Effects of genotyping errors,missing values and segregation distortion in molecular marker data on the construction of linkage maps

A simulation study was performed to investigate the effects of missing values, typing errors and distorted segregation ratios in molecular marker data on the construction of genetic linkage maps, and to compare the performance of three locus-ordering criteria (weighted least squares, maximum likelihood and minimum sum of adjacent recombination fractions criteria) in the presence of such effects. The study was based upon three linkage groups of 10 loci at 2, 6, and 10 cM spacings simulated from a doubled-haploid population of size 150. Criteria performance were assessed using the number of replicates with correctly estimated orders, the mean rank correlation between the estimated and the true order and the mean total map length. Bootstrap samples from replicates in the maximum likelihood analysis produced a measure of confidence in the estimated locus order. The effects of missing values and/or typing errors in the data are to reduce the proportion of correctly ordered maps, and this problem worsens as the distances between loci decreases. The maximum likelihood criterion is most successful at ordering loci correctly, but gives estimated map lengths, which are substantially inflated when typing errors are present. The presence of missing values in the data produces shorter map lengths for more widely spaced markers, especially under the weighted least-squares criterion. Overall, the presence of segregation distortion has little effect on this population.     

Linkage relations between A2M, HOX3, INT1, KRAS2, and PAH on bovine chromosome 5.

There is a high level of conservation between human chromosomes and bovine syntenic groups. One such comparison is between human chromosome 12 and bovine chromosome 5, where at least 16 loci have been shown to be conserved in an homologous segment. However, the degree of conservation of order of the loci on bovine chromosome 5 is unknown, and in general the conservation of order in comparisons between humans and cattle can only be speculated. We have estimated the recombination fractions between five of the loci that were previously published as mapping to bovine chromosome 5 by a combination of in situ hybridization and analysis of bovine-rodent somatic cell hybrid lines to determine whether order has been conserved in the homologous segment of bovine chromosome 5 and human chromosome 12. Recombination fractions were estimated in reference pedigrees of cattle. The loci were A2M, GSNL, HOX3, INT1, KRAS2, and PAH. Restriction fragment length polymorphisms for all loci were defined by screening a panel of eight restriction endonucleases. The linkage between loci was estimated using the lod score method, and all possible pairwise comparisons were made. A preliminary map was created by joining together loci that showed the smallest recombination fractions and the largest lod scores. A multipoint analysis was performed to estimate support for the most likely order. This order shows the relative inversion of some of the loci. Moreover, the distance spanned in cattle is less than a quarter the distance spanned in humans. Together, these data indicate that several chromosomal evolutionary events have occurred in the homologous segment shared by humans and cattle.     

A novel method for estimating linkage maps

The goal of linkage mapping is to find the true order of loci from a chromosome. Since the number of possible orders is large even for a modest number of loci, the problem of finding the optimal solution is known as a NP-hard problem or traveling salesman problem (TSP). Although a number of algorithms are available, many either are low in the accuracy of recovering the true order of loci or require tremendous amounts of computational resources, thus making them difficult to use for reconstructing a large-scale map. We developed in this article a novel method called unidirectional growth (UG) to help solve this problem. The UG algorithm sequentially constructs the linkage map on the basis of novel results about additive distance. It not only is fast but also has a very high accuracy in recovering the true order of loci according to our simulation studies. Since the UG method requires n-1 cycles to estimate the ordering of n loci, it is particularly useful for estimating linkage maps consisting of hundreds or even thousands of linked codominant loci on a chromosome.     

Constructing large-scale genetic maps using an evolutionary strategy algorithm

This article is devoted to the problem of ordering in linkage groups with many dozens or even hundreds of markers. The ordering problem belongs to the field of discrete optimization on a set of all possible orders, amounting to n!/2 for n loci; hence it is considered an NP-hard problem. Several authors attempted to employ the methods developed in the well-known traveling salesman problem (TSP) for multilocus ordering, using the assumption that for a set of linked loci the true order will be the one that minimizes the total length of the linkage group. A novel, fast, and reliable algorithm developed for the TSP and based on evolution-strategy discrete optimization was applied in this study for multilocus ordering on the basis of pairwise recombination frequencies. The quality of derived maps under various complications (dominant vs. codominant markers, marker misclassification, negative and positive interference, and missing data) was analyzed using simulated data with approximately 50-400 markers. High performance of the employed algorithm allows systematic treatment of the problem of verification of the obtained multilocus orders on the basis of computing-intensive bootstrap and/or jackknife approaches for detecting and removing questionable marker scores, thereby stabilizing the resulting maps. Parallel calculation technology can easily be adopted for further acceleration of the proposed algorithm. Real data analysis (on maize chromosome 1 with 230 markers) is provided to illustrate the proposed methodology.     

