Genome analyses and modelling the relationships between coding density, recombination rate and chromosome length

In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been observed that the recombination events are distributed unevenly along the chromosomes. We have found that many of such recombination properties can be predicted by computer simulations of population evolution based on the Monte Carlo methods. For example, these simulations have shown that the probability of acceptance of the recombination events by selection is higher at the ends of chromosomes and lower in their middle parts. The regions of high coding density are more prone to enter the strategy of haplotype complementation and to form clusters of genes, which are “recombination deserts”. The phenomenon of switching in-between the purifying selection and haplotype complementation has a phase transition character, and many relations between the effective population size, coding density, chromosome size and recombination frequency are those of the power law type.     

Probability distribution of haplotype frequencies under the two-locus Wright-Fisher model by diffusion approximation

The probability distribution of haplotype frequencies in a population, and the way it is influenced by genetical forces such as recombination, selection, random drift ...is a question of fundamental interest in population genetics. For large populations, the distribution of haplotype frequencies for two linked loci under the classical Wright-Fisher model is almost impossible to compute because of numerical reasons. However the Wright-Fisher process can in such cases be approximated by a diffusion process and the transition density can then be deduced from the Kolmogorov equations. As no exact solution has been found for these equations, we developed a numerical method based on finite differences to solve them. It applies to transient states and models including selection or mutations. We show by several tests that this method is accurate for computing the conditional joint density of haplotype frequencies given that no haplotype has been lost. We also prove that it is far less time consuming than other methods such as Monte Carlo simulations.     

Efficient inference of haplotypes from genotypes on a pedigree

We study haplotype reconstruction under the Mendelian law of inheritance and the minimum recombination principle on pedigree data. We prove that the problem of finding a minimum-recombinant haplotype configuration (MRHC) is in general NP-hard. This is the first complexity result concerning the problem to our knowledge. An iterative algorithm based on blocks of consecutive resolved marker loci (called block-extension) is proposed. It is very efficient and can be used for large pedigrees with a large number of markers, especially for those data sets requiring few recombinants (or recombination events). A polynomial-time exact algorithm for haplotype reconstruction without recombinants is also presented. This algorithm first identifies all the necessary constraints based on the Mendelian law and the zero recombinant assumption, and represents them using a system of linear equations over the cyclic group Z2. By using a simple method based on Gaussian elimination, we could obtain all possible feasible haplotype configurations. A C++ implementation of the block-extension algorithm, called PedPhase, has been tested on both simulated data and real data. The results show that the program performs very well on both types of data and will be useful for large scale haplotype inference projects.     

Fine-scale mapping of disease genes with multiple mutations via spatial clustering techniques

We present a method to perform fine mapping by placing haplotypes into clusters on the basis of risk. Each cluster has a haplotype "center." Cluster allocation is defined according to haplotype centers, with each haplotype assigned to the cluster with the "closest" center. The closeness of two haplotypes is determined by a similarity metric that measures the length of the shared segment around the location of a putative functional mutation for the particular cluster. Our method allows for missing marker information but still estimates the risks of complete haplotypes without resorting to a one-marker-at-a-time analysis. The dimensionality issues that can occur in haplotype analyses are removed by sampling over the haplotype space, allowing for estimation of haplotype risks without explicitly assigning a parameter to each haplotype to be estimated. In this way, we are able to handle haplotypes of arbitrary size. Furthermore, our clustering approach has the potential to allow us to detect the presence of multiple functional mutations.     

Haplotype-based linkage disequilibrium mapping via direct data mining

MOTIVATION: With the availability of large-scale, high-density single-nucleotide polymorphism markers and information on haplotype structures and frequencies, a great challenge is how to take advantage of haplotype information in the association mapping of complex diseases in case-control studies. RESULTS: We present a novel approach for association mapping based on directly mining haplotypes (i.e. phased genotype pairs) produced from case-control data or case-parent data via a density-based clustering algorithm, which can be applied to whole-genome screens as well as candidate-gene studies in small genomic regions. The method directly explores the sharing of haplotype segments in affected individuals that are rarely present in normal individuals. The measure of sharing between two haplotypes is defined by a new similarity metric that combines the length of the shared segments and the number of common alleles around any marker position of the haplotypes, which is robust against recent mutations/genotype errors and recombination events. The effectiveness of the approach is demonstrated by using both simulated datasets and real datasets. The results show that the algorithm is accurate for different population models and for different disease models, even for genes with small effects, and it outperforms some recently developed methods.     

