Unequal Gene Content Research Articles

Gene Transfer-Based Phylogenetics: Analytical Expressions and Additivity via Birth-Death Theory.

The genomic era has opened up vast opportunities in molecular systematics, one of which is deciphering the evolutionary history in fine detail. Under this mass of data, analyzing the point mutations of standard markers is often too crude and slow for fine-scale phylogenetics. Nevertheless, genome dynamics (GD) events provide alternative, often richer information. The synteny index (SI) between a pair of genomes combines gene order and gene content information, allowing the comparison of genomes of unequal gene content, together with order considerations of their common genes. Recently, genome dynamics has been modeled as a continuous-time Markov process, and gene distance in the genome as a birth-death-immigration process. Nevertheless, due to complexities arising in this setting, no precise and provably consistent estimators could be derived, resulting in heuristic solutions. Here, we extend this modeling approach by using techniques from birth-death theory to derive explicit expressions of the system's probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically accurate distances between organisms based on their SI. Subsequently, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). Applying the new measure in simulation studies shows that it provides accurate results in realistic settings and even under model extensions such as gene gain/loss or over a tree structure. In the real-data realm, we applied the new formulation to unique data structure that we constructed-the ordered orthology DB-based on a new version of the EggNOG database, to construct a tree with more than 4.5K taxa. To the best of our knowledge, this is the largest gene-order-based tree constructed and it overcomes shortcomings found in previous approaches. Constructing a GD-based tree allows to confirm and contrast findings based on other phylogenetic approaches, as we show.

Labeled Cycle Graph for Transposition and Indel Distance.

In the comparative genomics field, one way to infer the evolutionary distance between two organisms of related species is by finding the minimum number of large-scale mutations, called genome rearrangements, that transform one genome into the other. This number is referred to as the rearrangement distance. Since problems in this area emerged in the mid-1990s, several genome rearrangements have been proposed. Rearrangements that do not alter the genome content are called conservative, and in this group we have the following: the reversal, which inverts a segment of the genome; the transposition, which exchanges two consecutive segments; and the double cut and join, which cuts two different pairs of adjacent blocks and joins them differently. Seminal works compared genomes sharing the same set of conserved blocks, but nowadays, researchers started looking at genomes with unequal gene content, by allowing the use of nonconservative rearrangements such as insertion and deletion (jointly called indel). The transposition distance and the transposition and indel distance are both NP-hard. We investigate the transposition and indel distance and present a structure called labeled cycle graph, representing an instance of rearrangement distance problems for genomes with unequal gene content. This structure is used to devise a lower bound and a 2-approximation algorithm for the transposition and indel distance.

Sorting cancer karyotypes using double-cut-and-joins, duplications and deletions.

Problems of genome rearrangement are central in both evolution and cancer research. Most genome rearrangement models assume that the genome contains a single copy of each gene and the only changes in the genome are structural, i.e. reordering of segments. In contrast, tumor genomes also undergo numerical changes such as deletions and duplications, and thus the number of copies of genes varies. Dealing with unequal gene content is a very challenging task, addressed by few algorithms to date. More realistic models are needed to help trace genome evolution during tumorigenesis. Here, we present a model for the evolution of genomes with multiple gene copies using the operation types double-cut-and-joins, duplications and deletions. The events supported by the model are reversals, translocations, tandem duplications, segmental deletions and chromosomal amplifications and deletions, covering most types of structural and numerical changes observed in tumor samples. Our goal is to find a series of operations of minimum length that transform one karyotype into the other. We show that the problem is NP-hard and give an integer linear programming formulation that solves the problem exactly under some mild assumptions. We test our method on simulated genomes and on ovarian cancer genomes. Our study advances the state of the art in two ways: It allows a broader set of operations than extant models, thus being more realistic and it is the first study attempting to re-construct the full sequence of structural and numerical events during cancer evolution. Code and data are available in https://github.com/Shamir-Lab/Sorting-Cancer-Karyotypes. Supplementary data are available at Bioinformatics online.

