The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.     

Notch pathway plays a novel and critical role in regulating responses of T and antigen-presenting cells in aGVHD

Graft-versus-host disease (GVHD) induced by host antigen-presenting cells (APCs) and donor-derived T cells remains the major limitation of allogeneic bone marrow transplantation (allo-BMT). Notch signaling pathway is a highly conserved cell-cell communication that is important in T cell development. Recently, Notch signaling pathway is reported to be involved in regulating GVHD. To investigate the role of Notch inhibition in modulating GVHD, we established MHC-mismatched murine allo-BMT model. We found that inhibition of Notch signaling pathway by γ-secretase inhibitor in vivo could reduce aGVHD, which was shown by the onset time of aGVHD, body weight, clinical aGVHD scores, pathology aGVHD scores, and survival. Inhibition of Notch signaling pathway by DAPT ex vivo only reduced pathology aGVHD scores in the liver and intestine and had no impact on the onset time and clinical aGVHD scores. We investigated the possible mechanism by analyzing the phenotype of host APCs and donor-derived T cells. Notch signaling pathway had a broad effect on both host APCs and donor-derived T cells. The expressions of CD11c, CD40, and CD86 as the markers of activated dendritic cells (DCs) were decreased. The proliferative response of CD8+ T cell decreased, while CD4⁺ Notch-deprived T cells had preserved expansion with increased expressions of CD25 and Foxp3 as markers of regulatory T cells (Tregs). In conclusion, Notch inhibition may minimize aGVHD by decreasing proliferation and activation of DCs and CD8⁺ T cells while preserving Tregs expansion.     

Rice G protein γ subunit qPE9-1 modulates root elongation for phosphorus uptake by involving 14-3-3 protein OsGF14b and plasma membrane H+-ATPase

Heterotrimeric G protein is involved in plant growth and development, while the role of rice (Oryza sativa) G protein γ subunit qPE9-1 in response to low-phosphorus (LP) conditions remains unclear. The gene expression of qPE9-1 was significantly induced in rice roots under LP conditions. Rice varieties carrying the qPE9-1 allele showed a stronger primary root response to LP than the varieties carrying the qpe9-1 allele (mutant of the qPE9-1 allele). Transgenic rice plants with the qPE9-1 allele had longer primary roots and higher P concentrations than those with the qpe9-1 allele under LP conditions. The plasma membrane (PM) H⁺-ATPase was important for the qPE9-1-mediated response to LP. Furthermore, OsGF14b, a 14-3-3 protein that acts as a key component in activating PM H⁺-ATPase for root elongation, is also involved in the qPE9-1 mediation. Moreover, the overexpression of OsGF14b in WYJ8 (carrying the qpe9-1 allele) partially increased primary root length under LP conditions. Experiments using R18 peptide (a 14-3-3 protein inhibitor) showed that qPE9-1 is important for primary root elongation and H⁺ efflux under LP conditions by involving the 14-3-3 protein. In addition, rhizosheath weight, total P content, and the rhizosheath soil Olsen-P concentration of qPE9-1 lines were higher than those of qpe9-1 lines under soil drying and LP conditions. These results suggest that the G protein γ subunit qPE9-1 in rice plants modulates root elongation for phosphorus uptake by involving the 14-3-3 protein OsGF14b and PM H⁺-ATPase, which is required for rice P use.     

Dextrorphan: an antagonist for phencyclidine receptors

Radio-binding assay, bioassay and HPLC detection were used to observe the antagonistic effects of dextrorphan on PCP's actions. Dextrorphan displayed high affinity to PCP receptor in the rabbit mesenteric blood vessels. It had weak PCP-like bioactivity, but could antagonize PCP's action dose-dependently in vitro study with the rabbit ear artery preparation and shifted the dose-response curve of PCP to the right. After PCP administration, the content of norepinephrine in the vascular bath medium was increased, which was reversed by dextrorphan. Thus suggests that dextrorphan is an antagonist with very mild agonistic action for PCP receptors.     

The effect of berbamine derivatives on activated Ca2+-stimulated Mg2+-dependent ATPase in erythrocyte membranes.

Ca2+-stimulated Mg2+-dependent ATPase (Ca2+ + Mg2+-ATPase) stimulated by calmodulin, by partial proteolysis or by oleic acid in erythrocyte membranes was inhibited by various derivatives of the naturally occurring alkaloid berbamine. The ability of these derivatives to inhibit trypsin-activated Ca2+ + Mg2+-ATPase correlated well with their ability to inhibit the calmodulin-stimulated enzyme. Inhibition of the trypsin-activated Ca2+ + Mg2+-ATPase by O-4-(ethoxybutyl)berbamine (EBB) was competitive with respect to ATP. The Ki for inhibition was about 8 microM. These results suggest that the binding site of EBB on the activated Ca2+ + Mg2+-ATPase may bear structural similarity to that on calmodulin, and may be closely related to the ATP-binding site on the enzyme.     

Properties of bovine heart mitochondrial cytochrome b560

A large-scale preparation of the two-subunit protein complex (QPs) that converts succinate dehydrogenase into succinate-ubiquinone reductase from cytochrome b-c1 particles is achieved by a procedure involving Triton X-100 solubilization and calcium phosphate column chromatography at different pH values. The isolated two-subunit QPs contains 25 nmol of cytochrome b560/mg of protein and is able to reconstitute with soluble succinate dehydrogenase to form a TTFA-sensitive succinate-ubiquinone reductase. The maximum reconstitutive activity is 100 mumol of succinate oxidized per min per mg of QPs protein at 23 degrees C. Although cytochrome b560 in isolated QPs is not succinate reducible and its dithionite reduced form is reactive to carbon monoxide, cytochrome b560 is shown to be physically associated with succinate dehydrogenase by the following observations. The dithionite reduced form of cytochrome b560 in isolated QPs has a symmetrical alpha-absorption peak, which upon reconstitution with succinate dehydrogenase becomes slightly broadened and shows a shoulder at around 553 nm, identical to that of cytochrome b560 in succinate-ubiquinone reductase. Upon addition of succinate dehydrogenase to QPs, about 50% of the reduced form of cytochrome b560 in the QPs becomes insensitive to carbon monoxide treatment. The redox potential of cytochrome b560 in QPs is -144 mV which is higher than that of cytochrome b560 in succinate-ubiquinone reductase (-185 mV). Upon addition of succinate dehydrogenase, the redox potential of about 46% of the cytochrome b560 in QPs preparation becomes identical to that of cytochrome b560 in succinate-ubiquinone reductase. Cytochrome b560 in the QPs preparation shows two epr signals, g = 3.07 and g = 2.92, whereas cytochrome b560 in succinate-ubiquinone reductase exhibits only one epr signal at g = 3.46. When QPs is reconstituted with succinate dehydrogenase to form succinate-ubiquinone reductase, the g = 3.46 epr signal reappears at the expense of the g = 3.07 signal. Based on epr measurement at liquid helium temperature, about 18% of the total cytochrome b in the isolated active succinate-cytochrome c reductase is cytochrome b560, indicating that cytochrome b560 is indeed a unique cytochrome b and not a denatured product of cytochrome b562 or b565.