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

Dollo-CDP: a polynomial-time algorithm for the clade-constrained large Dollo parsimony problem

The last decade of phylogenetics has seen the development of many methods that leverage constraints plus dynamic programming. The goal of this algorithmic technique is to produce a phylogeny that is optimal with respect to some objective function and that lies within a constrained version of tree space. The popular species tree estimation method ASTRAL, for example, returns a tree that (1) maximizes the quartet score computed with respect to the input gene trees and that (2) draws its branches (bipartitions) from the input constraint set. This technique has yet to be used for parsimony problems where the input are binary characters, sometimes with missing values. Here, we introduce the clade-constrained character parsimony problem and present an algorithm that solves this problem for the Dollo criterion score in [Formula: see text] time, where n is the number of leaves, k is the number of characters, and [Formula: see text] is the set of clades used as constraints. Dollo parsimony, which requires traits/mutations to be gained at most once but allows them to be lost any number of times, is widely used for tumor phylogenetics as well as species phylogenetics, for example analyses of low-homoplasy retroelement insertions across the vertebrate tree of life. This motivated us to implement our algorithm in a software package, called Dollo-CDP, and evaluate its utility for analyzing retroelement insertion presence / absence patterns for bats, birds, toothed whales as well as simulated data. Our results show that Dollo-CDP can improve upon heuristic search from a single starting tree, often recovering a better scoring tree. Moreover, Dollo-CDP scales to data sets with much larger numbers of taxa than branch-and-bound while still having an optimality guarantee, albeit a more restricted one. Lastly, we show that our algorithm for Dollo parsimony can easily be adapted to Camin-Sokal parsimony but not Fitch parsimony.

Startle: A star homoplasy approach for CRISPR-Cas9 lineage tracing

CRISPR-Cas9-based genome editing combined with single-cell sequencing enables the tracing of the history of cell divisions, or cellular lineage, in tissues and whole organisms. Although standard phylogenetic approaches may be applied to reconstruct cellular lineage trees from this data, the unique features of the CRISPR-Cas9 editing process motivate the development of specialized models that describe the evolution of CRISPR-Cas9-induced mutations. Here, we introduce the "star homoplasy" evolutionary model that constrains a phylogenetic character to mutate at most once along a lineage, capturing the "non-modifiability" property of CRISPR-Cas9 mutations. We derive a combinatorial characterization of star homoplasy phylogenies and use this characterization to develop an algorithm, "Startle", that computes a maximum parsimony star homoplasy phylogeny. We demonstrate that Startle infers more accurate phylogenies on simulated lineage tracing data compared with existing methods and finds parsimonious phylogenies with fewer metastatic migrations on lineage tracing data from mouse metastatic lung adenocarcinoma.

Fast intratumor heterogeneity inference from single-cell sequencing data

We introduce HUNTRESS, a computational method for mutational intratumor heterogeneity inference from noisy genotype matrices derived from single-cell sequencing data, the running time of which is linear with the number of cells and quadratic with the number of mutations. We prove that, under reasonable conditions, HUNTRESS computes the true progression history of a tumor with high probability. On simulated and real tumor sequencing data, HUNTRESS is demonstrated to be faster than available alternatives with comparable or better accuracy. Additionally, the progression histories of tumors inferred by HUNTRESS on real single-cell sequencing datasets agree with the best known evolution scenarios for the associated tumors.

From Alpha to Zeta: Identifying Variants and Subtypes of SARS-CoV-2 Via Clustering

The availability of millions of SARS-CoV-2 (Severe Acute Respiratory Syndrome-Coronavirus-2) sequences in public databases such as GISAID (Global Initiative on Sharing All Influenza Data) and EMBL-EBI (European Molecular Biology Laboratory-European Bioinformatics Institute) (the United Kingdom) allows a detailed study of the evolution, genomic diversity, and dynamics of a virus such as never before. Here, we identify novel variants and subtypes of SARS-CoV-2 by clustering sequences in adapting methods originally designed for haplotyping intrahost viral populations. We asses our results using clustering entropy-the first time it has been used in this context. Our clustering approach reaches lower entropies compared with other methods, and we are able to boost this even further through gap filling and Monte Carlo-based entropy minimization. Moreover, our method clearly identifies the well-known Alpha variant in the U.K. and GISAID data sets, and is also able to detect the much less represented (<1% of the sequences) Beta (South Africa), Epsilon (California), and Gamma and Zeta (Brazil) variants in the GISAID data set. Finally, we show that each variant identified has high selective fitness, based on the growth rate of its cluster over time. This demonstrates that our clustering approach is a viable alternative for detecting even rare subtypes in very large data sets.

Studying the History of Tumor Evolution from Single-Cell Sequencing Data by Exploring the Space of Binary Matrices

Single-cell sequencing (SCS) data have great potential in reconstructing the evolutionary history of tumors. Rapid advances in SCS technology in the past decade were followed by the design of various computational methods for inferring trees of tumor evolution. Some of the earliest methods were based on the direct search in the space of trees with the goal of finding the maximum likelihood tree. However, it can be shown that instead of searching directly in the tree space, we can perform a search in the space of binary matrices and obtain maximum likelihood tree directly from the maximum likelihood matrix. The potential of the latter tree search strategy has recently been recognized by different research groups and several related methods were published in the past 2 years. Here we provide a review of the theoretical background of these methods and a detailed discussion, which are largely missing in the available publications, of the correlation between the two tree search strategies. We also discuss each of the existing methods based on the search in the space of binary matrices and summarize the best-known single-cell DNA sequencing data sets, which can be used in the future for assessing performance on real data of newly developed methods.

Effective Clustering for Single Cell Sequencing Cancer Data

Single cell sequencing (SCS) technologies provide a level of resolution that makes it indispensable for inferring from a sequenced tumor, evolutionary trees or phylogenies representing an accumulation of cancerous mutations. A drawback of SCS is elevated false negative and missing value rates, resulting in a large space of possible solutions, which in turn makes it difficult, sometimes infeasible using current approaches and tools. One possible solution is to reduce the size of an SCS instance --- usually represented as a matrix of presence, absence, and uncertainty of the mutations found in the different sequenced cells --- and to infer the tree from this reduced-size instance. In this work, we present a new clustering procedure aimed at clustering such categorical vector, or matrix data --- here representing SCS instances, called celluloid. We show that celluloid clusters mutations with high precision: never pairing too many mutations that are unrelated in the ground truth, but also obtains accurate results in terms of the phylogeny inferred downstream from the reduced instance produced by this method. We demonstrate the usefulness of a clustering step by applying the entire pipeline (clustering + inference method) to a real dataset, showing a significant reduction in the runtime, raising considerably the upper bound on the size of SCS instances which can be solved in practice. Our approach, celluloid: clustering single cell sequencing data around centroids is available at https://github.com/AlgoLab/celluloid/ under an MIT license, as well as on the Python Package Index (PyPI) at https://pypi.org/project/celluloid-clust/.