Rewriting the Mathematics of Tumor Growth; Teams Use Math Models to Sort Drivers from Passengers: Two JNCI Reviews by Mike Martin Regarding Genomics, Cancer, and Mutation
Curator: Stephen J. Williams, Ph.D.
Recently, there has been extensive interest in the cancer research and oncology community on detecting those mutations responsible for the initiation and propagation of a neoplastic cell (driver mutations) versus those mutations that are randomly (or by selective pressures) acquired due to the genetic instability of the transformed cell. The impact of either type of mutation has been a topic for debate, with a recent article showing that some passenger mutations may actually be responsible for tumor survival. In addition many articles, highlighted on this site (and referenced below) in recent years have described the importance of classifying driver and passenger mutations for the purposes of more effective personalized medicine strategies directed against tumors. Two review articles by Mike Martin in the Journal of the National Cancer Institute (JCNI) shed light on the current efforts and successes to discriminate between these passenger and driver mutations and determine impact of each type of mutation to tumor growth. However, as described in the associated article, the picture is not as clear cut as previously thought and highlights some revolutionary findings. In Rewriting the Mathematics of Tumor Growth, researchers discovered that driver mutations may confer such a small growth advantage that, multiple mutations, including the so called passenger mutations are necessary in order to sustain tumor growth. In fact, much experimental evidence has suggested at least six defined genetic events may be necessary for the in-vitro transformation of human cells. The following table shows some of the genetic events required for in-vitro transformation in cell culture systems.
Genetic events required for transformation
|Species||Cell type||# of genes required for tumor formation*||Genes used||Reference||Events required for priming|
|Human||FibroblastsEmbryonic kidney||3||hTERTH-rasLarge T||(a)Hahn(Weinberg)||2LT+hTERT|
|Mammary epithelialMyoblastsEmbryonic kidney||6||hTERTH-rasP53DDc-myc
|(b)Kendall(Counter)||Hras required for tumorigenesis so probably 5 events needed|
|Fibroblasts||4||Large TSmall TH-rashTERT||(c)Sun(Hornsby)||2Large T + H-ras|
|Fibroblasts||4||Large TSmall ThTERTRas||(d)Rangarajan(Weinberg)||3hTERT, Ras and either small or largeT|
|(e)Goessel(Opitz)||3 for anchorage independence (cyclin D1, dnp53, EGFR),Cyclin D1+dnp53 for immortalization|
|HOSE||6||CDK4, cyclin D, hTERT plus combination of either P53DD, myrAkt, and H-ras or P53DD, H-ras, c-myc Bcl2||(f)Sasaki(Kiyono)||5|
|HOSE||3||hTERTSV40 earlyH-ras orK-ras||(g)Liu(Bast)||2hTERT+ SV40 early|
|HOSE||3||Large ThTERTH-ras orc-erB-2||(h)Kusakari(Fujii)||2hTERT+large T|
|Rat||Fibroblasts||2||Large TH-ras||(i)Hirakawa||Did not analyze|
|Fibroblasts||2||Large TH-ras||(d)Rangarajan(Weinberg)||Large T|
|Mouse||MOSEIn p53-/- background||3||c-mycK-rasAkt||(j)Orsulic|
|(k)Adam(Counter)||5 need all butp53DD|
Note: priming means events required to immortalize but not fully transform. * Note that both ability to form colonies in soft agarose and subsequently tested for tumor formation in immunocompromised mice.
a. Hahn, W. C., Counter, C. M., Lundberg, A. S., Beijersbergen, R. L., Brooks, M. W., and Weinberg, R. A. (1999) Creation of human tumour cells with defined genetic elements, Nature 400, 464-468.
b. Kendall, S. D., Linardic, C. M., Adam, S. J., and Counter, C. M. (2005) A network of genetic events sufficient to convert normal human cells to a tumorigenic state, Cancer Res 65, 9824-9828.
c. Sun, B., Chen, M., Hawks, C. L., Pereira-Smith, O. M., and Hornsby, P. J. (2005) The minimal set of genetic alterations required for conversion of primary human fibroblasts to cancer cells in the subrenal capsule assay, Neoplasia 7, 585-593.
