Linearization of Ancestral Multichromosomal Genomes

Peer reviewed: 
Yes, item is peer reviewed.
Scholarly level: 
Final version published as: 

BMC Bioinformatics 2012, 13(Suppl 19):S11 doi:10.1186/1471-2105-13-S19-S11

Date created: 
Ancestral genome reconstruction methods
Linearization Problem
Binary matrices of degree two

BACKGROUND:Recovering the structure of ancestral genomes can be formalized in terms of properties of binary matrices such as the Consecutive-Ones Property (C1P). The Linearization Problem asks to extract, from a given binary matrix, a maximum weight subset of rows that satisfies such a property. This problem is in general intractable, and in particular if the ancestral genome is expected to contain only linear chromosomes or a unique circular chromosome. In the present work, we consider a relaxation of this problem, which allows ancestral genomes that can contain several chromosomes, each either linear or circular.RESULT:We show that, when restricted to binary matrices of degree two, which correspond to adjacencies, the genomic characters used in most ancestral genome reconstruction methods, this relaxed version of the Linearization Problem is polynomially solvable using a reduction to a matching problem. This result holds in the more general case where columns have bounded multiplicity, which models possibly duplicated ancestral genes. We also prove that for matrices with rows of degrees 2 and 3, without multiplicity and without weights on the rows, the problem is NP-complete, thus tracing sharp tractability boundaries.CONCLUSION:As it happened for the breakpoint median problem, also used in ancestral genome reconstruction, relaxing the definition of a genome turns an intractable problem into a tractable one. The relaxation is adapted to some biological contexts, such as bacterial genomes with several replicons, possibly partially assembled. Algorithms can also be used as heuristics for hard variants. More generally, this work opens a way to better understand linearization results for ancestral genome structure inference.

Document type: 
You are free to copy, distribute and transmit this work under the following conditions: You must give attribution to the work (but not in any way that suggests that the author endorses you or your use of the work); You may not use this work for commercial purposes; You may not alter, transform, or build upon this work. Any further uses require the permission of the rights holder (or author if no rights holder is listed). These rights are based on the Creative Commons Attribution-NonCommercial-NoDerivatives License.