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Single-cell sequencing provides a powerful approach for elucidating intratumor heterogeneity by resolving cell-to-cell variability. However, it also poses additional challenges including elevated error rates, allelic dropout and non-uniform coverage. A recently introduced single-cell-specific mutation detection algorithm leverages the evolutionary relationship between cells for denoising the data. However, due to its probabilistic nature, this method does not scale well with the number of cells. Here, we develop a novel combinatorial approach for utilizing the genealogical relationship of cells in detecting mutations from noisy single-cell sequencing data. Our method, called scVILP, jointly detects mutations in individual cells and reconstructs a perfect phylogeny among these cells. We employ a novel Integer Linear Program algorithm for deterministically and efficiently solving the joint inference problem. We show that scVILP achieves similar or better accuracy but significantly better runtime over existing methods on simulated data. We also applied scVILP to an empirical human cancer dataset from a high grade serous ovarian cancer patient.