First- and second-order necessary conditions with respect to components for discrete optimal control problems

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly

Annexin A1 Deficiency does not Affect Myofiber Repair but Delays Regeneration of Injured Muscles.

Repair and regeneration of the injured skeletal myofiber involves fusion of intracellular vesicles with sarcolemma and fusion of the muscle progenitor cells respectively. In vitro experiments have identified involvement of Annexin A1 (Anx A1) in both these fusion processes. To determine if Anx A1 contributes to these processes during muscle repair in vivo, we have assessed muscle growth and repair in Anx A1-deficient mouse (AnxA1-/-). We found that the lack of Anx A1 does not affect the muscle size and repair of myofibers following focal sarcolemmal injury and lengthening contraction injury. However, the lack of Anx A1 delayed muscle regeneration after notexin-induced injury. This delay in muscle regeneration was not caused by a slowdown in proliferation and differentiation of satellite cells. Instead, lack of Anx A1 lowered the proportion of differentiating myoblasts that managed to fuse with the injured myofibers by days 5 and 7 after notexin injury as compared to the wild type (w.t.) mice. Despite this early slowdown in fusion of Anx A1-/- myoblasts, regeneration caught up at later times post injury. These results establish in vivo role of Anx A1 in cell fusion required for myofiber regeneration and not in intracellular vesicle fusion needed for repair of myofiber sarcolemma

Delivery of steric block morpholino oligomers by (R-X-R)4 peptides: structure–activity studies

Redirecting the splicing machinery through the hybridization of high affinity, RNase H- incompetent oligonucleotide analogs such as phosphoramidate morpholino oligonucleotides (PMO) might lead to important clinical applications. Chemical conjugation of PMO to arginine-rich cell penetrating peptides (CPP) such as (R-Ahx-R)4 (with Ahx standing for 6-aminohexanoic acid) leads to sequence-specific splicing correction in the absence of endosomolytic agents in cell culture at variance with most conventional CPPs. Importantly, (R-Ahx-R)4–PMO conjugates are effective in mouse models of various viral infections and Duchenne muscular dystrophy. Unfortunately, active doses in some applications might be close to cytotoxic ones thus presenting challenge for systemic administration of the conjugates in those clinical settings. Structure–activity relationship studies have thus been undertaken to unravel CPP structural features important for the efficient nuclear delivery of the conjugated PMO and limiting steps in their internalization pathway. Affinity for heparin (taken as a model heparan sulfate), hydrophobicity, cellular uptake, intracellular distribution and splicing correction have been monitored. Spacing between the charges, hydrophobicity of the linker between the Arg-groups and Arg-stereochemistry influence splicing correction efficiency. A significant correlation between splicing correction efficiency, affinity for heparin and ability to destabilize model synthetic vesicles has been observed but no correlation with cellular uptake has been found. Efforts will have to focus on endosomal escape since it appears to remain the limiting factor for the delivery of these splice-redirecting ON analogs

Dengue Virus Ensures Its Fusion in Late Endosomes Using Compartment-Specific Lipids

Many enveloped viruses invade cells via endocytosis and use different environmental factors as triggers for virus-endosome fusion that delivers viral genome into cytosol. Intriguingly, dengue virus (DEN), the most prevalent mosquito-borne virus that infects up to 100 million people each year, fuses only in late endosomes, while activation of DEN protein fusogen glycoprotein E is triggered already at pH characteristic for early endosomes. Are there any cofactors that time DEN fusion to virion entry into late endosomes? Here we show that DEN utilizes bis(monoacylglycero)phosphate, a lipid specific to late endosomes, as a co-factor for its endosomal acidification-dependent fusion machinery. Effective virus fusion to plasma- and intracellular- membranes, as well as to protein-free liposomes, requires the target membrane to contain anionic lipids such as bis(monoacylglycero)phosphate and phosphatidylserine. Anionic lipids act downstream of low-pH-dependent fusion stages and promote the advance from the earliest hemifusion intermediates to the fusion pore opening. To reach anionic lipid-enriched late endosomes, DEN travels through acidified early endosomes, but we found that low pH-dependent loss of fusogenic properties of DEN is relatively slow in the presence of anionic lipid-free target membranes. We propose that anionic lipid-dependence of DEN fusion machinery protects it against premature irreversible restructuring and inactivation and ensures viral fusion in late endosomes, where the virus encounters anionic lipids for the first time during entry. Currently there are neither vaccines nor effective therapies for DEN, and the essential role of the newly identified DEN-bis(monoacylglycero)phosphate interactions in viral genome escape from the endosome suggests a novel target for drug design

