Ph.D. Summer School 1999 in Modelling Nonlinear Dynamics in Complex Chemical and Biological Systems.

Abstracts

Modeling biochemical and cellular rhythms

A. Goldbeter

Models for biochemical oscillations will be described, based on different types of cellular regulation. Considered in turn will be (1) Glycolytic oscillations in yeast which originate from the regulation of the allosteric enzyme phosphofructokinase; (2) Oscillations of cyclic AMP in the amoebae Dictyostelium discoideum, which appear to be based on receptor regulation through reversible phosphorylation; (3) Cytosolic calcium oscillations which originate from the regulation, of intracellular transport processes; (4) Circadian (24h-period) rhythms resulting from the regulation of gene expression. Theoretical models show that in each case the particular mode of cellular regulation gives rise to sustained oscillations of the limit cycle type. The models further indicate the conditions in which more complex oscillatory phenomena such as birhythmicity, bursting or chaos can originate from the coupling of multiple instability-generating mechanisms within the cell. Finally, the link between oscillations and waves will be illustrated in the cases of calcium and cyclic AMP signalling.