Individual haplotype assembly of Apis mellifera (honeybee) using a practical branch and bound algorithm

A haplotype is a single nucleotide polymorphism (SNP) sequence and a representative genetic marker describing the diversity of biological organs. Haplotypes have a wide range of applications such as pharmacology and medical applications. In particular, as a highly social species, haplotypes of the Apis mellifera (honeybee) benefit human health and medicine in diverse areas, including venom toxicology, infectious disease, and allergic disease. For this reason, assembling a pair of haplotypes from individual SNP fragments drives research and generates various computational models for this problem. The minimum error correction (MEC) model is an important computational model for an individual haplotype assembly problem. However, the MEC model has been proved to be NP-hard; therefore, no efficient algorithm is available to address this problem. In this study, we propose an improved version of a branch and bound algorithm that can assemble a pair of haplotypes with an optimal solution from SNP fragments of a honeybee specimen in practical time bound. First, we designed a local search algorithm to calculate the good initial upper bound of feasible solutions for enhancing the efficiency of the branch and bound algorithm. Furthermore, to accelerate the speed of the algorithm, we made use of the recursive property of the bounding function together with a lookup table. After conducting extensive experiments over honeybee SNP data released by the Human Genome Sequencing Center, we showed that our method is highly accurate and efficient for assembling haplotypes.     

A fast and accurate enumeration-based algorithm for haplotyping a triploid individual

Background

Haplotype assembly, reconstructing haplotypes from sequence data, is one of the major computational problems in bioinformatics. Most of the current methodologies for haplotype assembly are designed for diploid individuals. In recent years, genomes having more than two sets of homologous chromosomes have attracted many research groups that are interested in the genomics of disease, phylogenetics, botany and evolution. However, there is still a lack of methods for reconstructing polyploid haplotypes.

Results

In this work, the minimum error correction with genotype information (MEC/GI) model, an important combinatorial model for haplotyping a single individual, is used to study the triploid individual haplotype reconstruction problem. A fast and accurate enumeration-based algorithm enumeration haplotyping triploid with least difference (EHTLD) is proposed for solving the MEC/GI model. The EHTLD algorithm tries to reconstruct the three haplotypes according to the order of single nucleotide polymorphism (SNP) loci along them. When reconstructing a given SNP site, the EHTLD algorithm enumerates three kinds of SNP values in terms of the corresponding site’s genotype value, and chooses the one, which leads to the minimum difference between the reconstructed haplotypes and the sequenced fragments covering that SNP site, to fill the SNP loci being reconstructed.

Conclusion

Extensive experimental comparisons were performed between the EHTLD algorithm and the well known HapCompass and HapTree. Compared with algorithms HapCompass and HapTree, the EHTLD algorithm can reconstruct more accurate haplotypes, which were proven by a number of experiments.

     

HapScope: a software system for automated and visual analysis of functionally annotated haplotypes

We have developed a software analysis package, HapScope, which includes a comprehensive analysis pipeline and a sophisticated visualization tool for analyzing functionally annotated haplotypes. The HapScope analysis pipeline supports: (i) computational haplotype construction with an expectation-maximization or Bayesian statistical algorithm; (ii) SNP classification by protein coding change, homology to model organisms or putative regulatory regions; and (iii) minimum SNP subset selection by either a Brute Force Algorithm or a Greedy Partition Algorithm. The HapScope viewer displays genomic structure with haplotype information in an integrated environment, providing eight alternative views for assessing genetic and functional correlation. It has a user-friendly interface for: (i) haplotype block visualization; (ii) SNP subset selection; (iii) haplotype consolidation with subset SNP markers; (iv) incorporation of both experimentally determined haplotypes and computational results; and (v) data export for additional analysis. Comparison of haplotypes constructed by the statistical algorithms with those determined experimentally shows variation in haplotype prediction accuracies in genomic regions with different levels of nucleotide diversity. We have applied HapScope in analyzing haplotypes for candidate genes and genomic regions with extensive SNP and genotype data. We envision that the systematic approach of integrating functional genomic analysis with population haplotypes, supported by HapScope, will greatly facilitate current genetic disease research.     

Haplotype reconstruction from SNP alignment.

