A small number of tern cells replenishes the whole crypt

Fig. 4.1 The epithelium of the colon is organized into crypts. Each crypt contains about 103 cells. A small number of (stem) cells, which are thought to be located at the bottom of the crypt, divide asymmetrically to replenish the whole crypt. They give rise to differentiated cells which travel within 36 hours to the top of the crypt where they undergo apoptosis. Inactivation of both copies of the APC gene is believed to prevent apoptosis. The mutated cells remain on the top of the crypt, continue to divide and ultimately take over the crypt. This process gives rise to a dysplastic crypt, which represents the first step on the way to colorectal cancer.

give rise to differentiated cells which divide at a faster rate, and travel to the top of the crypt where they undergo apoptosis.

We start with the basic model of sporadic colorectal cancer initiation [Komarova et al. (2002)]. All the relevant parameters with their respective values are summarized in Table 4.1. Let us assume that the effective population size of a crypt is N\ this means that N cells are at risk of developing mutations which can lead to cancer. The value of N is unknown. As will be explained in detail in Chapter 5, one hypothesis is that only the stem cells are at risk of developing cancer, which gives AT ~ 1 — 10, and in this case the average turnover rate would be r = 1 — 20 days. Alternatively, we could assume that some differentiated cells are also at risk. In this case, N might be of the order of 100 and the average turnover rate could be less than 1 day. Here we will concentrate on the model with N ~ 1 — 10; some implications of the other model will also be discussed. In this chapter, we will not consider the details of the population structure. That is, the distinction between stem cell and differentiated cell division patterns will be ignored. Chapter 5 suggests a way of incorporating this in the model.

Table 4.1 Parameters, notations and possible numerical values; the mutation and LOH rates are given per gene per cell division.

Quantity

De finition

Range

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