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

Synchronized ATP oscillations have a critical role in prechondrogenic condensation during chondrogenesis

The skeletal elements of embryonic limb are prefigured by prechondrogenic condensation in which secreted molecules such as adhesion molecules and extracellular matrix have crucial roles. However, how the secreted molecules are controlled to organize the condensation remains unclear. In this study, we examined metabolic regulation of secretion in prechondrogenic condensation, using bioluminescent monitoring systems. We here report on ATP oscillations in the early step of chondrogenesis. The ATP oscillations depended on both glycolysis and mitochondrial respiration, and their synchronization among cells were achieved via gap junctions. In addition, the ATP oscillations were driven by Ca2+ oscillations and led to oscillatory secretion in chondrogenesis. Blockade of the ATP oscillations prevented cellular condensation. Furthermore, the degree of cellular condensation increased with the frequency of ATP oscillations. We conclude that ATP oscillations have a critical role in prechondrogenic condensation by inducing oscillatory secretion

Pulsatility of insulin release – a clinically important phenomenon

The mechanisms and clinical importance of pulsatile insulin release are presented against the background of more than half a century of companionship with the islets of Langerhans. The insulin-secreting β-cells are oscillators with intrinsic variations of cytoplasmic ATP and Ca2+. Within the islets the β-cells are mutually entrained into a common rhythm by gap junctions and diffusible factors (ATP). Synchronization of the different islets in the pancreas is supposed to be due to adjustment of the oscillations to the same phase by neural output of acetylcholine and ATP. Studies of hormone secretion from the perfused pancreas of rats and mice revealed that glucose induces pulses of glucagon anti-synchronous with pulses of insulin and somatostatin. The anti-synchrony may result from a paracrine action of somatostatin on the glucagon-producing α-cells. Purinoceptors have a key function for pulsatile release of islet hormones. It was possible to remove the glucagon and somatostatin pulses with maintenance of those of insulin with an inhibitor of the P2Y1 receptors. Knock-out of the adenosine A1 receptor prolonged the pulses of glucagon and somatostatin without affecting the duration of the insulin pulses. Studies of isolated human islets indicate similar relations between pulses of insulin, glucagon, and somatostatin as found during perfusion of the rodent pancreas. The observation of reversed cycles of insulin and glucagon adds to the understanding how the islets regulate hepatic glucose production. Current protocols for pulsatile intravenous infusion therapy (PIVIT) should be modified to mimic the anti-synchrony between insulin and glucagon normally seen in the portal blood

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