Danish Ph.D. School in Nonlinear Science

Sponsored by the Danish Research Agency

Research area: NONLINEAR DYNAMIC MODELS OF PHYSIOLOGICAL CONTROL SYSTEMS

Physiological control systems offer a particularly interesting area of application for the ideas and techniques of nonlinear science. Contrary to the concept of homoestasis that has dominated physiological thinking for such a long time, unstable phenomena are increasingly being recognized as essential in the regulation and function of normal physiological systems.

The heart beat and the respiratory and ovarian cycles have long been acknowledged as self-sustained oscillations. However, investigations performed during the last decades have revealed the existence of a great variety of additional rhythms with periods ranging from fractions of a second to several hours or even days. Many hormonal systems are unstable and operate in a pulsatile or oscillatory mode. This is true, for instance, for the release of insulin, growth hormone, and luteinizing hormone, and the interaction between two or more such pulsatile systems is likely to produce frequency-locking, chaos and a variety of other complicated nonlinear dynamic phenomena. It is clear that the disruption of certain hormonal rhythms can be associated with states of disease, and that new types of oscillations may appear in connection with other diseases.

Rhythmic signals are also essential for the function of the individual cell as well as for cell-to-cell signalling. Besides neurons and muscle cells that are known to sustain traveling electrical pulses, many other cells exhibit pulsatory variations in the membrane potential. The insulin producing -cells in the pancreas, for instance, exhibit oscillations in the hormonal release that are closely coupled to oscillations in the membrane potential, and observations indicate that signal transduction within the cell may be associated with oscillations and waves of intracellular messengers.

In many ways, the approaches of nonlinear science promise that for the first time we can develop a more detailed theoretical understanding of physiological control systems. Among the main topics considered under this heading are:

• oscillations and chaos in the regulation of kidney flows and pressures
• self-sustained oscillations in the insulin-glucose system
• hormonal oscillations and the role of receptor dynamics
• nonlinear dynamic phenomenon in coupled -cells.

The research is performed in collaboration with Dept. of Medicine, University of Copenhagen, Dept. of Medicine, University of Chicago, and Novo Nordisk A/S.