Many modeling studies have tried to capture this tightly regulated system, and three common approaches are to use compartmental, simulation or stochastic models (reviewed in ref. This general structure of stem, transit and differentiated cells is also found in many other biological systems, for example the hematopoietic system. 2 As the stem cells divide, their progeny migrate up the crypt wall, and once at the top they are shed into the lumen or undergo apoptosis. The single layer of epithelial cells that line the crypt is renewed every two to three days by a number of long-living stem cells that remain at the bottom of the crypt. 1 One such example is that of homeostasis in the colonic crypt. Mathematical modeling can be a powerful tool for understanding biologically observed phenomena which cannot be understood by verbal reasoning alone. 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. 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. 5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We use the cell population model by Johnston et al. 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. Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems.

Ip02 mathematical model block diagram