A simple model of short-range interactions II. The orientation dependence of the interaction between non-bonded hydrogen atoms

The simple model of short-range interactions described in the preceding paper has been applied to the study of the orientation dependence of the interaction between the non-bonded hydrogen atoms of two CH fragments. Calculation shows that for the same interatomic distance the interaction energy between non-bonded hydrogen atoms is strongly dependent on the relative orientation of the two bonds even for large values ofR.     

Mouse brain expression patterns of <Emphasis Type="Italic">Spg7</Emphasis>, <Emphasis Type="Italic">Afg3l1</Emphasis>, and <Emphasis Type="Italic">Afg3l2</Emphasis> transcripts,encoding for the mitochondrial <Emphasis Type="Italic">m</Emphasis>-AAA protease

Background  

The m-AAA (ATPases Associated with a variety of cellular Activities) is an evolutionary conserved metalloprotease complex located in the internal mitochondrial membrane. In the mouse, it is a hetero-oligomer variably formed by the Spg7, Afg3l1, and Afg3l2 encoded proteins, or a homo-oligomer formed by either Afg3l1 or Afg3l2. In humans, AFG3L2 and SPG7 genes are conserved, whereas AFG3L1 became a pseudogene. Both AFG3L2 and SPG7 are involved in a neurodegenerative disease, namely the autosomal dominant spinocerebellar ataxia SCA28 and a recessive form of spastic paraplegia, respectively.     

Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling

We consider the boundary value problem where Ω is a smooth and bounded domain in ℝ² and λ > 0. We prove that for any integer k ≧ 1 there exist at least two solutions u _λ with the property that the boundary flux satisfies up to subsequences λ → 0, where the ξ _j are points of ∂Ω ordered clockwise in j.     

A ketogenic diet increases succinic dehydrogenase (SDH) activity and recovers age-related decrease in numeric density of SDH-positive mitochondria in cerebellar Purkinje cells of late-adult rats

Ketogenic diets (KDs) have been applied in the therapy of paediatric epilepsy for nearly a century. Recently, beneficial results have also been reported on metabolic disorders and neurodegeneration, designating aged individuals as possible recipients. However, KDs efficacy decrease after the suckling period, and very little is known about their impact on the aging brain. In the present study, the effect on the neuronal energetic supply of a KD containing 20% of medium chain triglycerides (MCT) was investigated in Purkinje cells of the cerebellar vermis of late-adult (19-month-old) rats. The animals were fed with the KD for 8 weeks, and succinic dehydrogenase (SDH) activity was cytochemically determined. The following parameters of SDH-positive mitochondria were evaluated by the use of a computer-assisted image analysis system connected to a transmission electron microscope: numeric density (Nv), average volume (V), volume density (Vv), and cytochemical precipitate area/mitochondrial area (R). Young, age-matched, and old animals fed with a standard chow were used as controls. We found significantly higher Nv in MCT-KD-fed rats vs. all the control groups, in young vs. late-adult and old controls, and in late-adult vs. old controls. V and Vv showed no significant differences among the groups. R was significantly higher in MCT-KD-fed rats vs. all the control animals, and in old vs. young and late-adult controls. Present data indicate that the ketogenic treatment counteracted age-related decrease in numeric density of SDH-positive mitochondria, and enhanced their metabolic efficiency. Given the central role of mitochondrial impairment in age-related physio-pathological changes of the brain, these findings may represent a starting point to examine novel potentialities for KDs.     

Multispike solutions for the Brezis–Nirenberg problem in dimension three

We consider the problem $\mathrm{\Delta }u+\lambda u+u^5=0$, $u>0$, in a smooth bounded domain Ω in ${\mathbb{R}}^3$, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value ${\lambda }_0$, which we characterize in terms of the Green function of $?\mathrm{\Delta }?\lambda$.