Polyclonality of familial murine adenomas: analyses of mouse chimeras with low tumor multiplicity suggest short-range interactions

Abstract

In previous studies demonstrating the polyclonal structure of familial intestinal adenomas, high tumor multiplicity made it difficult to eliminate the possibility that polyclonality arose by the random collision of distinct initiated clones as opposed to some form of clonal interaction. We sought to test further the random collision hypothesis. Chimeric mice carrying the multiple intestinal neoplasia (Min) mutation of the adenomatous polyposis coli gene (Apc) and homozygous for the tumor resistance allele of the Mom1 locus were established. These chimeras also display a strong propensity for tumors of polyclonal structure, despite their markedly reduced tumor multiplicity. Considering tumor sizes and multiplicities, the observed fraction of overtly polyclonal heterotypic adenomas was significantly higher than predicted by the random collision hypothesis. This finding supports models of polyclonality involving interaction among multiple initiated clones. The extent of clonal interaction was assessed by statistical analyses that relate the observed frequency of overtly polyclonal heterotypic tumors to the geometry of the chimeric patches and the pattern of underlying crypts. These statistical calculations indicate that the familial adenomas of the Apc(Min/+) mouse may commonly form through interactions between clones as close as 1-2 crypt diameters apart.

Fig. 1.

Histological sections of a heterotypic small intestinal adenoma stained with X-Gal (blue). (A) Section also stained with hematoxylin and eosin. (B) An adjacent section also stained with Apc antibody 3122 (brown) and lightly counterstained with hematoxylin. (Bars: 200 μm.)

Fig. 2.

Characteristics of chimeric patches. (A) Image of a whole-mount small intestine adjacent to an adenoma stained with X-Gal. (Bar: 1 mm.) (B) Binary chimeric patch image. By threshholding, image A is transformed into a binary (blue/white) image. (C) Distance to boundary image. For each pixel p in B, the distance d(p) to the nearest point in image B that is of the opposite color is shown. Boundary regions where a heterotypic tumor could originate become highlighted as green. (D) Histogram of the imaged boundary distances from C.(E) Heterotypic fraction. The cumulative empirical distribution of distances d(p) from D is plotted. An equivalent interpretation is that if a disk of radius r (see Fig. 3) is placed uniformly at random on the image B, the height of the curve in E is the probability that this disk covers both blue and white pixels. (F) Multiimage summary. Computations A–E were repeated on images of regions near all 47 unambiguously phenotyped tumors in chimeric mice 100, 122, and 154. The median distance d(p) is plotted versus the proportion of white pixels in each image; color indicates the phenotype of the adjacent tumor (blue circle, homotypic blue tumor; white circle, homotypic white tumor; red triangle, heterotypic tumor).

Fig. 3.

Disk model analysis. (A) Log-likelihoods. For three choices of the polyclonal fraction parameter θ, the relative log-likelihood of the disk radius parameter r is plotted, based on the heterotypic tumor count being a binomial random variable with success probability θ F(r), where F(r) is the average of disk-heterotypic fractions (Fig. 2E), averaged over all available images. Relative log-likelihoods are plotted by subtracting the global maximum of the log-likelihood surface, maximized over both θ and r. All radius values within 2 units of log-likelihood from the maximum constitute an approximate 95% confidence interval for the interaction radius r.(B) Disk model interpretation. Disks of the maximum-likelihood radii from A, 30 μm for θ = 1 and 68 μm for θ = 0.5, are overlaid onto an image of crypt structure from a related mouse to illustrate the implied spatial extent of interaction. Crypt centers are marked with red dots.

Fig. 4.

Crypt reconstruction and analysis. (A) Crypt reconstruction. The arrangement of 5,462 crypts presumed to reside on the intestinal surface imaged in Fig. 2B is reconstructed by Metropolis chain simulation of a distribution over all possible crypt arrangements. This posterior distribution is informed by the known crypt arrangement from a ROSA11 mouse (expanded version of Fig. 3B), which constitutes a prior distribution of arrangements, and by the binary image (Fig. 2B), according to techniques from Bayesian image reconstruction (see Materials and Methods). The techniques give higher likelihood to arrangements in which all of the pixels within a crypt have the same color. Crypt centers from one realization of the posterior distribution are plotted; crypts are colored according to a majority rule of contained pixels. Crypt neighbors are determined by Delaunay triangulation, and the connecting edges are drawn in red if the adjacent crypts are heterotypic. This reconstruction contains 16,902 neighboring crypt pairs, 14% of which are heterotypic. If, for example, polyclonal tumors form by the interaction of two neighboring crypts in a chimeric intestinal surface like Fig. 2 A, then we estimate that 14% of such tumors would be heterotypic. This is the crypt pair phenotype index (2). (B) Crypt reconstruction detail. Shown is a higher magnification of the area marked in A.(C) Crypt neighborhood system. One crypt from B is highlighted in red and its neighbors of various orders are indicated by different colors. For instance, this crypt has 6 nearest neighbors (green) and 13 second-order neighbors (yellow). (D) Crypt neighborhood statistics. Crypt reconstructions as in A were obtained for 17 representative images, and neighborhoods were identified for all crypts. Plotted for various neighborhood orders is the average number of neighbors for each crypt. To avoid boundary problems, the average is computed over all interior crypts in all images, where a crypt is interior if it resides in the middle 80% of the image in both coordinates. On average, crypts are within a few steps of many other crypts. (E) Heterotypic crypt neighborhoods. Averaging as in D, we compute for each white crypt the average proportion of white crypts in its nth-order neighborhood (white circles) and for each blue crypt the average proportion of white crypts in its nth order neighborhood (blue circles). White crypts tend to lie near white crypts, and similarly for blue, but the patch sizes are such that two crypts seven or eight steps apart have independent colors. (F) Heterotypic tumor fraction. Averaging as in D and E we compute the probability ψ that a tumor is heterotypic, using various levels of crypt interaction. Shown in red is ψ when a tumor is formed from all crypts within an nth order neighborhood of some initiated crypt. Less than complete involvement is indicated by the other curves. For instance, the blue curve shows ψ when each curve within an nth-order neighborhood of an initiated crypt tosses a fair coin to decide whether or not to participate in the tumor. Importantly, the observed heterotypic fraction (22%) can be explained by intercryptal interactions between first- or second-order neighbors for a wide range of participation rates.