Positive Invariance for Linear Sampled-data Systems

Abstract: The sampled-data framework captures conventional sampled-data systems, and it also provides an adequate representational tool for contemporary cyber-physical and smart autonomous systems. One of the major concerns for analysis and synthesis of such systems is safe operation under constraints. This paper contributes to resolving this cornerstone aspect by focusing on related positive invariance notions within sampled-data setting. More specifically, we introduce generalized positive invariance notions that are topologically compatible with sampled-data framework and that overcome inevitable conservatism of the classical positive invariance notions. We propose exact generalized positive invariance and complement it with the guaranteed generalized positive invariance. The former notion is topologically nonconservative, while the latter notion is approximate and guaranteed but it leads to finitely parameterizable and practically computable generalized positively invariant sets. The limiting behaviour and computational aspects are also discussed, and an example illustrating the proposed notions is provided. Keywords:. Positive Invariance, Constrained Systems, Linear Sampled-data Dynamical Systems. Positive Invariance, Constrained Systems, Linear Sampled-data Dynamical Systems

Reachability and Invariance for Linear Sampled-data Systems

Abstract: We consider linear sampled-data dynamical systems subject to additive and bounded disturbances, and study properties of their forward and backward reach sets as well as robust positively invariant sets. We propose topologically compatible notions for the sampled-data forward and backward reachability as well as robust positive invariance. We also propose adequate notions for maximality and minimality of related robust positively invariant sets.Keywords: Reachability Analysis, Robust Positive Invariance, Sampled-data Systems

Reach and Robust Positively Invariant Sets Revisited

Abstract: This paper considers linear dynamical systems subject to additive and bounded disturbances, and studies properties of their forward reach, robust positively invariant (RPI) and the minimal RPI sets. The analysis is carried out for discrete-time (DT), continuous-time (CT), and sampled-data (SD) systems from a unified perspective. In the DT and CT cases, we review key existing results, while for the SD case novel results that reveal substantial structural differences to the DT and CT cases are presented. In particular, the main topological and computational properties associated with the DT and CT forward reach and RPI sets fail to be directly applicable to SD systems. In light of this, we introduce and develop topologically compatible notions for the SD forward reach, RPI and mRPI sets. We address and enhance computational aspects associated with these sets by complementing them with approximate, but guaranteed, and numerically more plausible notions.Keywords: Forward Reachability, Forward Reach Sets, Robust Positive Invariance, Robust Positively Invariant Sets, Minimal Robust Positively Invariant Sets, Bounded Disturbances, Discrete-Time, Continuous-Time, Sampled-data

Mutant Parkin Impairs Mitochondrial Function and Morphology in Human Fibroblasts

Background: Mutations in Parkin are the most common cause of autosomal recessive Parkinson disease (PD). The mitochondrially localized E3 ubiquitin-protein ligase Parkin has been reported to be involved in respiratory chain function and mitochondrial dynamics. More recent publications also described a link between Parkin and mitophagy.Methodology/Principal Findings: In this study, we investigated the impact of Parkin mutations on mitochondrial function and morphology in a human cellular model. Fibroblasts were obtained from three members of an Italian PD family with two mutations in Parkin (homozygous c.1072delT, homozygous delEx7, compound-heterozygous c.1072delT/delEx7), as well as from two relatives without mutations. Furthermore, three unrelated compound-heterozygous patients (delEx3-4/duplEx7-12, delEx4/c.924C>T and delEx1/c.924C>T) and three unrelated age-matched controls were included. Fibroblasts were cultured under basal or paraquat-induced oxidative stress conditions. ATP synthesis rates and cellular levels were detected luminometrically. Activities of complexes I-IV and citrate synthase were measured spectrophotometrically in mitochondrial preparations or cell lysates. The mitochondrial membrane potential was measured with 5,5',6,6'-tetrachloro-1,1',3,3'-tetraethylbenzimidazolylcarbocyanine iodide. Oxidative stress levels were investigated with the OxyBlot technique. The mitochondrial network was investigated immunocytochemically and the degree of branching was determined with image processing methods. We observed a decrease in the production and overall concentration of ATP coinciding with increased mitochondrial mass in Parkin-mutant fibroblasts. After an oxidative insult, the membrane potential decreased in patient cells but not in controls. We further determined higher levels of oxidized proteins in the mutants both under basal and stress conditions. The degree of mitochondrial network branching was comparable in mutants and controls under basal conditions and decreased to a similar extent under paraquat-induced stress.Conclusions: Our results indicate that Parkin mutations cause abnormal mitochondrial function and morphology in non-neuronal human cells

Selective inhibitors of cardiac ADPR cyclase as novel anti-arrhythmic compounds

ADP-ribosyl cyclases (ADPRCs) catalyse the conversion of nicotinamide adenine dinucleotide to cyclic adenosine diphosphoribose (cADPR) which is a second messenger involved in Ca2+ mobilisation from intracellular stores. Via its interaction with the ryanodine receptor Ca2+ channel in the heart, cADPR may exert arrhythmogenic activity. To test this hypothesis, we have studied the effect of novel cardiac ADPRC inhibitors in vitro and in vivo in models of ventricular arrhythmias. Using a high-throughput screening approach on cardiac sarcoplasmic reticulum membranes isolated from pig and rat and nicotinamide hypoxanthine dinuleotide as a surrogate substrate, we have identified potent and selective inhibitors of an intracellular, membrane-bound cardiac ADPRC that are different from the two known mammalian ADPRCs, CD38 and CD157/Bst1. We show that two structurally distinct cardiac ADPRC inhibitors, SAN2589 and SAN4825, prevent the formation of spontaneous action potentials in guinea pig papillary muscle in vitro and that compound SAN4825 is active in vivo in delaying ventricular fibrillation and cardiac arrest in a guinea pig model of Ca2+ overload-induced arrhythmia. Inhibition of cardiac ADPRC prevents Ca2+ overload-induced spontaneous depolarizations and ventricular fibrillation and may thus provide a novel therapeutic principle for the treatment of cardiac arrhythmias

Aberrant Cyclization Affords a C-6 Modified Cyclic Adenosine 5′-Diphosphoribose Analogue with Biological Activity in Jurkat T Cells

*S Supporting Information ABSTRACT: Two nicotinamide adenine dinucleotide (NAD +) analogues modified at the 6 position of the purine ring were synthesized, and their substrate properties toward Aplysia californica ADP-ribosyl cyclase were investigated. 6-N-Methyl NAD + (6-N-methyl nicotinamide adenosine 5′-dinucleotide 10) hydrolyzes to give the linear 6-N-methyl ADPR (adenosine 5′-diphosphoribose, 11), whereas 6-thio NHD + (nicotinamide 6-mercaptopurine 5′-dinucleotide, 17) generates a cyclic dinucleotide. Surprisingly, NMR correlation spectra confirm this compound to be the N1 cyclic product 6-thio N1-cIDPR (6-thio cyclic inosine 5′-diphosphoribose, 3), although the corresponding 6-oxo analogue is well-known to cyclize at N7. In Jurkat T cells, unlike the parent cyclic inosine 5′-diphosphoribose N1-cIDPR 2, 6-thio N1-cIDPR antagonizes both cADPR- and N1cIDPR-induced Ca 2+ release but possesses weak agonist activity at higher concentration. 3 is thus identified as the first C-6 modified cADPR (cyclic adenosine 5′-diphosphoribose) analogue antagonist; it represents the first example of a fluorescent N1cyclized cADPR analogue and is a new pharmacological tool for intervention in the cADPR pathway of cellular signaling