Scaffold filling,contig fusion and comparative gene order inference

Background

There has been a trend in increasing the phylogenetic scope of genome sequencing without finishing the sequence of the genome. Increasing numbers of genomes are being published in scaffold or contig form. Rearrangement algorithms, however, including gene order-based phylogenetic tools, require whole genome data on gene order or syntenic block order. How then can we use rearrangement algorithms to compare genomes available in scaffold form only? Can the comparative evidence predict the location of unsequenced genes?

Results

Our method involves optimally filling in genes missing from the scaffolds, while incorporating the augmented scaffolds directly into the rearrangement algorithms as if they were chromosomes. This is accomplished by an exact, polynomial-time algorithm. We then correct for the number of extra fusion/fission operations required to make scaffolds comparable to full assemblies. We model the relationship between the ratio of missing genes actually absent from the genome versus merely unsequenced ones, on one hand, and the increase of genomic distance after scaffold filling, on the other. We estimate the parameters of this model through simulations and by comparing the angiosperm genomes Ricinus communis and Vitis vinifera.

Conclusions

The algorithm solves the comparison of genomes with 18,300 genes, including 4500 missing from one genome, in less than a minute on a MacBook, putting virtually all genomes within range of the method.

     

Genetic distances between the Utah Mormons and related populations

Gene frequency data, consisting of six red cell antigen loci, nine electrophoretic systems, and HLA-A and -B are reported for the Utah Mormon population. These are compared statistically to gene frequencies from at U.S. population, 13 European populations, and seven populations from three religious isolates. The Mormon gene frequencies are similar to those of their northern European ancestors. This is explained by the large founding size of the Mormon population and high rates of gene flow. In contrast, the religious isolates (Amish, Hutterites, and Mennonites) show marked divergence from their ancestral populations and each other, due to isolation and random genetic drift. The HLA loci and electrophoretic loci presented here yield sets of genetic distances that are highly correlated (r = .734) and that both correspond closely to the actual geographic distances among the European populations. The genetic distances based on red cell antigen loci correspond less closely to the geographic distances and exhibit lower correlations with both the HLA and electrophoretic loci (r = .524 and r = .565, respectively).     

Multichromosomal median and halving problems under different genomic distances

Background  

Genome 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.     

Grain filling of cereals under soil drying

Monocarpic plants require the initiation of whole-plant senescence to remobilize and transfer assimilates pre-stored in vegetative tissues to grains. Delayed whole-plant senescence caused by either heavy use of nitrogen fertilizer or adoption of lodging-resistant cultivars/hybrids that remain green when the grains are due to ripen results in a low harvest index with much nonstructural carbohydrate (NSC) left in the straw. Usually, water stress during the grain-filling period induces early senescence, reduces photosynthesis, and shortens the grain-filling period; however, it increases the remobilization of NSC from the vegetative tissues to the grain. If mild soil drying is properly controlled during the later grain-filling period in rice (Oryza sativa) and wheat (Triticum aestivum), it can enhance whole-plant senescence, lead to faster and better remobilization of carbon from vegetative tissues to grains, and accelerate the grain-filling rate. In cases where plant senescence is unfavorably delayed, such as by heavy use of nitrogen and the introduction of hybrids with strong heterosis, the gain from the enhanced remobilization and accelerated grain-filling rate can outweigh the loss of reduced photosynthesis and the shortened grain-filling period, leading to an increased grain yield, better harvest index and higher water-use efficiency.     

