Old and new joint characterizations of leximin and variants of rank-weighted utilitarianism.

This paper proposes a new class of efficient and equitable social welfare orderings, a generalized leximin rule that includes rank-weighted utilitarianism, leximin, and their lexicographic compositions. While the famous Deschamps and Gevers' joint characterization theorem shows that a Paretian, anonymous, separable social welfare ordering must be either weak utilitarianism, leximin, or leximax under the assumption of cardinal full comparability, this study provides a new joint characterization theorem in which imposing rank-separability, instead of separability, enables acceptable social welfare ordering to be the generalized leximin rule. This result is proven by an intuitive and easy-to-understand method, which also helps show the mechanism by which a class of Paretian, anonymous, and separable social welfare orderings is limited to weak utilitarianism and leximin.

Polar-localized NPH3-like proteins regulate polarity and endocytosis of PIN-FORMED auxin efflux carriers.

PIN-FORMED (PIN)-dependent auxin transport is essential for plant development and its modulation in response to the environment or endogenous signals. A NON-PHOTOTROPIC HYPOCOTYL 3 (NPH3)-like protein, MACCHI-BOU 4 (MAB4), has been shown to control PIN1 localization during organ formation, but its contribution is limited. The Arabidopsis genome contains four genes, MAB4/ENP/NPY1-LIKE1 (MEL1), MEL2, MEL3 and MEL4, highly homologous to MAB4. Genetic analysis disclosed functional redundancy between MAB4 and MEL genes in regulation of not only organ formation but also of root gravitropism, revealing that NPH3 family proteins have a wider range of functions than previously suspected. Multiple mutants showed severe reduction in PIN abundance and PIN polar localization, leading to defective expression of an auxin responsive marker DR5rev::GFP. Pharmacological analyses and fluorescence recovery after photo-bleaching experiments showed that mel mutations increase PIN2 internalization from the plasma membrane, but affect neither intracellular PIN2 trafficking nor PIN2 lateral diffusion at the plasma membrane. Notably, all MAB4 subfamily proteins show polar localization at the cell periphery in plants. The MAB4 polarity was almost identical to PIN polarity. Our results suggest that the MAB4 subfamily proteins specifically retain PIN proteins in a polarized manner at the plasma membrane, thus controlling directional auxin transport and plant development.