Bisimulation and expressivity for conditional belief, degrees of belief, and safe belief

Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The logic of conditional belief contains that modality and also the knowledge modality, and similarly for the logic of degrees of belief and the logic of safe belief. With respect to these logics, plausibility models may contain too much information. A proper notion of bisimulation is required that characterises them. We define that notion of bisimulation and prove the required characterisations: on the class of image-finite and preimage-finite models (with respect to the plausibility relation), two pointed Kripke models are modally equivalent in either of the three logics, if and only if they are bisimilar. As a result, the information content of such a model can be similarly expressed in the logic of conditional belief, or the logic of degrees of belief, or that of safe belief. This, we found a surprising result. Still, that does not mean that the logics are equally expressive: the logics of conditional and degrees of belief are incomparable, the logics of degrees of belief and safe belief are incomparable, while the logic of safe belief is more expressive than the logic of conditional belief. In view of the result on bisimulation characterisation, this is an equally surprising result. We hope our insights may contribute to the growing community of formal epistemology and on the relation between qualitative and quantitative modelling

<em>Escherichia coli</em>- and <em>Staphylococcus aureus </em>- induced mastitis differentially modulate transcriptional responses in neighbouring uninfected bovine mammary gland quarters

BACKGROUND: The most important disease of dairy cattle is mastitis, caused by the infection of the mammary gland by various micro-organisms. Although the transcriptional response of bovine mammary gland cells to in vitro infection has been studied, the interplay and consequences of these responses in the in vivo environment of the mammary gland are less clear. Previously mammary gland quarters were considered to be unaffected by events occurring in neighbouring quarters. More recently infection of individual quarters with mastitis causing pathogens, especially Escherichia coli, has been shown to influence the physiology of neighbouring uninfected quarters. Therefore, the transcriptional responses of uninfected mammary gland quarters adjacent to quarters infected with two major mastitis causing pathogens, E. coli and Staphylococcus aureus, were compared. RESULTS: The bacteriologically sterile, within-animal control quarters exhibited a transcriptional response to the infection of neighbouring quarters. The greatest response was associated with E. coli infection, while a weaker, yet significant, response occurred during S. aureus infection. The transcriptional responses of these uninfected quarters included the enhanced expression of many genes previously associated with mammary gland infections. Comparison of the transcriptional response of uninfected quarters to S. aureus and E. coli infection identified 187 differentially expressed genes, which were particularly associated with cellular responses, e.g. response to stress. The most affected network identified by Ingenuity Pathway analysis has the immunosuppressor transforming growth factor beta 1 (TGFB1) at its hub and largely consists of genes more highly expressed in control quarters from S. aureus infected cows. CONCLUSIONS: Uninfected mammary gland quarters reacted to the infection of neighbouring quarters and the responses were dependent on pathogen type. Therefore, bovine udder quarters exhibit interdependence and should not be considered as separate functional entities. This suggests that mastitis pathogens not only interact directly with host mammary cells, but also influence discrete sites some distance away, which will affect their response to the subsequent spread of the infection. Understanding the underlying mechanisms may provide further clues for ways to control mammary gland infections. These results also have implications for the design of experimental studies investigating immune regulatory mechanisms in the bovine mammary gland

Ser649 and Ser650 Are the Major Determinants of Protein Kinase A-Mediated Activation of Human Hormone-Sensitive Lipase against Lipid Substrates

BACKGROUND: Hormone-sensitive lipase (HSL) is a key enzyme in the mobilization of fatty acids from stored triacylglycerols. Its activity is regulated by reversible protein phosphorylation. In rat HSL Ser563, Ser659 and Ser660 have been shown to be phosphorylated by protein kinase A (PKA) in vitro as well as in vivo. METHODOLOGY/PRINCIPAL FINDINGS: In this study we employed site-directed mutagenesis, in vitro phosphorylation and mass spectrometry to show that in vitro phosphorylation of human HSL by PKA occurs primarily on Ser649 and Ser650 (Ser659 and Ser660 in rat HSL). The wild type enzyme and four mutants were expressed in C-terminally His-tagged form in Sf9 insect cells and purified to homogeneity. HSL variants in which Ser552 and/or Ser554 were mutated to Ala or Glu retained both lipolytic and non-lipolytic activity and were phosphorylated by PKA and activated to a similar extent as the wild type enzyme. (32)P-labeling studies revealed that the bulk of the phosphorylation was on the Ser649/Ser650 site, with only a minor phosphorylation of Ser552 and Ser554. MS/MS analysis demonstrated that the peptide containing Ser649 and Ser650 was primarily phosphorylated on Ser650. The mutant lacking all four serines had severely reduced lipolytic activity, but a lesser reduction in non-lipolytic activity, had S(0.5) values for p-nitrophenol butyrate and triolein comparable to those of wild type HSL and was not phosphorylated by PKA. PKA phosphorylation of the wild type enzyme resulted in an increase in both the maximum turnover and S(0,5) using the TO substrate. CONCLUSIONS: Our results demonstrate that PKA activates human HSL against lipid substrates in vitro primarily through phosphorylation of Ser649 and Ser650. In addition the results suggest that Ser649 and Ser650 are located in the vicinity of a lipid binding region and that PKA phosphorylation controls the accessibility of this region