On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control - Supplementary Notes

By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to supplement a corresponding journal article. The results can be applied in a model predictive control context.Comment: 19 pages, 1 figur

Approximation of Continuous-Time Infinite-Horizon Optimal Control Problems Arising in Model Predictive Control - Supplementary Notes

These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a finite dimensional representation of the dynamics is obtained via a Galerkin approach. It is shown that the two approximations provide lower, respectively upper bounds on the optimal cost of the underlying infinite dimensional optimal control problem. These bounds get tighter as the number of basis functions is increased. In addition, conditions guaranteeing convergence to the cost of the underlying problem are provided.Comment: Supplementary notes, 10 page

Lupus autoantibodies interact directly with distinct glomerular and vascular cell surface antigens

Lupus autoantibodies interact directly with distinct glomerular and vascular cell surface antigens. We have identified monoclonal anti-DNA antibodies derived from lupus prone MRL-lpr/lpr mice that produce glomerular immune deposits and nephritis after passive transfer to normal mice. Particularly noteworthy is that the location of immune deposition varied among nephritogenic Ig, and this was associated with distinctive histologies and clinical disease profiles. Although their autoantigen binding properties differed, they were highly cross-reactive, in a manner similar to Ig deposited in glomeruli of lupus mice. This antigen binding profile was also typical of other previously described nephritogenic autoantibodies that bound directly to glomerular antigens to initiate immune deposit formation. In this study, we questioned whether ligation of different glomerular antigens by individual autoantibodies could contribute to the observed differences in the location of immune deposits. To examine this possibility, monoclonal anti-DNA antibodies (IgG2a) that produced glomerular immune deposits in different locations were evaluated. H221 produced mesangial, intracapillary (that is, intraluminal or within the capillary lumen) and subendothelial deposits associated with heavy proteinuria, whereas H147 produced mesangial, subendothelial and linear basement membrane deposits associated with proliferative glomerulonephritis. Initially, the capacity of H221 and H147 to bind directly to glomerular and vascular cell surfaces was evaluated. As demonstrated by FACS, H221 bound preferentially to mesangial cells whereas H147 bound preferentially to endothelial cells. To identify possible target cell surface antigens, Western blots, immunoprecipitation of surface labeled cells, and 2D gel electrophoresis were employed. H221 reacted with a 108kDa protein on mesangial cells not identified by H147, whereas H147 reacted with a 45kDa protein on endothelial cells not identified by H221. These results support the hypothesis that some nephritogenic lupus autoantibodies initiate immune deposit formation through direct interaction with glomerular antigens. Furthermore, they suggest that the site of immune deposition is determined by both antigen binding properties of the relevant antibody and the location of its target ligand within the glomerulus. In a given individual, therefore, the predominant autoantibody-glomerular antigen interaction may influence the morphologic and clinical phenotype expressed. Variation in the predominant interaction may also contribute to variations in disease expression among individuals with lupus nephritis

Small Intestinal Cannabinoid Receptor Changes Following a Single Colonic Insult with Oil of Mustard in Mice

Cannabinoids are known to be clinically beneficial for control of appetite disorders and nausea/vomiting, with emerging data that they can impact other GI disorders, such as inflammation. Post-inflammatory irritable bowel syndrome (PI-IBS) is a condition of perturbed intestinal function that occurs subsequent to earlier periods of intestinal inflammation. Cannabinoid 1 receptor (CB1R) and CB2R alterations in GI inflammation have been demonstrated in both animal models and clinically, but their continuing role in the post-inflammatory period has only been implicated to date. Therefore, to provide direct evidence for CBR involvement in altered GI functions in the absence of overt inflammation, we used a model of enhanced upper GI transit that persists for up to 4 weeks after a single insult by intracolonic 0.5% oil of mustard (OM) in mice. In mice administered OM, CB1R immunostaining in the myenteric plexus was reduced at day 7, when colonic inflammation is subsiding, and then increased at 28 days, compared to tissue from age-matched vehicle-treated mice. In the lamina propria CB2R immunostaining density was also increased at day 28. In mice tested 28 day after OM, either a CB1R-selective agonist, ACEA (1 and 3 mg/kg, s.c.) or a CB2R-selective agonist, JWH-133 (3 and 10 mg/kg, s.c.) reduced the enhanced small intestinal transit in a dose-related manner. Doses of ACEA and JWH-133 (1 mg/kg), alone or combined, reduced small intestinal transit of OM-treated mice to a greater extent than control mice. Thus, in this post-colonic inflammation model, both CBR subtypes are up-regulated and there is increased efficacy of both CB1R and CB2R agonists. We conclude that CBR remodeling occurs not only during GI inflammation but continues during the recovery phase. Thus, either CB1R- or CB2-selective agonists could be efficacious for modulating GI motility in individuals experiencing diarrhea-predominant PI-IBS

