We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G(alpha) subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes.

Whereas case rates for some childhood diseases (chickenpox) often vary according to an almost regular annual cycle, the incidence of more efficiently transmitted infections such as measles is more variable. Three hypotheses have been proposed to account for such fluctuations. (i) Irregular dynamics result from random shocks to systems with stable equilibria. (ii) The intrinsic dynamics correspond to biennial cycles that are subject to stochastic forcing. (iii) Aperiodic fluctuations are intrinsic to the epidemiology. Comparison of real world data and epidemiological models suggests that measles epidemics are inherently chaotic. Conversely, the extent to which chickenpox outbreaks approximate a yearly cycle depends inversely on the population size.

No abstract

Dynamic systems are usually thought to have either monotonic or periodic behaviour. Although the possibility of other types of behaviour has been recognised for many years, the existence of non-monotonic, non-periodic behaviour in dynamic systems has been firmly established only recently. It is termed chaotic behaviour. A review on the rapidly expanding literature on chaos in discrete model systems described by difference equations has been published by May. Rössler, on the other hand, has discussed a few published works on systems of differential equations with chaotic solutions, and he has proposed a three-component chemical model system which he argues has chaotic solutions [figure see text]. The argument is based on a theorem by Li and Yorke. Here we report the finding of chaotic behaviour as an experimental result in an enzyme system (peroxidase). Like Rössler we base our identification of chaos on the theorem by Li and Yorke.

We have studied mixed-mode oscillations (MMO) in the peroxidase-oxidase reaction at pH 6.3 and its dynamic behaviour as the stationary concentration of reduced nicotinamide adenine dinucleotide (NADH) is changed. At low NADH concentration, simple periodic relaxation oscillations of large amplitude are observed. As the concentration of NADH is increased, MMOs arise. They start with a simple 1' state where one oscillation with large amplitude is followed by one oscillation of small amplitude. Further increase in NADH results in 1' patterns where one large amplitude oscillation is followed by i small amplitude oscillations. The individual MMO states lose stability through period doubling sequences leading to narrow chaotic regions. These are followed by period-added regimes of MMOs. The period adding sequence of MMOs culminates in a broad region of homoclinic chaos. The experimental results are compared with numerical simulations of a detailed model of the reaction.Mixed-mode oscillations (MMOs) are oscillatory cycles that consist of a number of large-amplitude oscillations which are intercalated by a number of small-amplitude oscillations.