Relaxation of Selective Constraint on the Ultra-Large Mitochondrial Genomes of Arcidae (Mollusca: Bivalvia)

The mitochondrial genomes(mitogenomes)are purportedly under selection for smaller size to improve their replica-tion and translation efficiency.However,the mitogenomes of Arcidae species are larger than those of other bivalves,and are among the largest metazoan mitogenomes reported to date.In order to explore the differences of base composition and selective constraints between the large and small mitogenomes,we compared the mitogenomes of 9 large arcid mitogenomes and 77 small bivalves mitogenomes.Base composition analyses indicated that Arcidae mitogenomes have significantly greater GC skews in both their whole genomes and coding sequences.This result suggests that the replication of the large mitogenomes in Arcidae may be slower than those in other bivalves,exposing the parental strand to deamination for a longer time.Selection pressure analyses showed that the mitochondrial protein-coding genes of Arcidae species have significantly higher Ka/Ks ratios than other bivalves,suggesting that they have accumulated more nonsynonymous nucleotide substitutions.Seven protein-coding genes(atp6,cox1-3,nad1,nad4 and nad5)show significant difference for Ka/Ks ratios between the Arcidae and non-Arcidae groups.However,these divergences are not observed in the nuclear gene within histone H3.From these observations,we concluded that the large mitoge-nomes of Arcidae species experienced more relaxed selective constraints.As some Arcidae species are more tolerant to hypoxia that can lead to low metabolic rate,the relaxed selective constraints of mitogenomes may be energy-related.This study provides new insights into the evolution of Arcidae mitogenomes.

The Rolling Wheel Equations without Magic: A Combined Slip-Stiction Approach by the Udwadia-Kalaba Formulation with Constraints Relaxation for a Smooth Simulation

The Udwadia-Kalaba formulation is proposed to model the dynamics of the rolling wheel. A unified approach that addresses both the slip and the stiction in the contact section is considered. Purely rolling constraints are associated with stiction and are suitably lifted as slip occurs. An extended formulation for the Uwadia-Kalaba equations of motion is introduced for that matter. It resorts to the weighted minimum norm and the weighted semi-least-squares solutions of the constraints equations. This not only allows a bias on constraints, by an appropriate description of weight functions based on friction, it also leads to a smooth activation or deactivation of selected constraints without rewriting the equations of motion or upsetting their numerical integration.