A Nearly Linear-Time General Algorithm for Genome-Wide Bi-allele Haplotype Phasing

Abstract

The determination of feature maps, such as STSs (sequence tag sites), SNPs (single nucleotide polymorphisms) or RFLP (restriction fragment length polymorphisms) maps, for each chromosome copy or haplotype in an individual has important potential applications to genetics, clinical biology and association studies. We consider the problem of reconstructing two haplotypes of a diploid individual from genotype data generated by mapping experiments, and present an algorithm to recover haplotypes. The problem of optimizing existing methods of SNP phasing with a population of diploid genotypes has been investigated in [7] and found to be NP-hard. In contrast, using single molecule methods, we show that although haplotypes are not known and data are further confounded by the mapping error model, reasonable assumptions on the mapping process allow us to recover the co-associations of allele types across consecutive loci and estimate the haplotypes with an efficient algorithm. The haplotype reconstruction algorithm requires two stages: Stage I is the detection of polymorphic marker types, this is done by modifying an EM–algorithm for Gaussian mixture models and an example is given for RFLP sizing. Stage II focuses on the problem of phasing and presents a method of local maximum likelihood for the inference of haplotypes in an individual. The algorithm presented is nearly linear in the number of polymorphic loci. The algorithm results, run on simulated RFLP sizing data, are encouraging, and suggest that the method will prove practical for haplotype phasing.

Work reported in this paper is funded by grants from NSF Qubic program, DARPA, HHMI biomedical support research grant, US DOE, US Air Force, NIH, New York office of Science and Technology & Academic Research