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Keywords:

  • breast cancer;
  • oncogenesis;
  • stochastic model

Abstract

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

We used mathematical models to analyze the age-incidence curve of breast carcinoma for individuals carrying a germline mutation in the BRCA1 or BRCA2 gene locus. Although many genomic abnormalities have been identified in breast tumors, we found that a two-stage model fit the data well. A one-hit model was not, however, consistent with the data. The results supported the hypothesis that the first hit represents loss of the wild type BRCA1 or BRCA2 allele as this occurs at a rate very similar to that for loss of the wild-type RB allele in retinoblastoma. Loss of the wild-type BRCA1 or BRCA2 allele appears to destabilize the genome as the second event occurs at a much higher rate. The second event is “rate limiting” in the sense that its occurrence is constrained by the limited number of intermediate cells with doubly mutated BRCA1 or BRCA2 alleles. The second event may not be unique, however. Loss of the wild-type BRCA allele appears to result in an increased rate for subsequent genomic events. A second event increasing proliferation of the partially malignant intermediate clone may lead inexorably to production and selection of cells with additional mutations in genes that facilitate tumor progression. © 2007 Wiley-Liss, Inc.

Individuals carrying a germline mutation in the BRCA1 or BRCA2 genes have a lifetime risk of developing carcinoma of the breast in excess of 50%.1 We have attempted to indirectly ascertain the number of rate-limiting genomic changes involved in tumorogenesis of BRCA mediated breast cancer. Numerous genomic changes as well as over-expressed and silenced genes are observed in advanced breast tumors. Some of these changes may represent the results of clonal selection on a proliferating and genomically unstable cell population subject to numerous environmental pressures during invasion and metastatic dissemination. A smaller number of initial genomic changes presumably establish a tumor with deregulated growth control in which subsequent genomic changes take place. Our objective was to develop and fit stochastic models to the age-dependent incidence of breast carcinoma among women carrying germline BRCA1 or BRCA2 mutations in order to estimate the number of changes that occurred at rates characteristic of normal mammalian cells leading to tumorogenesis.

Material and methods

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

Struwing et al.,1 genotyped 5,318 individuals of Ashkenazi Jewish descent for 3 BRCA1/2 founder mutations and identified 120 mutation carriers. We used their published cumulative incidence curves for mutation carriers.

We considered models based on one or two events in addition to the germline mutation. Although models with more events fit the data, the additional events occurred at very high rates. The models assume that the cancer develops from a breast epithelial stem cell and that the number of such cells changes in an age dependent manner, increasing prior to puberty and decreasing after menopause. The one-stage or “one-hit” model assumes that stem cells carrying BRCA1 or BRCA2 mutations are subject to transformation to malignancy at a rate of μ1 per cell/year. The two-stage model assumes that the initial event occurs at rate μ1, that the intermediate cell population undergoes clonal expansion and that intermediate cells are subject to a final “hit” at a rate of μ2 per cell/year leading to malignancy. Both models assume that there is a 5 year silent period between the occurrence of the final mutational event and clinical detection of the tumor. Details on the mathematical models and methods for estimating the parameters to optimally fit the age-incidence data are described in the supplementary materials.

The parameters of these models were optimized to fit the data. The growth rates parameters were restricted to be nonnegative. We have considered various possible levels for the maximum number of progenitor cells (K). The number of progenitor cells decreases after age 45 at a rate estimated from the data.

Results

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

Figure 1 shows the cumulative risk of developing breast cancer for mutation carriers on the y axis as a function of age on the x-axis as well as the optimally fit one and two-stage models. One hit models are not consistent with this data but the two-stage models fit well. For the two-stage model, the predicted cancer incidence depends approximately on the product of the first event rate μ1 and the number of breast stem cells at puberty K (see supplementary materials). That product represents the net transition rate for the establishment of an intermediate clone of partially malignant cells. For the best-fitting two-stage model shown in Figure 1, the parameters were μ1K = 1.23 × 10−2 per year and μ2 = 1.54 × 10−4 per cell/year. The optimally fitted two-stage model had clonal expansion for intermediate cells with exponential growth rates of 0.62 per year. This net growth rate, which incorporates cell division and death, correspond to a compartment doubling time of 1.1 years.

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Figure 1. Cumulative risk breast cancer for BRCA mutation carriers and predictions of 1-hit and 2-hit models with parameters specified in Table 1.

