Reconstructing Intra-Tumor Heterogeneity via Convex Optimization and Branch-and-Bound Search.

Studies of intra-tumor heterogeneity using high-throughput sequencing data, i.e., assembly of tumor populations and inference of their relative frequencies, may provide highly valuable information about molecular signatures of cancer and point towards specific therapeutic treatments. Reconstructing heterogeneous tumor populations, however, is a challenging task rendered difficult by complex mutations and further exacerbated by the fact that high-throughput sequencing reads are short relative to genomic regions experiencing structural mutations. In this paper, we present a novel algorithmic framework for computationally efficient and accurate analysis of tumor clonal populations. Given locations of copy number aberrations, the proposed method quantifies gains and losses of the affected regions, and determines relative frequencies of the populations in a clonal mixture. This is achieved by formulating the reconstruction as a mixed-integer optimization problem and solved via a combination of convex optimization and branch-and-bound search. The developed algorithm was tested on realistic synthetic as well as experimental data and shown to outperform state-of-the art competing methods in a variety of scenarios.