Perturbed Rotations of a Rigid Body Close to the Lagrange Case under the Action of Unsteady Perturbation Torques

Perturbed rotations of a rigid body close to the Lagrange case under the action of perturbation torques slowly varying in time are investigated. Conditions are presented for the possibility of averaging the equations of motion with respect to the nutation angle and the averaged system of equations of motion is obtained. In the case of the rotational motion of the body in the linear-dissipative medium the numerical integration of the averaged system of equations is conducted

NADPH oxidases in Parkinson’s disease: a systematic review

Abstract Parkinson’s disease (PD) is a progressive movement neurodegenerative disease associated with a loss of dopaminergic neurons in the substantia nigra of the brain. Oxidative stress, a condition that occurs due to imbalance in oxidant and antioxidant status, is thought to play an important role in dopaminergic neurotoxicity. Nicotinamide adenine dinucleotide phosphate (NADPH) oxidases are multi-subunit enzymatic complexes that generate reactive oxygen species as their primary function. Increased immunoreactivities for the NADPH oxidases catalytic subunits Nox1, Nox2 and Nox4 have been reported in the brain of PD patients. Furthermore, knockout or genetic inactivation of NADPH oxidases exert a neuroprotective effect and reduce detrimental aspects of pathology in experimental models of the disease. However, the connections between NADPH oxidases and the biological processes believed to contribute to neuronal death are not well known. This review provides a comprehensive summary of our current understanding about expression and physiological function of NADPH oxidases in neurons, microglia and astrocytes and their pathophysiological roles in PD. It summarizes the findings supporting the role of both microglial and neuronal NADPH oxidases in cellular disturbances associated with PD such as neuroinflammation, alpha-synuclein accumulation, mitochondrial and synaptic dysfunction or disruption of the autophagy-lysosome system. Furthermore, this review highlights different steps that are essential for NADPH oxidases enzymatic activity and pinpoints major obstacles to overcome for the development of effective NADPH oxidases inhibitors for PD