A linear-time algorithm for reconstructing zero-recombinant haplotype configuration on a pedigree.

BACKGROUND: When studying genetic diseases in which genetic variations are passed on to offspring, the ability to distinguish between paternal and maternal alleles is essential. Determining haplotypes from genotype data is called haplotype inference. Most existing computational algorithms for haplotype inference have been designed to use genotype data collected from individuals in the form of a pedigree. A haplotype is regarded as a hereditary unit and therefore input pedigrees are preferred that are free of mutational events and have a minimum number of genetic recombinational events. These ideas motivated the zero-recombinant haplotype configuration (ZRHC) problem, which strictly follows the Mendelian law of inheritance, namely that one haplotype of each child is inherited from the father and the other haplotype is inherited from the mother, both without any mutation. So far no linear-time algorithm for ZRHC has been proposed for general pedigrees, even though the number of mating loops in a human pedigree is usually very small and can be regarded as constant. RESULTS: Given a pedigree with n individuals, m marker loci, and k mating loops, we proposed an algorithm that can provide a general solution to the zero-recombinant haplotype configuration problem in O(kmn + k2m) time. In addition, this algorithm can be modified to detect inconsistencies within the genotype data without loss of efficiency. The proposed algorithm was subject to 12000 experiments to verify its performance using different (n, m) combinations. The value of k was uniformly distributed between zero and six throughout all experiments. The experimental results show a great linearity in terms of execution time in relation to input size when both n and m are larger than 100. For those experiments where n or m are less than 100, the proposed algorithm runs very fast, in thousandth to hundredth of a second, on a personal desktop computer. CONCLUSIONS: We have developed the first deterministic linear-time algorithm for the zero-recombinant haplotype configuration problem. Our experimental results demonstrated the linearity of its execution time in relation to the input size. The proposed algorithm can be modified to detect inconsistency within the genotype data without loss of efficiency and is expected to be able to handle recombinant and missing data with further extension.

A new model of multi-marker correlation for genome-wide tag SNP selection.

Tag SNP selection is an important problem in computational biology and genetics because a small set of tag SNP markers may help reduce the cost of genotyping and thus genome-wide association studies. Several methods for selecting a smallest possible set of tag SNPs based on different formulations of tag SNP selection (block-based or genome-wide) and mathematical models of marker correlation have been investigated in the literature. In this paper, we propose a new model of multi-marker correlation for genome-wide tag SNP selection, and a simple greedy algorithm to select a smallest possible set of tag SNPs according to the model. Our experimental results on several real datasets from the HapMap project demonstrate that the new model yields more succinct tag SNP sets than the previous methods.

Detection of homologous recombination events in bacterial genomes.

We study the detection of mutations, sequencing errors, and homologous recombination events (HREs) in a set of closely related microbial genomes. We base the model on single nucleotide polymorphisms (SNPs) and break the genomes into blocks to handle the rearrangement problem. Then we apply a dynamic programming algorithm to model whether changes within each block are likely a result of mutations, sequencing errors, or HREs. Results from simulation experiments show that we can detect 31%-61% of HREs and the precision of our detection is about 48%-90% depending on the rates of mutation and missing data. The HREfinder software for predicting HREs in a set of whole genomes is available as open source (http://sourceforge.net/projects/hrefinder/).

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.