New facets to Knudsen’s “two-hit” hypothesis have been proposed recently in relation to adenomatous polyposis coli (APC): protein inactivation may be selected weakly, and the two hits may be interdependent. We reviewed published data on 165 sporadic and 102 familial adenomatous polyposis-associated colorectal tumors with two characterized mutations. Using a Poisson model, we redefined the mutation cluster region (MCR) to residues 1281–1556 and confirmed that the locations of pairs of APC mutations are interdependent (P < 0.0001). A mathematical model, based on the data for sporadic tumors, implied different growth advantages for different combinations of APC mutations: genotype I/I (I: mutation inside MCR) was 3.9 times more likely to be selected than IO or IL (O: mutation outside MCR, L: allelic loss), which were 27.8 times more likely to be selected than OO or OL.

The APC3 gene acts as a gate-keeper for the development of colorectal adenomas and carcinomas. Biallelic APC mutations are found in very early adenomas in both sporadic and FAP-associated disease (1), and APC has been regarded as a classical Knudsen-type tumor suppressor gene. Pathogenic mutations affecting the 2843 amino acid APC sequence are nonrandomly distributed, and >60% of reported somatic mutations occur between codons 1286 and 1513, a region referred to as the MCR (2). Recently, new facets to Knudsen’s “two-hit” model have been proposed in relation to APC (3). In both sporadic and FAP-associated colorectal tumors, an interdependence of the two hits has been proposed, with mere protein inactivation appearing to be selected weakly, if at all (4, 5). This interdependence of mutations has led to the suggestion that different combinations of APC mutation confer tumors with different selective advantages and that both mutations need to be considered together when their functional consequences are being investigated (3). We have compiled a comprehensive literature-based list of >260 sporadic and FAP-associated colorectal tumors in which two truncating APC mutations have been identified. These data allow us to confirm previous suggestions that the two hits in both sporadic and FAP-associated tumors are highly significantly associated. Furthermore, we developed a mathematical model, based on all data available for sporadic tumors, which suggests that different combinations of APC mutations have different growth advantages.

### Data Compilation.

We reviewed literature reports on the characterization of somatic APC mutations in sporadic or FAP-associated colorectal tumors. The search covered all publications cited in the APC mutation database4 and publications from the period 1991–2001 as identified through a PubMed5 search. A comprehensive list of tumors with two truncating APC mutations was compiled from a total of 18 articles (1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19). Reports of truncating mutations that were inconsistent with the published cDNA sequence (accession nos. M74088 and M73548) were excluded, as were putative missense mutations, because the evidence for their pathogenicity was inconclusive. Data on 165 sporadic tumors containing two somatic APC mutations (on-line Table 1)6 and on 102 FAP-associated tumors containing an inherited and a somatic mutation (on-line Table 2) were retrieved for analysis. Although in some tumors it was impossible to confirm whether the two truncating mutations were on different alleles, this was generally assumed to have been the case.

### Statistical Analysis.

To redefine the MCR on a statistical basis, we used a Poisson model for the observed number of intragenic APC mutations in sporadic tumors per amino acid residue. To this end, the APC amino acid sequence was considered to be divided into three consecutive regions, namely 5′MCR, MCR, and 3′MCR, each with its own Poisson parameter λ5′MCR, λMCR, and λ3′MCR, respectively. For each positioning of the first (f) and last (l) residue of the MCR, the overall likelihood of a given set of mutations equals:

$Lik(f,\ l){=}e^{{-}{\lambda}_{5{^\prime}MCR}}{{\sum}_{j{=}1}^{f{-}1}}\ \frac{{\lambda}_{5{^\prime}MCR}^{n_{j}}}{n_{j}!}{+}e^{{-}{\lambda}_{MCR}}{{\sum}_{j{=}f}^{l}}\ \frac{{\lambda}_{MCR}^{n_{j}}}{n_{j}!}{+}e^{{-}{\lambda}_{3{^\prime}MCR}}{{\sum}_{j{=}l{+}1}^{2843}}\ \frac{{\lambda}_{3{^\prime}MCR}^{n_{j}}}{n_{j}!}$

where nj is the number of mutations observed at the j-th residue. “Quasi” 99% confidence intervals for f and l were obtained by considering all positionings that were at most 100 times less likely than the most likely one. For a given significance level α (α = 0.95 or 0.99), significant outlier residues in terms of the observed number n of mutations were identified by reference to the critical number nα,

$n_{{\alpha}}{=}{min_{z}}\ P(n{<}z)^{s}{\geq}{\alpha}$

Here, s is the size of the section in question (i.e., 5′MCR, MCR, or 3′MCR). Critical n values for the sporadic tumor database are listed in Table 1.

