a big variety of Max-Product operators under Caputo fractional differentiability. Our study is based on our general fractional results about positive sublinear operators. We produce Jackson type inequalities under simple initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of fractional derivative of the function under approximation. It follows Anastassiou, Caputo fractional approximation by sublinear operators (2017, submitted) [4]

Choquet Integral Analytical Type Inequalities

Based on an amazing result of Sugeno [16], we are able to transfer classic analytic integral inequalities to Choquet integral setting. We give Choquet integral inequalities of the following types: fractional-Polya, Ostrowski, fractional Ostrowski, Hermite–Hadamard, Simpson and Iyengar. We provide several examples for the involved distorted Lebesgue measure. See also [5]