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Fig. 4 | BMC Systems Biology

Fig. 4

From: Multitype Bellman-Harris branching model provides biological predictors of early stages of adult hippocampal neurogenesis

Fig. 4

Hierarchical structure of the neurogenic cascade modeled by the Multitype Bellman-Harris branching process with different cell types as different compartments. Consider a collection of particles of I types, which proliferate according to the following rules: At time t=0, an ancestor particle of type i is born, which lives for a random time Ï„ with cumulative distribution function (cdf) T i and upon death, it produces a random number of progeny of all types, described by a vector (X 1,...,X I ) with multivariate probability generating function h i (s 1,...,s I ) At time t=Ï„, each first-generation progeny particle of type j lives for a random time with cumulative distribution function (cdf) T j and upon death, produces a random number of progeny of all types, described by vector of multivariate pgf h j (s 1,...,s I ), independently of other progeny particles. The cycle of life, death and progeny production is repeated indefinitely by each generation of particles. ÊŽ= intensity of influx of new ANPs from NSCs, X 2 = cell doubling rate, D i = cell death rate of the cell i, p = renewal probability of ANPs, T i = duration time of cell in stage i. G1, S, G2M = stages of cell cycle. NonPr ANP = non-proliferating ANP. Astro = astrocyte

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