Breakpoint Distance Research Articles

SCJ: A Breakpoint-Like Distance that Simplifies Several Rearrangement Problems

The breakpoint distance is one of the most straightforward genome comparison measures. Surprisingly, when it comes to defining it precisely for multichromosomal genomes with both linear and circular chromosomes, there is more than one way to go about it. Pevzner and Tesler gave a definition in a 2003 paper, Tannier et al. defined it differently in 2008, and in this paper we provide yet another alternative, calling it SCJ for single-cut-or-join, in analogy to the popular double cut and join (DCJ) measure. We show that several genome rearrangement problems, such as median and halving, become easy for SCJ, and provide linear and higher polynomial time algorithms for them. For the multichromosomal linear genome median problem, this is the first polynomial time algorithm described, since for other distances this problem is NP-hard. In addition, we show that small parsimony under SCJ is also easy, and can be solved by a variant of Fitch's algorithm. In contrast, big parsimony is NP-hard under SCJ. This new distance measure may be of value as a speedily computable, first approximation to distances based on more realistic rearrangement models.

A Statistically Fair Comparison of Ancestral Genome Reconstructions, Based on Breakpoint and Rearrangement Distances

We introduce a way of evaluating two mathematically different optimization approaches to the same problem, namely how good or bad each is with respect to the other's criterion. We illustrate this in a comparison of breakpoint and rearrangement distances between the endpoints of a branch, where total branch-length is minimized in reconstructing ancestral genomes at the nodes of a given phylogeny. We apply this to mammalian genome evolution and simulations under various hypotheses about breakpoint re-use. Reconstructions based on rearrangement distance are superior in terms of branch length and dispersion of the multiple optimal reconstructions, but simulations show that both sets of reconstructions are equally close to the simulated ancestors.

Reconstructing genome trees of prokaryotes using overlapping genes.

BackgroundOverlapping genes (OGs) are defined as adjacent genes whose coding sequences overlap partially or entirely. In fact, they are ubiquitous in microbial genomes and more conserved between species than non-overlapping genes. Based on this property, we have previously implemented a web server, named OGtree, that allows the user to reconstruct genome trees of some prokaryotes according to their pairwise OG distances. By analogy to the analyses of gene content and gene order, the OG distance between two genomes we defined was based on a measure of combining OG content (i.e., the normalized number of shared orthologous OG pairs) and OG order (i.e., the normalized OG breakpoint distance) in their whole genomes. A shortcoming of using the concept of breakpoints to define the OG distance is its inability to analyze the OG distance of multi-chromosomal genomes. In addition, the amount of overlapping coding sequences between some distantly related prokaryotic genomes may be limited so that it is hard to find enough OGs to properly evaluate their pairwise OG distances.ResultsIn this study, we therefore define a new OG order distance that is based on more biologically accurate rearrangements (e.g., reversals, transpositions and translocations) rather than breakpoints and that is applicable to both uni-chromosomal and multi-chromosomal genomes. In addition, we expand the term "gene" to include both its coding sequence and regulatory regions so that two adjacent genes whose coding sequences or regulatory regions overlap with each other are considered as a pair of overlapping genes. This is because overlapping of regulatory regions of distinct genes suggests that the regulation of expression for these genes should be more or less interrelated. Based on these modifications, we have reimplemented our OGtree as a new web server, named OGtree2, and have also evaluated its accuracy of genome tree reconstruction on a testing dataset consisting of 21 Proteobacteria genomes. Our experimental results have finally shown that our current OGtree2 indeed outperforms its previous version OGtree, as well as another similar server, called BPhyOG, significantly in the quality of genome tree reconstruction, because the phylogenetic tree obtained by OGtree2 is greatly congruent with the reference tree that coincides with the taxonomy accepted by biologists for these Proteobacteria.ConclusionsIn this study, we have introduced a new web server OGtree2 at http://bioalgorithm.life.nctu.edu.tw/OGtree2.0/ that can serve as a useful tool for reconstructing more precise and robust genome trees of prokaryotes according to their overlapping genes.