Fixation probability in a two-locus model by the ancestral recombination-selection graph

We use the ancestral influence graph (AIG) for a two-locus, two-allele selection model in the limit of a large population size to obtain an analytic approximation for the probability of ultimate fixation of a single mutant allele A. We assume that this new mutant is introduced at a given locus into a finite population in which a previous mutant allele B is already segregating with a wild type at another linked locus. We deduce that the fixation probability increases as the recombination rate increases if allele A is either in positive epistatic interaction with B and allele B is beneficial or in no epistatic interaction with B and then allele A itself is beneficial. This holds at least as long as the recombination fraction and the selection intensity are small enough and the population size is large enough. In particular this confirms the Hill-Robertson effect, which predicts that recombination renders more likely the ultimate fixation of beneficial mutants at different loci in a population in the presence of random genetic drift even in the absence of epistasis. More importantly, we show that this is true from weak negative epistasis to positive epistasis, at least under weak selection. In the case of deleterious mutants, the fixation probability decreases as the recombination rate increases. This supports Muller's ratchet mechanism to explain the accumulation of deleterious mutants in a population lacking recombination.     

Structural similarity of the HLA-DQ region in DQ3 and DQ4 haplotypes and structural diversity of the HLA-DQ region in HLA-DR7 haplotypes.

Genomic DNA obtained from a B lymphoblastoid cell line was digested with appropriate restriction endonuclease and hybridized with several probes specific for genes encoding HLA-DQ. Southern hybridization with a DQA1 3'untranslated (UT) region probe showed DQ2-type hybridization pattern in DR7DQ3 haplotype. On the contrary, DQB1 3'UT probe showed DQ3-type pattern in the same haplotype. Gene cloning and DNA sequencing analysis revealed a repetitive sequence, (TG)19, between DQA1 and DQB1 gene in the DR7DQ3 haplotype. These results suggest that a recombination event has occurred near this potential Z-DNA structure in the haplotype, DR7DQ3. The 3'UT region probes of DQA1 and DQB1 genes failed to detect restriction fragment length polymorphism (RFLP) differences between DR4DQ3 and DR4DQ4 haplotypes in this experiment, suggesting that the gene structure between DQA1 and DQB1 is conserved in these haplotypes.     

Size of donor chromosome segments around introgressed loci and reduction of linkage drag in marker-assisted backcross programs.

This article investigates the efficiency of marker-assisted selection in reducing the length of the donor chromosome segment retained around a locus held heterozygous by backcrossing. First, the efficiency of marker-assisted selection is evaluated from the length of the donor segment in backcrossed individuals that are (double) recombinants for two markers flanking the introgressed gene on each side. Analytical expressions for the probability density function, the mean, and the variance of this length are given for any number of backcross generations, as well as numerical applications. For a given marker distance, the number of backcross generations performed has little impact on the reduction of donor segment length, except for distant markers. In practical situations, the most important parameter is the distance between the introgressed gene and the flanking markers, which should be chosen to be as closely linked as possible to the introgressed gene. Second, the minimal population sizes required to obtain double recombinants for such closely linked markers are computed and optimized in the context of a multigeneration backcross program. The results indicate that it is generally more profitable to allow for three or more successive backcross generations rather than to favor recombinations in early generations.     

Distribution of recombination crossovers and the origin of haplotype blocks: the interplay of population history,recombination, and mutation

Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure.     

Inference about recombination from haplotype data: lower bounds and recombination hotspots.

