By Catherine A. Macken, Alan S. Perelson
The physique comprises many mobile platforms that require the continual construction of latest, absolutely practical, differentiated cells to switch cells missing or having restricted self-renewal functions that die or are broken through the life of anyone. Such platforms comprise the dermis, the epithelial lining of the intestine, and the blood. for instance, erythrocytes (red blood cells) lack nuclei and therefore are incapable of self-replication. they've got a lifestyles span within the flow of approximately one hundred twenty days. Mature granulocytes, which additionally lack proliferative means, have a far shorter existence span - regularly 12 hours, notwithstanding this can be lowered to just or 3 hours in occasions of significant tissue an infection. maybe a extra time-honored instance is the outermost layer of the surface. this sediment consists of totally mature, useless epidermal cells that has to be changed by means of the descendants of stem cells lodged in reduce layers of the skin (cf. Alberts et al. , 1983). In overall, to provide the conventional steady-state calls for of cells, a typical human needs to produce nearly three. 7 x 1011 cells an afternoon all through lifestyles (Dexter and Spooncer, 1987). universal to every of those mobile structures is a primitive (undifferentiated) stem phone which replenishes cells in the course of the creation of offspring, a few of which proliferate and progressively differentiate until eventually mature, totally practical cells are produced.
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Extra info for Stem Cell Proliferation and Differentiation: A Multitype Branching Process Model
Example text
In this case numerical solutions axe easily obtained, and such numerical solutions axe used later in the text. The mean and variance of Zn provide convenient summaries of some of the major features of the full distribution function for Zn obtained by the generating function approach above. , higher order moments do not decrease to zero with increasing n. 3 Modeling Unknown Types of Colony Initiating Cells One further modeling step is necessary before we have a theory that can be compared with experiment.
Posable Galton-Watson processes (cf. Kesten and Stigum, 1967; Mode, 1971). The essenc~ of these theorems is that, under conditions in which a colony can grow without bound, the limiting proportion of each cell type is a constant that can be calculated as a function of the branching probabilities, ps, Pm, and Pe. The theorems require calculation of the eigenvalues and eigenvectors of the matrix of means of the offspring distribution for parents of each type. We shall consider separately the cases of colonies with an M -cell parent and colonies with an S-cell parent.
The total variability observed among plated colonies (var[ZnD is composed of two separable components. The first component (Ezo(var[Zn\ZO)])) measures the average variability within a colony, where the average is taken over all possible types of initiating cells. The "within" variability is due to the stochastic nature of the proliferative process. The second component (varzo(E[Zn\Zo])) measures the variability among the average behavior of colonies due to different types of initiating cells. Chapter 3 Characterization of Colony Growth with Time In the previous chapter, we alluded to the problem of iteration of the generating functions: Essentially it is computationally infeasible to evaluate Eq.