## Hnpcc

Patients with HNPCC inherit one mutation in an MSI gene. The corresponding mutation-selection network is presented in Figure 4.4b. The solutions for X2 and Y2 in this case are identical to those for sporadic colorectal cancers and are given by equations (4.2). The solution for Z2 is as follows:

= (u + p0)[a2Eb - b2Ea + (q - b){uabt/T - (a + &))] abu(a — b) '

in the limit where u is a fast rate we have Z2(t) — (u +po)t/r. In the opposite limit, where u is a slow rate, Z2H) = N(u+po)u(u+po)(t/t)3/3. If we assume that the second copy of the MSI gene is silenced by methylation, we need to replace u by umet in the expression for ^(i).

The solutions for X2 and I2 in this case are quadratic in time (two rate-limiting steps), and the quantity Zz(i) grows slower than linear but faster than quadratic, because it requires one rate-limiting and two intermediate steps (note that we are talking about linear and quadratic functions of an argument smaller than one). In Table 4.6 we present the expected number of dysplastic crypts and the fraction of MSI crypts, calculated for t = 40. We have explored two possibilities: (1) inactivation of the second copy of an MSI gene happens by means of a point mutation, with the rate u, and (2) inactivation of the second copy of an MSI gene happens by methylation. There is evidence that the second scenario is less likely in the case of HNPCC [Yamamoto et al. (2002)]. In a recent study, DNA methylation of the hMLHl gene was found in 80% of 40 sporadic MSI cancers and in 0% of 30 cancers in HNPCC patients [Esteller et al. (2001)].

Our model predicts that the majority of dysplastic crypts in HNPCC patients are expected to have MSI. However, we do not find that 100% of dysplastic crypts will contain MSI. On the other hand, we know that virtually all tumors in HNPCC patients have MSI. This might suggest that selection for MSI also happens at later stages of carcinogenesis: dysplastic crypts with MSI might have a faster rate of progression to cancer than dysplastic crypts containing CIN or normal cells.

Finally we note that the total number of dysplastic crypts in HNPCC patients, as predicted by our model, is of the order 10 at age 40, which is only slightly larger than the expected number of dysplastic crypts in normal individuals and is not nearly as high as in the case of FAP (of the order 10,000, Table 4.6). This is also consistent with observations.

Condition |
Total No of dyspl. crypts |
% of CIN |
% of MSI |

HNPCCby mutation |

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