Chromosome structures: reduction of certain problems with unequal gene content and gene paralogs to integer linear programming

BackgroundChromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs.ResultsWe proved that these problems can be reduced to integer linear programming formulations, which allows an algorithm to redefine the problems to implement a very special case of the integer linear programming tool. The results were tested on synthetic and biological samples.ConclusionsThree well-known problems were reduced to a very special case of integer linear programming, which is a new method of their solutions. Integer linear programming is clearly among the main computational methods and, as generally accepted, is fast on average; in particular, computation systems specifically targeted at it are available. The challenges are to reduce the size of the corresponding integer linear programming formulations and to incorporate a more detailed biological concept in our model of the reconstruction.

Fast ancestral gene order reconstruction of genomes with unequal gene content.

BackgroundDuring evolution, genomes are modified by large scale structural events, such as rearrangements, deletions or insertions of large blocks of DNA. Of particular interest, in order to better understand how this type of genomic evolution happens, is the reconstruction of ancestral genomes, given a phylogenetic tree with extant genomes at its leaves. One way of solving this problem is to assume a rearrangement model, such as Double Cut and Join (DCJ), and find a set of ancestral genomes that minimizes the number of events on the input tree. Since this problem is NP-hard for most rearrangement models, exact solutions are practical only for small instances, and heuristics have to be used for larger datasets. This type of approach can be called event-based. Another common approach is based on finding conserved structures between the input genomes, such as adjacencies between genes, possibly also assigning weights that indicate a measure of confidence or probability that this particular structure is present on each ancestral genome, and then finding a set of non conflicting adjacencies that optimize some given function, usually trying to maximize total weight and minimizing character changes in the tree. We call this type of methods homology-based.ResultsIn previous work, we proposed an ancestral reconstruction method that combines homology- and event-based ideas, using the concept of intermediate genomes, that arise in DCJ rearrangement scenarios. This method showed better rate of correctly reconstructed adjacencies than other methods, while also being faster, since the use of intermediate genomes greatly reduces the search space. Here, we generalize the intermediate genome concept to genomes with unequal gene content, extending our method to account for gene insertions and deletions of any length. In many of the simulated datasets, our proposed method had better results than MLGO and MGRA, two state-of-the-art algorithms for ancestral reconstruction with unequal gene content, while running much faster, making it more scalable to larger datasets.ConclusionStuding ancestral reconstruction problems under a new light, using the concept of intermediate genomes, allows the design of very fast algorithms by greatly reducing the solution search space, while also giving very good results. The algorithms introduced in this paper were implemented in an open-source software called RINGO (ancestral Reconstruction with INtermediate GenOmes), available at https://github.com/pedrofeijao/RINGO.

Lateral gene transfer, rearrangement, reconciliation

BackgroundModels of ancestral gene order reconstruction have progressively integrated different evolutionary patterns and processes such as unequal gene content, gene duplications, and implicitly sequence evolution via reconciled gene trees. These models have so far ignored lateral gene transfer, even though in unicellular organisms it can have an important confounding effect, and can be a rich source of information on the function of genes through the detection of transfers of clusters of genes.ResultWe report an algorithm together with its implementation, DeCoLT, that reconstructs ancestral genome organization based on reconciled gene trees which summarize information on sequence evolution, gene origination, duplication, loss, and lateral transfer. DeCoLT optimizes in polynomial time on the number of rearrangements, computed as the number of gains and breakages of adjacencies between pairs of genes. We apply DeCoLT to 1099 gene families from 36 cyanobacteria genomes.ConclusionDeCoLT is able to reconstruct adjacencies in 35 ancestral bacterial genomes with a thousand gene families in a few hours, and detects clusters of co-transferred genes. DeCoLT may also be used with any relationship between genes instead of adjacencies, to reconstruct ancestral interactions, functions or complexes.Availabilityhttp://pbil.univ-lyon1.fr/software/DeCoLT/

