Nonlinear modelling of calcium metabol ism — first attempt in the calcium-deficient rat

Abstract

A nonlinear model of calcium metabolism in the calcium-deficient rat is pro posed. It takes fully into account the experimental time-courses of plasma calcium and its radionuclide concentrations, circadian variations included. Through its mathematical representation (a set offive first-order differential equations incorporating a nonlinearity representing a second-order autocatalysis), calcium metabolism is considered as a self-organised system and its circadian behaviour is dictated mainly by nonlinear processes involved in bone calcification. From our identification procedure, a probably unique set of parameters is obtained and both temporal stability and the time-course of calcium distribution within the model are studied. The model exhibits a stable limit cycle corresponding to two observed characteristics of calcium metabolism: stability and circadian periodicity. Simulated behaviour of different compartments is discussed in relation to calcium deficiency. In conclusion, this investigation represents the first attempt to elucidate a quantitative study of calcium metabolism, visualised as a self-oscillating system, ie, in a non-steady stable state.

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