The Research Of Linkage Disequilibrium Measures For The Gene Mapping Of Complex Traits Locus In Human Beings

BackgroundMapping genes associated with various traits and diseases is one of the most important tasks in human genetics research. For diseases and quantitative traits with complex genetic and environmental determinations, the traditional linkage analyses and quantitative-trait locus (QTL) mapping in humans generally can locate a trait locus to a genomic region of～10cM. However, physical mapping of such genes generally is not feasible, unless a genomic region containing such a gene can be reduced, through the use of fine-scale mapping, to a region of <1cM. With the availability of high-density maps of single nucleotide polymorphism (SNP) markers, population-based linkage disequilibrium (LD) mapping or association studies are widely used to identify genetic variants that influence human complex trait. The simplest LD method is to use measures which quantify LD between the trait locus and each marker locus, because of the values of the measures account for genetic distance between the trait locus and each marker locus. The common LD measure is based on case-control analysis which is to compare the marker allele or haplotype frequencies between affected and unaffected individuals (or selective samples). However, this method is not uniformly the most powerful. Amplifying the difference in allele or haplotype frequencies may increase the power of the measure and/or statistic in gene mapping. Shannon entropy, which is a nonlinear function of frequencies, can be used to amplify the differences in marker allele or haplotype frequencies. One implicit assumption in above research is that there are no genotyping errors. However, maybe there are genotyping errors in practical research, and genotyping errors can lead to erroneous inferences. ObjectivesBased on entropy theory, two measures l and Ix are proposed for fine-scale mapping of human complex trait using high-density marker maps. The effects that genotype errors have on the LD measures are investigated under a stochastic model in this paper.MethodsThe mapping performances of the two measures are investigated in both analytic and simulation scenarios of a single QTL or DSL linked to a single marker, and also compared with the common LD measure. The effects that genotype errors have on the LD measures are investigated under a stochastic model.ResultsThe measure l, which compares the entropy and conditional entropy in a marker by use of case-control samples and high-density marker maps, is used for fine-scale·mapping of disease susceptibility locus (DSL). The measure Ix is presented using high-density marker maps in extreme samples for fine-scale mapping of QTL. The measure Ix compares the entropy and the conditional entropy of a marker in the admixture population combined with the upper sample and the lower sample. The results show that the values of Ix and l in the presence of genotyping errors is less than the values when there are no genotyping errors.ConclusionsThe two measures are the function of LD between the marker and the QTL or DSL. They are the decrease function of genetic distance between the marker and the QTL or DSL and do not depend on the marker allele frequencies across the loci under the following assumptions: there is initial complete LD between the marker allele and the trait allele, there are no new mutations at both the marker locus and the QTL or DSL, and the population under study is large. The analytic results also show that the power of the two measures in fine mapping is higher than that of the common measure p_excess . We also investigate the effect of initialincomplete linkage disequilibrium between the marker allele and the trait allele and new mutations on l and lx. Both the two measures are affected slightly by initial incomplete linkage disequilibrium and new mutations and they are still suitable for fine-scale mapping when the mutation rates at the trait locus and the marker loci are relatively low. The fine mapping performances are investigated extensively by simulation study under various genetic parameters. The simulation results show that the two LD measures l and Ix can accurately map the QTL or DSL.The values of lx and l in the presence of genotyping errors is less than the values when there are no genotyping errors. The proportion of the decrease will increase with the increasing of the marker allele frequencies. The proportion of the decrease are below 10 % as genotyping errors rate is relatively low (0.01) and the marker allele frequencies are not very high(<0.9). When genotyping errors rate is relatively high (0.03, 0.05), the proportion of the decrease exceeds 10%, and the trait associated allele frequency is small (0.10) and the marker allele frequencies are relatively high (0.9), the proportion of the decrease are 50% even exceeds 50%. The effects of the genotype errors are evaluated by a simulation study on the basis of the haplotype frequencies of 10 SNPs of ACE genes. We suggest to minimize, if not eliminate, the extent of genotyping errors in genetic research.