FastTagger: an efficient algorithm for genome-wide tag SNP selection using multi-marker linkage disequilibrium

<p>Abstract</p> <p>Background</p> <p>Human genome contains millions of common single nucleotide polymorphisms (SNPs) and these SNPs play an important role in understanding the association between genetic variations and human diseases. Many SNPs show correlated genotypes, or linkage disequilibrium (LD), thus it is not necessary to genotype all SNPs for association study. Many algorithms have been developed to find a small subset of SNPs called tag SNPs that are sufficient to infer all the other SNPs. Algorithms based on the <it>r</it>²LD statistic have gained popularity because <it>r</it>²is directly related to statistical power to detect disease associations. Most of existing <it>r</it>²based algorithms use pairwise LD. Recent studies show that multi-marker LD can help further reduce the number of tag SNPs. However, existing tag SNP selection algorithms based on multi-marker LD are both time-consuming and memory-consuming. They cannot work on chromosomes containing more than 100 k SNPs using length-3 tagging rules.</p> <p>Results</p> <p>We propose an efficient algorithm called FastTagger to calculate multi-marker tagging rules and select tag SNPs based on multi-marker LD. FastTagger uses several techniques to reduce running time and memory consumption. Our experiment results show that FastTagger is several times faster than existing multi-marker based tag SNP selection algorithms, and it consumes much less memory at the same time. As a result, FastTagger can work on chromosomes containing more than 100 k SNPs using length-3 tagging rules.</p> <p>FastTagger also produces smaller sets of tag SNPs than existing multi-marker based algorithms, and the reduction ratio ranges from 3%-9% when length-3 tagging rules are used. The generated tagging rules can also be used for genotype imputation. We studied the prediction accuracy of individual rules, and the average accuracy is above 96% when <it>r</it>²≥ 0.9.</p> <p>Conclusions</p> <p>Generating multi-marker tagging rules is a computation intensive task, and it is the bottleneck of existing multi-marker based tag SNP selection methods. FastTagger is a practical and scalable algorithm to solve this problem.</p

Single nucleotide polymorphisms in bone turnover-related genes in Koreans: ethnic differences in linkage disequilibrium and haplotype

<p>Abstract</p> <p>Background</p> <p>Osteoporosis is defined as the loss of bone mineral density that leads to bone fragility with aging. Population-based case-control studies have identified polymorphisms in many candidate genes that have been associated with bone mass maintenance or osteoporotic fracture. To investigate single nucleotide polymorphisms (SNPs) that are associated with osteoporosis, we examined the genetic variation among Koreans by analyzing 81 genes according to their function in bone formation and resorption during bone remodeling.</p> <p>Methods</p> <p>We resequenced all the exons, splice junctions and promoter regions of candidate osteoporosis genes using 24 unrelated Korean individuals. Using the common SNPs from our study and the HapMap database, a statistical analysis of deviation in heterozygosity depicted.</p> <p>Results</p> <p>We identified 942 variants, including 888 SNPs, 43 insertion/deletion polymorphisms, and 11 microsatellite markers. Of the SNPs, 557 (63%) had been previously identified and 331 (37%) were newly discovered in the Korean population. When compared SNPs in the Korean population with those in HapMap database, 1% (or less) of SNPs in the Japanese and Chinese subpopulations and 20% of those in Caucasian and African subpopulations were significantly differentiated from the Hardy-Weinberg expectations. In addition, an analysis of the genetic diversity showed that there were no significant differences among Korean, Han Chinese and Japanese populations, but African and Caucasian populations were significantly differentiated in selected genes. Nevertheless, in the detailed analysis of genetic properties, the LD and Haplotype block patterns among the five sub-populations were substantially different from one another.</p> <p>Conclusion</p> <p>Through the resequencing of 81 osteoporosis candidate genes, 118 unknown SNPs with a minor allele frequency (MAF) > 0.05 were discovered in the Korean population. In addition, using the common SNPs between our study and HapMap, an analysis of genetic diversity and deviation in heterozygosity was performed and the polymorphisms of the above genes among the five populations were substantially differentiated from one another. Further studies of osteoporosis could utilize the polymorphisms identified in our data since they may have important implications for the selection of highly informative SNPs for future association studies.</p

A Sequence of Service Stations with Arbitrary Input and Regular Service Times

In a queuing system with an ordered sequence of stations, the arrivals process is arbitrary and service times are regular at all stations. The case where each station consists of the same number of servers in parallel and the service times at all servers belonging to one station are the same is investigated and shown to possess the following properties: (a) The time spent in the system by any customer is independent of the order of the stations and of the allowable sizes of the intermediate queues; (b) The waiting time (not including service) of any customer equals the time the same customer would have been waiting in the queue of a single station system with regular service time, equaling the longest service time of the sequence (assuming the same arrivals process in both systems). These properties enable one to obtain waiting time distributions and other characteristics of such queuing processes.