COMPUTING THE REVERSAL DISTANCE BETWEEN GENOMES IN THE PRESENCE OF MULTI-GENE FAMILIES VIA BINARY INTEGER PROGRAMMING

Flanked Block-Interchange Distance on Strings

Rearrangement sorting problems impact profoundly in measuring genome similarities and tracing historic scenarios of species. However, recent studies on genome rearrangement mechanisms disclosed a statistically significant evidence, repeats are situated at the ends of rearrangement relevant segments and stay unchanged before and after rearrangements.To reflect the principle behind this evidence, we propose flanked block-interchange, an operation on strings that exchanges two substrings flanked by identical left and right symbols in a string. The flanked block-interchange distance problem is formulated as finding a shortest sequence of flanked block-interchanges to transform a string into the other. We propose a sufficient and necessary condition for deciding whether two strings can be transformed into each other by flanked block-interchanges. This condition is linear time verifiable. Under this condition for two strings, we present a [Formula: see text]-approximation algorithm for the flanked block-interchange distance problem where each symbol occurs at most k times in a string and a polynomial algorithm for this problem where each symbol occurs at most twice in a string. We show that the problem of flanked block-interchange distance is NP-hard at last.

A unified ILP framework for core ancestral genome reconstruction problems

MOTIVATION

One of the key computational problems in comparative genomics is the reconstruction of genomes of ancestral species based on genomes of extant species. Since most dramatic changes in genomic architectures are caused by genome rearrangements, this problem is often posed as minimization of the number of genome rearrangements between extant and ancestral genomes. The basic case of three given genomes is known as the genome median problem. Whole-genome duplications (WGDs) represent yet another type of dramatic evolutionary events and inspire the reconstruction of preduplicated ancestral genomes, referred to as the genome halving problem. Generalization of WGDs to whole-genome multiplication events leads to the genome aliquoting problem.

RESULTS

In this study, we propose polynomial-size integer linear programming (ILP) formulations for the aforementioned problems. We further obtain such formulations for the restricted and conserved versions of the median and halving problems, which have been recently introduced to improve biological relevance of the solutions. Extensive evaluation of solutions to the different ILP problems demonstrates their good accuracy. Furthermore, since the ILP formulations for the conserved versions have linear size, they provide a novel practical approach to ancestral genome reconstruction, which combines the advantages of homology- and rearrangements-based methods.

AVAILABILITY AND IMPLEMENTATION

Code and data are available in https://github.com/AvdeevPavel/ILP-WGD-reconstructor.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.