The binary perfect phylogeny with persistent characters

Bonizzoni, Paola; Braghin, Chiara; Dondi, Riccardo; Trucco, Gabriella

doi:10.1016/j.tcs.2012.05.035

Cited by 62 publications

(72 citation statements)

References 23 publications

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“…The converse also holds, that is given a sequence C of edge labels, we can reconstruct the unique persistent perfect phylogeny T (if it exists) such that C is the sequence of edge labels traversed during a depth-first visit of T [21]. …”

Section: Introductionmentioning

confidence: 99%

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Explaining evolution via constrained persistent perfect phylogeny

et al. 2014

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BackgroundThe perfect phylogeny is an often used model in phylogenetics since it provides an efficient basic procedure for representing the evolution of genomic binary characters in several frameworks, such as for example in haplotype inference. The model, which is conceptually the simplest, is based on the infinite sites assumption, that is no character can mutate more than once in the whole tree. A main open problem regarding the model is finding generalizations that retain the computational tractability of the original model but are more flexible in modeling biological data when the infinite site assumption is violated because of e.g. back mutations. A special case of back mutations that has been considered in the study of the evolution of protein domains (where a domain is acquired and then lost) is persistency, that is the fact that a character is allowed to return back to the ancestral state. In this model characters can be gained and lost at most once. In this paper we consider the computational problem of explaining binary data by the Persistent Perfect Phylogeny model (referred as PPP) and for this purpose we investigate the problem of reconstructing an evolution where some constraints are imposed on the paths of the tree.ResultsWe define a natural generalization of the PPP problem obtained by requiring that for some pairs (character, species), neither the species nor any of its ancestors can have the character. In other words, some characters cannot be persistent for some species. This new problem is called Constrained PPP (CPPP). Based on a graph formulation of the CPPP problem, we are able to provide a polynomial time solution for the CPPP problem for matrices whose conflict graph has no edges. Using this result, we develop a parameterized algorithm for solving the CPPP problem where the parameter is the number of characters.ConclusionsA preliminary experimental analysis shows that the constrained persistent perfect phylogeny model allows to explain efficiently data that do not conform with the classical perfect phylogeny model.

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Section: Introductionmentioning

confidence: 99%

“…The sequence

scriptC

obtained by a depth-first visit of the tree is a sequence of edge labels whose realization results in an edgeless red-black graph [21]. Such sequence

scriptC

is called successful c-reduction of the red-black graph.…”

Section: Introductionmentioning

confidence: 99%

Explaining evolution via constrained persistent perfect phylogeny

et al. 2014

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“…This problem can be formulated and efficiently solved as an instance of ILP. Later, a similar formulation was proposed in [21] to solve the Persistent Phylogeny Problem [22,23]. In this problem, the goal is to compute a persistent phylogeny that is defined as a phylogeny in which each mutation is allowed to be "lost" at most once.…”

Section: Introductionmentioning

confidence: 99%

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

Malikić

Ciccolella

Mehrabadi

et al. 2018

Preprint

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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.

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“…We will focus on three main character-based models that generalize the Perfect Phylogeny: the Persistent Phylogeny [1] (where each character can be gained once and lost at most once), the Camin-Sokal [6] (where each character can be gained several times, but never lost), and the Dollo [11] (where each character can be gained at most once, but lost several times). We denote by Camin-Sokal(k) the restriction of the Camin-Sokal model where each character can be gained at most k times in the entire tree.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

Does relaxing the infinite sites assumption give better tumor phylogenies? An ILP-based comparative approach

Bonizzoni

Ciccolella

Vedova

et al. 2017

Preprint

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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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The binary perfect phylogeny with persistent characters

Cited by 62 publications

References 23 publications

Explaining evolution via constrained persistent perfect phylogeny

Explaining evolution via constrained persistent perfect phylogeny

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

Does relaxing the infinite sites assumption give better tumor phylogenies? An ILP-based comparative approach

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