Topological analysis of gene expression arrays identifies high risk molecular subtypes in breast cancer

  • Javier Arsuaga
  • Nils A. Baas
  • Daniel DeWoskin
  • Hideaki Mizuno
  • Aleksandr Pankov
  • Catherine Park
Original Paper


Genomic technologies measure thousands of molecular signals with the goal of understanding complex biological processes. In cancer these molecular signals have been used to characterize disease subtypes, signaling pathways and to identify subsets of patients with specific prognosis. However molecular signals for any disease type are so vast and complex that novel mathematical approaches are required for further analyses. Persistent and computational homology provide a new method for these analyses. In our previous work we presented a new homology-based supervised classification method to identify copy number aberrations from comparative genomic hybridization arrays. In this work we first propose a theoretical framework for our classification method and second we extend our analysis to gene expression data. We analyze a published breast cancer data set and find that that our method can distinguish most, but not all, different breast cancer subtypes. This result suggests that specific relationships between genes, captured by our algorithm, help distinguish between breast cancer subtypes. We propose that topological methods can be used for the classification and clustering of gene expression profiles.


Computational homology Breast cancer subtypes Gene expression 


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  1. 1.
    Adelaide J., Finetti P., Bekhouche I. et al.: Integrated profiling of basal and luminal breast cancers. Cancer Res. 67, 11565–11575 (2007)CrossRefGoogle Scholar
  2. 2.
    Ahmed S., Thomas G., Ghoussaini M. et al.: Newly discovered breast cancer susceptibility loci on 3p24 and 17q23.2. Nat. Genet. 41, 585–590 (2009)CrossRefGoogle Scholar
  3. 3.
    Balmain A., Gray J., Ponder B.: The genetics and genomics of cancer. Nat. Genet. 33(Suppl), 238–244 (2003)CrossRefGoogle Scholar
  4. 4.
    Benjamini Y., Hochberg Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B 57, 289–300 (1995)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Bild A.H., Yao G., Chang J.T., Wang Q., Potti A., Chasse D., Joshi M.-B., Harpole D., Lancaster J.M., Berchuck A. et al.: Oncogenic pathway signatures in human cancers as a guide to targeted therapies. Nature 439, 353–357 (2006)CrossRefGoogle Scholar
  6. 6.
    Carlsson G.: Topology and data. Bull. Am. Math. Soc. 46, 255–308 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Chang J.C., Makris A., Gutierrez M.C. et al.: Gene expression patterns in formalin-fixed, paraffin-embedded core biopsies predict docetaxel chemosensitivity in breast cancer patients. Breast Cancer Res Treat. 108, 233–240 (2008)CrossRefGoogle Scholar
  8. 8.
    Chin K., DeVries S., Fridlyand J. et al.: Genomic and transcriptional aberrations linked to breast cancer pathophysiologies. Cancer Cell 10, 529–541 (2006)CrossRefGoogle Scholar
  9. 9.
    Collins A., Zomorodian A., Carlsson G., Guibas L.J.: A barcode shape descriptor for curve point cloud data. Comput. Graphics 28, 881–894 (2004)CrossRefGoogle Scholar
  10. 10.
    Cowin P.A., Anglesio M., Etemadmoghadam D., Bowtell D.D.: Profiling the cancer genome. Ann. Rev. Genomics Hum. Genet. 11, 133–159 (2010)CrossRefGoogle Scholar
  11. 11.