In this paper, we describe a method for statistical reconstruction of haplotypes from a set of aligned SNP fragments. We consider the case of a pair of homologous human chromosomes, one from the mother and the other from the father. After fragment assembly, we wish to reconstruct the two haplotypes of the parents. Given a set of potential SNP sites inferred from the assembly alignment, we wish to divide the fragment set into two subsets, each of which represents one chromosome. Our method is based on a statistical model of sequencing errors, compositional information, and haplotype memberships. We calculate probabilities of different haplotypes conditional on the alignment. Due to computational complexity, we first determine phases for neighboring SNPs. Then we connect them and construct haplotype segments. Also, we compute the accuracy or confidence of the reconstructed haplotypes. We discuss other issues, such as alternative methods, parameter estimation, computational efficiency, and relaxation of assumptions.     

Haplotype inference by maximum parsimony

MOTIVATION: Haplotypes have been attracting increasing attention because of their importance in analysis of many fine-scale molecular-genetics data. Since direct sequencing of haplotype via experimental methods is both time-consuming and expensive, haplotype inference methods that infer haplotypes based on genotype samples become attractive alternatives. RESULTS: (1) We design and implement an algorithm for an important computational model of haplotype inference that has been suggested before in several places. The model finds a set of minimum number of haplotypes that explains the genotype samples. (2) Strong supports of this computational model are given based on the computational results on both real data and simulation data. (3) We also did some comparative study to show the strength and weakness of this computational model using our program. AVAILABILITY: The software HAPAR is free for non-commercial uses. Available upon request (lwang@cs.cityu.edu.hk).     

Efficient reconstruction of haplotype structure via perfect phylogeny

Each person's genome contains two copies of each chromosome, one inherited from the father and the other from the mother. A person's genotype specifies the pair of bases at each site, but does not specify which base occurs on which chromosome. The sequence of each chromosome separately is called a haplotype. The determination of the haplotypes within a population is essential for understanding genetic variation and the inheritance of complex diseases. The haplotype mapping project, a successor to the human genome project, seeks to determine the common haplotypes in the human population. Since experimental determination of a person's genotype is less expensive than determining its component haplotypes, algorithms are required for computing haplotypes from genotypes. Two observations aid in this process: first, the human genome contains short blocks within which only a few different haplotypes occur; second, as suggested by Gusfield, it is reasonable to assume that the haplotypes observed within a block have evolved according to a perfect phylogeny, in which at most one mutation event has occurred at any site, and no recombination occurred at the given region. We present a simple and efficient polynomial-time algorithm for inferring haplotypes from the genotypes of a set of individuals assuming a perfect phylogeny. Using a reduction to 2-SAT we extend this algorithm to handle constraints that apply when we have genotypes from both parents and child. We also present a hardness result for the problem of removing the minimum number of individuals from a population to ensure that the genotypes of the remaining individuals are consistent with a perfect phylogeny. Our algorithms have been tested on real data and give biologically meaningful results. Our webserver (http://www.cs.columbia.edu/compbio/hap/) is publicly available for predicting haplotypes from genotype data and partitioning genotype data into blocks.     

The new HNO donor, 1-nitrosocyclohexyl acetate, increases contractile force in normal and β-adrenergically desensitized ventricular myocytes

Haplotype, which is the sequence of SNPs in a specific chromosome, plays an important role in disease association studies. However, current sequencing techniques can detect the presence of SNP sites, but they cannot tell which copy of a pair of chromosomes the alleles belong to. Moreover, sequencing errors that occurred in sequencing SNP fragments make it difficult to determine a pair of haplotypes from SNP fragments. To help overcome this difficulty, the haplotype assembly problem is defined from the viewpoint of computation, and several models are suggested to tackle this problem. However, there are no freely available web-based tools to overcome this problem as far as we are aware. In this paper, we present a web-based application based on the genetic algorithm, named HapAssembler, for assembling a pair of haplotypes from SNP fragments. Numerical results on real biological data show that the correct rate of the proposed application in this paper is greater than 95% in most cases. HapAssembler is freely available at http://alex.chonnam.ac.kr/~drminor/hapHome.htm. Users can choose any model among four models for their purpose and determine haplotypes from their input data.     

