1,868 research outputs found
Cross sections for geodesic flows and \alpha-continued fractions
We adjust Arnoux's coding, in terms of regular continued fractions, of the
geodesic flow on the modular surface to give a cross section on which the
return map is a double cover of the natural extension for the \alpha-continued
fractions, for each in (0,1]. The argument is sufficiently robust to
apply to the Rosen continued fractions and their recently introduced
\alpha-variants.Comment: 20 pages, 2 figure
Monomeric Alpha-Synuclein Exerts a Physiological Role on Brain ATP Synthase
Misfolded α-synuclein is a key factor in the pathogenesis of Parkinson's disease (PD). However, knowledge about a physiological role for the native, unfolded α-synuclein is limited. Using brains of mice lacking α-, β-, and γ-synuclein, we report that extracellular monomeric α-synuclein enters neurons and localizes to mitochondria, interacts with ATP synthase subunit α, and modulates ATP synthase function. Using a combination of biochemical, live-cell imaging and mitochondrial respiration analysis, we found that brain mitochondria of α-, β-, and γ-synuclein knock-out mice are uncoupled, as characterized by increased mitochondrial respiration and reduced mitochondrial membrane potential. Furthermore, synuclein deficiency results in reduced ATP synthase efficiency and lower ATP levels. Exogenous application of low unfolded α-synuclein concentrations is able to increase the ATP synthase activity that rescues the mitochondrial phenotypes observed in synuclein deficiency. Overall, the data suggest that α-synuclein is a previously unrecognized physiological regulator of mitochondrial bioenergetics through its ability to interact with ATP synthase and increase its efficiency. This may be of particular importance in times of stress or PD mutations leading to energy depletion and neuronal cell toxicity.
SIGNIFICANCE STATEMENT: Misfolded α-synuclein aggregations in the form of Lewy bodies have been shown to be a pathological hallmark in histological staining of Parkinson's disease (PD) patient brains. It is known that misfolded α-synuclein is a key driver in PD pathogenesis, but the physiological role of unfolded monomeric α-synuclein remains unclear. Using neuronal cocultures and isolated brain mitochondria of α-, β-, and γ-synuclein knock-out mice and monomeric α-synuclein, this current study shows that α-synuclein in its unfolded monomeric form improves ATP synthase efficiency and mitochondrial function. The ability of monomeric α-synuclein to enhance ATP synthase efficiency under physiological conditions may be of importance when α-synuclein undergoes the misfolding and aggregation reported in PD
On the construction of generalized Grassmann representatives of state vectors
Generalized -graded Grassmann variables are used to label coherent
states related to the nilpotent representation of the q-oscillator of
Biedenharn and Macfarlane when the deformation parameter is a root of unity.
These states are then used to construct generalized Grassmann representatives
of state vectors.Comment: 8 page
Symmetry of bound and antibound states in the semiclassical limit
We consider one dimensional scattering and show how the presence of a mild
positive barrier separating the interaction region from infinity implies that
the bound and antibound states are symmetric modulo exponentially small errors
in 1/h. This simple result was inspired by a numerical experiment and we
describe the numerical scheme for an efficient computation of resonances in one
dimension
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