Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

Monophosphothreonyl extracellular signal-regulated kinases 1 and 2 (ERK1/2) are formed endogenously in intact cardiac myocytes and are enzymically active

ERK1 and ERK2 (ERK1/2) are central to the regulation of cell division, growth and survival. They are activated by phosphorylation of the Thr- and the Tyr- residues in their Thr-Glu-Tyr activation loops. The dogma is that dually-phosphorylated ERK1/2 constitute the principal activities in intact cells. We previously showed that, in neonatal rat cardiac myocytes, endothelin-1 and phorbol 12-myristate 13-acetate (PMA) powerfully and rapidly (maximal at ~ 5 min) activate ERK1/2. Here, we show that dually-phosphorylated ERK1/2 rapidly (< 2 min) appear in the nucleus following stimulation with endothelin-1. We characterized the active ERK1/2 species in myocytes exposed to endothelin-1 or PMA using MonoQ FPLC. Unexpectedly, two peaks of ERK1 and two peaks of ERK2 activity were resolved using in vitro kinase assays. One of each of these represented the dually-phosphorylated species. The other two represented activities for ERK1 or ERK2 which were phosphorylated solely on the Thr- residue. Monophosphothreonyl ERK1/2 represented maximally ~ 30% of total ERK1/2 activity after stimulation with endothelin-1 or PMA, and their kcat values were estimated to be minimally ~ 30% of the dually-phosphorylated species. Appearance of monophosphothreonyl ERK1/2 was rapid but delayed in comparison with dually-phosphorylated ERK1/2. Of 10 agonists studied, endothelin-1 and PMA were most effective in terms of ERK1/2 activation and in stimulating the appearance of monophosphothreonyl and dually-phosphorylated ERK1/2. Thus, enzymically active monophosphothreonyl ERK1/2 are formed endogenously following activation of the ERK1/2 cascade and we suggest that monophosphothreonyl ERK1/2 arise by protein tyrosine phosphatase-mediated dephosphorylation of dually-phosphorylated ERK1/2.

Recommendations for the viability assessment of probiotics as concentrated cultures and in food matrices

Due to the fact that probiotic cells need to be alive when they are consumed, culture-based analysis (plate count) is critical in ascertaining the quality (numbers of viable cells) of probiotic products. Since probiotic cells are typically stressed, due to various factors related to their production, processing and formulation, the standard methodology for total plate counts tends to underestimate the cell numbers of these products. Furthermore, products such as microencapsulated cultures require modifications in the release and sampling procedure in order to correctly estimate viable counts. This review examines the enumeration of probiotic bacteria in the following commercial products: powders, microencapsulated cultures, frozen concentrates, capsules, foods and beverages. The parameters which are specifically examined include: sample preparation (rehydration, thawing), dilutions (homogenization, media) and plating (media, incubation) procedures. Recommendations are provided for each of these analytical steps to improve the accuracy of the analysis. Although the recommendations specifically target the analysis of probiotics, many will apply to the analysis of commercial lactic starter cultures used in food fermentations as well.

Formation of atypical podosomes in extravillous trophoblasts regulates extracellular matrix degradation

Throughout pregnancy the cytotrophoblast, the stem cell of the placenta, gives rise to the differentiated forms of trophoblasts. The two main cell lineages are the syncytiotrophoblast and the invading extravillous trophoblast. A successful pregnancy requires extravillous trophoblasts to migrate and invade through the decidua and then remodel the maternal spiral arteries. Many invasive cells use specialised cellular structures called invadopodia or podosomes in order to degrade extracellular matrix. Despite being highly invasive cells, the presence of invadapodia or podosomes has not previously been investigated in trophoblasts. In this study these structures have been identified and characterised in extravillous trophoblasts. The role of specialised invasive structures in trophoblasts in the degradation of the extracellular matrix was compared with well characterised podosomes and invadopodia in other invasive cells and the trophoblast specific structures were characterised by using a sensitive matrix degradation assay which enabled visualisation of the structures and their dynamics. We show trophoblasts form actin rich protrusive structures which have the ability to degrade the extracellular matrix during invasion. The degradation ability and dynamics of the structures closely resemble podosomes, but have unique characteristics that have not previously been described in other cell types. The composition of these structures does not conform to the classic podosome structure, with no distinct ring of plaque proteins such as paxillin or vinculin. In addition, trophoblast podosomes protrude more deeply into the extracellular matrix than established podosomes, resembling invadopodia in this regard. We also show several significant pathways such as Src kinase, MAPK kinase and PKC along with MMP-2 and 9 as key regulators of extracellular matrix degradation activity in trophoblasts, while podosome activity was regulated by the rigidity of the extracellular matrix.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Staphylococcal extracellular adherence protein induces platelet activation by stimulation of thiol isomerases