    Creighton C.J., Kent Osborne C., van de Vijver M.J. et al.: Molecular profiles of progesterone receptor loss in human breast tumors. Breast Cancer Res. Treat. 114, 287–299 (2009)CrossRefGoogle Scholar
  12. 12.
    de Silva V., Ghrist R.: Coverage in sensor networks via persistent homology. Algebraic Geometr. Topol. 7, 339–358 (2007)zbMATHCrossRefGoogle Scholar
  13. 13.
    DeWoskin D., Climent J., Cruz-White I., Vazquez M., Park C., Arsuaga J.: Applications of computational homology to prediction of treatment response in breast cancer patients. Topol. Its Appl. 157, 157–164 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Edelsbrunner, H., Harer, J.: Persistent homology—a survey. In: Twenty Years After, AMS (2007)Google Scholar
  15. 15.
    Hartung J.A.: Note on combining dependent tests of significance. Biometr. J. 41, 849–855 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Horlings H., Lai C., Nuyten D.S.A. et al.: Integration of DNA copy number alterations and prognostic gene expression signatures in breast cancer patients. Clin. Cancer Res. 16, 651–663 (2010)CrossRefGoogle Scholar
  17. 17.
    Kaczynski, T., Mischaikow, K., Mrozek, M.: Computational Homology Applied Mathematical Sciences 157. Springer, Berlin (2004)Google Scholar
  18. 18.
    Krishan K., Kurtuldu H., Schatz M.F., Gameiro M., Mischaikow K., Madruga S.: Homology and symmetry breaking in Rayleigh-Bnard convection: experiments and simulations. Phys. Fluids 19, 117105–117106 (2007)CrossRefGoogle Scholar
  19. 19.
    Loi S., Haibe-Kains B., Desmedt C., Lallemand F., Tutt A.M., Gillet C., Ellis P., Harris A., Bergh J., Foekens J.A. et al.: Definition of clinically distinct molecular subtypes in estrogen receptor-positive breast carcinomas through genomic grade. J. Clin. Oncol. 25, 1239–1246 (2007)CrossRefGoogle Scholar
  20. 20.
    Ma X.-J., Wang Z., Ryan P.D., Isakoff S.J., Barmettler A., Fuller A., Muir B., Mohapatra G., Salunga R., Tuggle J.T. et al.: A two-gene expression ratio predicts clinical outcome in breast cancer patients treated with tamoxifen. Cancer Cell 5, 607–616 (2004)CrossRefGoogle Scholar
  21. 21.
    Miller L.D., Smeds J., George J., Vega V.B., Vergara L., Ploner A., Pawitan Y., Hall P., Klaar S., Liu E.T. et al.: An expression signature for p53 status in human breast cancer predicts mutation status, transcriptional effects, and patient survival. Proc. Natl. Acad. Sci. USA 102, 13550–13555 (2005)CrossRefGoogle Scholar
  22. 22.
    Nakanishi Y.: Application of homology theory to topology optimization of three-dimensional structures using genetic algorithm. Comput. Methods Appl. Mech. Eng. 190, 3849–3863 (2001)zbMATHCrossRefGoogle Scholar
  23. 23.
    Neve R.M., Chin K. et al.: A collection of breast cancer cell lines for the study of functionally distinct cancer subtypes. Cancer Cell 10, 515–527 (2006)CrossRefGoogle Scholar
  24. 24.
    Perou C.M., Sørlie T., Eisen M.B., van de Rijn M., Jeffrey S.S., Rees C.A., Pollack J.R., Ross D.T., Johnsen H., Akslen L.A. et al.: Molecular portraits of human breast tumors. Nature 406, 747–752 (2000)CrossRefGoogle Scholar
  25. 25.
    Pinkel D., Albertson D.G.: Array comparative genomic hybridization and its applications in cancer. Nat. Genet. 37, 11–17 (2005)CrossRefGoogle Scholar
  26. 26.
    Potti A., Dressman H.K., Bild A., Riedel R.F., Chan G., Sayer R., Cragun J., Cottrill H., Kelley M.J., Petersen R. et al.: Genomic signatures to guide the use of chemotherapeutics. Nat. Med. 12, 1294–1300 (2006)CrossRefGoogle Scholar
  27. 27.
