The multivariate L1-median and associated data depth

This paper gives three related results: (i) a new, simple, fast, monotonically converging algorithm for deriving the L1-median of a data cloud in ℝd, a problem that can be traced to Fermat and has fascinated applied mathematicians for over three centuries; (ii) a new general definition for depth functions, as functions of multivariate medians, so that different definitions of medians will, correspondingly, give rise to different dept functions; and (iii) a simple closed-form formula of the L1-depth function for a given data cloud in ℝd.

Interaction between like-charged colloidal spheres in electrolyte solutions

How colloidal particles interact with each other is one of the key issues that determines our ability to interpret experimental results for phase transitions in colloidal dispersions and our ability to apply colloid science to various industrial processes. The long-accepted theories for answering this question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractive force between identical macroions in electrolyte solutions containing divalent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macroions in the presence of added salt ions for the conditions where the interacting macroion pair is not affected by any other macroions that may be in the solution. This attractive force follows from the internal-energy contribution of counterion mediation. Contrary to conventional expectations, for charged macroions in an electrolyte solution, the entropic force is repulsive at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin–Landau–Verwey–Overbeek theory and Sogami–Ise theory fail to describe the attractive interactions found in our simulations; the former predicts only repulsive interaction and the latter predicts a long-range attraction that is too weak and occurs at macroion separations that are too large. Our simulations provide fundamental “data” toward an improved theory for the potential of mean force as required for optimum design of new materials including those containing nanoparticles.

Mutation R120G in αB-crystallin, which is linked to a desmin-related myopathy, results in an irregular structure and defective chaperone-like function

αB-crystallin, a member of the small heat shock protein family, possesses chaperone-like function. Recently, it has been shown that a missense mutation in αB-crystallin, R120G, is genetically linked to a desmin-related myopathy as well as to cataracts [Vicart, P., Caron, A., Guicheney, P., Li, A., Prevost, M.-C., Faure, A., Chateau, D., Chapon, F., Tome, F., Dupret, J.-M., et al. (1998) Nat. Genet. 20, 92–95]. By using α-lactalbumin, alcohol dehydrogenase, and insulin as target proteins, in vitro assays indicated that R120G αB-crystallin had reduced or completely lost chaperone-like function. The addition of R120G αB-crystallin to unfolding α-lactalbumin enhanced the kinetics and extent of its aggregation. R120G αB-crystallin became entangled with unfolding α-lactalbumin and was a major portion of the resulting insoluble pellet. Similarly, incubation of R120G αB-crystallin with alcohol dehydrogenase and insulin also resulted in the presence of R120G αB-crystallin in the insoluble pellets. Far and near UV CD indicate that R120G αB-crystallin has decreased β-sheet secondary structure and an altered aromatic residue environment compared with wild-type αB-crystallin. The apparent molecular mass of R120G αB-crystallin, as determined by gel filtration chromatography, is 1.4 MDa, which is more than twice the molecular mass of wild-type αB-crystallin (650 kDa). Images obtained from cryoelectron microscopy indicate that R120G αB-crystallin possesses an irregular quaternary structure with an absence of a clear central cavity. The results of this study show, through biochemical analysis, that an altered structure and defective chaperone-like function of αB-crystallin are associated with a point mutation that leads to a desmin-related myopathy and cataracts.

Increased mitochondrial oxidative stress in the Sod2 (+/−) mouse results in the age-related decline of mitochondrial function culminating in increased apoptosis

To determine the importance of mitochondrial reactive oxygen species toxicity in aging and senescence, we analyzed changes in mitochondrial function with age in mice with partial or complete deficiencies in the mitochondrial antioxidant enzyme manganese superoxide dismutase (MnSOD). Liver mitochondria from homozygous mutant mice, with a complete deficiency in MnSOD, exhibited substantial respiration inhibition and marked sensitization of the mitochondrial permeability transition pore. Mitochondria from heterozygous mice, with a partial deficiency in MnSOD, showed evidence of increased proton leak, inhibition of respiration, and early and rapid accumulation of mitochondrial oxidative damage. Furthermore, chronic oxidative stress in the heterozygous mice resulted in an increased sensitization of the mitochondrial permeability transition pore and the premature induction of apoptosis, which presumably eliminates the cells with damaged mitochondria. Mice with normal MnSOD levels show the same age-related mitochondrial decline as the heterozygotes but occurring later in life. The premature decline in mitochondrial function in the heterozygote was associated with the compensatory up-regulation of oxidative phosphorylation enzyme activity. Thus mitochondrial reactive oxygen species production, oxidative stress, functional decline, and the initiation of apoptosis appear to be central components of the aging process.