Experimental investigation of mobile radio propagation at 1.8 GHz over macrocellular dense urban regions of Delhi

The design of future-generation mobile communication systems depends critically on the suitability of path loss prediction methods and their suitability to various regions. To investigate the radio channel behavior, experimental measurements in the 1.8 GHz band were conducted in the dense urban regions of New Delhi for six GSM base stations. Path loss exponents and break point distances have been deduced, and observed results have been compared with various prediction methods, and their standard deviations have been presented. Measured regression line exhibited lowest standard deviations followed by rooftop propagation method compared with Cost 231 Hata and Cost 231 Walfisch–Ikegami (WI) prediction methods. Variation of observed results has been explained in terms of vertical and horizontal propagation mechanisms which is the novelty of this paper.

Genetic Map Refinement Using a Comparative Genomic Approach

Following various genetic mapping techniques conducted on different segregating populations, one or more genetic maps are obtained for a given species. However, recombination analyzes and other methods for gene mapping often fail to resolve the ordering of some pairs of neighboring markers, thereby leading to sets of markers ambiguously mapped to the same position. Each individual map is thus a partial order defined on the set of markers, and can be represented as a Directed Acyclic Graph (DAG). In this article, given a phylogenetic tree with a set of DAGs labeling each leaf (species), the goal is to infer, at each leaf, a single combined DAG that is as resolved as possible, considering the complementary information provided by individual maps, and the phylogenetic information provided by the species tree. After combining the individual maps of a leaf into a single DAG, we order incomparable markers by using two successive heuristics for minimizing two distances on the species tree: the breakpoint distance, and the Kemeny distance. We apply our algorithms to the plant species represented in the Gramene database, and we evaluate the simplified maps we obtained.

An Approximation Algorithm for the Minimum Breakpoint Linearization Problem

In the recent years, there has been a growing interest in inferring the total order of genes or markers on a chromosome, since current genetic mapping efforts might only suffice to produce a partial order. Many interesting optimization problems were thus formulated in the framework of genome rearrangement. As an important one among them, the minimum breakpoint linearization (MBL) problem is to find the total order of a partially ordered genome that minimizes its breakpoint distance to a reference genome whose genes are already totally ordered. It was previously shown to be NP-hard, and the algorithms proposed so far are all heuristic. In this paper, we present an {m(2)+m/2}-approximation algorithm for the MBL problem, where m is the number of gene maps that are combined together to form a partial order of the genome under investigation.

WCDMA downlink capacity of cigar‐shaped microcells for underground metro service

AbstractIn this paper, the wideband code division multiple access (WCDMA) downlink capacity and the interference statistics of underground cigar‐shaped microcells utilised to serve users within metros are analysed. The hybrid model of propagation is used in the analysis where a model of eight cigar‐shaped microcells is used. The downlink capacity is given for different sector radio R, train length Ltrain, break point distance Rb and propagation parameters (s and γ). It is found that increasing the sector range up to 1250 m will increase the sector downlink capacity. Also, it is found that the effect of changing the value of the propagation parameter s is very small. It is noticed that increasing the train length Ltrain will increase the downlink capacity. Also, it is noticed that, increasing the propagation parameter γ will reduce the sector downlink. Finally, it is found that, the effect of changing the break point distance Rb is quasi‐null. Copyright © 2008 John Wiley & Sons, Ltd.

Multichromosomal median and halving problems under different genomic distances.

BackgroundGenome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.ResultsWe settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.ConclusionThis theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

Downlink capacity and interference statistics of wideband code division multiple access microcells for trains in long tunnels

The wideband code division multiple access downlink interference statistics and the capacity of equally spaced tunnel cigar-shaped microcells, used to serve users travelling in trains or metros, are analysed. The hybrid propagation model, with two defined modes, is used in the analysis. Fast fading because of multipath interference is superimposed with the main value of the loss and the slow fading up to a certain distance beyond which it can be neglected. To calculate the interference statistics and the capacity, a scenario with ten cigar-shaped microcells has been considered. The downlink capacity is then derived for different sector radii, train lengths, break point distances and propagation parameters. It is found that increasing the sector range up to 1250 m increases the sector downlink capacity. It is noticed that the maximum downlink capacity can be obtained for a sector radius of 1250–1750 m. It is also found that the increment of the propagation parameter γ reduces the sector downlink capacity. It is also noticed that increasing the train length increases the downlink capacity. It is also found that the bend loss increases the downlink capacity and reduces the maximum sector range.

