A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Proteomic characterization of thiazolidinedione regulation of obese adipose secretome in Zucker obese rats

Signaling molecules released by adipose tissue have been implicated in inflammation, adipocyte dysfunction and systemic insulin resistance. In this study, we used 2-D LC-MS/MS and quantitative proteomics approaches to characterize the obese adipose secretory proteins that are responsive to the thiazolidinediones class of PPAR-γ agonizts. We first showed the differential secretion profiling between obese and lean adipose tissue; 87 proteins were detected from the conditioned medium of adipose tissue of Zucker obese rats compared with 31 from lean rats. A total of 57 proteins comprising immune factors, inflammatory molecules, collagens, proteases, and extracellular matrix proteins were detected from obese, but not lean adipose tissue. More importantly, a quantitative proteomics approach using ^(18)O proteolytic labeling allowed quantification of the difference in the secretion levels of 77 proteins, and thiazolidinediones treatment suppressed the secretion of most of the obese adipose tissue secretome, thus resembling a lean tissue. We have demonstrated an application of identifying the obese adipose secretome and characterizing the regulation of adipose secretion in obesity and insulin resistance. Our data provide the first evidence of changes in adipose secretion in obesity at a global level and show that such changes are correlated with systemic insulin resistance

Waves of Adipose Tissue Growth in the Genetically Obese Zucker Fatty Rat

In mammals, calories ingested in excess of those used are stored primarily as fat in adipose tissue; consistent ingestion of excess calories requires an enlargement of the adipose tissue mass. Thus, a dysfunction in adipose tissue growth may be a key factor in insulin resistance due to imbalanced fat storage and disrupted insulin action. Adipose tissue growth requires the recruitment and then the development of adipose precursor cells, but little is known about these processes in vivo.In this study, adipose cell-size probability distributions were measured in two Zucker fa/fa rats over a period of 151 and 163 days, from four weeks of age, using micro-biopsies to obtain subcutaneous (inguinal) fat tissue from the animals. These longitudinal probability distributions were analyzed to assess the probability of periodic phenomena.Adipose tissue growth in this strain of rat exhibits a striking temporal periodicity of approximately days. A simple model is proposed for the periodicity, with PPAR signaling driven by a deficit in lipid uptake capacity leading to the periodic recruitment of new adipocytes. This model predicts that the observed period will be diet-dependent