In the field of cancer biology, there is currently great interest in the development of "targeted therapeutics" that attack specific molecular abnormalities characterizing subsets of cancers. Computational methods have been essential in identifying subsets of tumors sharing a common molecular mechanism, making it possible to identify meaningful groupings for targeted therapy. To date, such approaches have been limited in their ability to infer the specific sequences of molecular changes, or progression pathways, by which a tumor forms and increases in aggressiveness. In the present work, we develop computational methods for inferring progression pathways from cell-bycell assays. Our methods bypass important limitations of the current approaches by recognizing and taking advantage of tumor heterogeneity. We define a model for tumor progression and introduce a procedure for cancer phylogenetics based on the inference of likely progression pathways in individual patients. This procedure is formulated as a set of easily tractable graph problems. We demonstrate the methods on a set of fluorescence in situ hybridization (FISH) assays, which measure gene and chromosome gain and loss from a collection of fifty tumor samples. The results are consistent with prior knowledge about the role of the genes examined in cancer progression, and they suggest additional features of progression pathways involving the genes studied.

16 pages

*Allegheny Singer Research Institute, Allegheny General Hospital, Pittsburgh, PA 15212
**Department of Biological Sciences, Carnegie Mellon University, Pittsburgh PA 15213

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