Algorithms to Model Single Gene, Single Chromosome, and Whole Genome Copy Number Changes Jointly in Tumor Phylogenetics

Abstract

We present methods to construct phylogenetic models of tumor progression at the cellular level that include copy number changes at the scale of single genes, entire chromosomes, and the whole genome. The methods are designed for data collected by fluorescence in situ hybridization (FISH), an experimental technique especially well suited to characterizing intratumor heterogeneity using counts of probes to genetic regions frequently gained or lost in tumor development. Here, we develop new provably optimal methods for computing an edit distance between the copy number states of two cells given evolution by copy number changes of single probes, all probes on a chromosome, or all probes in the genome. We then apply this theory to develop a practical heuristic algorithm, implemented in publicly available software, for inferring tumor phylogenies on data from potentially hundreds of single cells by this evolutionary model. We demonstrate and validate the methods on simulated data and published FISH data from cervical cancers and breast cancers. Our computational experiments show that the new model and algorithm lead to more parsimonious trees than prior methods for single-tumor phylogenetics and to improved performance on various classification tasks, such as distinguishing primary tumors from metastases obtained from the same patient population.

The evolution of tumour phylogenetics: principles and practice

“…The majority of published tools for single-cell phylogenetics are still based on pre-scSeq technologies 84,148,151–153 , with just a handful having been developed specifically for scSeq. Kim and Simon 89 introduced the muttree program, which uses a custom combinatorial inference to find trees optimized for a specialized probabilistic model that differs from the models used by other tools which accept the same input.…”

The Copy-Number Tree Mixture Deconvolution Problem and Applications to Multi-sample Bulk Sequencing Tumor Data

“…However, the single event model is not a good representation of true copy number aberrations in cancer, as the length distribution of somatic copy number aberrations is not simply a function of length [30]. Such a copy number model was used by [19] and [3] for inferring the evolution comprising the minimum number of single events from the profile of clones inferred independently from each sample. Figure 3 shows an example highlighting the weaknesses of all the alternative methods presented above.…”

“…Thus, methods that simultaneously identify CNAs and perform phylogeny inference from CNAs and SNVs are an important direction for future work. Finally, one could augment the phylogenetic reconstructions with single-cell measurements including FISH [3] or single-cell sequencing [4]. Together, these improvements would enable high-fidelity phylogenetic reconstructions of tumor evolution.…”

“…A number of models have been introduced to study CNA evolution, and these models can be classified into two categories. The first considers single events such that each of those independently affects the copy number of a single segment [3,19]. However, these models do not account for dependency between adjacent segments in the genome.…”

Genetic Heterogeneity of Kidney Cancer

“…However, this analysis revealed that mutations with different allele frequencies within the population had different mutational spectra, suggesting that clear cell RCC "may be more genetically complex than previously thought" [ 19 ]. Novel algorithms to construct phylogenetic models of tumor progression at the cellular levelincorporating copy number changes at the scale of single genes, entire chromosomes, and the whole genome -are currently under development and may help shed additional light on the implications of single-cell sequencing [ 20 ].…”