Andre Rodrigues Oliveira

In this work, we explore heuristics for the Adjacency Graph Packing problem, which can be applied to the Double Cut and Join (DCJ) Distance Problem. The DCJ is a rearrangement operation and the distance problem considering it is a well established method for genome comparison. Our heuristics will use the structure called adjacency graph adapted to include information about intergenic regions, multiple copies of genes in the genomes, and multiple circular or linear chromosomes. The only required property from the genomes is that it must be possible to turn one into the other with DCJ operations. We propose one greedy heuristic and one heuristic based on Genetic Algorithms. Our experimental tests in artificial genomes show that the use of heuristics is capable of finding good results that are superior to a simpler random strategy.

Genome Rearrangement distance problems are used in Computational Biology to estimate the evolutionary distance between genomes. These problems consist of minimizing the number of rearrangement events necessary to transform one genome into another. Two commonly used rearrangement events are reversal and transposition. The first studied problems ignored nucleotides outside genes (called intergenic regions), or assumed that genomes have a single copy of each gene. Recent works made advancements in more general problems considering the number of nucleotides in intergenic regions, and replicated genes. Nevertheless, genomes tend to have wildly different quantities of nucleotides on their intergenic regions, which poses a problem when comparing these regions exactly. To overcome this limitation, our work considers some flexibility when matching intergenic regions that do not have the same number of nucleotides. We propose new problems seeking the minimum number of reversals, or reversals and transpositions, necessary to transform one genome into another, while considering flexible intergenic region information. We show approximations for these problems by exploring their relationship with the Signed Minimum Common Flexible Intergenic String Partition problem. We also present different heuristics for the partition problem, and conduct experimental tests on simulated genomes to assess the performance of our algorithms

One of the challenges in the Comparative Genomics field is to infer how close two organisms are based on the similarities and differences between their genetic materials. Recent advances in DNA sequencing have made complete genomes increasingly available. That said, several new algorithms trying to infer the distance between two organisms based on genome rearrangements have been proposed in the literature. However, given the diversity of approaches, the diversity of genome rearrangement events, or even how each work models the genomes and what assumptions are made by each of them, finding the ideal algorithm for each situation or simply knowing the range of applicable approaches can be challenging. In this work, we review these approaches having the algorithmic and combinatorial advances since 2010 as our main focus. This survey aims to organize the recently published papers using a concise notation and to indicate the gaps filled by each of them in the literature. This makes it easier to understand what still needs to be done and what has room for enhancement.

The most common way to calculate the rearrangement distance between two genomes is to use the size of a minimum length sequence of rearrangements that transforms one of the two given genomes into the other, where the genomes are represented as permutations using only their gene order, based on the assumption that genomes have the same gene content. With the advance of research in genome rearrangements, new works extended the classical models by either considering genomes with different gene content (unbalanced genomes) or including more genomic characteristics to the mathematical representation of the genomes, such as the distribution of intergenic regions sizes. In this study, we study the Reversal, Transposition, and Indel (Insertion and Deletion) Distance using intergenic information, which allows comparing unbalanced genomes, because indels are included in the rearrangement model (i.e., the set of possible rearrangements allowed when we compute the distance). For the particular case of transpositions and indels on unbalanced genomes, we present a 4-approximation algorithm, improving a previous 4.5 approximation. This algorithm is extended so as to deal with gene orientation and to maintain the 4-approximation factor for the Reversal, Transposition, and Indel Distance on unbalanced genomes. Furthermore, we evaluate the proposed algorithms using experiments on simulated data.