d. Rangarajan, A., Hong, S. J., Gifford, A., and Weinberg, R. A. (2004) Species- and cell type-specific requirements for cellular transformation, Cancer Cell 6, 171-183.
e. Goessel, G., Quante, M., Hahn, W. C., Harada, H., Heeg, S., Suliman, Y., Doebele, M., von Werder, A., Fulda, C., Nakagawa, H., Rustgi, A. K., Blum, H. E., and Opitz, O. G. (2005) Creating oral squamous cancer cells: a cellular model of oral-esophageal carcinogenesis, Proc Natl Acad Sci U S A 102, 15599-15604.
f. Sasaki, R., Narisawa-Saito, M., Yugawa, T., Fujita, M., Tashiro, H., Katabuchi, H., and Kiyono, T. (2009) Oncogenic transformation of human ovarian surface epithelial cells with defined cellular oncogenes, Carcinogenesis 30, 423-431.
g. Liu, J., Yang, G., Thompson-Lanza, J. A., Glassman, A., Hayes, K., Patterson, A., Marquez, R. T., Auersperg, N., Yu, Y., Hahn, W. C., Mills, G. B., and Bast, R. C., Jr. (2004) A genetically defined model for human ovarian cancer, Cancer Res 64, 1655-1663.
h. Kusakari, T., Kariya, M., Mandai, M., Tsuruta, Y., Hamid, A. A., Fukuhara, K., Nanbu, K., Takakura, K., and Fujii, S. (2003) C-erbB-2 or mutant Ha-ras induced malignant transformation of immortalized human ovarian surface epithelial cells in vitro, Br J Cancer 89, 2293-2298.
i. Hirakawa, T., and Ruley, H. E. (1988) Rescue of cells from ras oncogene-induced growth arrest by a second, complementing, oncogene, Proc Natl Acad Sci U S A 85, 1519-1523.
j. Orsulic, S., Li, Y., Soslow, R. A., Vitale-Cross, L. A., Gutkind, J. S., and Varmus, H. E. (2002) Induction of ovarian cancer by defined multiple genetic changes in a mouse model system, Cancer Cell 1, 53-62.
k. Adam, S. J., Rund, L. A., Kuzmuk, K. N., Zachary, J. F., Schook, L. B., and Counter, C. M. (2007) Genetic induction of tumorigenesis in swine, Oncogene 26, 1038-1045.
However it may be argued that the aforementioned experimental examples were produced in cell lines with a more stable genome than that which is seen in most tumors and had used traditional assays of transformation, such as growth in soft agarose and tumorigenicity in immunocompromised mice, as endpoints of transformation, and not representative of the tumor growth seen in the clinical setting.
Therefore Bert Vogelstein, M.D., along with collaborators around the world developed a model they termed the “sequential driver mutation theory”, in which they describe that driver mutations multiply over time with each mutation “slightly increasing the tumor growth rate through a process that depends on three factors”:
- Driver mutation rate
- The 0.4% selective growth advantage
- Cell division time
This model was based on a combination of experimental data and computer simulations of gliobastoma multiforme and pancreatic adenocarcinoma. Most tumor models follow a Gompertz kinetics, which show how tumor growth is exponential but eventually levels off over time.
This new theory shows though that a tumor cell with only one driver mutation can only grow so much, until a second driver mutation is required. Using data for the COSMIC database (Catalog of Somatic Mutations in Cancer) together with analysis software CHASM (Cancer-specific High-throughput Annotation of Somatic Mutations) the researchers analyzed 713 mutations sequenced from 14 glioma patients and 562 mutations in nine pancreatic adenocarcinomas, revealing at least 100 tumor suppressor genes and 100 oncogenes altered. Therefore, the authors suggested these may be possible driver mutations, or at least mutations required for the sustained growth of these tumors. Applying this new model to data obtained from Dr. Giardiello’s publication concerning familial adenopolypsis in New England Journal of medicine in 19993 and 2000, the sequential driver mutation model predicted age distribution of FAP patients, number and size of polyps, and polyp growth rate than previous models. This surprising number of required driver mutations for full transformation was also verified in a study led by University of Texas Southwestern Medical Center biologist Jerry Shay, Ph.D., who noted “this team’s surprise nearly 45% of all colorectal candidate oncogenes (65 mutations) drove malignant proliferation”.