OBJECTIVE: Staphylococcus aureus can induce platelet aggregation. The rapidity and degree of this correlates with the severity of disseminated intravascular coagulation, and depends on platelet peptidoglycans. Surface-located thiol isomerases play an important role in platelet activation. The staphylococcal extracellular adherence protein (Eap) functions as an adhesin for host plasma proteins. Therefore we tested the effect of Eap on platelets. METHODS AND RESULTS: We found a strong stimulation of the platelet-surface thiol isomerases protein disulfide isomerase, endoplasmic reticulum stress proteins 57 and 72 by Eap. Eap induced thiol isomerase-dependent glycoprotein IIb/IIIa activation, granule secretion, and platelet aggregation. Treatment of platelets with thiol blockers, bacitracin, and anti-protein disulfide isomerase antibody inhibited Eap-induced platelet activation. The effect of Eap on platelets and protein disulfide isomerase activity was completely blocked by glycosaminoglycans. Inhibition by the hydrophobic probe bis(1-anilinonaphthalene 8-sulfonate) suggested the involvement of hydrophobic sites in protein disulfide isomerase and platelet activation by Eap. CONCLUSIONS: In the present study, we found an additional and yet unknown mechanism of platelet activation by a bacterial adhesin, involving stimulation of thiol isomerases. The thiol isomerase stimulatory and prothrombotic features of a microbial secreted protein are probably not restricted to S aureus and Eap. Because many microorganisms are coated with amyloidogenic proteins, it is likely that the observed mechanism is a more general one.

Extracellular release of a heterologous phytase from roots of transgenic plants: does manipulation of rhizosphere biochemistry impact microbial community structure?

To maintain the sustainability of agriculture, it is imperative that the reliance of crops on inorganic phosphorus (P) fertilizers is reduced. One approach is to improve the ability of crop plants to acquire P from organic sources. Transgenic plants that produce microbial phytases have been suggested as a possible means to achieve this goal. However, neither the impact of heterologous expression of phytase on the ecology of microorganisms in the rhizosphere nor the impact of rhizosphere microorganisms on the efficacy of phytases in the rhizosphere of transgenic plants has been tested. In this paper, we demonstrate that the presence of rhizosphere microorganisms reduced the dependence of plants oil extracellular secretion of phytase from roots when grown in a P-deficient soil. Despite this, the expression of phytase in transgenic plants had little or no impact on the microbial community structure as compared with control plant lines, whereas soil treatments, such as the addition of inorganic P, had large effects. The results demonstrate that soil microorganisms are explicitly involved in the availability of P to plants and that the microbial community in the rhizosphere appears to be resistant to the impacts of single-gene changes in plants designed to alter rhizosphere biochemistry and nutrient cycling.

Layer-by-layer coating of alginate matrices with chitosan–alginate for the improved survival and targeted delivery of probiotic bacteria after oral administration

The oral administration of probiotic bacteria has shown potential in clinical trials for the alleviation of specific disorders of the gastrointestinal tract. However, cells must be alive in order to exert these benefits. The low pH of the stomach can greatly reduce the number of viable microorganisms that reach the intestine, thereby reducing the efficacy of the administration. Herein, a model probiotic, Bifidobacterium breve, has been encapsulated into an alginate matrix before coating in multilayers of alternating alginate and chitosan. The intention of this formulation was to improve the survival of B. breve during exposure to low pH and to target the delivery of the cells to the intestine. The material properties were first characterized before in vitro testing. Biacore™ experiments allowed for the polymer interactions to be confirmed; additionally, the stability of these multilayers to buffers simulating the pH of the gastrointestinal tract was demonstrated. Texture analysis was used to monitor changes in the gel strength during preparation, showing a weakening of the matrices during coating as a result of calcium ion sequestration. The build-up of multilayers was confirmed by confocal laser-scanning microscopy, which also showed the increase in the thickness of coat over time. During exposure to in vitro gastric conditions, an increase in viability from <3 log(CFU) per mL, seen in free cells, up to a maximum of 8.84 ± 0.17 log(CFU) per mL was noted in a 3-layer coated matrix. Multilayer-coated alginate matrices also showed a targeting of delivery to the intestine, with a gradual release of their loads over 240 min.

CLSM method for the dynamic observation of pH change within polymer matrices for oral delivery

If acid-sensitive drugs or cells are administered orally, there is often a reduction in efficacy associated with gastric passage. Formulation into a polymer matrix is a potential method to improve their stability. The visualization of pH within these materials may help better understand the action of these polymer systems and allow comparison of different formulations. We herein describe the development of a novel confocal laser-scanning microscopy (CLSM) method for visualizing pH changes within polymer matrices and demonstrate its applicability to an enteric formulation based on chitosan-coated alginate gels. The system in question is first shown to protect an acid-sensitive bacterial strain to low pH, before being studied by our technique. Prior to this study, it has been claimed that protection by these materials is a result of buffering, but this has not been demonstrated. The visualization of pH within these matrices during exposure to a pH 2.0 simulated gastric solution showed an encroachment of acid from the periphery of the capsule, and a persistence of pHs above 2.0 within the matrix. This implies that the protective effect of the alginate-chitosan matrices is most likely due to a combination of buffering of acid as it enters the polymer matrix and the slowing of acid penetration.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.