### Colorectal Tumors with Two Truncating APC Mutations.

Of the 165 sporadic tumors, 57 carried two intragenic APC mutations (Fig. 1,a), and 108 carried an intragenic APC mutation together with allelic loss (Fig. 1,b). Of the 102 FAP-associated tumors, 37 carried two intragenic APC mutations (Fig. 1,a), and 65 carried an intragenic APC mutation together with allelic loss (Fig. 1 b).

### Redefinition of the MCR.

To redefine the MCR, a Poisson model was used. Maximization of the likelihood function yielded estimates of f = 1281 and l = 1556 for the first and last residue of the MCR, respectively (quasi 99% confidence interval, f: 1266 to 1286, and l: 1556). Significant outliers in terms of the observed number of mutations were residues 876 (11 mutations) and 1114 (6) in the region 5′ to the MCR and nos. 1309 (11), 1367 (6), 1450 (12), and 1556 (10) within the redefined MCR (Table 1).

### Interdependence of the Two Hits in Sporadic Colorectal Tumors.

Table 2 shows the distribution of APC gene mutation pairs in sporadic tumors, classified according to whether they occurred inside the MCR (I), outside the MCR (O), or represented allelic loss (L). Under the null hypothesis that the two hits are independent, the cell probabilities of Table 2 belong to an extended Bernoulli distribution with parameters pI, pO, and pL = 1 − pI − pO. Maximum likelihood estimates of these parameters were pI = 0.427, pO = 0.245, and pL = 0.327, and the validity of the independence model was assessed by a χ2 goodness-of-fit test. Because χ2 = 63.88 (3 df, P < 0.0001), it can be concluded that the two hits are not independent but are instead highly significantly associated.

Under the assumption that the primary occurrences of the two mutations in a sporadic tumor were unrelated events, followed by selection with a genotype-specific probability πgenotype, a mathematical model for the combined distribution of the two APC hits was derived (Model S0; Table 3,a). The absence of LL tumors (Table 2) implies that there is currently no evidence for the LL genotype being tumorigenic, thereby justifying the assumption πLL = 0. Furthermore, closer inspection of Table 2 and Fig. 1 suggests that the selection probabilities of the other genotypes only depend on the presence or absence of at least one MCR mutation (because ratios IL:IO and OL:OO are similar), which is equivalent to introducing constraints (πII = πIO = πIL = πI) and (πOO = πOL = πO) into model S0. Under this simplified model (S1, Table 3 a), maximum likelihood estimates of the parameters involved were pI = 0.128, pO = 0.293, and πIO = 7.1. Because χ2 = 0.43 (1 df, P > 0.5) for the goodness-of-fit test, it may be concluded that, for genotypes other than LL, the respective selection probabilities indeed only depend on the presence or absence of at least one mutation within the MCR. The selection probability of cells containing an MCR mutation would then be 7.1 times higher than of those without.

Although the MCR comprises only 10% of the APC coding sequence, model S1 would nevertheless predict that 24% [i.e., 100 × (1 − [1 − pI]2)] of primary mutations would be located within the MCR. Modification of the model by introducing constraint (pO = 9pI) resulted in a poor fit to the data in Table 22 = 16.47, 2 df, P = 2.7 × 10−4). However, subsequent introduction of separate selection probabilities πI′ and πII, respectively, for tumors with one or two mutations within the MCR gave a very good fit (χ2 = 0.44, 1 df, P > 0.5). Maximum likelihood estimates of the parameters involved in modified model S2 (Table 3 a) were pI = 0.036, πIII′ = 3.9, and πIIO = 108.7. This implies that, if primary mutations are uniformly distributed along the APC coding sequence, cells with two MCR mutations are 3.9 times more likely to be selected than those with one MCR mutation and 108.7 times more likely to be selected than cells lacking an MCR mutation. Genotype IO/IL would be 108.7/3.9 = 27.9 times more likely to be selected than OO/OL.