Recombination is an important evolutionary mechanism responsible for creating the patterns of haplotype variation observable in human populations. Recently, there has been extensive research on understanding the fine-scale variation in recombination across the human genome using DNA polymorphism data. Historical recombination events leave signature patterns in haplotype data. A nonparametric approach for estimating the number of historical recombination events is to compute the minimum number of recombination events in the history of a set of haplotypes. In this paper, we provide new and improved methods for computing lower bounds on the minimum number of recombination events. These methods are shown to detect a higher number of recombination events for a haplotype dataset from a region in the lipoprotein lipase gene than previous lower bounds. We apply our methods to two datasets for which recombination hotspots have been experimentally determined and demonstrate a high density of detectable recombination events in the regions annotated as recombination hotspots. The programs implementing the methods in this paper are available at www.cs.ucsd.edu/users/vibansal/RecBounds/.     

Genetic analysis of the proximal portion of the mouse t complex: evidence for a second inversion within t haplotypes

Genomic sequences derived from the mouse t complex by a microdissection cloning technique have been used as tools to obtain high resolution genetic maps of the wild-type and t haplotype forms of the most proximal portion of chromosome 17. Genetic mapping was performed through a recombinant inbred strain analysis and an analysis of partial t haplotypes. The accumulated data demonstrate the existence of a large inversion of genetic material, encompassing the loci of T and qk, within the proximal portion of t haplotypes. This newly described proximal inversion and the previously described distal inversion provide an explanation for the suppression of recombination observed along the length of t haplotype DNA in heterozygous mice.     

Meiotic recombination in Turnera (Turneraceae): extreme sexual difference in rates, but no evidence for recombination suppression associated with the distyly (S) locus

To explore the rate of recombination resulting from male vs female meiosis, crosses were performed using distylous Turnera subulata as well as a cross involving the introgression of genes from T. krapovickasii into T. subulata. We assayed four loci on the chromosome bearing the S-locus as well as two loci on each of two other linkage groups. Substantial and consistent dimorphism in recombination rates was found with female meiosis resulting in as much as a approximately 6-fold increase relative to male. Aberrant single locus segregation ratios occurred for some loci, particularly when the male (pollen) parent was heterozygous and the cross involved introgressed genes. The extreme trend of greater recombination resulting from female meiosis was, however, maintained in crosses where no aberrant ratios occurred, indicating that the sex dimorphism in recombination is not the result of aberrant segregation. We also exploited this distylous species and tested whether there is recombination suppression around the S-locus because of an inversion or other chromosome rearrangement(s). We found no significant evidence for recombination suppression.     

A large inverted duplication allows homologous recombination between chromosomes heterozygous for the proximal t complex inversion

We have examined the molecular organization of a region of mouse chromosome 17 that allows homologous recombination between wild-type and t haplotype chromosomes across a large inversion. We have used a combination of genetic mapping of restriction fragment length polymorphisms, molecular characterization of cloned regions isolated on overlapping cosmids, and subchromosomal restriction mapping using the pulsed field gel technique. Our analyses show that the wild-type form of chromosome 17 contains an inverted duplication of an element of at least 650 kb that is present in only one copy in the t haplotype form. Two chromosomes, th45 and tAE5, arose by homologous recombination across the element that is present in both chromosomal variants in the same orientation.     

Restimulation in secondary MLC by a non-D-locus determinant within the MHC

By testing a family in which one offspring had inherited a chromosome including a recombination between theHLA-B andD loci, we sought to obtain some insight into whether determinants other than those atHLA-D are capable of restimulating in a secondary MLC. Results obtained in the primary MLC indicated that the recombinant child did not express products of theHLA-D region normally associated with this haplotype. When sensitization in a primary MLC was to the entire haplotype, everyone who had the sensitizing haplotype restimulated strongly and specifically. In addition, however, weak to moderate stimulation was obtained when the cells of the recombinant child were used to restimulate. Presumably these cells possessed determinants coded for within theHLA-A toB chromosomal segments of the sensitizing haplotype, but not those coded for by theHLA-D locus. Our results indicate that a simple structure atHLA-D is not the sole factor in the secondary MLC. Either the products of loci outside theHLA-D locus can also restimulate or the recombination occurred within theD locus, suggesting that theD region contains more than one locus coding for restimulating determinants.     

