Abstract
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 varphi-MCPS (Minimum Cost Parsimonious Scenario), that are based on labeled graphs. We show how to compute solutions to general instances of varphi-MCPS, given an algorithm to compute varphi-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.
Highlights
Context The practical study of genome rearrangement scenarios has been limited by a lack of mathematical models capable of incorporating biological constraints, since foundational models focused on minimum length scenarios transforming one genome into another
double cut and join (DCJ) can naturally be interpreted as a graph edit model with the use of the breakpoint graph, where there is an edge between gene extremities a and b for each adjacent pair
In [11] we presented an O(n4) time algorithm solving φcMCPS for a labeled breakpoint graph with the gray edges labeled by τ
Summary
Context The practical study of genome rearrangement scenarios has been limited by a lack of mathematical models capable of incorporating biological constraints, since foundational models focused on minimum length scenarios transforming one genome into another. One way to incorporate biological information into the inference of evolutionary scenarios is to consider models that weight rearrangements according to their likelihood of occurring; a breakpoint may be more likely to occur in some intergenic regions than others. To this end, the study of length-weighted reversals was started in the late nineties by Blanchette et al [1]. DCJ can naturally be interpreted as a graph edit model with the use of the breakpoint graph, where there is an edge between gene extremities a and b for each adjacent pair. This edge edit operation on a graph is called a 2-break
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