### Interdependence of the Two Hits in FAP-associated Tumors.

Table 3,b summarizes the combinations of germ-line and somatic mutations observed in FAP-associated tumors. Because χ2 = 71.83 (3 df, P < 0.0001) under an independence model, it can be concluded that the two hits are again highly associated. Because each entry in Table 3,b represents a separate tumor, a meaningful model for the distribution of the second, somatic hit, conditional on the respective germ-line mutation, could potentially be derived using the mutation and selection probabilities as defined and estimated for sporadic tumors (Table 3,b). However, regardless of whether these probabilities were derived from model S1 or S2, the model ensuing for the FAP-associated somatic mutation was the same and provided a poor fit to the data in Table 3 b, irrespective of whether the germ-line mutation was located within the MCR (χ2 = 32.37, 2 df, P < 0.0001) or outside the MCR (χ2 = 11.12, 2 df, P = 0.0038).

In the present study, we have been able to redefine the APC MCR based on statistical theory as opposed to subjective assessment of somatic mutation clustering (2). Thus, we located the MCR to residues 1281–1556, which is larger than the region initially reported (1286–1513, Ref. 2), although the inclusion of residues up to codon 1556 has been suggested before (5). Six codons harbored significantly more mutations than expected. Three of these (codons 876, 1114, and 1450) showed recurrent C to T substitution at a CpG dinucleotide, one (codon 1309) harbored a recurrent 5-bp deletion at an AAAAG direct repeat, one (codon 1367) showed recurrent C to T transition at a non-CpG dinucleotide, and one (codon 1556) was characterized by the recurrent insertion of a single A into an A6 repeat. The recurrence of most of these mutations was readily explicable in terms of well-characterized mechanisms of hypermutagenesis (e.g., spontaneous deamination of methyl-cytosines or slipped strand mispairing during DNA replication).

On the basis of a comprehensive survey of the published literature, we have been able to confirm previous suggestions that the two APC hits in both sporadic and FAP-associated colorectal tumors are strongly associated (4, 5). In addition, a mathematical model, based on data from sporadic tumors, allowed us to estimate the relative growth advantages conferred by different combinations of APC mutations. In developing our model, we assumed that the two primary mutations occurred as unrelated events, but it is possible that the nature of the first mutation could have an (yet unknown) effect on the occurrence of the second. APC has recently been shown to play a role in maintaining correct chromosome segregation by binding to kinetochores with EB1 (20); however, because all APC gene mutations reported to date are predicted to lead to the loss of the EB1 binding domain, it seems unlikely that mutant APC itself is a direct determinant of the frequency at which allelic loss is observed.

Although a clear interdependence of the two mutational hits in APC was also observed in FAP-associated tumors, our model of selection based on observations in sporadic tumors does not explain the genotype distribution in FAP-associated tumors. Genotype Ig + Ls has been reported more frequently than expected, whereas Ig + Os has been reported less frequently (Table 3 b). This discrepancy may reflect a difference between the mechanisms of sporadic and FAP-associated tumorigenesis. However, most of the data on FAP tumors were derived from a single study that reported allelic loss in numerous adenomas from a small number of patients, all carrying the most common germ-line mutation 1309 del5bp (4). In the same study, only the MCR-containing exon 15 was screened for somatic mutations, whereas exons 1–14 were not. Therefore, the data for FAP-associated tumors may have been subject to considerable ascertainment bias. Sporadic tumors, by contrast, show a wider spectrum of first hits, have been isolated from a larger number of cases, and have been analyzed by numerous investigators using a wide variety of screening strategies. Nonetheless, there remains a theoretical possibility that some of the observed differences are attributable to publication bias rather than tumor selection. Future analyses of tumors from FAP patients with a wider spectrum of germ-line mutations may help to resolve whether similar genotype-specific growth advantages pertain to sporadic and FAP-associated tumors. Indeed, it would be preferable to test separate models for sporadic and FAP-associated tumors against a single model for a combined data set, where more data are available for the FAP setting.

