PhISCS - A Combinatorial Approach for Sub-perfect Tumor Phylogeny Reconstruction via Integrative use of Single Cell and Bulk Sequencing Data

Recent technological advances in single cell sequencing (SCS) provide high resolution data for studying intra-tumor heterogeneity and tumor evolution. Available computational methods for tumor phylogeny inference via SCS typically aim to identify the most likely perfect phylogeny tree satisfying infinite sites assumption (ISA). However limitations of SCS technologies such as frequent allele dropout or highly variable sequence coverage, commonly result in mutational call errors and prohibit a perfect phylogeny. In addition, ISA violations are commonly observed in tumor phylogenies due to the loss of heterozygosity, deletions and convergent evolution. In order to address such limitations, we, for the first time, introduce a new combinatorial formulation that integrates single cell sequencing data with matching bulk sequencing data, with the objective of minimizing a linear combination of (i) potential false negatives (due to e.g. allele dropout or variance in sequence coverage) and (ii) potential false positives (due to e.g. read errors) among mutation calls, as well as (iii) the number of mutations that violate ISA - to define the optimal sub-perfect phylogeny. Our formulation ensures that several lineage constraints imposed by the use of variant allele frequencies (VAFs, derived from bulk sequence data) are satisfied. We express our formulation both in the form of an integer linear program (ILP) and - for the first time in the context of tumor phylogeny reconstruction - a boolean constraint satisfaction problem (CSP) and solve them by leveraging state-of-the-art ILP/CSP solvers. The resulting method, which we name PhISCS, is the first to integrate SCS and bulk sequencing data under the finite sites model. Using several simulated and real SCS data sets, we demonstrate that PhISCS is not only more general but also more accurate than the alternative tumor phylogeny inference tools. PhISCS is very fast especially when its CSP based variant is used returns the optimal solution, except in rare instances for which it provides an optimality gap. PhISCS is available at https://github.com/haghshenas/PhISCS.