Regulatory network of inflammation downstream of proteinase-activated receptors

BACKGROUND: Protease-activated receptors (PAR) are present in the urinary bladder, and their expression is altered in response to inflammation. PARs are a unique class of G protein-coupled that carry their own ligands, which remain cryptic until unmasked by proteolytic cleavage. Although the canonical signal transduction pathway downstream of PAR activation and coupling with various G proteins is known and leads to the rapid transcription of genes involved in inflammation, the effect of PAR activation on the downstream transcriptome is unknown. We have shown that intravesical administration of PAR-activating peptides leads to an inflammatory reaction characterized by edema and granulocyte infiltration. Moreover, the inflammatory response to intravesical instillation of known pro-inflammatory stimuli such as E. coli lipopolysaccharide (LPS), substance P (SP), and antigen was strongly attenuated by PAR1- and to a lesser extent by PAR2-deficiency. RESULTS: Here, cDNA array experiments determined inflammatory genes whose expression is dependent on PAR1 activation. For this purpose, we compared the alteration in gene expression in wild type and PAR1(-/- )mice induced by classical pro-inflammatory stimuli (LPS, SP, and antigen). 75 transcripts were considered to be dependent on PAR-1 activation and further annotated in silico by Ingenuity Pathways Analysis (IPA) and gene ontology (GO). Selected transcripts were target validated by quantitative PCR (Q-PCR). Among PAR1-dependent transcripts, the following have been implicated in the inflammatory process: b2m, ccl7, cd200, cd63, cdbpd, cfl1, dusp1, fkbp1a, fth1, hspb1, marcksl1, mmp2, myo5a, nfkbia, pax1, plaur, ppia, ptpn1, ptprcap, s100a10, sim2, and tnfaip2. However, a balanced response to signals of injury requires a transient cellular activation of a panel of genes together with inhibitory systems that temper the overwhelming inflammation. In this context, the activation of genes such as dusp1 and nfkbia seems to counter-balance the inflammatory response to PAR activation by limiting prolonged activation of p38 MAPK and increased cytokine production. In contrast, transcripts such as arf6 and dcnt1 that are involved in the mechanism of PAR re-sensitization would tend to perpetuate the inflammatory reaction in response to common pro-inflammatory stimuli. CONCLUSION: The combination of cDNA array results and genomic networks reveals an overriding participation of PAR1 in bladder inflammation, provides a working model for the involvement of downstream signaling, and evokes testable hypotheses regarding the transcriptome downstream of PAR1 activation. It remains to be determined whether or not mechanisms targeting PAR1 gene silencing or PAR1 blockade will ameliorate the clinical manifestation of cystitis

Mandatory role of proteinase-activated receptor 1 in experimental bladder inflammation

BACKGROUND: In general, inflammation plays a role in most bladder pathologies and represents a defense reaction to injury that often times is two edged. In particular, bladder neurogenic inflammation involves the participation of mast cells and sensory nerves. Increased mast cell numbers and tryptase release represent one of the prevalent etiologic theories for interstitial cystitis and other urinary bladder inflammatory conditions. The activity of mast cell-derived tryptase as well as thrombin is significantly increased during inflammation. Those enzymes activate specific G-protein coupled proteinase-activated receptors (PAR)s. Four PARs have been cloned so far, and not only are all four receptors highly expressed in different cell types of the mouse urinary bladder, but their expression is altered during experimental bladder inflammation. We hypothesize that PARs may link mast cell-derived proteases to bladder inflammation and, therefore, play a fundamental role in the pathogenesis of cystitis. RESULTS: Here, we demonstrate that in addition to the mouse urinary bladder, all four PA receptors are also expressed in the J82 human urothelial cell line. Intravesical administration of PAR-activating peptides in mice leads to an inflammatory reaction characterized by edema and granulocyte infiltration. Moreover, the inflammatory response to intravesical instillation of known pro-inflammatory stimuli such as E. coli lipopolysaccharide (LPS), substance P, and antigen was strongly attenuated by PAR1-, and to a lesser extent, by PAR2-deficiency. CONCLUSION: Our results reveal an overriding participation of PAR1 in bladder inflammation, provide a working model for the involvement of downstream signaling, and evoke testable hypotheses regarding the role of PARs in bladder inflammation. It remains to be determined whether or not mechanisms targeting PAR1 gene silencing or PAR1 blockade will ameliorate the clinical manifestations of cystitis

Evaluation of E. coli inhibition by plain and polymer-coated silver nanoparticles

Escherichia coli causes various ailments such as septicemia, enteritis, foodborne illnesses, and urinary tract infections which are of concern in the public health field due to antibiotic resistance. Silver nanoparticles (AgNP) are known for their biocompatibility and antibacterial activity, and may prove to be an alternative method of treatment, especially as wound dressings. In this study, we compared the antibacterial efficacy of two polymer-coated silver nanoparticles either containing 10% Ag (Ag 10% + Polymer), or 99% Ag (AgPVP) in relation to plain uncoated silver nanoparticles (AgNP). Atomic force microscopy was used to characterize the nanoparticles, and their antibacterial efficacy was compared by the minimum inhibitory concentration (MIC) and bacterial growth curve assays, followed by molecular studies using scanning electron microscopy (SEM) and (qRT- PCR). AgNP inhibited the growth of E. coli only at 0.621 mg/mL, which was double the concentration required for both coated nanoparticles (0.312 mg/mL). Similarly, bacterial growth was impeded as early as 8 h at 0.156 mg/mL of both coated nanoparticles as compared to 0.312 mg/mL for plain AgNP. SEM data showed that nanoparticles damaged the cell membrane, resulting in bacterial cell lysis, expulsion of cellular contents, and complete disintegration of some cells. The expression of genes associated with the TCA cycle (aceF and frdB) and amino acid metabolism (gadB, metL, argC) were substantially downregulated in E. coli treated with nanoparticles. The reduction in the silver ion (Ag+) concentration of polymer-coated AgNP did not affect their antibacterial efficacy against E. coli