In conclusion, we have confirmed a clear interdependence of the two APC hits in both sporadic and FAP-associated tumors and developed, for the first time, a model that allows quantification of how different combinations of APC mutations confer different growth advantages. Whether differential genotype selection reflects novel (pathogenic) functions associated with a subset of mutant APC proteins, an imbalance of different lost and retained physiological roles of APC, or an as yet unsuspected mechanism will require further investigation. It also remains to be determined whether mutations in other tumor suppressor genes are subject to similar genotype-specific selection.

Fig. 1.

a, pairwise distribution of intragenic APC mutations in sporadic and FAP-associated colorectal tumors. Each tumor is represented by the location of its most 5′ mutation on the X axis, and its most 3′ mutation is on the Y axis. b, distribution of intragenic APC mutations associated with allelic loss in sporadic and FAP-associated tumors. ----, the MCR (amino acids 1281–1556) as determined by a Poisson model.

Fig. 1.

a, pairwise distribution of intragenic APC mutations in sporadic and FAP-associated colorectal tumors. Each tumor is represented by the location of its most 5′ mutation on the X axis, and its most 3′ mutation is on the Y axis. b, distribution of intragenic APC mutations associated with allelic loss in sporadic and FAP-associated tumors. ----, the MCR (amino acids 1281–1556) as determined by a Poisson model.

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The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

1

Supported by grants from Tenovus and the King Saud University via the Saudi Cultural Bureau.

3

The abbreviations used are: APC, adenomatous polyposis coli; FAP, familial adenomatous polyposis; MCR, mutation cluster region.

4

5

6

Table 1

Characterization of the APC gene MCR and flanking regions

Region5′MCRMCR3′MCR
Range 1–1280 1281–1556 1557–2843
Size 1280 276 1287
λ 0.060 0.518 0.003
N0.95
N0.99
Region5′MCRMCR3′MCR
Range 1–1280 1281–1556 1557–2843
Size 1280 276 1287
λ 0.060 0.518 0.003
N0.95
N0.99
Table 2

Pattern of pairwise APC mutation in sporadic colorectal tumoursa

IOLLocation
40 83
25

IOLLocation
40 83
25

a

I, inside MCR; O, outside MCR; L, allelic loss.

Table 3A

Models of APC mutation distribution in sporadic colorectal tumoursa

GenotypeModel S0Model S1Model S2
IIb PI2πII pI2πI pI2πII
IO 2pIpOπIO 2pIpOπI 18pI2πI′
IL 2pI(1 − pI − pOIL 2pI(1 − pI − pOI 2pI(1 − 10pII′
OO PO2πOO pO2πO 81pI2πO
OL 2pO(1 − pI − pOOL 2pO(1 − pI − pOO 18pI(1 − 10pIO
LL (1 − pI − pO)2πLL
GenotypeModel S0Model S1Model S2
IIb PI2πII pI2πI pI2πII
IO 2pIpOπIO 2pIpOπI 18pI2πI′
IL 2pI(1 − pI − pOIL 2pI(1 − pI − pOI 2pI(1 − 10pII′
OO PO2πOO pO2πO 81pI2πO
OL 2pO(1 − pI − pOOL 2pO(1 − pI − pOO 18pI(1 − 10pIO
LL (1 − pI − pO)2πLL
Table 3B

Pattern of germ-line and somatic APC mutation in FAP-associated colorectal tumours

GenotypeNModelExpected
Ig +Isb pIπII 8.8
Ig +Os pOπIO 20.2
Ig +Ls 63 (1 − pI − pOIL 40.0
Og +Is 25 pIπIO 16.8
Og +Os pOπOO 5.4
Og +Ls (1 − pI − pOOL 10.7
GenotypeNModelExpected
Ig +Isb pIπII 8.8
Ig +Os pOπIO 20.2
Ig +Ls 63 (1 − pI − pOIL 40.0
Og +Is 25 pIπIO 16.8
Og +Os pOπOO 5.4
Og +Ls (1 − pI − pOOL 10.7
a

Note: cell probabilities are given without norming to an overall sum of unity.

b

I, inside MCR; O, outside MCR; L, allelic loss; Px, probability of primary mutation in section x; πx, selection probability of genotype x; g, germ-line; s, somatic.

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