Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

Anticoagulant and antiprotease profiles of a novel natural heparinomimetic mannopentaose phosphate sulfate (PI-88)

Heparinomimetic mannopentaose phosphate sulfate (PI-88) (Progen Industries Ltd. Brisbane, Australia), currently developed as an anticoagulant and antiproliferative agent, mainly is composed of a pentomannan. However, tetrasaccharide and disaccharide components are also present. The molecular profile and the anticoagulant potency of PI-88 are investigated in this study. Gel permeation chromatography and polyacrylamide gel electrophoresis analyses were carried out to determine the molecular profile and separation of components of PI-88, respectively. Potentiation of antithrombin III (ATIII) and heparin cofactor-II (HC-LI) activity were measured using chromogenic substrate assay. In order to determine anticoagulant and antiprotease effects of PI-88, various global anticoagulant tests, such as the prothrombin time (PT), activated partial thromboplastin time (APTT), thrombin time (TT), Heptest(R) (Haemachem Inc., St. Louis), ecarin clotting time (ECT), activated clotting time (ACT), and thromboelastography (TEG) were used. Anti-Xa and anti-IIa activities also were measured. The effect of PI-88 on the release of tissue factor pathway inhibitor (TFPI) was performed in nonhuman primates who received PI-88 and in endothelial cell culture systems. The relative susceptibility of PI-88 to heparinase I, protamine sulfate (PS), and platelet factor 4 (PF4) also was evaluated. The high-performance liquid chromatography profiles of PI-88 showed that its average molecular weight is approximately 2300 Da. Separation and gradient electrophoretic patterns of PI-88 showed that it is composed of five different fractions. This agent activates HC-II through inhibiting the thrombin generation but not inhibiting ATIII. Although PI-88 produced a concentration-dependent prolongation of all of the clotting tests, ECT gave the best correlation in the dose-response curve (ECT, r(2) = 0.94; TT, r(2) = 0.84; APTT, r(2) = 0.69). Heparinomimetic mannopentaose phosphate sulfate (PI-88) exhibited marked inhibition of FIIa, but not of FXa. Heparinase I failed to produce significant neutralization of PI-88 in all the assays used, whereas PS and PF4 partially neutralized the effects of this compound. Heparinomimetic mannopentaose phosphate sulfate (PI-88) produced fivefold increase in the TFPI levels at 15 minutes after intravenous (IV) injection to primates. The incubation of PI-88 in endothelial cell culture system also showed a strong effect on TFPI release. These results suggest that PI-88 exhibited strong antithrombotic and anticoagulant activity in addition to its known antiproliferative properties. Because of the molecular characteristics and the dual nature of the pharmacologic action of PI-88, this agent represents an attractive pharmacologic agent for the control of thrombotic and proliferative disorders

Preparation and anticoagulant activity of the phosphosulfomannan PI-88

A yeast-derived phosphomannan mixture was chemically sulfonated and the composition and structure of the product mixture was studied. This phosphosulfomannan mixture, PI-88, is currently under clinical evaluation as an anti-cancer agent. Analysis using capillary electrophoresis demonstrated that PI-88 was a multi-component mixture. Gel permeation chromatography provided four fractions of PI-88 that contained components which differed in size from disaccharide to hexasaccharide, and by degree of sulfation. These fractions were characterised by spectroscopic and chromatographic methods and the structure of PI-88 is that expected based On the structure of the phosphomannan starting material. The anticoagulant activity of these fractions was evaluated and the structural requirements for,activity are described. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved

Neural Synchronization at Tonic-to-Bursting Transitions

We studied the synchronous behavior of two electrically-coupled model neurons as a function of the coupling strength when the individual neurons are tuned to different activity patterns that ranged from tonic firing via chaotic activity to burst discharges. We observe asynchronous and various synchronous states such as out-of-phase, in-phase and almost in-phase chaotic synchronization. The highest variety of synchronous states occurs at the transition from tonic firing to chaos where the highest coupling strength is also needed for in-phase synchronization which is, essentially, facilitated towards the bursting range. This demonstrates that tuning of the neuron’s internal dynamics can have significant impact on the synchronous states especially at the physiologically relevant tonic-to-bursting transitions