Genome Rearrangement: A Planning Approach

Evolutionary trees of species can be reconstructed by pairwise comparison of their entire genomes. Such a comparison can be quantified by determining the number of events that change the order of genes in a genome. Earlier Erdem and Tillier formulated the pairwise comparison of entire genomes as the problem of planning rearrangement events that transform one genome to the other. We reformulate this problem as a planning problem to extend its applicability to genomes with multiple copies of genes and with unequal gene content, and illustrate its applicability and effectiveness on three real datasets: mitochondrial genomes of Metazoa, chloroplast genomes of Campanulaceae, chloroplast genomes of various land plants and green algae.

ProgressiveMauve: Multiple Genome Alignment with Gene Gain, Loss and Rearrangement

BackgroundMultiple genome alignment remains a challenging problem. Effects of recombination including rearrangement, segmental duplication, gain, and loss can create a mosaic pattern of homology even among closely related organisms.Methodology/Principal FindingsWe describe a new method to align two or more genomes that have undergone rearrangements due to recombination and substantial amounts of segmental gain and loss (flux). We demonstrate that the new method can accurately align regions conserved in some, but not all, of the genomes, an important case not handled by our previous work. The method uses a novel alignment objective score called a sum-of-pairs breakpoint score, which facilitates accurate detection of rearrangement breakpoints when genomes have unequal gene content. We also apply a probabilistic alignment filtering method to remove erroneous alignments of unrelated sequences, which are commonly observed in other genome alignment methods. We describe new metrics for quantifying genome alignment accuracy which measure the quality of rearrangement breakpoint predictions and indel predictions. The new genome alignment algorithm demonstrates high accuracy in situations where genomes have undergone biologically feasible amounts of genome rearrangement, segmental gain and loss. We apply the new algorithm to a set of 23 genomes from the genera Escherichia, Shigella, and Salmonella. Analysis of whole-genome multiple alignments allows us to extend the previously defined concepts of core- and pan-genomes to include not only annotated genes, but also non-coding regions with potential regulatory roles. The 23 enterobacteria have an estimated core-genome of 2.46Mbp conserved among all taxa and a pan-genome of 15.2Mbp. We document substantial population-level variability among these organisms driven by segmental gain and loss. Interestingly, much variability lies in intergenic regions, suggesting that the Enterobacteriacae may exhibit regulatory divergence.ConclusionsThe multiple genome alignments generated by our software provide a platform for comparative genomic and population genomic studies. Free, open-source software implementing the described genome alignment approach is available from http://gel.ahabs.wisc.edu/mauve.

Genome Rearrangement and Planning: Revisited

Evolutionary trees of species can be reconstructed by pairwise comparison of their entire genomes. Such a comparison can be quantified by determining the number of events that change the order of genes in a genome. Earlier Erdem and Tillier formulated the pairwise comparison of entire genomes as the problem of planning rearrangement events that transform one genome to the other. We reformulate this problem as a planning problem to extend its applicability to genomes with multiple copies of genes and with unequal gene content, and illustrate its applicability and effectiveness on three real datasets: mitochondrial genomes of Metazoa, chloroplast genomes of Campanulaceae, chloroplast genomes of various land plants and green algae.

Genome rearrangements with duplications

BackgroundFinding sequences of evolutionary operations that transform one genome into another is a classical problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well - most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions, especially if the duplicated or deleted segments are of arbitrary size.ResultsWe recently proposed a heuristic algorithm for sorting unichromosomal genomes by reversals, block interchanges, tandem duplications, and deletions. In this paper, we extend this approach to multichromosomal genomes. We are now able to sort a multichromosomal ancestral genome into a genome of a descendant by a large set of different operations, including tandem duplications and deletions of segments of arbitrary size.ConclusionExperimental results show that our algorithm finds sorting sequences that have a weight close to the true evolutionary distance.

