Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow

The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.Comment: 23 pages, no figures. Completely revised and improved version of dg-ga/970301

The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

GABA, glutamine, glutamate oxidation and succinic semialdehyde dehydrogenase expression in human gliomas

Bioenergetic characterisation of malignant tissues revealed that different tumour cells can catabolise multiple substrates as salvage pathways, in response to metabolic stress. Altered metabolism in gliomas has received a lot of attention, especially in relation to IDH mutations, and the associated oncometabolite D-2-hydroxyglutarate (2-HG) that impact on metabolism, epigenetics and redox status. Astrocytomas and oligodendrogliomas, collectively called diffuse gliomas, are derived from astrocytes and oligodendrocytes that are in metabolic symbiosis with neurons; astrocytes can catabolise neuron-derived glutamate and gamma-aminobutyric acid (GABA) for supporting and regulating neuronal functions.Metabolic characteristics of human glioma cell models - including mitochondrial function, glycolytic pathway and energy substrate oxidation - in relation to IDH mutation status and after 2-HG incubation were studied to understand the Janus-faced role of IDH1 mutations in the progression of gliomas/astrocytomas. The metabolic and bioenergetic features were identified in glioma cells using wild-type and genetically engineered IDH1-mutant glioblastoma cell lines by metabolic analyses with Seahorse, protein expression studies and liquid chromatography-mass spectrometry.U251 glioma cells were characterised by high levels of glutamine, glutamate and GABA oxidation. Succinic semialdehyde dehydrogenase (SSADH) expression was correlated to GABA oxidation. GABA addition to glioma cells increased proliferation rates. Expression of mutated IDH1 and treatment with 2-HG reduced glutamine and GABA oxidation, diminished the pro-proliferative effect of GABA in SSADH expressing cells. SSADH protein overexpression was found in almost all studied human cases with no significant association between SSADH expression and clinicopathological parameters (e.g. IDH mutation).Our findings demonstrate that SSADH expression may participate in the oxidation and/or consumption of GABA in gliomas, furthermore, GABA oxidation capacity may contribute to proliferation and worse prognosis of gliomas. Moreover, IDH mutation and 2-HG production inhibit GABA oxidation in glioma cells. Based on these data, GABA oxidation and SSADH activity could be additional therapeutic targets in gliomas/glioblastomas