On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Phosphofructo-2-kinase/Fructose-2,6-bisphosphatase Modulates Oscillations of Pancreatic Islet Metabolism

Pulses of insulin from pancreatic beta-cells help maintain blood glucose in a narrow range, although the source of these pulses is unclear. It has been proposed that a positive feedback circuit exists within the glycolytic pathway, the autocatalytic activation of phosphofructokinase-1 (PFK1), which endows pancreatic beta-cells with the ability to generate oscillations in metabolism. Flux through PFK1 is controlled by the bifunctional enzyme PFK2/FBPase2 (6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase) in two ways: via (1) production/degradation of fructose-2,6-bisphosphate (Fru2,6-BP), a potent allosteric activator of PFK1, as well as (2) direct activation of glucokinase due to a protein-protein interaction. In this study, we used a combination of live-cell imaging and mathematical modeling to examine the effects of inducibly-expressed PFK2/FBPase2 mutants on glucose-induced Ca2+ pulsatility in mouse islets. Irrespective of the ability to bind glucokinase, mutants of PFK2/FBPase2 that increased the kinase:phosphatase ratio reduced the period and amplitude of Ca2+ oscillations. Mutants which reduced the kinase:phosphatase ratio had the opposite effect. These results indicate that the main effect of the bifunctional enzyme on islet pulsatility is due to Fru2,6-BP alteration of the threshold for autocatalytic activation of PFK1 by Fru1,6-BP. Using computational models based on PFK1-generated islet oscillations, we then illustrated how moderate elevation of Fru-2,6-BP can increase the frequency of glycolytic oscillations while reducing their amplitude, with sufficiently high activation resulting in termination of slow oscillations. The concordance we observed between PFK2/FBPase2-induced modulation of islet oscillations and the models of PFK1-driven oscillations furthermore suggests that metabolic oscillations, like those found in yeast and skeletal muscle, are shaped early in glycolysis

Chagas Cardiomyopathy in the Context of the Chronic Disease Transition

Latin America is undergoing a transition from disease patterns characteristic of developing countries with high rates of infectious disease and premature deaths to a pattern more like industrialized countries, in which chronic conditions such as obesity, hypertension and diabetes are more common. Many rural residents with Chagas disease have now migrated to cities, taken on new habits and may suffer from both types of disease. We studied heart disease among 394 adults seen by cardiologists in a public hospital in the city of Santa Cruz, Bolivia; 64% were infected with T. cruzi, the parasite that causes Chagas disease. Both T. cruzi infected and uninfected patients had a high rate of hypertension (64%) and overweight (67%), with no difference by infection status. Nearly 60% of symptomatic congestive heart failure was due to Chagas disease; mortality was also higher for infected than uninfected patients. Males and older patients had more severe Chagas heart disease. Chagas heart disease remains an important cause of congestive heart failure in this hospital population, but often occurs in patients who also have obesity, hypertension and/or other cardiac risk factors

Substrates for Efficient Fluorometric Screening Employing the NAD-Dependent Sirtuin 5 Lysine Deacylase (KDAC) Enzyme

The class III lysine deacylases (KDACs), also known as the sirtuins, have emerged as interesting drug targets for therapeutic intervention in a variety of diseases. To gain a deeper understanding of the processes affected by sirtuins, the development of selective small molecule modulators of individual isozymes has been a longstanding goal. Essential for the discovery of novel modulators, however, are good screening protocols and mechanistic insights with regard to the targets in question. We therefore evaluated the activities of the seven human sirtuin hydrolases against a panel of fluorogenic substrates. Both commonly used, commercially available substrates and novel chemotypes designed to address recent developments in the field of lysine post-translational modification were evaluated. Our investigations led to the discovery of two new fluorogenic ε-N-succinyllysine-containing substrates that enable highly efficient and enzyme-economical screening employing sirtuin 5 (SIRT5). Furthermore, optimized protocols for facile kinetic investigations were developed, which should be valuable for enzyme kinetic investigations. Finally, these protocols were applied to a kinetic analysis of the inhibition of SIRT5 by suramin, a potent sirtuin inhibitor previously shown by X-ray crystallography to bind the substrate pocket of the human SIRT5 KDAC enzyme