Reconstruction of clone- and haplotype-specific cancer genome karyotypes from bulk tumor samples

Ambiguity and errors in inferring segment copy number (SCN) profiles for a heterogeneous sample S = (G₁, G₂) under different assumptions about the sample composition. (A) A two-genome proper sample S = (G₁, G₂): each genome G_i ∈ S is depicted as collections of adjacent blocks (top), and the corresponding sequences of signed blocks (bottom). (B) The copy number profile c = [c₁, c₂, c₃, c₄] inferred under the assumption that the sample is homogeneous (i.e., comprised of a single derived genome) and the reference genome is haploid (i.e., each segment has only a single haplotype in the reference). Each value c_j is the weighted average of the sums of haplotype-specific (or allele-specific) copy numbers over the genomes G_i ∈ S. (C) Allele-specific copy number profiles and inferred under the assumption that the sample is homogeneous and the reference genome is diploid (i.e., each segment has two haplotypes labeled A and B). Here, the entries and for segment j are averages and of genome- and allele-specific copy number values. Note that the vectors and č do not preserve the true A/B label of each allele: dark blue are true counts of allele A and light blue are true counts of allele B. Here, segments 2 and 4 are flipped. (D) Genome-specific copy number profiles c₁ = [c_1,1, c_1,2, c_1,3, c_1,4] and c₂ = [c_2,1, c_2,2, c_2,3, c_2,4] inferred under the assumption that the sample is heterogeneous, but the reference genome is haploid. Here, the entry c_i,j for a segment j and genome G_i is the sum of allele-specific copy number values in a genome G_i. (E) Allele- and genome-specific copy number matrices inferred under the assumption that the sample is heterogeneous and the reference genome is diploid. Segments 2 and 4 are flipped alleles: and .