Adiponectin gene haplotype is associated with preeclampsia

We determined whether the polymorphism of the gene encoding adiponectin contributes to susceptibility to preeclampsia. The study involved 133 Finnish women with preeclampsia and 245 healthy control subjects. All women were genotyped for two single nucleotide polymorphisms (SNPs), SNP45 in exon 2 and SNP276 in intron 2, in the adiponectin gene. Chi2 analysis was used to assess genotype and allele frequency differences between the preeclamptic and control groups. In addition, the pair of loci haplotype analysis, using the expectation-maximization (EM) algorithm, was used to examine the estimated haplotype frequencies of the two SNPs, among the two groups. The TT genotype versus the pooled G genotypes in SNP276 was associated with protection against preeclampsia (p = 0.012) at an odds ratio of 0.27 (95% confidence interval [CI]: 0.09-0.80). Also the genotype and allele frequency distributions of SNP276 differed significantly between the preeclampsia group and the control group (p = 0.035 and p = 0.043, respectively). Single-point genotype and allele distributions in SNP45 of the adiponectin gene were not statistically different between the groups. In the haplotype estimation analysis, the pooled G haplotypes versus the TT haplotype were significantly overrepresented in the preeclampsia group (p = 0.042 +/- 0.005). Polymorphisms of the adiponectin gene show a weak, but statistically significant, haplotype association with susceptibility to preeclampsia in Finnish women.     

Inference on haplotype effects in case-control studies using unphased genotype data

A variety of statistical methods exist for detecting haplotype-disease association through use of genetic data from a case-control study. Since such data often consist of unphased genotypes (resulting in haplotype ambiguity), such statistical methods typically apply the expectation-maximization (EM) algorithm for inference. However, the majority of these methods fail to perform inference on the effect of particular haplotypes or haplotype features on disease risk. Since such inference is valuable, we develop a retrospective likelihood for estimating and testing the effects of specific features of single-nucleotide polymorphism (SNP)-based haplotypes on disease risk using unphased genotype data from a case-control study. Our proposed method has a flexible structure that allows, among other choices, modeling of multiplicative, dominant, and recessive effects of specific haplotype features on disease risk. In addition, our method relaxes the requirement of Hardy-Weinberg equilibrium of haplotype frequencies in case subjects, which is typically required of EM-based haplotype methods. Also, our method easily accommodates missing SNP information. Finally, our method allows for asymptotic, permutation-based, or bootstrap inference. We apply our method to case-control SNP genotype data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus (FUSION) Genetics study and identify two haplotypes that appear to be significantly associated with type 2 diabetes. Using the FUSION data, we assess the accuracy of asymptotic P values by comparing them with P values obtained from a permutation procedure. We also assess the accuracy of asymptotic confidence intervals for relative-risk parameters for haplotype effects, by a simulation study based on the FUSION data.     

An optimal algorithm for perfect phylogeny haplotyping.

Inferring haplotype data from genotype data is a crucial step in linking SNPs to human diseases. Given n genotypes over m SNP sites, the haplotype inference (HI) problem deals with finding a set of haplotypes so that each given genotype can be formed by a combining a pair of haplotypes from the set. The perfect phylogeny haplotyping (PPH) problem is one of the many computational approaches to the HI problem. Though it was conjectured that the complexity of the PPH problem was O(nm), the complexity of all the solutions presented until recently was O(nm (2)). In this paper, we make complete use of the column-ordering that was presented earlier and show that there must be some interdependencies among the pairwise relationships between SNP sites in order for the given genotypes to allow a perfect phylogeny. Based on these interdependencies, we introduce the FlexTree (flexible tree) data structure that represents all the pairwise relationships in O(m) space. The FlexTree data structure provides a compact representation of all the perfect phylogenies for the given set of genotypes. We also introduce an ordering of the genotypes that allows the genotypes to be added to the FlexTree sequentially. The column ordering, the FlexTree data structure, and the row ordering we introduce make the O(nm) OPPH algorithm possible. We present some results on simulated data which demonstrate that the OPPH algorithm performs quiet impressively when compared to the previous algorithms. The OPPH algorithm is one of the first O(nm) algorithms presented for the PPH problem.     

