On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased; author's version of the published pape

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Bafilomycin A1 activates respiration of neuronal cells via uncoupling associated with flickering depolarization of mitochondria

Bafilomycin A1 (Baf) induces an elevation of cytosolic Ca2+ and acidification in neuronal cells via inhibition of the V-ATPase. Also, Baf uncouples mitochondria in differentiated PC12 (dPC12), dSH-SY5Y cells and cerebellar granule neurons, and markedly elevates their respiration. This respiratory response in dPC12 is accompanied by morphological changes in the mitochondria and decreases the mitochondrial pH, Ca2+ and ΔΨm. The response to Baf is regulated by cytosolic Ca2+ fluxes from the endoplasmic reticulum. Inhibition of permeability transition pore opening increases the depolarizing effect of Baf on the ΔΨm. Baf induces stochastic flickering of the ΔΨm with a period of 20 ± 10 s. Under conditions of suppressed ATP production by glycolysis, oxidative phosphorylation impaired by Baf does not provide cells with sufficient ATP levels. Cells treated with Baf become more susceptible to excitation with KCl. Such mitochondrial uncoupling may play a role in a number of (patho)physiological conditions induced by Baf

Compound heterozygous <em>SPATA5</em> variants in four families and functional studies of SPATA5 deficiency.

Variants in the SPATA5 gene were recently described in a cohort of patients with global developmental delay, sensorineural hearing loss, seizures, cortical visual impairment and microcephaly. SPATA5 protein localizes predominantly in the mitochondria and is proposed to be involved in mitochondrial function and brain developmental processes. However no functional studies have been performed. This study describes five patients with psychomotor developmental delay, microcephaly, epilepsy and hearing impairment, who were thought clinically to have a mitochondrial disease with subsequent whole-exome sequencing analysis detecting compound heterozygous variants in the SPATA5 gene. A summary of clinical data of all the SPATA5 patients reported in the literature confirms the characteristic phenotype. To assess SPATA5&#39; s role in mitochondrial dynamics, functional studies were performed on rat cortical neurons. SPATA5-deficient neurons had a significant imbalance in the mitochondrial fusion-fission rate, impaired energy production and short axons. In conclusion, SPATA5 protein has an important role in mitochondrial dynamics and axonal growth. Biallelic variants in the SPATA5 gene can affect mitochondria in cortical neurons and should be considered in patients with a neurodegenerative disorder and/or with clinical presentation resembling a mitochondrial disorder