Models and algorithms for genome rearrangement with positional constraints

Genome Rearrangement Analysis : Cut and Join Genome Rearrangements and Gene Cluster Preserving Approaches

Genome rearrangements are mutations that change the gene content of a genome or the arrangement of the genes on a genome. Several years of research on genome rearrangements have established different algorithmic approaches for solving some fundamental problems in comparative genomics based on gene order information. This review summarizes the literature on genome rearrangement analysis along two lines of research. The first line considers rearrangement models that are particularly well suited for a theoretical analysis. These models use rearrangement operations that cut chromosomes into fragments and then join the fragments into new chromosomes. The second line works with rearrangement models that reflect several biologically motivated constraints, e.g., the constraint that gene clusters have to be preserved. In this chapter, the border between algorithmically "easy" and "hard" rearrangement problems is sketched and a brief review is given on the available software tools for genome rearrangement analysis.

A general framework for genome rearrangement with biological constraints

This paper generalizes previous studies on genome rearrangement under biological constraints, using double cut and join (DCJ). We propose a model for weighted DCJ, along with a family of optimization problems called \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi$$\end{document}φ-MCPS (Minimum Cost Parsimonious Scenario), that are based on labeled graphs. We show how to compute solutions to general instances of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi$$\end{document}φ-MCPS, given an algorithm to compute \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi$$\end{document}φ-MCPS on a circular genome with exactly one occurrence of each gene. These general instances can have an arbitrary number of circular and linear chromosomes, and arbitrary gene content. The practicality of the framework is displayed by presenting polynomial-time algorithms that generalize the results of Bulteau, Fertin, and Tannier on the Sorting by wDCJs and indels in intergenes problem, and that generalize previous results on the Minimum Local Parsimonious Scenario problem.

Large-scale mammalian genome rearrangements coincide with chromatin interactions

Motivation

Genome rearrangements drastically change gene order along great stretches of a chromosome. There has been initial evidence that these apparently non-local events in the 1D sense may have breakpoints that are close in the 3D sense. We harness the power of the Double Cut and Join model of genome rearrangement, along with Hi-C chromosome conformation capture data to test this hypothesis between human and mouse.

Results

We devise novel statistical tests that show that indeed, rearrangement scenarios that transform the human into the mouse gene order are enriched for pairs of breakpoints that have frequent chromosome interactions. This is observed for both intra-chromosomal breakpoint pairs, as well as for inter-chromosomal pairs. For intra-chromosomal rearrangements, the enrichment exists from close (<20 Mb) to very distant (100 Mb) pairs. Further, the pattern exists across multiple cell lines in Hi-C data produced by different laboratories and at different stages of the cell cycle. We show that similarities in the contact frequencies between these many experiments contribute to the enrichment. We conclude that either (i) rearrangements usually involve breakpoints that are spatially close or (ii) there is selection against rearrangements that act on spatially distant breakpoints.

Availability and implementation

Our pipeline is freely available at https://bitbucket.org/thekswenson/locality.

Supplementary information

Supplementary data are available at Bioinformatics online.

Position and Content Paradigms in Genome Rearrangements: The Wild and Crazy World of Permutations in Genomics

Modellers of large-scale genome rearrangement events, in which segments of DNA are inverted, moved, swapped, or even inserted or deleted, have found a natural syntax in the language of permutations. Despite this, there has been a wide range of modelling choices, assumptions and interpretations that make navigating the literature a significant challenge. Indeed, even authors of papers that use permutations to model genome rearrangement can struggle to interpret each others' work, because of subtle differences in basic assumptions that are often deeply ingrained (and consequently sometimes not even mentioned). In this paper, we describe the different ways in which permutations have been used to model genomes and genome rearrangement events, presenting some features and limitations of each approach, and show how the various models are related. This paper will help researchers navigate the landscape of permutation-based genome rearrangement models and make it easier for authors to present clear and consistent models.

Finding local genome rearrangements

Background

The double cut and join (DCJ) model of genome rearrangement is well studied due to its mathematical simplicity and power to account for the many events that transform gene order. These studies have mostly been devoted to the understanding of minimum length scenarios transforming one genome into another. In this paper we search instead for rearrangement scenarios that minimize the number of rearrangements whose breakpoints are unlikely due to some biological criteria. One such criterion has recently become accessible due to the advent of the Hi-C experiment, facilitating the study of 3D spacial distance between breakpoint regions.

Results

We establish a link between the minimum number of unlikely rearrangements required by a scenario and the problem of finding a maximum edge-disjoint cycle packing on a certain transformed version of the adjacency graph. This link leads to a 3/2-approximation as well as an exact integer linear programming formulation for our problem, which we prove to be NP-complete. We also present experimental results on fruit flies, showing that Hi-C data is informative when used as a criterion for rearrangements.

Conclusions

A new variant of the weighted DCJ distance problem is addressed that ignores scenario length in its objective function. A solution to this problem provides a lower bound on the number of unlikely moves necessary when transforming one gene order into another. This lower bound aids in the study of rearrangement scenarios with respect to chromatin structure, and could eventually be used in the design of a fixed parameter algorithm with a more general objective function.

Genome Rearrangement Analysis: Cut and Join Genome Rearrangements and Gene Cluster Preserving Approaches

Genome rearrangements are mutations that change the gene content of a genome or the arrangement of the genes on a genome. Several years of research on genome rearrangements have established different algorithmic approaches for solving some fundamental problems in comparative genomics based on gene order information. This review summarizes the literature on genome rearrangement analysis along two lines of research. The first line considers rearrangement models that are particularly well suited for a theoretical analysis. These models use rearrangement operations that cut chromosomes into fragments and then join the fragments into new chromosomes. The second line works with rearrangement models that reflect several biologically motivated constraints, e.g., the constraint that gene clusters have to be preserved. In this chapter, the border between algorithmically "easy" and "hard" rearrangement problems is sketched and a brief review is given on the available software tools for genome rearrangement analysis.