TagSNP Selection Problems based on Linkage Disequilibrium and Lagrangian Relaxation

• Main Authors: Chia-Yi Ma, 馬家宜
• Other Authors: I-Lin Wang
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/55381888411320540603

碩士 === 國立成功大學 === 工業與資訊管理學系碩博士班 === 96 === Among all possible DNA sequence variations, Single Nucleotide Polymorphism （SNP）is the most common genetic variation. Sequence of closely linked SNPs composes the haplotype. Changes in the sequence can have significant influence on disease occurrences and the phenotype of human traits. The changes can be applied for identifying diseases and other medical research. At present, there are voluminous data of discovered SNPs. To make SNP database more cost-effective, many researchers propose tagging SNPs, a minimal subset of SNPs called tagSNP, to capture the full information of the original SNP sequence（haplotype）. Various SNP tagging methods have been proposed in the literature, based on different purpose of applications. This paper focuses on the most commonly cited definition of tagSNP and proposes methods to select them. In particular, we first seek the smallest SNP subset to identify all Haplotype patterns. The tagSNP Selection Problem can be modeled as a 0-1 binary integer programming problem with multiple optimal solutions. Previously, scholars focused on improving the efficiency of their solution methods, and ignored the differences among multiple optimal solutions. To this end, we proposes a Heuristic algorithm based on graph theory that first solves for all the multiple optimal solutions and then recommend a more informative set of optimal solution based on the concept of Linkage Disequilibrium（LD）. Our method calculates the relevancy between a selected tagSNP and the other SNPs, which later serves as an indicator for assessing the amount of information it carries. Among all the multiple optimal solutions, we recommend the one with the highest calculated LD value. In addition, we also propose a bi-objective integer programming model which tries to minimize the number of tagSNPs while maximize its associated LD value at the same time. To deal with large-scale tagSNP selection problems, we propose a heuristic called LRH, based on the theory of Lagrangian Relaxation. In particular, a modified subgradient method is proposed to update the Lagrangian multiplier which in turn approaches to the optimal solution step by step. In LRH, we incorporate the concept of Greedy Algorithm which selects some good SNP column, gradually reduces the problem size, and thus greatly improves the speed and quality of the calculated solution. The computation results show that LRH has good efficiency and effectiveness, since it can quickly converges to a better solution. Moreover, we also give a two-stage solution method（MIX） which first uses LRH to select good candidate SNP columns and then solve a reduced tagSNP selection problem of much smaller size based on the selected candidate SNPs. The computational results show that the proposed two-stage approach converges to a better solution in a much shorter time. Finally, in a suggested future research topic, we consider the case where the selected tagSNPs is to be included in a biochip, while the capacity for the biochip is sufficiently large. In this case, we no longer have to select the SNPs of minimum size. Instead, we focus on selecting those tagSNPs that can be used to differentiate haplotypes as many as possible so that the selected SNPs are more robust or reliable.