Genetic Evidence for Two T Complex Tail Interaction (Tct) Loci in T Haplotypes

The t complex on chromosome 17 of the house mouse is an exceptional model for studying the genetic control of transmission ratio, gametogenesis, and embryogenesis. Partial haplotypes derived through rare recombination between a t haplotype and its wild-type homolog have been essential in the genetic analysis of these various properties of the t complex. A new partial t haplotype, which was derived from the complete tw71 haplotype and which is called tw71Jr1, was shown to have unexpected effects on tail length and unique recombination breakpoints. This haplotype, either when homozygous or when heterozygous with the progenitor tw71 haplotype, produced short-tailed rather than normal-tailed mice on certain genetic backgrounds. Genetic analysis of this exceptional haplotype showed that the recombination breakpoints were different from those leading to any other partial t haplotype. Based on this haplotype, a model is proposed that accounts for genetic interactions between the brachyury locus (T), the t complex tail interaction (tct) locus, and their wild-type homolog(s) that determine tail length. An important part of this model is the hypothesis that the tct locus, which enhances the tail-shortening effect of T mutations, is in fact at least two, genetically separable genes with different genetic activities. Genetic analysis of parental and recombinant haplotypes also suggests that intrachromosomal recombination involving an inverted duplicated segment can account for the variable orientation of loci within an inverted duplication on wild-type homologs of the t haplotype.     

Genotyping error detection through tightly linked markers

The identification of genotyping errors is an important issue in mapping complex disease genes. Although it is common practice to genotype multiple markers in a candidate region in genetic studies, the potential benefit of jointly analyzing multiple markers to detect genotyping errors has not been investigated. In this article, we discuss genotyping error detections for a set of tightly linked markers in nuclear families, and the objective is to identify families likely to have genotyping errors at one or more markers. We make use of the fact that recombination is a very unlikely event among these markers. We first show that, with family trios, no extra information can be gained by jointly analyzing markers if no phase information is available, and error detection rates are usually low if Mendelian consistency is used as the only standard for checking errors. However, for nuclear families with more than one child, error detection rates can be greatly increased with the consideration of more markers. Error detection rates also increase with the number of children in each family. Because families displaying Mendelian consistency may still have genotyping errors, we calculate the probability that a family displaying Mendelian consistency has correct genotypes. These probabilities can help identify families that, although showing Mendelian consistency, may have genotyping errors. In addition, we examine the benefit of available haplotype frequencies in the general population on genotyping error detections. We show that both error detection rates and the probability that an observed family displaying Mendelian consistency has correct genotypes can be greatly increased when such additional information is available.     

Bayesian fine-scale mapping of disease loci, by hidden Markov models

We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers-in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain-Monte Carlo simulation methods, we obtain posterior distributions of model parameter estimates including disease-gene location and the age of the disease-predisposing mutation. In addition, we allow for heterogeneity in recombination rates, across the candidate region, to account for recombination hot and cold spots. We also obtain, for the ancestral marker haplotype, a posterior distribution that is unique to our method and that, unlike maximum-likelihood estimation, can properly account for uncertainty. We apply the method to data for cystic fibrosis and Huntington disease, for which mutations in disease genes have already been identified. The new method performs well compared with existing multi-locus mapping methods.     

Maize genome structure variation: interplay between retrotransposon polymorphisms and genic recombination

Although maize (Zea mays) retrotransposons are recombinationally inert, the highly polymorphic structure of maize haplotypes raises questions regarding the local effect of intergenic retrotransposons on recombination. To examine this effect, we compared recombination in the same genetic interval with and without a large retrotransposon cluster. We used three different bz1 locus haplotypes, McC, B73, and W22, in the same genetic background. We analyzed recombination between the bz1 and stc1 markers in heterozygotes that differ by the presence and absence of a 26-kb intergenic retrotransposon cluster. To facilitate the genetic screen, we used Ds and Ac markers that allowed us to identify recombinants by their seed pigmentation. We sequenced 239 recombination junctions and assigned them to a single nucleotide polymorphism-delimited interval in the region. The genetic distance between the markers was twofold smaller in the presence of the retrotransposon cluster. The reduction was seen in bz1 and stc1, but no recombination occurred in the highly polymorphic intergenic region of either heterozygote. Recombination within genes shuffled flanking retrotransposon clusters, creating new chimeric haplotypes and either contracting or expanding the physical distance between markers. Our findings imply that haplotype structure will profoundly affect the correlation between genetic and physical distance for the same interval in maize.     

