Co-evolution of AR gene copy number and structural complexity in endocrine therapy resistant prostate cancer.

Androgen receptor (AR) inhibition is standard of care for advanced prostate cancer (PC). However, efficacy is limited by progression to castration-resistant PC (CRPC), usually due to AR re-activation via mechanisms that include AR amplification and structural rearrangement. These two classes of AR alterations often co-occur in CRPC tumors, but it is unclear whether this reflects intercellular or intracellular heterogeneity of AR. Resolving this is important for developing new therapies and predictive biomarkers. Here, we analyzed 41 CRPC tumors and 6 patient-derived xenografts (PDXs) using linked-read DNA-sequencing, and identified 7 tumors that developed complex, multiply-rearranged AR gene structures in conjunction with very high AR copy number. Analysis of PDX models by optical genome mapping and fluorescence in situ hybridization showed that AR residing on extrachromosomal DNA (ecDNA) was an underlying mechanism, and was associated with elevated levels and diversity of AR expression. This study identifies co-evolution of AR gene copy number and structural complexity via ecDNA as a mechanism associated with endocrine therapy resistance.

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 φ -MCPS (Minimum Cost Parsimonious Scenario), that are based on labeled graphs. We show how to compute solutions to general instances of φ -MCPS, given an algorithm to compute 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.

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.

Models and algorithms for genome rearrangement with positional constraints.

BACKGROUND: Traditionally, the merit of a rearrangement scenario between two gene orders has been measured based on a parsimony criteria alone; two scenarios with the same number of rearrangements are considered equally good. In this paper, we acknowledge that each rearrangement has a certain likelihood of occurring based on biological constraints, e.g. physical proximity of the DNA segments implicated or repetitive sequences. RESULTS: We propose optimization problems with the objective of maximizing overall likelihood, by weighting the rearrangements. We study a binary weight function suitable to the representation of sets of genome positions that are most likely to have swapped adjacencies. We give a polynomial-time algorithm for the problem of finding a minimum weight double cut and join scenario among all minimum length scenarios. In the process we solve an optimization problem on colored noncrossing partitions, which is a generalization of the Maximum Independent Set problem on circle graphs. CONCLUSIONS: We introduce a model for weighting genome rearrangements and show that under simple yet reasonable conditions, a fundamental distance can be computed in polynomial time. This is achieved by solving a generalization of the Maximum Independent Set problem on circle graphs. Several variants of the problem are also mentioned.