    Singh G., Memoli F., Ishkhanov T., Carlsson G., Sapiro G., Ringach D.: Topological structure of population activity in primary visual cortex. J. Vis. 8, 1–18 (2008)CrossRefGoogle Scholar
  28. 28.
    Sørlie T., Perou C.M., Tibshirani R., Aas T., Geisler S., Johnsen H., Hastie T., Eisen M.B., van de Rijn M., Jeffrey S.S. et al.: Gene expression patterns of breast carcinomas distinguish tumor subclasses with clinical implications. Proc. Natl. Acad. Sci. USA 98, 10869–10874 (2001)CrossRefGoogle Scholar
  29. 29.
    Sørlie T., Tibshirani R., Parker J. et al.: Repeated observation of breast tumor subtypes in independent gene expression data sets. Proc. Natl. Acad. Sci. USA 100, 8418–8423 (2003)CrossRefGoogle Scholar
  30. 30.
    Sørlie T., Perou C.M., Fan C. et al.: Gene expression profiles do not consistently predict the clinical treatment response in locally advanced breast cancer. Mol. Cancer Ther. 5, 2914–2918 (2006)CrossRefGoogle Scholar
  31. 31.
    Sotiriou C., Neo S.-Y., McShane L.M., Korn E.L., Long P.M., Jazaeri A., Martiat P., Fox S.B., Harris A.L., Liu E.T.: Breast cancer classification and prognosis based on gene expression profiles from a population-based study. Proc. Natl. Acad. Sci. USA 100, 10393–10398 (2003)CrossRefGoogle Scholar
  32. 32.
    Swanton C., Caldas C.: From genomic landscapes to personalized cancer management-is there a roadmap?. Ann. NY. Acad. Sci. 1210, 34–44 (2010)CrossRefGoogle Scholar
  33. 33.
    Takens, F.: Detecting strange attractors in turbulence, Springer Lecture Notes in Mathematics, vol. 898, 366–381 (1981)Google Scholar
  34. 34.
    Troester M.A., Hoadley K.A., Sørlie T. et al.: Cell-type-specific responses to chemotherapeutics in breast cancer. Cancer Res. 64, 4218–4226 (2004)CrossRefGoogle Scholar
  35. 35.
    vant Veer L.J., dai H., van de Vijver M.J., He Y.D. et al.: Gene expression profiling predicts clinical outcome of breast cancer. Nature 415, 530–536 (2002)CrossRefGoogle Scholar
  36. 36.
    van de Vijver M.J., He Y.D., vant Veer L.J., Dai H., Hart A.A., Voskuil D.W., Schreiber G.J., Peterse J.L., Roberts C., Marton M.J.: A gene-expression signature as a predictor of survival in breast cancer. N. Engl. J. Med. 347, 1999–2009 (2002)CrossRefGoogle Scholar
  37. 37.
    Wang Y., Klijn J.G., Zhang Y., Sieuwerts A.M., Look M.P., Yang F., Talantov D., Timmermans M., Meijer-van Gelder M.E., Yu J.: Gene-expression profiles to predict distant metastasis of lymph-node-negative primary breast cancer. Lancet 365, 671–679 (2005)Google Scholar
  38. 38.
    Yang Q., Yoshimura G., Mori I., Sakurai T., Kakudo K.: Chromosome 3p and breast cancer. J. Hum. Genet. 47, 453–459 (2002)CrossRefGoogle Scholar
  39. 39.
    Zomorodian A.J.: Topology for Computing. Cambridge University Press, Cambridge (2005)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Javier Arsuaga
    • 1
  • Nils A. Baas
    • 2
  • Daniel DeWoskin
    • 3
  • Hideaki Mizuno
    • 4
  • Aleksandr Pankov
    • 1
  • Catherine Park
    • 5
  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of MathematicsNorwegian University of Science and TechnologyTrondheimNorway
  3. 3.Department of MathematicsUniversity of MichiganAnn ArborUSA
  4. 4.Discovery Science and Technology DepartmentChugai Pharmaceuticals Co. Ltd.Kamakura, KanagawaJapan
  5. 5.Department of Radiation Oncology, Helen Diller Family Comprehensive Cancer CenterUniversity of California San FranciscoSan FranciscoUSA

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