Recombination locations and rates in beef cattle assessed from parent-offspring pairs

Background

Recombination events tend to occur in hotspots and vary in number among individuals. The presence of recombination influences the accuracy of haplotype phasing and the imputation of missing genotypes. Genes that influence genome-wide recombination rate have been discovered in mammals, yeast, and plants. Our aim was to investigate the influence of recombination on haplotype phasing, locate recombination hotspots, scan the genome for Quantitative Trait Loci (QTL) and identify candidate genes that influence recombination, and quantify the impact of recombination on the accuracy of genotype imputation in beef cattle.

Methods

2775 Angus and 1485 Limousin parent-verified sire/offspring pairs were genotyped with the Illumina BovineSNP50 chip. Haplotype phasing was performed with DAGPHASE and BEAGLE using UMD3.1 assembly SNP (single nucleotide polymorphism) coordinates. Recombination events were detected by comparing the two reconstructed chromosomal haplotypes inherited by each offspring with those of their sires. Expected crossover probabilities were estimated assuming no interference and a binomial distribution for the frequency of crossovers. The BayesB approach for genome-wide association analysis implemented in the GenSel software was used to identify genomic regions harboring QTL with large effects on recombination. BEAGLE was used to impute Angus genotypes from a 7K subset to the 50K chip.

Results

DAGPHASE was superior to BEAGLE in haplotype phasing, which indicates that linkage information from relatives can improve its accuracy. The estimated genetic length of the 29 bovine autosomes was 3097 cM, with a genome-wide recombination distance averaging 1.23 cM/Mb. 427 and 348 windows containing recombination hotspots were detected in Angus and Limousin, respectively, of which 166 were in common. Several significant SNPs and candidate genes, which influence genome-wide recombination were localized in QTL regions detected in the two breeds. High-recombination rates hinder the accuracy of haplotype phasing and genotype imputation.

Conclusions

Small population sizes, inadequate half-sib family sizes, recombination, gene conversion, genotyping errors, and map errors reduce the accuracy of haplotype phasing and genotype imputation. Candidate regions associated with recombination were identified in both breeds. Recombination analysis may improve the accuracy of haplotype phasing and genotype imputation from low- to high-density SNP panels.     

Heterokaryon formation and parasexual recombination between vegetatively incompatible lineages in a population of the chestnut blight fungus, Cryphonectria parasitica

Heterokaryosis was recently reported in the chestnut blight fungus, Cryphonectria parasitica, in which individuals contain nuclei that are isogenic except at the mating-type locus (MAT). MAT heterokaryons were found in several natural populations, including a putatively clonal population in West Salem, Wisconsin, providing an opportunity to address the question of how heterokaryons arise. We represented relationships among RFLP fingerprint haplotypes as networks in which loop formation is considered evidence of recombination. From 1990 to 1995, this population was clonal, as indicated by a simple haplotype network without loops, and the correlation of vegetative compatibility (vc) types and mating types with haplotype lineages. By 1999, we observed loops in the haplotype network involving isolates of two vc types (WS-2 and WS-3). Isolates with haplotypes in the loops were either MAT heterokaryons, carried the opposite mating type from other isolates of the same vc type, and/or had two alleles at two or more codominant SCAR (sequence-characterized amplified region) loci. Segregation of markers and recombination were evident among single-spore isolates from one heterokaryon; these single-spore isolates had novel fingerprint haplotypes, also within the loops. In contrast, vc type WS-1, which comprises 85% of the population, was represented by a simple network with no loops, indicating a clonal lineage varying only by mutation. Almost all isolates of WS-1 had the same mating type; the exceptions were five isolates that were MAT heterokaryons. These results are consistent with the hypothesis that heterokaryons formed between vegetatively incompatible individuals, and recombination occurred by a parasexual process.