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The number of normal mammary stem cells is not known2, 3 but the plausible range of K between 104 and 106 results in an estimated range of values for the rate for the first hit of μ1 = 1.11 × 10−6 to 1.23 × 10−8 per stem cell/year.

Although the two-stage model provides an excellent fit to the data, the rate of the second event μ2 is not precisely determined by the data. Values for μ2 ranging from 10−5 to 10−3 events per intermediate cell per year provided almost equivalent fits to the data, with lower rates compensated for by higher rates of clonal expansion. The inferred range of second events represents an annual rate of one to many orders of magnitude greater than the rate for the first event.

We also examined 3-stage models. The fit of the 3-stage model was indistinguishable from that of the 2-stage model and so is not shown in Figure 1. Since the 3-stage model contains more parameters, their values were not well determined by the data, but at least one event occurred at a rate greater than the second event of the two-stage models.

Discussion

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

Our results suggest that in BRCA1 and BRCA2 germline mutation carriers there are two events which may occur at rates similar to mutation rates for normal mammalian cells leading to breast cancer. This is consistent with our previous study of breast carcinoma in the general population where we found that the age-incidence data was most consistent with 3 such events.4 In our analysis of BRCA1 and BRCA2 mutation carriers, the first event occurs at a rate of 1.11 × 10−6 to 1.23 × 10−8 per stem cell/year and the other at a much greater rate of 10−5 to 10−3 events per intermediate cell/year. Several studies have indicated that the wild-type BRCA allele is lost in the large majority of breast cancers in patients carrying BRCA germline mutations.5, 6 For example, in the study by Osorio et al., loss of the wild-type BRCA allele was found in 14 of the 16 breast cancer patients who carried deleterious germline mutations in BRCA1 or BRCA2. The most plausible interpretation of our data is that the first event in our two-stage model represents the loss of the wild-type BRCA allele as in Knudson's model for tumor suppressor genes.7 Knudson estimated the probability that a cell with the inherited mutation in the retinoblastoma gene will develop into a tumor cell as 2 × 10−7 per year, quite similar to our estimated range of 1.11 × 10−6 to 1.23 × 10−8. A second event is required for our data, but occurs at a much higher rate than that corresponding to the point mutation rate for normal mammalian cells which has been estimated as 2.2 × 10−9 per base pair/year.8 The loss of the wild-type BRCA allele presumably leads to an increased mutation rate and the second event in our two-stage model is probably just one of many mutational events that occur and are selected for during tumor invasion and progression. The second event is “rate-limiting” in the sense that there are only a limited number of intermediate cell targets initially available containing a deleted BRCA allele. The second event may not be unique, however, in the sense of occurring in a specific gene or pathway that needs to be inactivated as the second event. Many genes and pathways may be subsequently deregulated as a result of the genomic instability caused by loss of the wild type BRCA allele and which one is deregulated first may not be crucial.

BRCA1 and BRCA2 are large proteins that have been implicated in many key cellular processes. Both are involved in repair of double-stranded DNA breaks by homologous recombination, and BRCA1 is also thought to be involved in nucleotide-excision repair.9 BRCA1 appears to be involved in checkpoint control; p53, MYC, RB and ZBRK1 all bind to a region of BRCA1 that includes the nuclear localization signals. BRCA1 also has cellular growth suppression effects via interaction with NF-kappa B10 and to be involved in chromatin remodeling.9 Both BRCA1 and BRCA2 bind to Rad51, a protein involved in maintaining the integrity of the genome, and both are considered “caretaker” genes.11 Inactivation of a caretaker gene leads to genetic instabilities that result in an increased mutation rate of all genes, including gate-keepers such as p53.12 Consequently, loss of the wild-type BRCA allele may result in an increased rate for subsequent genomic events via chromosomal instability or loss of homologous repair of double strand breaks in DNA.9 A second event increasing proliferation of the partially malignant intermediate clone, may in this way, lead inexorably to production and selection of cells with additional mutations in genes that facilitate tumor progression.13 Although our results are biologically plausible, our inferences are indirect, based only on the age-incidence curve, and do not prove the correctness of the two-stage model or our interpretations of the nature of the events involved.

References

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Material and methods
  4. Results
  5. Discussion
  6. References
  7. Supporting Information

This article contains supplementary material available via the Internet at http://www.interscience.wiley.com/jpages/0020-7136/suppmat .

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ijc23323-Supplementary-BRCA-mod3.rtf4155KSupporting Information file ijc23323-Supplementary-BRCA-mod3.rtf

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