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Examples of Mathematical Modeling: Tales from the Crypt

Matthew D. Johnston, Carina M. Edwards, Walter F. Bodmer, Philip K. Maini and S. Jonathan Chapman

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Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters.

Authors

Matthew D. Johnston

University of Oxford; Oxford UK

Carina M. Edwards

University of Oxford; Oxford UK

Walter F. Bodmer

University of Oxford; Oxford UK

Philip K. Maini

University of Oxford; Oxford UK

S. Jonathan Chapman

University of Oxford; Oxford UK

Purchase article for $19

Subscribe to this journal for $129/year