Emergence of Complex Dynamics in a Simple Model of Signaling Networks

A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by $1/f$-scaling of their power spectra, can emerge in networks of simple signaling units. We find that under general conditions, complex dynamics can be generated by systems fulfilling two requirements: i) a ``small-world'' topology and ii) the presence of noise. Our findings support two notable conclusions: first, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions (i) and (ii) are robust to some degree of degradation, i.e., they will still be able to generate $1/f$-dynamics

Glucose metabolism and oscillatory behavior of pancreatic islets

A variety of oscillations are observed in pancreatic islets.We establish a model, incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic beta-cells and the other is the glucose-insulin feedback model which considers direct and indirect feedback of secreted insulin. These two are coupled to interact with each other in the combined model, and two basic assumptions are made on the basis of biological observations: The conductance g_{K(ATP)} for the ATP-dependent potassium current is a decreasing function of the glucose concentration whereas the insulin secretion rate is given by a function of the intracellular calcium concentration. Obtained via extensive numerical simulations are complex oscillations including clusters of bursts, slow and fast calcium oscillations, and so on. We also consider how the intracellular glucose concentration depends upon the extracellular glucose concentration, and examine the inhibitory effects of insulin.Comment: 11 pages, 16 figure

Complex Patterns of Metabolic and Ca²⁺ Entrainment in Pancreatic Islets by Oscillatory Glucose

Glucose-stimulated insulin secretion is pulsatile and driven by intrinsic oscillations in metabolism, electrical activity, and Ca(2+) in pancreatic islets. Periodic variations in glucose can entrain islet Ca(2+) and insulin secretion, possibly promoting interislet synchronization. Here, we used fluorescence microscopy to demonstrate that glucose oscillations can induce distinct 1:1 and 1:2 entrainment of oscillations (one and two oscillations for each period of exogenous stimulus, respectively) in islet Ca(2+), NAD(P)H, and mitochondrial membrane potential. To our knowledge, this is the first demonstration of metabolic entrainment in islets, and we found that entrainment of metabolic oscillations requires voltage-gated Ca(2+) influx. We identified diverse patterns of 1:2 entrainment and showed that islet synchronization during entrainment involves adjustments of both oscillatory phase and period. All experimental findings could be recapitulated by our recently developed mathematical model, and simulations suggested that interislet variability in 1:2 entrainment patterns reflects differences in their glucose sensitivity. Finally, our simulations and recordings showed that a heterogeneous group of islets synchronized during 1:2 entrainment, resulting in a clear oscillatory response from the collective. In summary, we demonstrate that oscillatory glucose can induce complex modes of entrainment of metabolically driven oscillations in islets, and provide additional support for the notion that entrainment promotes interislet synchrony in the pancreas

Modelling the regulatory system for diabetes mellitus with a threshold window

Piecewise (or non-smooth) glucose-insulin models with threshold windows for type 1 and type 2 diabetes mellitus are proposed and analyzed with a view to improving understanding of the glucose-insulin regulatory system. For glucose-insulin models with a single threshold, the existence and stability of regular, virtual, pseudo-equilibria and tangent points are addressed. Then the relations between regular equilibria and a pseudo-equilibrium are studied. Furthermore, the sufficient and necessary conditions for the global stability of regular equilibria and the pseudo-equilibrium are provided by using qualitative analysis techniques of non-smooth Filippov dynamic systems. Sliding bifurcations related to boundary node bifurcations were investigated with theoretical and numerical techniques, and insulin clinical therapies are discussed. For glucose-insulin models with a threshold window, the effects of glucose thresholds or the widths of threshold windows on the durations of insulin therapy and glucose infusion were addressed. The duration of the effects of an insulin injection is sensitive to the variation of thresholds. Our results indicate that blood glucose level can be maintained within a normal range using piecewise glucose-insulin models with a single threshold or a threshold window. Moreover, our findings suggest that it is critical to individualize insulin therapy for each patient separately, based on initial blood glucose levels

The stability of metal complexes with 8-mercaptoquinoline and alkyl-substituted 8-mercaptoquinolines in dimethylformamide

The stoichiometry and stability constants of 8-mercaptoquinoline and alkyl-8-mercaptoquinoline complexes of Zn(II), Cd(II), Pb(II), Ni(II), Bi(III) and Ag(I) were determined potentiometrically in dimethylformamide. The stability of the 8-mercaptoquinolinates decreases in the order Ag(I) ≫ Bi(III) ≫ Ni(II) ≫ Pb(II) ≫ Cd(II) ≫ Zn(II). Metal 7-methyl-8-mercaptoquinolinates are the most stable. The presence of the alkyl group in the 2-position (which has a steric effect) lowers the strength of metal-ligand bonding. © 1984

Review article: a comparison of glucagon-like peptides 1 and 2.

BACKGROUND: Recent advancements in understanding the roles and functions of glucagon-like peptide 1 (GLP-1) and 2 (GLP-2) have provided a basis for targeting these peptides in therapeutic strategies. AIM: To summarise the preclinical and clinical research supporting the discovery of new therapeutic molecules targeting GLP-1 and GLP-2. METHODS: This review is based on a comprehensive PubMed search, representing literature published during the past 30 years related to GLP-1 and GLP-2. RESULTS: Although produced and secreted together primarily from L cells of the intestine in response to ingestion of nutrients, GLP-1 and GLP-2 exhibit distinctive biological functions that are governed by the expression of their respective receptors, GLP-1R and GLP-2R. Through widespread expression in the pancreas, intestine, nervous tissue, et cetera, GLP-1Rs facilitates an incretin effect along with effects on appetite and satiety. GLP-1 analogues resistant to degradation by dipeptidyl peptidase-IV and inhibitors of dipeptidyl peptidase-IV have been developed to aid treatment of diabetes and obesity. The GLP-2R is expressed almost exclusively in the stomach and bowel. The most apparent role for GLP-2 is its promotion of growth and function of intestinal mucosa, which has been targeted for therapies that promote repair and adaptive growth. These are used as treatments for intestinal failure and related conditions. CONCLUSIONS: Our growing understanding of the biology and function of GLP-1, GLP-2 and corresponding receptors has fostered further discovery of fundamental biological function as well as new categories of potent therapeutic medicines