2SNP: scalable phasing method for trios and unrelated individuals

Emerging microarray technologies allow affordable typing of very long genome sequences. A key challenge in analyzing of such huge amount of data is scalable and accurate computational inferring of haplotypes (i.e., splitting of each genotype into a pair of corresponding haplotypes). In this paper, we first phase genotypes consisting only of two SNPs using genotypes frequencies adjusted to the random mating model and then extend phasing of two-SNP genotypes to phasing of complete genotypes using maximum spanning trees. Runtime of the proposed 2SNP algorithm is O(nm (n + log m), where n and m are the numbers of genotypes and SNPs, respectively, and it can handle genotypes spanning entire chromosomes in a matter of hours.On datasets across 23 chromosomal regions from HapMap[11], 2SNP is several orders of magnitude faster than GERBIL and PHASE while matching them in quality measured by the number of correctly phased genotypes, single-site and switching errors. For example the 2SNP software phases entire chromosome (10(5) SNPs from HapMap) for 30 individuals in 2 hours with average switching error 7.7%.We have also enhanced 2SNP algorithm to phase family trio data and compared it with four other well-known phasing methods on simulated data from [15]. 2SNP is much faster than all of them while loosing in quality only to PHASE. 2SNP software is publicly available at http://alla.cs.gsu.edu/~software/2SNP.     

HapTree: A Novel Bayesian Framework for Single Individual Polyplotyping Using NGS Data

As the more recent next-generation sequencing (NGS) technologies provide longer read sequences, the use of sequencing datasets for complete haplotype phasing is fast becoming a reality, allowing haplotype reconstruction of a single sequenced genome. Nearly all previous haplotype reconstruction studies have focused on diploid genomes and are rarely scalable to genomes with higher ploidy. Yet computational investigations into polyploid genomes carry great importance, impacting plant, yeast and fish genomics, as well as the studies of the evolution of modern-day eukaryotes and (epi)genetic interactions between copies of genes. In this paper, we describe a novel maximum-likelihood estimation framework, HapTree, for polyploid haplotype assembly of an individual genome using NGS read datasets. We evaluate the performance of HapTree on simulated polyploid sequencing read data modeled after Illumina sequencing technologies. For triploid and higher ploidy genomes, we demonstrate that HapTree substantially improves haplotype assembly accuracy and efficiency over the state-of-the-art; moreover, HapTree is the first scalable polyplotyping method for higher ploidy. As a proof of concept, we also test our method on real sequencing data from NA12878 (1000 Genomes Project) and evaluate the quality of assembled haplotypes with respect to trio-based diplotype annotation as the ground truth. The results indicate that HapTree significantly improves the switch accuracy within phased haplotype blocks as compared to existing haplotype assembly methods, while producing comparable minimum error correction (MEC) values. A summary of this paper appears in the proceedings of the RECOMB 2014 conference, April 2–5.     

Haplotyping in pedigrees via a genetic algorithm.

Genome-wide screening for localization of disease genes necessitates the efficient reconstruction of haplotypes of members of a pedigree from genotype data at multiple loci. We propose a genetic algorithmic approach to haplotyping and show that it works fast, efficiently and reliably. This algorithm uses certain principles of biological evolution to find optimal solutions to complex problems. The optimality criterion used in the present problem is the minimum number of recombinations over possible haplotype configurations of members of a pedigree. The proposed algorithm is much less demanding in terms of data and assumption requirements compared to the currently used likelihood-based methods of haplotype reconstruction. It also provides multiple optimal haplotype configurations of a pedigree, if such multiple optima exist.     

Inferring haplotypes from genotypes on a pedigree with mutations, genotyping errors and missing alleles

Inferring the haplotypes of the members of a pedigree from their genotypes has been extensively studied. However, most studies do not consider genotyping errors and de novo mutations. In this paper, we study how to infer haplotypes from genotype data that may contain genotyping errors, de novo mutations, and missing alleles. We assume that there are no recombinants in the genotype data, which is usually true for tightly linked markers. We introduce a combinatorial optimization problem, called haplotype configuration with mutations and errors (HCME), which calls for haplotype configurations consistent with the given genotypes that incur no recombinants and require the minimum number of mutations and errors. HCME is NP-hard. To solve the problem, we propose a heuristic algorithm, the core of which is an integer linear program (ILP) using the system of linear equations over Galois field GF(2). Our algorithm can detect and locate genotyping errors that cannot be detected by simply checking the Mendelian law of inheritance. The algorithm also offers error correction in genotypes/haplotypes rather than just detecting inconsistencies and deleting the involved loci. Our experimental results show that the algorithm can infer haplotypes with a very high accuracy and recover 65%-94% of genotyping errors depending on the pedigree topology.     

Model-based inference of haplotype block variation.

