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 $\alpha$ 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

THE ROLE OF PUBLIC ORGANIZATIONS IN THE ORGANIZATION OF MEDICAL CARE: ACCORDING TO A SURVEY OF PARENTS OF CHILDREN SUFFERING FROM ORPHAN DISEASES

The activities of public patient organizations are multifaceted: providing legal support to patients in order to protect their legal rights; information and educational work, conducting “schools”, providing specific types of assistance that can provide those involved in the problem. Public patient organizations are the “voice” of all patients with orphan diseases in solving their problems at the level of the highest echelons of power. From 2016-2017 years in the Reference center of congenital hereditary diseases, genetic disorders, orphan and other rare diseases of GBUZ “Morozovskaya DGKB DZM” on a specially designed questionnaire conducted a sociological study on awareness of parents of children suffering ABOUT the public patient organizations. Public organizations provide information and legal support, contact with pharmaceutical companies, participate in solving the problems of patients at the state level. Taking into account the rights and opportunities of public associations, it is necessary for doctors to inform parents about the existence of charitable organizations and their involvement in public patient organizations, as well as to participate in the work of health schools for parents

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Adsorption of cis-dichlorodiammineplatinum by nanostructures based on single-domain magnetite

Magnetosensitive nanocomposites on the basis of monodomain magnetite Fe3O4/meso-2,3-dimercaptosuccinic acid, Fe3O4/c-aminopropyltriethoxysilane, Fe3O4/polyacrylamide, Fe3O4/hydroxyapatite were synthesized. Size distribution of magnetite nanoparticles in ensemble and their magnetic properties were studied. It has been shown that the magnetization curve of the liquid containing monodomain magnetite has a form that is characteristic for superparamagnetics, and its calculations in the framework of Langeven’s paramagnetism theory match satisfactorily to the experimental results. The highest adsorption parameters were observed for magnetosensitive nanocomposites Fe3O4/ polyacrylamide and Fe3O4/c-aminopropyltriethoxysilane. Prospects of the studied nanostructures for medicobiological and technical applications as adsorbents of cis-dichlorodiammineplatinum were shown