A non-linear optimization procedure to estimate distances and instantaneous substitution rate matrices under the GTR model

MOTIVATION: The general-time-reversible (GTR) model is one of the most popular models of nucleotide substitution because it constitutes a good trade-off between mathematical tractability and biological reality. However, when it is applied for inferring evolutionary distances and/or instantaneous rate matrices, the GTR model seems more prone to inapplicability than more restrictive time-reversible models. Although it has been previously noted that the causes for intractability are caused by the impossibility of computing the logarithm of a matrix characterised by negative eigenvalues, the issue has not been investigated further. RESULTS: Here, we formally characterize the mathematical conditions, and discuss their biological interpretation, which lead to the inapplicability of the GTR model. We investigate the relations between, on one hand, the occurrence of negative eigenvalues and, on the other hand, both sequence length and sequence divergence. We then propose a possible re-formulation of previous procedures in terms of a non-linear optimization problem. We analytically investigate the effect of our approach on the estimated evolutionary distances and transition probability matrix. Finally, we provide an analysis on the goodness of the solution we propose. A numerical example is discussed.     

Divide-and-conquer approach for the exemplar breakpoint distance

MOTIVATION: A one-to-one correspondence between the sets of genes in the two genomes being compared is necessary for the notions of breakpoint and reversal distances. To compare genomes where there are paralogous genes, Sankoff formulated the exemplar distance problem as a general version of the genome rearrangement problem. Unfortunately, the problem is NP-hard even for the breakpoint distance. RESULTS: This paper proposes a divide-and-conquer approach for calculating the exemplar breakpoint distance between two genomes with multiple gene families. The combination of our approach and Sankoff's branch-and-bound technique leads to a practical program to answer this question. Tests with both simulated and real datasets show that our program is much more efficient than the existing program that is based only on the branch-and-bound technique. AVAILABILITY: Code for the program is available from the authors.     

Scaling of diastolic intraventricular pressure gradients is related to filling time duration

In early diastole, pressure is lower in the apex than in the base of the left ventricle (LV). This early intraventricular pressure difference (IVPD) facilitates LV filling. We assessed how LV diastolic IVPD and intraventricular pressure gradient (IVPG), defined as IVPD divided by length, scale to the heart size and other physiological variables. We studied 10 mice, 10 rats, 5 rabbits, 12 dogs, and 21 humans by echocardiography. Color Doppler M-mode data were postprocessed to reconstruct IVPD and IVPG. Normalized LV filling time was calculated by dividing filling time by RR interval. The relationship between IVPD, IVPG, normalized LV filling time, and LV end-diastolic volume (or mass) as fit to the general scaling equation Y = kM beta, where M is LV heart size parameter, Y is a dependent variable, k is a constant, and beta is the power of the scaling exponent. LV mass varied from 0.049 to 194 g, whereas end-diastolic volume varied from 0.011 to 149 ml. The beta values relating normalized LV filling time with LV mass and end-diastolic volume were 0.091 (SD 0.011) and 0.083 (SD 0.009), respectively (P < 0.0001 vs. 0 for both). The beta values relating IVPD with LV mass and end-diastolic volume were similarly significant at 0.271 (SD 0.039) and 0.243 (SD 0.0361), respectively (P < 0.0001 vs. 0 for both). Finally, beta values relating IVPG with LV mass and end-diastolic volume were -0.118 (SD 0.013) and -0.104 (SD 0.011), respectively (P < 0.0001 vs. 0 for both). As a result, there was an inverse relationship between IVPG and normalized LV filling time (r = -0.65, P < 0.001). We conclude that IVPD decrease, while IVPG increase with decreasing animal size. High IVPG in small mammals may be an adaptive mechanism to short filling times.     

Bias-corrected paralinear and LogDet distances and tests of molecular clocks and phylogenies under nonstationary nucleotide frequencies

The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, we developed formulas for correcting the estimation biases of the paralinear and LogDet distances, i.e., the bias-corrected distance is estimated by dc = d - 2var(d), where d and var(d) are the estimated distance and sampling variance, respectively. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, we developed a method for estimating the variance- covariance matrix of paralinear distances, so that statistical tests of DNA phylogenies can be conducted in the nonstationary case. Third, a new LogDet-based method for testing the molecular clock hypothesis was developed under nonstationary nucleotide frequencies.      

