Dynamic changes in cellular free-calcium concentrations are essential for a great variety of cellular processes, including intra- and extra-cellular signalling processes, muscle contraction, and cell motility. Using modern techniques in calcium imaging, experimentalists have recently resolved spatio-temporal patterns (oscillations and various types of nonlinear waves) in both isolated cells and tissue. These dynamical phenomena involve specific molecular mechanisms controlling calcium influx and efflux through the cell's outer membrane (voltage-gated ion channels, calcium exhangers and pumps) as well as calcium release mechanisms from internal compartments (sarcoplasmic or endoplasmic reticulum and mitochondria). A number of complex signalling pathways coupling these mechanisms have been uncovered in the laboratory, and realistic models of these processes are being developed. The workshop was preceded by a two-day tutorial that provides the necessary biological background for non-experts and an overview of current models. Workshop participants included a mix of experimental cell biologists, theorists currently developing mathematical models, and mathematicians from the dynamical systems community. The workshop explored important current biological questions such as the role of local calcium gradients in cells, how the stochastic properties of individual molecular entities (e.g., ion channels and hormone receptors) lead to organized dynamical behavior, and how calcium signals are transduced into physiological function. The workshop closed with an extended discussion of new mathematical challenges that this area presents in dynamical systems theory.

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1997-1998 Emerging Applications of Dynamical Systems