Abstract
A genealogical model describing the dynamics of a binary branching system of astrocytes and microglia which takes into account a developmental hierarchy, is proposed. The model consists of a scheme of developmental pathways interconnecting the elements at various stages of development from a common progenitor to a nonproliferating end stage. To the elements at each stage are attributed probabilities of division, differentiation and quiescence. The pathway of any particular element at the end of each cycle is determined by a random-number generator according to the predetermined probabilities. The model is applied to colony formation in vitro. The development of each colony is followed for several cycles of division and theoretical results are compared to experimental values. Comparison of values obtained from several variants of the theoretical model with experimental data is then used to derive the most plausible scheme of branching pathways under given experimental conditions. The model is defined as follows: a common unlabeled progenitor with a high self-renewal potential differentiates into unlabeled monopotential precursors which further develop into astrocytes and microglia, identified experimentally as GFAP-positive cells and CR3-positive cells, respectively. Both the monopotential unlabeled cells and the identifiable progeny also have the capability of self-renewal.
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