Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary Patterns

  • Sakellarios Zairis
  • Hossein Khiabanian
  • Andrew J. Blumberg
  • Raul Rabadan
Conference paper

DOI: 10.1007/978-3-319-09891-3_48

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8609)
Cite this paper as:
Zairis S., Khiabanian H., Blumberg A.J., Rabadan R. (2014) Moduli Spaces of Phylogenetic Trees Describing Tumor Evolutionary Patterns. In: Ślȩzak D., Tan AH., Peters J.F., Schwabe L. (eds) Brain Informatics and Health. BIH 2014. Lecture Notes in Computer Science, vol 8609. Springer, Cham

Abstract

Cancers follow a clonal Darwinian evolution, with fitter subclones replacing more quiescent cells, ultimately giving rise to macroscopic disease. High-throughput genomics provides the opportunity to investigate these processes and determine specific genetic alterations driving disease progression. Genomic sampling of a patient’s cancer provides a molecular history, represented by a phylogenetic tree. Cohorts of patients represent a forest of related phylogenetic structures. To extract clinically relevant information, one must represent and statistically compare these collections of trees. We propose a framework based on an application of the work by Billera, Holmes and Vogtmann on phylogenetic tree spaces to the case of unrooted trees of intra-individual cancer tissue samples. We observe that these tree spaces are globally nonpositively curved, allowing for statistical inference on populations of patient histories. A projective tree space is introduced, permitting visualizations of evolutionary patterns. Published data from four types of human malignancies are explored within our framework.

Keywords

phylogenetic tree moduli space tumor evolution genomics 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sakellarios Zairis
    • 1
    • 2
  • Hossein Khiabanian
    • 1
    • 2
  • Andrew J. Blumberg
    • 3
  • Raul Rabadan
    • 1
    • 2
  1. 1.Department of Systems BiologyColumbia UniversityNew YorkUSA
  2. 2.Department of Biomedical InformaticsColumbia UniversityNew YorkUSA
  3. 3.Department of MathematicsUniversity of Texas at AustinAustinUSA

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