ComPhy: prokaryotic composite distance phylogenies inferred from whole-genome gene sets

BackgroundWith the increasing availability of whole genome sequences, it is becoming more and more important to use complete genome sequences for inferring species phylogenies. We developed a new tool ComPhy, 'Composite Distance Phylogeny', based on a composite distance matrix calculated from the comparison of complete gene sets between genome pairs to produce a prokaryotic phylogeny.ResultsThe composite distance between two genomes is defined by three components: Gene Dispersion Distance (GDD), Genome Breakpoint Distance (GBD) and Gene Content Distance (GCD). GDD quantifies the dispersion of orthologous genes along the genomic coordinates from one genome to another; GBD measures the shared breakpoints between two genomes; GCD measures the level of shared orthologs between two genomes. The phylogenetic tree is constructed from the composite distance matrix using a neighbor joining method. We tested our method on 9 datasets from 398 completely sequenced prokaryotic genomes. We have achieved above 90% agreement in quartet topologies between the tree created by our method and the tree from the Bergey's taxonomy. In comparison to several other phylogenetic analysis methods, our method showed consistently better performance.ConclusionComPhy is a fast and robust tool for genome-wide inference of evolutionary relationship among genomes. It can be downloaded from .

A fast algorithm for the multiple genome rearrangement problem with weighted reversals and transpositions

BackgroundDue to recent progress in genome sequencing, more and more data for phylogenetic reconstruction based on rearrangement distances between genomes become available. However, this phylogenetic reconstruction is a very challenging task. For the most simple distance measures (the breakpoint distance and the reversal distance), the problem is NP-hard even if one considers only three genomes.ResultsIn this paper, we present a new heuristic algorithm that directly constructs a phylogenetic tree w.r.t. the weighted reversal and transposition distance. Experimental results on previously published datasets show that constructing phylogenetic trees in this way results in better trees than constructing the trees w.r.t. the reversal distance, and recalculating the weight of the trees with the weighted reversal and transposition distance. An implementation of the algorithm can be obtained from the authors.ConclusionThe possibility of creating phylogenetic trees directly w.r.t. the weighted reversal and transposition distance results in biologically more realistic scenarios. Our algorithm can solve today's most challenging biological datasets in a reasonable amount of time.

Sensitivity of the System Performance to the Propagation Parameters in LOS Microcellular Environments

Propagation loss is a fundamental phenomenon that affects the performance of any wireless network. Although propagation characteristics in line-of-sight (LOS) microcellular systems are well known, so far, only a few papers have investigated its effect on system performance in a comprehensive manner. In this paper, the impact of both system parameters (i.e., cell size, antenna height, operating frequency, and reuse factor) and propagation loss parameters (i.e., breakpoint distance, path loss exponents, standard deviation of the shadowing component, signals correlation, and effective road height) on the performance of both time-division multiple access (TDMA)- and code-division multiple access (CDMA)-based LOS microcellular networks is studied. Performance is evaluated in terms of outage probability in TDMA-based systems and in terms of the other-cell interference factor in CDMA-based systems. This paper includes substantial numerical results and new insights into the behavior of wireless system performance. For instance, novel insights into the impact of both distance-dependent shadowing and the effective road height on system performance are provided. In particular, nontypical fluctuational and discontinuous behavior on performance metrics are observed, and at microwave frequencies, the spectral efficiency is greater for heavy vehicular traffic conditions (i.e., during daytime) than for light vehicular traffic conditions (i.e., during nighttime). Such an understanding of interference engineering issues is vital for the planning, designing, dimensioning, and the optimization of mobile LOS microcellular networks for present and future wireless systems beyond third generation.

COMPUTING THE BREAKPOINT DISTANCE BETWEEN PARTIALLY ORDERED GENOMES

The total order of genes or markers on a chromosome is crucial for most comparative genomics studies. However, current gene mapping efforts might only suffice to provide a partial order of the genes on a chromosome. Several different genes or markers might be mapped at the same position due to the low resolution of gene mapping or missing data. Moreover, conflicting datasets might give rise to the ambiguity of gene order. In this paper, we consider the reversal distance and breakpoint distance problems for partially ordered genomes. We first prove that these problems are nondeterministic polynomial-time (NP)-hard, and then give an efficient heuristic algorithm to compute the breakpoint distance between partially ordered genomes. The algorithm is based on an efficient approximation algorithm for a natural generalization of the well-known feedback vertex set problem, and has been tested on both simulated and real biological datasets. The experimental results demonstrate that our algorithm is quite effective for estimating the breakpoint distance between partially ordered genomes and for inferring the gene (total) order.

