Mitochondrial contribution to Parkinson's disease pathogenesis

The identification of the etiologies and pathogenesis of Parkinson's disease (PD) should play an important role in enabling the development of novel treatment strategies to prevent or slow the progression of the disease. The last few years have seen enormous progress in this respect. Abnormalities of mitochondrial function and increased free radical mediated damage were described in post mortem PD brain before the first gene mutations causing familial PD were published. Several genetic causes are now known to induce loss of dopaminergic cells and parkinsonism, and study of the mechanisms by which these mutations produce this effect has provided important insights into the pathogenesis of PD and confirmed mitochondrial dysfunction and oxidative stress pathways as central to PD pathogenesis. Abnormalities of protein metabolism including protein mis-folding and aggregation are also crucial to the pathology of PD. Genetic causes of PD have specifically highlighted the importance of mitochondrial dysfunction to PD: PINK1, parkin, DJ-1 and most recently alpha-synuclein proteins have been shown to localise to mitochondria and influence function. The turnover of mitochondria by autophagy (mitophagy) has also become a focus of attention. This review summarises recent discoveries in the contribution of mitochondrial abnormalities to PD etiology and pathogenesis

An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

The cotangent bundle $T^*X$ to a complex manifold $X$ is classically endowed with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where \cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X] as a subalgebra and an extra central parameter $t$. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If $P$ is any section of order zero of \W[T^*X], we show that \exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page

The biochemical basis of interactions between Glucocerebrosidase and alpha‐synuclein in GBA1 mutation carriers

The discovery of genes involved in familial as well as sporadic forms of Parkinson disease (PD) constitutes an important milestone in understanding this disorder's pathophysiology and potential treatment. Among these genes, GBA1 is one of the most common and well-studied, but it is still unclear how mutations in GBA1 translate into an increased risk for developing PD. In this review, we provide an overview of the biochemical and structural relationship between GBA1 and PD to help understand the recent advances in the development of PD therapies intended to target this pathway

Targeting the GBA1 pathway to slow Parkinson disease: Insights into clinical aspects, pathogenic mechanisms and new therapeutic avenues

The GBA1 gene encodes the lysosomal enzyme glucocerebrosidase (GCase), which is involved in sphingolipid metabolism. Biallelic variants in GBA1 cause Gaucher disease (GD), a lysosomal storage disorder characterised by loss of GCase activity and aberrant intracellular accumulation of GCase substrates. Carriers of GBA1 variants have an increased risk of developing Parkinson disease (PD), with odds ratio ranging from 2.2 to 30 according to variant severity. GBA1 variants which do not cause GD in homozygosis can also increase PD risk. Patients with PD carrying GBA1 variants show a more rapidly progressive phenotype compared to non-carriers, emphasising the need for disease modifying treatments targeting the GBA1 pathway. Several mechanisms secondary to GCase dysfunction are potentially responsible for the pathological changes leading to PD. Misfolded GCase proteins induce endoplasmic reticulum stress and subsequent unfolded protein response and impair the autophagy-lysosomal pathway. This results in α-synuclein accumulation and spread, and promotes neurodegenerative changes. Preclinical evidence also shows that products of GCase activity can promote accumulation of α-synuclein, however there is no convincing evidence of substrate accumulation in GBA1-PD brains. Altered lipid homeostasis secondary to loss of GCase activity could also contribute to PD pathology. Treatments that target the GBA1 pathway could reverse these pathological processes and halt/slow the progression of PD. These range from augmentation of GCase activity via GBA1 gene therapy, restoration of normal intracellular GCase trafficking via molecular chaperones, and substrate reduction therapy. This review discusses the pathways associated with GBA1-PD and related novel GBA1-targeted interventions for PD treatment

Who is at Risk of Parkinson Disease? Refining the Preclinical Phase of GBA1 and LRRK2 Variant Carriers: a Clinical, Biochemical, and Imaging Approach

Purpose of Review: Genetic variants in GBA1 and LRRK2 genes are the commonest genetic risk factor for Parkinson disease (PD); however, the preclinical profile of GBA1 and LRRK2 variant carriers who will develop PD is unclear. This review aims to highlight the more sensitive markers that can stratify PD risk in non-manifesting GBA1 and LRRK2 variant carriers. Recent Findings: Several case–control and a few longitudinal studies evaluated clinical, biochemical, and neuroimaging markers within cohorts of non-manifesting carriers of GBA1 and LRRK2 variants. Summary: Despite similar levels of penetrance of PD in GBA1 and LRRK2 variant carriers (10–30%), these individuals have distinct preclinical profiles. GBA1 variant carriers at higher risk of PD can present with prodromal symptoms suggestive of PD (hyposmia), display increased α-synuclein levels in peripheral blood mononuclear cells, and show dopamine transporter abnormalities. LRRK2 variant carriers at higher risk of PD might show subtle motor abnormalities, but no prodromal symptoms, higher exposure to some environmental factors (non-steroid anti-inflammatory drugs), and peripheral inflammatory profile. This information will help clinicians tailor appropriate screening tests and counseling and facilitate researchers in the development of predictive markers, disease-modifying treatments, and selection of healthy individuals who might benefit from preventive interventions

Structural and Compositional Changes in Aging Bone: Osteopenia in Lumbar Vertebrae of Wistar Female Rats

Changes in vertebral bone mineral content and density during aging were quantified in female Wistar rats. This study represents a longitudinal follow up utilizing single photon absorptiometry for the measurement of bone mineral content (BMC), quantitative computed tomography (OCT) for the measurement of bone mineral density (BMD), and image analysis histomorphometry for the measurement of trabecular bone volume (TBV) and bone cortical area (BCA). The above measurements were accompanied by biochemical assays of calcium concentrations in the respective bones. All aging animals experienced significant decreases in BMC, BMD, TBV, BCA and in the calcium content of their bones. The above features have been further emphasized through the use of scanning electron micrographs showing the age-related structural changes in a three-dimentional fashion. New, advanced technologies will enable the quantitation of 3-dimensional images that are currently obtained from the scanning electron micrograph; thus will provide new consideration as related to trabecular bone compactness (density). Energy dispersive x-ray spectroscopy indicated that the nature of crystals in aging bones does not differ markedly from that encountered in young specimens. Data are also provided with regard to the health of the animals, and it became apparent that aging rats undergo changes in their kidneys yet do not show any significant change in renal functional parameters as measured in both the serum and the urine. Hence, new noninvasive methodologies are currently available for longitudinal studies related to the skeleton in laboratory animals enabling reliable monitoring of age-related and hormonally induced changes in bones (spine and hip) of well defined experimental models

Euler-Bessel and Euler-Fourier Transforms

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible \zed-valued functions to continuous $\real$-valued functions over a vector space. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the logarithmic blowup of the topological Fourier transform; and a novel Morse index formula for the transforms. We then apply the theory to problems of target reconstruction from enumerative sensor data, including localization and shape discrimination. This last application utilizes an extension of spatially variant apodization (SVA) to mitigate sidelobe phenomena