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.     

Recruitment of Nox4 to a Plasma Membrane Scaffold Is Required for Localized Reactive Oxygen Species Generation and Sustained Src Activation in Response to Insulin-like Growth Factor-I

Nox4-derived ROS is increased in response to hyperglycemia and is required for IGF-I-stimulated Src activation. This study was undertaken to determine the mechanism by which Nox4 mediates sustained Src activation. IGF-I stimulated sustained Src activation, which occurred primarily on the SHPS-1 scaffold protein. In vitro oxidation experiments indicated that Nox4-derived ROS was able to oxidize Src when they are in close proximity, and Src oxidation leads to its activation. Therefore we hypothesized that Nox4 recruitment to the plasma membrane scaffold SHPS-1 allowed localized ROS generation to mediate sustained Src oxidation and activation. To determine the mechanism of Nox4 recruitment, we analyzed the role of Grb2, a component of the SHPS-1 signaling complex. We determined that Nox4 Tyr-491 was phosphorylated after IGF-I stimulation and was responsible for Nox4 binding to the SH2 domain of Grb2. Overexpression of a Nox4 mutant, Y491F, prevented Nox4/Grb2 association. Importantly, it also prevented Nox4 recruitment to SHPS-1. The role of Grb2 was confirmed using a Pyk2 Y881F mutant, which blocked Grb2 recruitment to SHPS-1. Cells expressing this mutant had impaired Nox4 recruitment to SHPS-1. IGF-I-stimulated downstream signaling and biological actions were also significantly impaired in Nox4 Y491F-overexpressing cells. Disruption of Nox4 recruitment to SHPS-1 in aorta from diabetic mice inhibited IGF-I-stimulated Src oxidation and activation as well as cell proliferation. These findings provide insight into the mechanism by which localized Nox4-derived ROS regulates the sustained activity of a tyrosine kinase that is critical for mediating signal transduction and biological actions.     

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.     

Iron plaque enhances phosphorus uptake by rice (Oryza sativa) growing under varying phosphorus and iron concentrations

Both solution culture and pot experiments were performed to investigate (a) the effects of external Fe (II) concentrations and forms on the formation of iron plaque on the roots of rice (Oryza sativa) and subsequent P adsorption on iron plaque and shoot P concentrations and (b) the effects of soil moisture regimes on the formation of iron plaque and P adsorption on root surfaces and P accumulation in shoots. The results showed that iron plaque was significantly increased with increasing Fe²⁺ concentrations in the solution culture. The amounts of P adsorbed on the iron plaque were increased significantly with external Fe²⁺ concentrations. Although shoot P concentration was not significantly affected by Fe²⁺ treatment after incubation for 2 days, it was significantly increased in the Fe‐treated plants compared with Fe‐deprived ones after incubation for 4 days. Soil culture experiment showed that the formation of iron plaque on root surfaces was promoted by exogenous iron, with greater amount of iron plaque being formed by addition of ferric hydroxide than of ferric oxide. Phosphorus adsorption on iron plaque also increased with the addition of iron oxides, and increasing soil P increased the amounts of P associated with the iron plaque and shoot P concentration. The amounts of iron plaque were almost sixfold higher under flooding condition than under field capacity condition. Plants pretreated under flooding condition generally had higher shoot P concentrations when they were transplanted to solutions with varying P levels, and this was most pronounced in the treatment with highest solution P concentration. The results suggest that iron plaque acts as a nutrient reservoir for phosphorus in the rhizosphere and helps enhance P acquisition by rice.     

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.