Mathematical modeling for the aging process: normal, abnormal and self-terminating phenomena in spatio-temporal organization.
An elucidation of the aging process is attempted using a simple one-dimensional multicellular system, a prototype of living organisms. This model analysis has the advantage of making us investigate the two types of modes of their dynamical behavior: (i) the local modes of behavior of individual cells and (ii) the global modes of behavior of the total system. At first, each cell is assumed to have biochemically excitable kinetics for local modes, and then what kind of the global modes results with change in intercellular interaction is examined. With a simple interaction as possibly occurs in the early stage of differentiation, the model displays well-coordinated spatio-temporal patterns. This may be interpreted as a normal state. With a more complex interaction as possibly occurs in the late stage of growth, however, the model produces much more erratic patterns. This may refer to an abnormal state. Interestingly, these abnormal patterns can be transformed into normal patterns, when the activity of some parts of this model is turned 'off'; the system can survive at the sacrifice of its parts. This makes us imagine that programmed cell death plays an important role in development during morphogenesis. When individual cells become less sensitive to intercellular signals and still possess intrinsic excitability, then the normal patterns are developed for a short while before being replaced by rather irregular patterns. As time proceeds, however, all activity of them disappears. We call this a 'self-terminating' phenomenon, which may refer to aging. This strongly suggests that the loss of the total system function, leading to death, results from a global mode of system failure but not from a local mode of subsystem failure.
Murase
M
M
Tokyo Metropolitan Institute of Gerontology, Japan.
Matsuo
M
M
D000375:Aging / Q000473:pathology / Q000502:physiology; D000818:Animals; D002468:Cell Physiological Phenomena; D004594:Electrophysiology; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D013598:Systems Theory