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Modeling Stem Cell Population Growth: Incorporating Terms for Proliferative Heterogeneity

^a Departments of Orthopaedic Surgery, Molecular Genetics, Biochemistry and Bioengineering, University of Pittsburgh School of Medicine;
^b Growth and Development Laboratory, Children’s Hospital of Pittsburgh;
^c Department of Radiation Oncology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, USA

Key Words. Nonexponential • Mathematical model • Kinetics • Muscle-derived stem cell • Proliferation

Johnny Huard, Ph.D., Growth and Development Laboratory, Children’s Hospital of Pittsburgh; Departments of Orthopedic Surgery, Molecular Genetics, Biochemistry, and Bioengineering, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania 15213, USA. Telephone: 412-692-8148; Fax: 412-692-7095; e-mail: jhuard{at}pitt.edu

Expansion of the undifferentiated stem cell phenotype is one of the most challenging aspects in stem cell research. Clinical protocols for stem cell therapeutics will require standardization of defined culture conditions. A first step in the development of predictable and reproducible, scalable bioreactor processes is the development of mathematical growth models. This paper provides practical models for describing cell growth in general, which are particularly well suited for examining stem cell populations. The nonexponential kinetics of stem cells derive from proliferative heterogeneity, which is biologically recognized as mitosis, quiescence, senescence, differentiation, or death. Here, we examined the assumptions of the Sherley model, which describes heterogeneous expansion in the absence of cell loss. We next incorporated terms into the model to account for A) cell loss or apoptosis and B) cell differentiation. We conclude that the basic assumptions of the model are valid and a high correlation between the modified equations and experimental data obtained using muscle-derived stem cells was observed. Finally, we demonstrate an improved estimation of the kinetic parameters. This study contributes to both the biological and mathematical understanding of stem cell dynamics. Further, it is expected that the models will prove useful in establishing standardization of cell culture conditions and scalable systems and will be required to develop clinical protocols for stem cell therapeutics.

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