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Chromosomal rearrangements can initiate and drive cancer progression, yet it has been challenging to evaluate their impact, especially in genetically heterogeneous solid cancers. To address this problem we developed HiDENSEC, a new computational framework for analyzing chromatin conformation capture in heterogeneous samples, which can infer somatic copy number alterations, characterize large-scale chromosomal rearrangements, and estimate cancer cell fractions. We validated HiDENSEC within silicoandin vitrocontrols, and then characterized chromosome-scale evolution during melanoma progression in formalin-fixed tumor samples from three patients. The resulting comprehensive annotation of the genomic events includes copy number neutral translocations that disrupt tumor suppressor genes such as NF1, whole chromosome arm exchanges that result in loss of CDKN2A, and whole-arm copy-number neutral loss of homozygosity involving PTEN. These findings show that large-scale chromosomal rearrangements occur throughout cancer evolution and characterizing these events yields insights into drivers of melanoma progression.

A wealth of problems occurring naturally in the applied sciences can be reformulated as optimization tasks whose argument is constrained to the solution set of a system of linear equations. Solving these efficiently typically requires computation of feasible descent directions and proper step sizes - the quality of which depends largely on conditioning of the linear equality constraint. In this paper we present a way of transforming such ill-conditioned problems into easily solvable, equivalent formulations by means of directly changing the singular values of the system’s associated matrix. This transformation allows us to solve problems for which corresponding routines in the LAPACK library as well as widely used projection methods converged either very slowly or not at all.