Structure, Complexity and Chaos in Living Systems
Although homeostasis of the internal environment is almost axiomatic in the physiological sciences, it is apparent that rhythms occur in the levels of a variety of bodily functions, ranging in time from a few cycles per millisecond for the firing of the central nervous system to the monthly period of the menstrual cycle. As an example of such a rhythm, this introductory overview describes how self-sustained oscillations arise in the pressure and flow regulation of individual nephrons as a result of a delayed action of the juxtaglomerular apparatus. The same problem is dealt with in considerably more detail in the contribution by Marsh et al., and one of the purposes of the present discussion is to speculate on the biological significance of such cycles.
A viral or bacterial infection is an example of an instability where a small initial population of foreign agents is allowed to multiply over several decades before the immune system or other reactions of the body finally establishes the defence required to cope with the infection. In a recent paper by Anderson and May, it was suggested that the response of the immune system to the simultaneous infection by HIV and another virus that activates the same T-cells can produce chaotic bursts of free HIV with intervals of the order of 20 weeks. We have performed a more detailed mathematical analysis of this model, including a construction of phase space trajectories as well as Poincaré sections and return maps. At least one route to chaos in the model has been identified and found to proceed through a cascade of period-doubling bifurcations. Even though more recent observations seem to indicate that the Anderson and May model is incorrect in certain respects, it can still be expected that the immune system is capable of producing very complicated responses.
In contrast to the conventional picture of a relatively quiescent dynamics, it has always been acknowledged that the spatial structure of physiological systems is exceedingly complicated. Advances in experimental techniques over recent decades have made it possible to illuminate this complexity in even more detail, and the time has come when we must try to relate the complexity of the physiological structures with the dynamical processes involved in their formation and maintenance. As a final problem we thus discuss some of the difficulties involved in relating bone structure with bone remodeling processes. This problem will also be dealt with at greater length in a subsequent contribution by Lis Mosekilde.
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