Characterization of the rearranged tpr-met oncogene breakpoint.

We determined the nucleotide sequence of the rearranged trp-met genomic locus and the corresponding portions of the unrearranged tpr and met genomic fragments. The breakpoints occur at one end of a stretch of 21 A residues that follow an Alu repetitive sequence in the tpr locus and within a group of 3 A residues in the met proto-oncogene locus. We conclude that the fusion between the tpr locus on chromosome 1 and the met locus on chromosome 7 resulted from a recombination event.     

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.     

Sequence-based detection and breakpoint assembly of polymorphic inversions

Inversion polymorphisms have occupied a privileged place in Drosophila genetic research since their discovery in the 1920s. Indeed, inversions seem to be nearly ubiquitous, and the majority of species that have been thoroughly surveyed have been found to be polymorphic for one or more chromosomal inversions. Despite enduring interest, however, inversions remain difficult to study because their effects are often cryptic, and few efficient assays have been developed. Even in Drosophila melanogaster, in which inversions can be reliably detected and have received considerable attention, the breakpoints of only three inversions have been characterized molecularly. Hence, inversion detection and assay design remain important unsolved problems. Here, we present a method for identification and local de novo assembly of inversion breakpoints using next-generation paired-end reads derived from D. melanogaster isofemale lines. PCR and cytological confirmations demonstrate that our method can reliably assemble inversion breakpoints, providing tools for future research on D. melanogaster inversions as well as a framework for detection and assay design of inversions and other chromosome aberrations in diverse taxa.     

Family distances and human lymphocyte antigens

We compared family distances of homozygotes and heterozygotes for HLA-A and -B. When matched on number of inhabitants per birthplace, no significant differences were found. However, when homozygotes were compared with heterozygotes from larger birthplaces, homozygotes showed significantly smaller family distances in the grandparental generation. We suggest that matching for population size of birthplace and the choice of the geographic study area are important factors in studies of family distances.     

Breakpoint medians and breakpoint phylogenies: a fixed-parameter approach

With breakpoint distance, the genome rearrangement field delivered one of the currently most popular measures in phylogenetic studies for related species. Here, BREAKPOINT MEDIAN, which is NP-complete already for three given species (whose genomes are represented as signed orderings), is the core basic problem. For the important special case of three species, approximation (ratio 7/6) and exact heuristic algorithms were developed. Here, we provide an exact, fixed-parameter algorithm with provable performance bounds. For instance, a breakpoint median for three signed orderings over nelements that causes at most d breakpoints can be computed in time O((2.15)(d).n). We show the algorithm's practical usefulness through experimental studies. In particular, we demonstrate that a simple implementation of our algorithm combined with a new tree construction heuristic allows for a new approach to breakpoint phylogeny, yielding evolutionary trees that are competitive in comparison with known results developed in a recent series of papers that use clever algorithm engineering methods.     

Intercondylar distances of the human temporomandibular joints

In a sample which included subjects of the Croatian population we made measurements of intercondylar distances between the temporomandibular joints in radiographs. A total of 101 subjects of both sexes ranging in age from 20 to 80 years, mostly residents in Zagreb, were evaluated. We measured the intercondylar distances from the condyle centers in the postero-anterior cranial radiographs which had previously been examined and traced on acetate paper. The measuring points were digitized prior to measurements. A special system of coordinates was devised for each radiograph. The results of our measurements were assessed by ANOVA analysis. The intercondylar distance between the two temporomandibular joints was within the range of 110 and 145 mm, with the mean of 126 mm. In men the intercondylar distance was within the range of 116 and 145 mm, with the mean of 130.2 mm. In women the distance ranged from 110 to 138 mm, with the mean of 123.5 mm. There was a significant difference between the two sexes. From a review of the literature, it is apparent that the results of our measurements do not support the results of similar studies assessed by a number of researchers in other countries. The intercondylar distance in the Croatian sample was 5.25% larger than the maximal values of the same parameters in other populations suggesting larger craniofacial skeletons. The development of this radiographic assessment method should improve evaluation of subjects seeking treatment.     

