Pedro Feijão

Reconstruction of ancestral gene orders using intermediate genomes

BackgroundThe problem of reconstructing ancestral genomes in a given phylogenetic tree arises in many different comparative genomics fields. Here, we focus on reconstructing the gene order of ancestral genomes, a problem that has been largely studied in the past 20 years, especially with the increasing availability of whole genome DNA sequences. There are two main approaches to this problem: event-based methods, that try to find the ancestral genomes that minimize the number of rearrangement events in the tree; and homology-based, that look for conserved structures, such as adjacent genes in the extant genomes, to build the ancestral genomes.ResultsWe propose algorithms that use the concept of intermediate genomes, arising in optimal pairwise rearrangement scenarios. We show that intermediate genomes have combinatorial properties that make them easy to reconstruct, and develop fast algorithms with better reconstructed ancestral genomes than current event-based methods. The proposed framework is also designed to accept extra information, such as results from homology-based approaches, giving rise to combined algorithms with better results than the original methods.

On the family-free DCJ distance and similarity

Structural variation in genomes can be revealed by many (dis)similarity measures. Rearrangement operations, such as the so called double-cut-and-join (DCJ), are large-scale mutations that can create complex changes and produce such variations in genomes. A basic task in comparative genomics is to find the rearrangement distance between two given genomes, i.e., the minimum number of rearragement operations that transform one given genome into another one. In a family-based setting, genes are grouped into gene families and efficient algorithms have already been presented to compute the DCJ distance between two given genomes. In this work we propose the problem of computing the DCJ distance of two given genomes without prior gene family assignment, directly using the pairwise similarities between genes. We prove that this new family-free DCJ distance problem is APX-hard and provide an integer linear program to its solution. We also study a family-free DCJ similarity and prove that its computation is NP-hard.

Approximating the DCJ distance of balanced genomes in linear time

BackgroundRearrangements are large-scale mutations in genomes, responsible for complex changes and structural variations. Most rearrangements that modify the organization of a genome can be represented by the double cut and join (DCJ) operation. Given two balanced genomes, i.e., two genomes that have exactly the same number of occurrences of each gene in each genome, we are interested in the problem of computing the rearrangement distance between them, i.e., finding the minimum number of DCJ operations that transform one genome into the other. This problem is known to be NP-hard.ResultsWe propose a linear time approximation algorithm with approximation factor O(k) for the DCJ distance problem, where k is the maximum number of occurrences of any gene in the input genomes. Our algorithm works for linear and circular unichromosomal balanced genomes and uses as an intermediate step an O(k)-approximation for the minimum common string partition problem, which is closely related to the DCJ distance problem.ConclusionsExperiments on simulated data sets show that our approximation algorithm is very competitive both in efficiency and in quality of the solutions.

On the Multichromosomal Hultman Number

The number of cycles of a breakpoint graph is one of the notable parameters to solve distance problems in comparative genomics. For a fixed c, the number of linear unichromosomal genomes with n genes such that the breakpoint graph has c disjoint cycles, the Hultman number, is already determined. In this work we extend this result to multichromosomal genomes, providing formulas to compute the number of multichromosal genomes having a fixed number of cycles and/or paths.

On the Family-Free DCJ Distance

Structural variation in genomes can be revealed by many (dis)similarity measures. Rearrangement operations, such as the so called double-cut-and-join (DCJ), are large-scale mutations that can create complex changes and produce such variations in genomes. A basic task in comparative genomics is to find the rearrangement distance between two given genomes, i.e., the minimum number of rearragement operations that transform one given genome into another one. In a family-based setting, genes are grouped into gene families and efficient algorithms were already proposed to compute the DCJ distance between two given genomes. In this work we propose the problem of computing the DCJ distance of two given genomes without prior gene family assignment, directly using the pairwise similarity between genes. We propose a new family-free DCJ distance, prove that the family-free DCJ distance problem is APX-hard, and provide an integer linear program to its solution.

The gene family-free median of three

BackgroundThe gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the breakpoint median of three genomes, which asks for the construction of a fourth genome that minimizes the sum of breakpoint distances to the input genomes.MethodsWe present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We study its computational complexity and we describe an integer linear program (ILP) for its exact solution. We further discuss a related problem called family-free adjacencies for k genomes for the special case of

Fast ancestral gene order reconstruction of genomes with unequal gene content

k \le 3

The Rooted SCJ Median with Single Gene Duplications

k≤3 and present an ILP for its solution. However, for this problem, the computation of exact solutions remains intractable for sufficiently large instances. We then proceed to describe a heuristic method, FFAdj-AM, which performs well in practice.ResultsThe developed methods compute accurate positional orthologs for genomes comparable in size of bacterial genomes on simulated data and genomic data acquired from the OMA orthology database. In particular, FFAdj-AM performs equally or better when compared to the well-established gene family prediction tool MultiMSOAR.ConclusionsWe study the computational complexity of a new family-free model and present algorithms for its solution. With FFAdj-AM, we propose an appealing alternative to established tools for identifying higher confidence positional orthologs.