[The notion of the internal and external limitations of monotonic growth functions. A reformulation of the logistic equation].
The boundary value (plateau) of non-periodic growth functions constitutes one of the parameters of various usual models such as the logistic equation. Its double interpretation involves either a limit of an internal or endogenous nature or an external environment-dependent limit. Using the autocatalytic model of structured cell populations (Buis, model II, 2003), a reformulation of the logistic equation is put forward and illustrated in the case of three cell classes (juvenile, mature, senescing). The agonistic component corresponds exactly to the only active fraction of the population (non-senescing mature cells), whereas the antagonistic component is interpreted in terms of an external limit (available substrate or source). The occurrence and properties of an external limit are investigated using the same autocatalytic model with two major modifications: the absence of competition (non-limiting source) and the occurrence of a maximum number of mitoses per cell filiation (Lück and Lück, 1978). The analysis, which is carried out according to the principle of deterministic cell automata (L-systems), shows the flexibility of the model, which exhibits a diversity of kinetic properties: shifts from the sigmoidal form, number and position of growth rate extremums, number of phases of the temporal structure. These characteristics correspond to the diversity of the experimental growth curves where the singularities of the growth rate gradient are often not accounted for satisfactorily by the usual global models.
Buis
Roger
R
Biotechnologie et amélioration des plantes, Institut national polytechnique de Toulouse, Ensa, 31326 Auzeville, France. buis.roger@wanadoo.fr
Lück
Jacqueline
J
D000465:Algorithms; D000818:Animals; D049109:Cell Proliferation; D004777:Environment; D006128:Growth / Q000502:physiology*; D016015:Logistic Models; D008954:Models, Biological; D015233:Models, Statistical