Stochastic model of human granulocyte-macrophage progenitor cell proliferation and differentiation. I. Setting up the model.

A mathematical model is constructed for the proliferation and differentiation of granulocyte-macrophage progenitor cells in response to the specific proliferation/differentiation stimulus granulocyte-macrophage colony stimulating activity (gm-CSA). The major objective of this model was to test an earlier conceptual model in which we proposed that clone size potential and sensitivity to gm-CSA are functional properties of granulocyte-macrophage progenitor cells, properties that gradually change as the cells differentiate down the granulocyte-monocyte pathway. Another aim was to provide a tool for further analysis of the regulation of granulopoiesis and granulocyte-macrophage progenitor cell proliferation and differentiation. To formulate and then test the mathematical model, available experimental data were divided, one part being used to construct the model, and the other, the results of different and independent experiments, being used for model validation. This report describes the mathematical model and the estimation of model parameters using in vitro experimental results on the relationship between clone number and gm-CSA concentration and on the clone size distributions obtained under conditions of maximal stimulation by gm-CSA. The accompanying article shows how the model was then tested using data from three other types of experiment.