Cytosol-dependent membrane fusion in ER, nuclear envelope and nuclear pore assembly: Biological implications

Endoplasmic reticulum and nuclear envelope rearrangements after mitosis are often studied in the reconstitution system based on Xenopus egg extract. In our recent work we partially replaced the membrane vesicles in the reconstitution mix with protein-free liposomes to explore the relative contributions of cytosolic and transmembrane proteins. Here we discuss our finding that cytosolic proteins mediate fusion between membranes lacking functional transmembrane proteins and the role of membrane fusion in endoplasmic reticulum and nuclear envelope reorganization. Cytosol-dependent liposome fusion has allowed us to restore, without adding transmembrane nucleoporins, functionality of nuclear pores, their spatial distribution and chromatin decondensation in nuclei formed at insufficient amounts of membrane material and characterized by only partial decondensation of chromatin and lack of nuclear transport. Both the mechanisms and the biological implications of the discovered coupling between spatial distribution of nuclear pores, chromatin decondensation and nuclear transport are discussed

First- and second-order necessary conditions with respect to components for discrete optimal control problems

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly

Cytoplasmic free Ca²⁺ is essential for multiple steps in malaria parasite egress from infected erythrocytes

<p>Abstract</p> <p>Background</p> <p>Egress of <it>Plasmodium falciparum,</it> from erythrocytes at the end of its asexual cycle and subsequent parasite invasion into new host cells, is responsible for parasite dissemination in the human body. The egress pathway is emerging as a coordinated multistep programme that extends in time for tens of minutes, ending with rapid parasite extrusion from erythrocytes. While the Ca²⁺ regulation of the invasion of <it>P. falciparum</it> in erythrocytes is well established, the role of Ca²⁺ in parasite egress is poorly understood. This study analysed the involvement of cytoplasmic free Ca²⁺ in infected erythrocytes during the multistep egress programme of malaria parasites.</p> <p>Methods</p> <p>Live-cell fluorescence microscopy was used to image parasite egress from infected erythrocytes, assessing the effect of drugs modulating Ca²⁺ homeostasis on the egress programme.</p> <p>Results</p> <p>A steady increase in cytoplasmic free Ca²⁺ is found to precede parasite egress. This increase is independent of extracellular Ca²⁺ for at least the last two hours of the cycle, but is dependent upon Ca²⁺ release from internal stores. Intracellular BAPTA chelation of Ca²⁺ within the last 45 minutes of the cycle inhibits egress prior to parasitophorous vacuole swelling and erythrocyte membrane poration, two characteristic morphological transformations preceding parasite egress. Inhibitors of the parasite endoplasmic reticulum (ER) Ca²⁺-ATPase accelerate parasite egress, indicating that Ca²⁺ stores within the ER are sufficient in supporting egress. Markedly accelerated egress of apparently viable parasites was achieved in mature schizonts using Ca²⁺ ionophore A23187. Ionophore treatment overcomes the BAPTA-induced block of parasite egress, confirming that free Ca²⁺ is essential in egress initiation. Ionophore treatment of immature schizonts had an adverse effect inducing parasitophorous vacuole swelling and killing the parasites within the host cell.</p> <p>Conclusions</p> <p>The parasite egress programme requires intracellular free Ca²⁺ for egress initiation, vacuole swelling, and host cell cytoskeleton digestion. The evidence that parasitophorous vacuole swelling, a stage of unaffected egress, is dependent upon a rise in intracellular Ca²⁺ suggests a mechanism for ionophore-inducible egress and a new target for Ca²⁺ in the programme liberating parasites from the host cell. A regulatory pathway for egress that depends upon increases in intracellular free Ca²⁺ is proposed.</p