However, some investigators do not believe the model is complex enough to account for other factors involved in oncogenesis, such as epigenetic factors like methylation and acetylation. In addition the review also discusses host and tissue factors which may complicate the models, such as location where a tumor develops. However, most of the investigators interviewed for this review agreed that focusing on this long-term progression of the disease may give us clues to other potential druggable targets.
Teams Use Math Models to Sort Drivers From Passengers
A related review from Mike Martin in JNCI  describes a statistical method, published in 2009 Cancer Informatics, which distinguishes chromosomal abnormalities that can drive oncogenesis from passenger abnormalities. Chromosomal abnormalities, such as deletions, additions, and translocations are common in cancer. For instance, the well-known Philadelphia chromosome, a translocation between chromosome 9 and 22 which results in the BCR-ABL tyrosine kinase fusion protein is the molecular basis of chronic myelogenous leukemia.
In the report, Eytan Domany, Ph.D., from Weizmann Institute and several colleagues from University of Lausanne, University of Haifa and the Broad Institute were analyzing chromosomal aberrations in a subset of medulloblastoma, which had more gain and losses in chromosomes than had been attributed to the disease. Using a statistical method they termed a “volumetric sieve”, the investigators were able to identify driver versus passenger aberrations based on three filters:
- Fraction of patients with the abnormality
- Length of DNA involved in the aberrant chromosome
- Abnormality’s copy number
Another method to sort the most “important” chromosomal aberrations from less relevant alterations is termed GISTIC, as the website describes is: a tool to identify genes targeted by somatic copy-number alterations (SCNAs) that drive cancer growth (at the Broad Institute website http://www.broadinstitute.org/software/cprg/?q=node/31). The method allows for comparison across multiple tumors so noise is eliminated and improves consistency of analysis. This method had been successfully used to determine driver aberrations is mesotheliomas, leukemias, and identify new oncogenes in adenocarcinomas of the lung and squamous cell carcinoma of the esophagus.
Main references for the two Mike Martin articles are as follows:
1. Martin M: Rewriting the mathematics of tumor growth. Journal of the National Cancer Institute 2011, 103(21):1564-1565.
2. Martin M: Aberrant chromosomes: teams use math models to sort drivers from passengers. Journal of the National Cancer Institute 2010, 102(6):369-371.
3. Eskiocak U, Kim SB, Ly P, Roig AI, Biglione S, Komurov K, Cornelius C, Wright WE, White MA, Shay JW: Functional parsing of driver mutations in the colorectal cancer genome reveals numerous suppressors of anchorage-independent growth. Cancer research 2011, 71(13):4359-4365.
4. Shay T, Lambiv WL, Reiner-Benaim A, Hegi ME, Domany E: Combining chromosomal arm status and significantly aberrant genomic locations reveals new cancer subtypes. Cancer informatics 2009, 7:91-104.
5. Beroukhim R, Getz G, Nghiemphu L, Barretina J, Hsueh T, Linhart D, Vivanco I, Lee JC, Huang JH, Alexander S et al: Assessing the significance of chromosomal aberrations in cancer: methodology and application to glioma. Proceedings of the National Academy of Sciences of the United States of America 2007, 104(50):20007-20012.
Further posts on CANCER and GENOMICS and Sequencing published on the site include:
 Michor F, Iwasa Y, and Nowak MA (2004) Dynamics of cancer
progression. Nature Reviews Cancer 4, 197-205.
 Crespi B and Summers K (2005) Evolutionary biology of cancer.
 Merlo LMF, et al. (2006) Cancer as an evolutionary and ecological
process. Nature Reviews Cancer 6, 924-935.
 McFarland C, et al. “Accumulation of deleterious passenger mutations
in cancer,” in preparation.
 Birkbak NJ, et al. (2011) Paradoxical relationship between
chromosomal instability and survival outcome in cancer. Cancer