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  • 1
    Publication Date: 2015-09-19
    Description: In this paper, the spatial, temporal and spatiotemporal dynamics of a reaction–diffusion predator–prey system with mutual interference described by the Crowley–Martin-type functional response, under homogeneous Neumann boundary conditions, are studied. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equations is presented. For the reaction–diffusion model, firstly the invariance, uniform persistence and global asymptotic stability of the coexistence equilibrium are discussed. Then it is shown that Turing (diffusion-driven) instability occurs, which induces spatial inhomogeneous patterns. Next it is proved that the model exhibits Hopf bifurcation which produces temporal inhomogeneous patterns. Furthermore, at the points where the Turing instability curve and Hopf bifurcation curve intersect, it is demonstrated that the model undergoes Turing–Hopf bifurcation and exhibits spatiotemporal patterns. Finally, the existence and non-existence of positive non-constant steady states of the reaction–diffusion model are established. Numerical simulations are presented to verify and illustrate the theoretical results.
    Print ISSN: 0272-4960
    Electronic ISSN: 1464-3634
    Topics: Mathematics
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  • 2
    Publication Date: 2014-05-30
    Description: Insulin constitutes a principal evolutionarily conserved hormonal axis for maintaining glucose homeostasis; dysregulation of this axis causes diabetes. PGC-1alpha (peroxisome-proliferator-activated receptor-gamma coactivator-1alpha) links insulin signalling to the expression of glucose and lipid metabolic genes. The histone acetyltransferase GCN5 (general control non-repressed protein 5) acetylates PGC-1alpha and suppresses its transcriptional activity, whereas sirtuin 1 deacetylates and activates PGC-1alpha. Although insulin is a mitogenic signal in proliferative cells, whether components of the cell cycle machinery contribute to its metabolic action is poorly understood. Here we report that in mice insulin activates cyclin D1-cyclin-dependent kinase 4 (Cdk4), which, in turn, increases GCN5 acetyltransferase activity and suppresses hepatic glucose production independently of cell cycle progression. Through a cell-based high-throughput chemical screen, we identify a Cdk4 inhibitor that potently decreases PGC-1alpha acetylation. Insulin/GSK-3beta (glycogen synthase kinase 3-beta) signalling induces cyclin D1 protein stability by sequestering cyclin D1 in the nucleus. In parallel, dietary amino acids increase hepatic cyclin D1 messenger RNA transcripts. Activated cyclin D1-Cdk4 kinase phosphorylates and activates GCN5, which then acetylates and inhibits PGC-1alpha activity on gluconeogenic genes. Loss of hepatic cyclin D1 results in increased gluconeogenesis and hyperglycaemia. In diabetic models, cyclin D1-Cdk4 is chronically elevated and refractory to fasting/feeding transitions; nevertheless further activation of this kinase normalizes glycaemia. Our findings show that insulin uses components of the cell cycle machinery in post-mitotic cells to control glucose homeostasis independently of cell division.〈br /〉〈br /〉〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4076706/" target="_blank"〉〈img src="https://static.pubmed.gov/portal/portal3rc.fcgi/4089621/img/3977009" border="0"〉〈/a〉   〈a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4076706/" target="_blank"〉This paper as free author manuscript - peer-reviewed and accepted for publication〈/a〉〈br /〉〈br /〉〈span class="detail_caption"〉Notes: 〈/span〉Lee, Yoonjin -- Dominy, John E -- Choi, Yoon Jong -- Jurczak, Michael -- Tolliday, Nicola -- Camporez, Joao Paulo -- Chim, Helen -- Lim, Ji-Hong -- Ruan, Hai-Bin -- Yang, Xiaoyong -- Vazquez, Francisca -- Sicinski, Piotr -- Shulman, Gerald I -- Puigserver, Pere -- DK059635/DK/NIDDK NIH HHS/ -- F32 DK083871/DK/NIDDK NIH HHS/ -- P30 DK034989/DK/NIDDK NIH HHS/ -- R01 CA083688/CA/NCI NIH HHS/ -- R01 CA108420/CA/NCI NIH HHS/ -- R01 DK069966/DK/NIDDK NIH HHS/ -- R01 DK089098/DK/NIDDK NIH HHS/ -- R01069966/PHS HHS/ -- R03 DA032468/DA/NIDA NIH HHS/ -- R03 MH092174/MH/NIMH NIH HHS/ -- R24 DK080261/DK/NIDDK NIH HHS/ -- R24DK080261-06/DK/NIDDK NIH HHS/ -- U24 DK059635/DK/NIDDK NIH HHS/ -- England -- Nature. 2014 Jun 26;510(7506):547-51. doi: 10.1038/nature13267. Epub 2014 May 25.〈br /〉〈span class="detail_caption"〉Author address: 〈/span〉1] Department of Cancer Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA [2] Department of Cell Biology, Harvard Medical School, Boston, Massachusetts 02115, USA [3] Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA. ; 1] Department of Cancer Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA [2] Department of Cell Biology, Harvard Medical School, Boston, Massachusetts 02115, USA. ; 1] Department of Cancer Biology, Dana-Farber Cancer Institute, Boston, Massachusetts 02115, USA [2] Department of Genetics, Harvard Medical School, Boston, Massachusetts 02115, USA. ; Yale's Mouse Metabolic Phenotyping Center and Departments of Internal Medicine and Cellular and Molecular Physiology, Yale University School of Medicine, New Haven, Connecticut 06510, USA. ; Chemical Biology Platform, Broad Institute of Harvard and MIT, 7 Cambridge Center, Cambridge, Massachusetts 02141, USA.〈br /〉〈span class="detail_caption"〉Record origin:〈/span〉 〈a href="http://www.ncbi.nlm.nih.gov/pubmed/24870244" target="_blank"〉PubMed〈/a〉
    Keywords: Acetylation ; Amino Acids/pharmacology ; Animals ; *Cell Cycle ; Cell Line, Tumor ; Cell Nucleus/metabolism ; Cells, Cultured ; Cyclin D1/deficiency/genetics/*metabolism ; Cyclin-Dependent Kinase 4/antagonists & inhibitors/*metabolism ; Diabetes Mellitus/metabolism ; Enzyme Activation ; Fasting ; Gene Deletion ; Gluconeogenesis/genetics ; Glucose/*metabolism ; Glycogen Synthase Kinase 3/metabolism ; Hepatocytes/cytology/drug effects/metabolism ; Histone Acetyltransferases/metabolism ; Homeostasis ; Humans ; Hyperglycemia/metabolism ; Hyperinsulinism/metabolism ; Insulin/*metabolism ; Male ; Mice ; Phosphorylation ; RNA, Messenger/analysis/genetics ; *Signal Transduction ; Transcription Factors/metabolism ; Transcription, Genetic/drug effects
    Print ISSN: 0028-0836
    Electronic ISSN: 1476-4687
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
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