WCDMA Multiservice Uplink Capacity of Highways Cigar-Shaped Microcells

The multiservice uplink capacity and the interference (intracellular and intercellular) statistics (mean and variance) of the sectors of cigar-shaped wideband code-division multiple access (WCDMA) microcell are studied using a model of 5 highway microcells in rural zone. The two-slope propagation loss model with lognormal shadowing is used in the analysis. The capacity and the interference statistics of the microcell are studied for different sector ranges, antenna side lobe levels, standard deviation of the power control error, breakpoint distance, and different intersites correlation coefficient. It is shown that reducing the antenna side lobe level increases the sector capacity. Also, it is shown that the sector range that gives the quasi the maximum sector capacity is in the order of 800 to 1200 m.

Duplication and Inversion History of a Tandemly Repeated Genes Family

Given a phylogenetic tree for a family of tandemly repeated genes and their signed order on the chromosome, we aim to find the minimum number of inversions compatible with an evolutionary history of this family. This is the first attempt to account for inversions in an evolutionary model of tandemly repeated genes. We present a branch-and-bound algorithm that finds the exact solution, and a polynomial-time heuristic based on the breakpoint distance. We show, on simulated data, that those algorithms can be used to improve phylogenetic inference of tandemly repeated gene families. An application on a published phylogeny of KRAB zinc finger genes is presented.

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.

On the Similarity of Sets of Permutations and Its Applications to Genome Comparison

The comparison of genomes with the same gene content relies on our ability to compare permutations, either by measuring how much they differ, or by measuring how much they are alike. With the notable exception of the breakpoint distance, which is based on the concept of conserved adjacencies, measures of distance do not generalize easily to sets of more than two permutations. In this paper, we present a basic unifying notion, conserved intervals, as a powerful generalization of adjacencies, and as a key feature of genome rearrangement theories. We also show that sets of conserved intervals have elegant nesting and chaining properties that allow the development of compact graphic representations, and linear time algorithms to manipulate them.

The Relationship Between the Rate of Molecular Evolution and the Rate of Genome Rearrangement in Animal Mitochondrial Genomes

Evolution of mitochondrial genes is far from clock-like. The substitution rate varies considerably between species, and there are many species that have a significantly increased rate with respect to their close relatives. There is also considerable variation among species in the rate of gene order rearrangement. Using a set of 55 complete arthropod mitochondrial genomes, we estimate the evolutionary distance from the common ancestor to each species using protein sequences, tRNA sequences, and breakpoint distances (a measure of the degree of genome rearrangement). All these distance measures are correlated. We use relative rate tests to compare pairs of related species in several animal phyla. In the majority of cases, the species with the more highly rearranged genome also has a significantly higher rate of sequence evolution. Species with higher amino acid substitution rates in mitochondria also have more variable amino acid composition in response to mutation pressure. We discuss the possible causes of variation in rates of sequence evolution and gene rearrangement among species and the possible reasons for the observed correlation between the two rates.

SPRING: a tool for the analysis of genome rearrangement using reversals and block-interchanges

SPRING () is a tool for the analysis of genome rearrangement between two chromosomal genomes using reversals and/or block-interchanges. SPRING takes two or more chromosomes as its input and then computes a minimum series of reversals and/or block-interchanges between any two input chromosomes for transforming one chromosome into another. The input of SPRING can be either bacterial-size sequences or gene/landmark orders. If the input is a set of chromosomal sequences then the SPRING will automatically search for identical landmarks, which are homologous/conserved regions shared by all input sequences. In particular, SPRING also computes the breakpoint distance between any pair of two chromosomes, which can be used to compare with the rearrangement distance to confirm whether they are correlated or not. In addition, SPRING shows phylogenetic trees that are reconstructed based on the rearrangement and breakpoint distance matrixes.

W-CDMA Uplink Practical Capacity and Interference Statistics of Rural Highways Cigar-Shaped Microcells with Imperfect Power Control and Finite Transmitted Power

The capacity and the interference statistics of the sectors of the cigar-shaped W-CDMA microcell are studied. A model of 5 microcells is used to analyze the uplink. The microcells are assumed to exist in rural zones. The capacity and the interference statistics of the microcell are studied for different sector range, different antenna side lobe levels, different values of the break point distance, different values of the propagation parameter s 2 and different standard deviation of the power control error.