Histone Modifications and the Chromatin Scaffold for Meiotic Chromosome Architecture

Chromosomes are capable of remarkable structural adaptability that enables their diverse functions. Histone modifications play pivotal roles in conferring structural diversity to chromosomes by influencing the compactness of chromatin. Several multi-protein complexes bind to chromatin and affect chromosome dynamics, including cohesin, condensin, the chromosome passenger complex, and the synaptonemal complex. The roles of these complexes in promoting chromosome functions include cohesion, condensation and synapsis. It is now crucial to define the relationship between the protein complexes that affect chromosome architecture and the underlying state of the chromatin. During meiosis chromosomes undergo striking morphological changes, including alignment of homologous chromosomes, double-strand break formation and repair, and establishment of meiosis-specific chromosome structures. These dynamic chromosome arrangements are accompanied by the recruitment and expulsion of multi-protein complexes from chromatin. Meiotic chromosome dynamics ensure proper chromosome segregation and production of healthy gametes. Meiosis thus affords an excellent opportunity to determine how histone modifications impact higher order chromosome dynamics by affecting localization and function of chromosome protein complexes. A meiotic mutation in the Drosophila histone kinase, NHK-1, uncovered a critical requirement for histone modifications in chromosome architecture, underscoring the power of this approach.     

Testing chromosomal phylogenies and inversion breakpoint reuse in Drosophila

A combination of cytogenetic and bioinformatic procedures was used to test the chromosomal phylogeny relating Drosophila buzzatii with D. repleta. Chromosomes X and 2, harboring most of the inversions fixed between these two species, were analyzed. First, chromosomal segments conserved during the divergence of the two species were identified by comparative in situ hybridization to the D. repleta chromosomes of 180 BAC clones from a BAC-based physical map of the D. buzzatii genome. These conserved segments were precisely delimited with the aid of clones containing inversion breakpoints. Then GRIMM software was used to estimate the minimum number of rearrangements necessary to transform one genome into the other and identify all possible rearrangement scenarios. Finally, the most plausible inversion trajectory was tested by hybridizing 12 breakpoint-bearing BAC clones to the chromosomes of seven other species in the repleta group. The results show that chromosomes X and 2 of D. buzzatii and D. repleta differ by 12 paracentric inversions. Nine of them are fixed in chromosome 2 and entail two breakpoint reuses. Our results also show that the cytological relationship between D. repleta and D. mercatorum is closer than that between D. repleta and D. peninsularis, and we propose that the phylogenetic relationships in this lineage of the repleta group be reconsidered. We also estimated the rate of rearrangement between D. repleta and D. buzzatii and conclude that rates within the genus Drosophila vary substantially between lineages, even within a single species group.     

Genetic distances,geographic distances and migration between four villages of a single region in Slovakia

Genetic microdifferentiation has been studied among four endogamous villages of the Bystrica Valley in the Kysuce region of northwest Slovakia, which arose from a single ancestral population about 15 generations ago. Genetic distances and sample kinship between the villages were estimated from the gene frequencies of seven serum-group and isozyme genetic markers. The genetic distance was found to correlate positively (though insignificantly) with the geographic distance, and negatively with the intensity of migration between villages; the sample kinship correlates negatively with geography as well as with the genetic distance. This pattern of genetic structure within the area indicates that the genetic variation among the villages is attributable to the genetic drift. Thus, drift has brought about a detectable differentiation in the area within a limited period of approximately 300 years, in spite of the fact that the villages were not completely genetically isolated from each other. The finding of a negative correlation between the sample kinship and geographic distance indicates that the recent breakdown of genetic isolates in Slovakia is likely to be accompanied with an overall increase of heterozygosity.