H-PoP and H-PoPG: heuristic partitioning algorithms for single individual haplotyping of polyploids

Abstract

Motivation: Some economically important plants including wheat and cotton have more than two copies of each chromosome. With the decreasing cost and increasing read length of next-generation sequencing technologies, reconstructing the multiple haplotypes of a polyploid genome from its sequence reads becomes practical. However, the computational challenge in polyploid haplotyping is much greater than that in diploid haplotyping, and there are few related methods. Results: This paper models the polyploid haplotyping problem as an optimal poly-partition problem of the reads, called the Polyploid Balanced Optimal Partition (PBOP) model. For the reads sequenced from a k -ploid genome, the model tries to divide the reads into k groups such that the difference between the reads of the same group is minimized while the difference between the reads of different groups is maximized. When the genotype information is available, the model is extended to the Polyploid Balanced Optimal Partition with Genotype constraint (PBOPG) problem. These models are all NP-hard. We propose two heuristic algorithms, H-PoP and H-PoPG, based on dynamic programming and a strategy of limiting the number of intermediate solutions at each iteration, to solve the two models, respectively. Extensive experimental results on simulated and real data show that our algorithms can solve the models effectively, and are much faster and more accurate than the recent state-of-the-art polyploid haplotyping algorithms. The experiments also show that our algorithms can deal with long reads and deep read coverage effectively and accurately. Furthermore, H-PoP might be applied to help determine the ploidy of an organism. Availability: https://github.com/MinzhuXie/H-PoPG Contact:

Hap10: reconstructing accurate and long polyploid haplotypes using linked reads

“…We calculate this criterion for each haplotype block and report the average. The vector error rate is calculated by finding the minimum number of switches needed in haplotype segments in order to match • to ; this number is then divided by the haplotype length [7,15].…”

“…SDhaP [6] solves a correlation clustering problem using a gradient method to estimate the haplotypes. H-PoP [7], a heuristic algorithm, solves a combinatorial optimization problem called "polyploid balanced optimal partition". Another approach is to use the minimum fragment removal (MFR) model in which conflicting fragments (due to erroneous reads) are removed.…”

A Graph Auto-Encoder for Haplotype Assembly and Viral Quasispecies Reconstruction

“…The vast majority of existing haplotype assembly methods attempt to remove the aforementioned ambiguity by altering or even discarding the data, leading to minimum SNP removal (Lancia 2001), maximum fragments cut (Duitama 2010), and minimum error correction (MEC) score optimization criteria. Majority of haplotype assembly methods developed in recent years are focused on optimizing the MEC score, i.e., determining the smallest possible number of nucleotides in sequencing reads that should be altered such that the resulting dataset is consistent with having originated from k haplotypes (k denotes the ploidy of an organism) (Xie 2016;Pirola 2015;Kuleshov 2014;Patterson 2015;Bonizzoni 2016). These include the branch-and-bound scheme (Wang 2005), an integer linear programming formulation in (Chen 2013), and a dynamic programming framework in (Kuleshov 2014).…”

“…Among the aforementioned methods, only HapCompass (Aguiar 2012), SD-haP (Das 2015) and BP (Puljiz 2016) are capable of solving the haplotype assembly problem for k > 2. Other techniques that can handle reconstruction of haplotypes for both diploid and polyploid genomes include a Bayesian method HapTree (Berger 2014), a dynamic programming method H-PoP (Xie 2016) shown to be more accurate than the techniques in (Aguiar 2012;Berger 2014;Das 2015), and the matrix factorization schemes in (Cai 2016;Hashemi 2018).…”

Overlap graph-based generation of haplotigs for diploids and polyploids

“…Examples for diploid haplotype assembly are WhatsHap (Patterson et al, 2015), Phaser (Castel et al, 2016), Hap-Cut2 (Edge et al, 2017), ProbHap (Kuleshov, 2014) and HapCol (Pirola et al, 2016). Examples for polyploid haplotype assembly are Hap-Compass (Aguiar and Istrail, 2012), HapTree (Berger et al, 2014), SDhaP (Das and Vikalo, 2015), and H-PoP (Xie et al, 2016). The disadvantage of haplotype assembly programs is that they depend on high-quality reference sequence as a backbone, and, in addition, also on external variant call sets, which are major external factors that can introduce non-negligible biases.…”