A colored graph approach to perfect phylogeny with persistent characters

MotivationCancer is characterized by intra-tumor heterogeneity, the presence of distinct cell populations with distinct complements of somatic mutations, which include single-nucleotide variants (SNVs) and copy-number aberrations (CNAs). Single-cell sequencing technology enables one to study these cell populations at single-cell resolution. Phylogeny estimation algorithms that employ appropriate evolutionary models are key to understanding the evolutionary mechanisms behind intra-tumor heterogeneity.ResultsWe introduce Single-cell Phylogeny Reconstruction (SPhyR), a method for tumor phylogeny estimation from single-cell sequencing data. In light of frequent loss of SNVs due to CNAs in cancer, SPhyR employs the k-Dollo evolutionary model, where a mutation can only be gained once but lost k times. Underlying SPhyR is a novel combinatorial characterization of solutions as constrained integer matrix completions, based on a connection to the cladistic multi-state perfect phylogeny problem. SPhyR outperforms existing methods on simulated data and on a metastatic colorectal cancer.Availability and implementationSPhyR is available on https://github.com/elkebir-group/SPhyR.Supplementary information Supplementary data are available at Bioinformatics online.

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“…We note that the binary matrix used in these papers is precisely the binary factor matrix obtained from the multi-state matrix A and state trees

. While a restricted variant of the k = 1 case was recently shown to be solvable in polynomial time ( Bonizzoni et al. , 2017a ), the hardness for

remains an open question.…”

Section: Methodsmentioning

confidence: 99%

SPhyR: tumor phylogeny estimation from single-cell sequencing data under loss and error

2018

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“…We denote as Dollo(k) the evolutionary model in which each mutation can be acquired exactly once and can be lost at most k times. In this way Dollo(0) and Dollo(1) correspond to the perfect [21] and persistent [37][38][39] phylogeny models, respectively. In the tree generation process for the Dollo(k) model (k > 0) we are required to augment a perfect phylogeny representing the cancer progression by adding nodes which represent the loss of a mutation, i.e., a node labeled m − l , representing the potential losses.…”

Section: Methodsmentioning

confidence: 99%

gpps: an ILP-based approach for inferring cancer progression with mutation losses from single cell data

et al. 2020

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Background Cancer progression reconstruction is an important development stemming from the phylogenetics field. In this context, the reconstruction of the phylogeny representing the evolutionary history presents some peculiar aspects that depend on the technology used to obtain the data to analyze: Single Cell DNA Sequencing data have great specificity, but are affected by moderate false negative and missing value rates. Moreover, there has been some recent evidence of back mutations in cancer: this phenomenon is currently widely ignored. Results We present a new tool, , that reconstructs a tumor phylogeny from Single Cell Sequencing data, allowing each mutation to be lost at most a fixed number of times. The General Parsimony Phylogeny from Single cell () tool is open source and available at https://github.com/AlgoLab/gpps. Conclusions provides new insights to the analysis of intra-tumor heterogeneity by proposing a new progression model to the field of cancer phylogeny reconstruction on Single Cell data.

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“…(1), (2). We stress the fact that decision problem of determine if an incomplete matrix admits a Perfect Phylogeny can be seen as checking if the former problem has zero value or equivalently a feasible solution for restrictions (1) and (3). The total number of variables and constraints in the formulation are in O(nm + m 2 ) and O(nm 2 ) respectively.…”

Section: Objective Functionmentioning

confidence: 99%

“…Moreover, we denote by Dollo(k) the restriction of the Dollo model where each character can be lost at most k times in the entire tree. Clearly, the Persistent Phylogeny [1] corresponds to the Dollo(1) model which has been recently investigated in several works aiming to develop efficient solutions for the model [3,4,16] since its use is motivated also in other contexts [2,26]. In particular, in [1] it is proved that the Persistent Phylogeny Problem over a binary matrix M can be formulated as finding a special completion of an extended matrix M e that is a Perfect Phylogeny.…”

Section: Introductionmentioning

confidence: 99%

Does Relaxing the Infinite Sites Assumption Give Better Tumor Phylogenies? An ILP-Based Comparative Approach

Bonizzoni

Ciccolella

Vedova

et al. 2019

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Most of the evolutionary history reconstruction approaches are based on the infinite site assumption, which is underlying the Perfect Phylogeny model and whose main consequence is that acquired mutation can never lost. This results in the clonal model used to explain cancer evolution. Some recent results gives a strong evidence that recurrent and back mutations are present in the evolutionary history of tumors [5,21], thus showing that more general models then the Perfect Phylogeny are required. We propose a new approach that incorporates the possibility of losing a previously acquired mutation, extending the Persistent Phylogeny model [1].We exploit our model to provide an ILP formulation of the problem of reconstructing trees on mixed populations, where the input data consists of the fraction of cells in a set of samples that have a certain mutation. This is a fundamental problem in cancer genomics, where the goal is to study the evolutionary history of a tumor. An experimental analysis shows the usefulness of allowing mutation losses, by studying some real and simulated datasets where our ILP approach provides a better interpretation than the one obtained under perfect phylogeny assumption. Finally, we show how to incorporate multiple back mutations and recurrent mutations in our model.

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A colored graph approach to perfect phylogeny with persistent characters

Cited by 16 publications

References 16 publications

SPhyR: tumor phylogeny estimation from single-cell sequencing data under loss and error

SPhyR: tumor phylogeny estimation from single-cell sequencing data under loss and error

gpps: an ILP-based approach for inferring cancer progression with mutation losses from single cell data

Does Relaxing the Infinite Sites Assumption Give Better Tumor Phylogenies? An ILP-Based Comparative Approach

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