The haplotype block structure of SNP variation in human DNA has been demonstrated by several recent studies. The presence of haplotype blocks can be used to dramatically increase the statistical power of genetic mapping. Several criteria have already been proposed for identifying these blocks, all of which require haplotypes as input. We propose a comprehensive statistical model of haplotype block variation and show how the parameters of this model can be learned from haplotypes and/or unphased genotype data. Using real-world SNP data, we demonstrate that our approach can be used to resolve genotypes into their constituent haplotypes with greater accuracy than previously known methods.     

Direct maximum parsimony phylogeny reconstruction from genotype data

Background  

Maximum parsimony phylogenetic tree reconstruction from genetic variation data is a fundamental problem in computational genetics with many practical applications in population genetics, whole genome analysis, and the search for genetic predictors of disease. Efficient methods are available for reconstruction of maximum parsimony trees from haplotype data, but such data are difficult to determine directly for autosomal DNA. Data more commonly is available in the form of genotypes, which consist of conflated combinations of pairs of haplotypes from homologous chromosomes. Currently, there are no general algorithms for the direct reconstruction of maximum parsimony phylogenies from genotype data. Hence phylogenetic applications for autosomal data must therefore rely on other methods for first computationally inferring haplotypes from genotypes.     

SNP Haplotype Mapping in a Small ALS Family

The identification of genes for monogenic disorders has proven to be highly effective for understanding disease mechanisms, pathways and gene function in humans. Nevertheless, while thousands of Mendelian disorders have not yet been mapped there has been a trend away from studying single-gene disorders. In part, this is due to the fact that many of the remaining single-gene families are not large enough to map the disease locus to a single site in the genome. New tools and approaches are needed to allow researchers to effectively tap into this genetic gold-mine. Towards this goal, we have used haploid cell lines to experimentally validate the use of high-density single nucleotide polymorphism (SNP) arrays to define genome-wide haplotypes and candidate regions, using a small amyotrophic lateral sclerosis (ALS) family as a prototype. Specifically, we used haploid-cell lines to determine if high-density SNP arrays accurately predict haplotypes across entire chromosomes and show that haplotype information significantly enhances the genetic information in small families. Panels of haploid-cell lines were generated and a 5 centimorgan (cM) short tandem repeat polymorphism (STRP) genome scan was performed. Experimentally derived haplotypes for entire chromosomes were used to directly identify regions of the genome identical-by-descent in 5 affected individuals. Comparisons between experimentally determined and in silico haplotypes predicted from SNP arrays demonstrate that SNP analysis of diploid DNA accurately predicted chromosomal haplotypes. These methods precisely identified 12 candidate intervals, which are shared by all 5 affected individuals. Our study illustrates how genetic information can be maximized using readily available tools as a first step in mapping single-gene disorders in small families.     

Association analysis of the RGS4 gene in Han Chinese and Scottish populations with schizophrenia

We investigated the RGS4 as a susceptibility gene for schizophrenia in Chinese Han (184 trios and 138 sibling pairs, a total of 322 families) and Scottish (580 cases and 620 controls) populations using both a family trio and case-control design. Both the samples had statistical power greater than 70% to detect a heterozygote genotype relative risk of >1.2 for frequent RGS4-risk alleles. We genotyped four single nucleotide polymorphisms (SNPs) which have previously been associated with schizophrenia as either individually or part of haplotypes. Allele frequencies and linkage disequilibrium between the SNPs was similar in the two populations. In the Chinese sample, no individual SNPs or any of their haplotypes were associated with schizophrenia. In the Scottish population, one SNP (SNP7) was significantly over-represented in the cases compared with the controls (0.44 vs. 0.38; A allele; chi(2) 7.08, P = 0.011 after correction for correlation between markers by permutation testing). One two-marker haplotype, composed of alleles T and A of SNP4 and SNP7, respectively, showed individual significance after correction by permutation testing (chi(2) 6.8; P = 0.04). None of the full four-marker haplotypes showed association, including the G-G-G-G haplotype previously associated with schizophrenia in more than one sample and the A-T-A-A haplotype. Thus, our data do not directly replicate previous associations of RGS4, but association with SNP 7 in the Scottish population provides some support for a role in schizophrenia susceptibility. We cannot conclusively exclude RGS4, as associated haplotypes are likely to be surrogates for unknown causative alleles, whose relationship with overlying haplotypes may differ between the population groups. Differences in the association seen across the two populations could result from methodological factors such as diagnostic differences but most likely result from ethnic differences in haplotype structures within RGS4.