Efficient Inference of Haplotypes from Genotypes on a Pedigree with Mutations and Missing Alleles (Extented Abstract)

Abstract

Abstract. Driven by the international HapMap project, the haplotype inference problem has become an important topic in the computational biology community. In this paper, we study how to efficiently infer haplotypes from genotypes of related individuals as given by a pedigree. Our assumption is that the input pedigree data may contain de novo mutations and missing alleles but is free of genotyping errors and recombinants, which is usually true for tightly linked markers. We formulate the problem as a combinatorial optimization problem, called the minimum mutation haplotype configuration (MMHC) problem, where we seek haplotypes consistent with the given genotypes that incur no recombinants and require the minimum number of mutations. This extends the well studied zero-recombinant haplotype configuration (ZRHC) problem. Although ZRHC is polynomial-time solvable, MMHC is NP-hard. We construct an integer linear program (ILP) for MMHC using the system of linear equations over the field F (2) that has been developed recently to solve ZRHC. Since the number of constraints in the ILP is large (exponentially large in the general case), we present an incremental approach for solving the ILP where we gradually add the constraints to a standard ILP solver until a feasible haplotype configuration is found. Our preliminary experiments on simulated data demonstrate that the method is very efficient on large pedigrees and can infer haplotypes very accurately as well as recover most of the mutations and missing alleles correctly.

Inferring Haplotypes From Genotypes on a Pedigree With Mutations, Genotyping Errors and Missing Alleles

“…If it is not consistent, we add more constraints and then invoke the ILP solver again. The ILP solver together with the Gaussian elimination subroutine will be referred to as the black box, which was introduced in our previous work 13 . The temporary h-variable assignment from the black box is often optimal and, in this case, we can compute an optimal haplotype configuration with the assignment.…”

“…As in Ref. 13 and 29, we can convert the system to an equivalent linear system involving only the h-variables, mutation variables, and error variables.…”

“…Haplotype inference methods can be divided into three groups according to the type of given genotype data: methods for population data collected from unrelated individuals [3][4][5] , methods for pedigree data collected from individuals (typically from an extended family) that are related by the parent-child relationship [6][7][8][9][10][11][12][13][14] , and methods for pooled samples 15,16 . Here, we are interested in only pedigree data.…”

“…8,12 and 29 for solving ZRHC in almost linear time. We use the incremental approach introduced in a previous work 13 to reduce the number of constraints in the ILP instance.…”

“…In this paper, we will follow Ref. 13 to consider only tree pedigrees, which are very common among human pedigrees. From now on, when we talk about paths and cycles in a pedigree, we will consider it as a graph form.…”