Biomedical subjects

O Decroly

Publications and source records attributed to O Decroly.

5 recordsLinked to original sources

PubMed1988

Finding complex oscillatory phenomena in biochemical systems. An empirical approach.

Starting with a model for a product-activated enzymatic reaction proposed for glycolytic oscillations, we show how more complex oscillatory phenomena may develop when the basic model is modified by addition of product recycling into substrate or by coupling in parallel or in series two autocatalytic enzyme reactions. Among the new modes of behavior are the coexistence between two stable types of oscillations (birhythmicity), bursting, and aperiodic oscillations (chaos). On the basis of these results, we outline an empirical method for finding complex oscillatory phenomena in autonomous biochemical systems, not subjected to forcing by a periodic input. This procedure relies on finding in parameter space two domains of instability of the steady state and bringing them close to each other until they merge. Complex phenomena occur in or near the region where the two domains overlap. The method applies to the search for birhythmicity, bursting and chaos in a model for the cAMP signalling system of Dictyostelium discoideum amoebae.

Cyclic AMP↗

PubMed1987

From simple to complex oscillatory behaviour: analysis of bursting in a multiply regulated biochemical system.

We analyze the transition from simple to complex oscillatory behaviour in a three-variable biochemical system that consists of the coupling in series of two autocatalytic enzyme reactions. Complex periodic behaviour occurs in the form of bursting in which clusters of spikes are separated by phases of relative quiescence. The generation of such temporal patterns is investigated by a series of complementary approaches. The dynamics of the system is first cast into two different time-scales, and one of the variables is taken as a slowly-varying parameter influencing the behaviour of the two remaining variables. This analysis shows how complex oscillations develop from simple periodic behaviour and accounts for the existence of various modes of bursting as well as for the dependence of the number of spikes per period on key parameters of the model. We further reduce the number of variables by analyzing bursting by means of one-dimensional return maps obtained from the time evolution of the three-dimensional system. The analysis of a related piecewise linear map allows for a detailed understanding of the complex sequence leading from a bursting pattern with p spikes to a pattern with p + 1 spikes per period. We show that this transition possesses properties of self-similarity associated with the occurrence of more and more complex patterns of bursting. In addition to bursting, period-doubling bifurcations leading to chaos are observed, as in the differential system, when the piecewise-linear map becomes nonlinear.

Catalysis↗

PubMed1985

Selection between multiple periodic regimes in a biochemical system: complex dynamic behaviour resolved by use of one-dimensional maps.

We analyse a model biochemical system in which two autocatalytic enzyme reactions are coupled in series, in conditions where multiple stable periodic regimes coexist for the same set of parameter values. We determine how the periodic regimes are reached from different initial conditions. The structure of the attraction basins is generally simple in the case of two coexisting limit cycles (birhythmicity). This structure and the associated behaviour may, however, become highly complex. In particular, the system exhibits enhanced sensitivity to initial conditions when the boundaries of the attraction basins are fractal. In the latter case, it becomes difficult to predict the evolution towards either one of two limit cycles, a phenomenon known as final state sensitivity. We show how these complex phenomena can be explained in a unified and simple manner by means of one-dimensional return maps derived from the time evolution of the model and from fifth degree polynomial equations. We suggest experimental tests of the sensitivity to initial conditions in chemical systems presenting birhythmicity. The physiological significance of the results is discussed with respect to the sensitivity of regulatory systems admitting multiple stable biological rhythms.

Allosteric Regulation↗

PubMed1983

Temporal self-organization in biochemical systems: periodic behavior vs. chaos.

The patterns of temporal self-organization in regulated biochemical systems are examined. Simple periodic oscillations are the most frequent type of such organization, as exemplified by glycolytic oscillations in yeast and muscle and by the periodic synthesis of adenosine 3',5'-cyclic monophosphate in Dictyostelium discoideum amoebas. These phenomena originate, respectively, from the periodic operation of the product-activated phosphofructokinase and adenylate cyclase reactions. The analysis of a model for a multiply regulated biochemical system shows more complex oscillatory phenomena, e.g., the coexistence between two stable periodic regimes for the same set of parameter values (birhythmicity) and chaos. The latter phenomenon of aperiodic oscillations occurs in a narrow range of parameter values and is much less frequent than simple or complex periodic behavior. It is suggested that a sufficient condition for the occurrence of birhythmicity and chaos in a regulated biological system subjected to a constant environment (i.e., in the absence of periodic forcing) may be the simultaneous presence and interaction of two mechanisms capable of producing oscillations.

Animals↗

PubMed1982

Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system.

We analyze on a model biochemical system the effect of a coupling between two instability-generating mechanisms. The system considered is that of two allosteric enzymes coupled in series and activated by their respective products. In addition to simple periodic oscillations, the system can exhibit a variety of new modes of dynamic behavior; coexistence between two stable periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable periodic regime with a stable steady state (hard excitation) or with chaos. The relationship between these patterns of temporal self-organization is analyzed as a function of the control parameters of the model. Chaos and birhythmicity appear to be rare events in comparison with simple periodic behavior. We discuss the relevance of these results with respect to the regularity of most biological rhythms.

Enzymes↗