DCJ Path Formulation for Genome Transformations which Include Insertions, Deletions, and Duplications

We extend the double cut and join operation (DCJ) paradigm to perform genome rearrangements on pairs of genomes having unequal gene content and/or multiple copies by permitting genes in one genome which are completely or partially unmatched in the other. The existence of unmatched gene ends introduces new kinds of paths in the adjacency graph, since some paths can now terminate internal to a chromosome and not on telomeres. We introduce "ghost adjacencies" to supply the missing gene ends in the genome not containing them. Ghosts enable us to close paths that were due to incomplete matching, just as null points enable us to close even paths terminating in telomeres. We define generalized DCJ operations on the generalized adjacency graph, and give a prescription for calculating the DCJ distance for the expanded repertoire of operations, which includes insertions, deletions, and duplications. For the case of insertions and deletions, with linear as well as circular chromosomes, we suggest permitting a "nugh" (half ghost, half null), which can shorten the distance. We give algorithms for the optimal closure, with and without nughs, and give the resulting distance formula in terms of paths. For certain simplest cases, we calculate the number of optimal ways to close the graph.

Sorting by reversals, block interchanges, tandem duplications, and deletions

BackgroundFinding sequences of evolutionary operations that transform one genome into another is a classic problem in comparative genomics. While most of the genome rearrangement algorithms assume that there is exactly one copy of each gene in both genomes, this does not reflect the biological reality very well – most of the studied genomes contain duplicated gene content, which has to be removed before applying those algorithms. However, dealing with unequal gene content is a very challenging task, and only few algorithms allow operations like duplications and deletions. Almost all of these algorithms restrict these operations to have a fixed size.ResultsIn this paper, we present a heuristic algorithm to sort an ancestral genome (with unique gene content) into a genome of a descendant (with arbitrary gene content) by reversals, block interchanges, tandem duplications, and deletions, where tandem duplications and deletions are of arbitrary size.ConclusionExperimental results show that our algorithm finds sorting sequences that are close to an optimal sorting sequence when the ancestor and the descendant are closely related. The quality of the results decreases when the genomes get more diverged or the genome size increases. Nevertheless, the calculated distances give a good approximation of the true evolutionary distances.

Gene Maps Linearization Using Genomic Rearrangement Distances

A preliminary step to most comparative genomics studies is the annotation of chromosomes as ordered sequences of genes. Different genetic mapping techniques often give rise to different maps with unequal gene content and sets of unordered neighboring genes. Only partial orders can thus be obtained from combining such maps. However, once a total order O is known for a given genome, it can be used as a reference to order genes of a closely related species characterized by a partial order P. Our goal is to find a linearization of P that is as close as possible to O, in term of a given genomic distance. We first prove NP-completeness complexity results considering the breakpoint and the common interval distances. We then focus on the breakpoint distance and give a dynamic programming algorithm whose running time is exponential for general partial orders, but polynomial when the partial order is derived from a bounded number of genetic maps. A time-efficient greedy heuristic is then given for the general case and is empirically shown to produce solutions within 10% of the optimal solution, on simulated data. Applications to the analysis of grass genomes are presented.

Common Intervals and Symmetric Difference in a Model-Free Phylogenomics, with an Application to Streptophyte Evolution

The common intervals of two permutations on n elements are the subsets of terms contiguous in both permutations. They constitute the most basic representation of conserved local order. We use d, the size of the symmetric difference (the complement of the common intervals) of the two subsets of 2({1,n}) thus determined by two permutations, as an evolutionary distance between the gene orders represented by the permutations. We consider the Steiner Tree problem in the space (2({1,n}), d) as the basis for constructing phylogenetic trees, including ancestral gene orders. We extend this to genomes with unequal gene content and to genomes containing gene families. Applied to streptophyte phylogeny, our method does not support the positioning of the complex algae Charales as a sister group to the land plants. Simulations show that the method, though unmotivated by any specific model of genome rearrangement, accurately reconstructs a tree from artificial genome data generated by random inversions deriving each genome from its ancestor on this tree.