Stem Cell Proliferation and Differentiation: A Multitype Branching Process Model

ISBN-13: 9783540501831 / Angielski / Miękka / 1988 / 113 str.

Catherine A. Macken; Alan S. Perelson

Opis

The book develops a model for stem cell proliferation and differentiation. It is a substantial generalization of the famous Till and McCulloch model. It describes the growth of stem cells in culture and the formation of both progenitor cells and end cells. The book contains a biologically realistic application of branching processes and should be of interest to mathematics students and teachers of stochastic process courses.

Spis treści

1. Introduction.- 2. A Multitype Branching Process Model.- 2.1 Probability Generating Functions.- 2.2 Moments.- 2.3 Modeling Unknown Types of Colony Initiating Cells.- 3. Characterization of Colony Growth with Time.- 3.1 Total Colony Size After n Generations.- 3.2 Probability of Completion of Growth.- 3.3 Stem Cell Growth.- 4. Colonies Reaching Completion.- 4.1 Number of Generations to Completion.- 4.2 Colony Size at Completion.- 5. Colonies Growing without Bound.- 5.1 Asymptotic Proportions of Cell Types in Colonies with an M-Cell Parent.- 5.2 Asymptotic Proportions of Cell Types in Colonies with an S-Cell Parent.- 6. Critical Processes.- 7. Results.- 7.1 Parameter Estimation.- 7.2 Total Colony Size After n Generations.- 7.3 Completion of Growth.- 7.4 Size at Completion of Growth.- 7.5 Asymptotic Proportion of Each Cell Type.- 8. Conclusions and Extensions.- Appendices.- B. Estimation of Branching Probabilities.- References.