[Contribution to the logistic theory of growth: temporal structure and growth potential].
The analysis of a structured population according to three (juvenile, mature and senescent) cellular states is carried out within the framework of Delattre's transformation systems theory. Growth in number, with the dissymmetry of cell divisions, is determined by an autocatalysis process under the constraint of the availability of a source. Two models are presented: their dynamics results in a growth of the exponential type or of the sigmoidal type, respectively. In the sigmoidal case, the logistic equation (Richards-Nelder's function with adjunction of a lower asymptote Y not equal to 0) fits satisfactorily the simulated data of the total cell number Y. The growth potential is defined as the instantaneous capacity of autocatalysis, which is expressed in relation to the present 'mitotic resources' (source + non-senescing mature cells). The acceleration variations d2Y/dt2 are in close agreement with the growth potential gradient. The analysis is then generalized to other population structuring. As a result, the logistic equation can be interpreted in terms of a formal model of growth of a structured population submitted to autocatalysis and competition.
Buis
Roger
R
Laboratoire de biotechnologie et amélioration des plantes, Institut national polytechnique de Toulouse, Ensa, 31326 Auzeville, France. buis@ensat.fr
D000818:Animals; D016923:Cell Death; D002455:Cell Division; D016922:Cellular Senescence; D006128:Growth; D016015:Logistic Models; D008954:Models, Biological