Linkage of an autosomal dominant clefting syndrome (Van der Woude) to loci on chromosome Iq

Van der Woude syndrome (VWS) is an autosomal dominant disorder in which affected individuals have one or more of the following manifestations: cleft lip, cleft palate, hypodontia, or paramedian lower-lip pits. VWS is a well-characterized example of a single-gene abnormality that disturbs normal craniofacial morphogenesis. As a first step in identifying genes involved in human development, we used a candidate-gene-and-region approach to look for a linkage to VWS. Six families with 3 or more generations of affected individuals were studied. Evidence for linkage (theta = 0.02, lod score = 9.09) was found between the renin (REN) gene on 1q and VWS. Other linked loci included CR1, D1S58, and D1S53. The genes for laminin B2 (LAMB2), a basement-membrane protein, and for decay-accelerating factor (DAF) were studied as possible candidate genes on 1q. Recombinants between VWS and both LAMB2 and DAF excluded these genes from a causal role in the etiology of VWS for the families studied in this report. Multipoint linkage analysis indicated that the VWS locus was flanked by REN and D1S65 at a lod score of 10.83. This tight linkage with renin and other nearby loci provides a first step in identifying the molecular abnormality underlying this disturbance of human development.     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Structures for polyinosinic acid and polyguanylic acid

X-ray-diffraction analysis of oriented, partially crystalline fibres of polyinosinic acid has resulted in a new molecular model. This model consists of four identical polynucleotide chains related to one another by a fourfold rotation axis. The coaxial helices are righthanded (screw symmetry 23(2)) and have an axial translation per residue h=0.341nm and a rotation per residue t=31.3 degrees . Incorporated in the model are standard bond lengths, bond angles and C-2-endo furanose rings. The nucleotide conformation angles, determined by linked-atom least-squares methods, are orthodox and the fit with the X-ray intensities is good. Each hypoxanthine base is linked to two others by hydrogen bonds involving O-6 and N-1. Further stability may arise from intrachain hydrogen bonds between each ribose hydroxyl group and the phosphate oxygen O-3. If guanine were to be substituted for hypoxanthine in an isogeometrical molecular structure, additional hydrogen bonds could be made between every N-2 and N-7.     

A genome-wide search for genes predisposing to manic-depression, assuming autosomal dominant inheritance.

Manic-depressive illness (MDI), also known as "bipolar affective disorder," is a common and devastating neuropsychiatric illness. Although pivotal biochemical alterations underlying the disease are unknown, results of family, twin, and adoption studies consistently implicate genetic transmission in the pathogenesis of MDI. In order to carry out linkage analysis, we ascertained eight moderately sized pedigrees containing multiple cases of the disease. For a four-allele marker mapping 5 cM from the disease gene, the pedigree sample has > 97% power to detect a dominant allele under genetic homogeneity and has > 73% power under 20% heterogeneity. To date, the eight pedigrees have been genotyped with 328 polymorphic DNA loci throughout the genome. When autosomal dominant inheritance was assumed, 273 DNA markers gave lod scores < -2.0 at recombination fraction (theta) = .0, 174 DNA loci produced lod scores < -2.0 at theta = .05, and 4 DNA marker loci yielded lod scores > 1 (chromosome 5--D5S39, D5S43, and D5S62; chromosome 11--D11S85). Of the markers giving lod scores > 1, only D5S62 continued to show evidence for linkage when the affected-pedigree-member method was used. The D5S62 locus maps to distal 5q, a region containing neurotransmitter-receptor genes for dopamine, norepinephrine, glutamate, and gamma-aminobutyric acid. Although additional work in this region may be warranted, our linkage results should be interpreted as preliminary data, as 68 unaffected individuals are not past the age of risk.     

Probable genetic linkage between a locus for human urinary pepsinogen and the HL-A loci.

The genetic basis of familial variation in the relative intensities of human urinary pepsinogen isozymes is not completely clear from family studies. An investigation of the linkage relationships of pepsinogen isozyme 5, considering only segregation for the presence or absence of Pg 5, yields a peak lod score of 4.1 at theta = .1 for linkage with HL-A1 or HL-A2. Added to data from segregation interpreted according to a scheme proposed for the inheritance of intensity differences in Pg 5, the peak lod score becomes 3.0 at theta = .2. Data derived from the segregation of pepsinogen isozyme 4, possibly determined by an allele to that controlling the presence or absence of Pg 5, further reduces the total lod score at theta = .2 to 2.9. The results indicate probable linkage between a locus for urinary pepsinogen and the HL-A loci, but are insufficient to permit any conclusion concerning possible heterogeneity in the linkage relationships of Pg 4 and Pg 5 to HL-A.     

Absence of linkage of hereditary motor and sensory neuropathy type I to chromosome 1 markers

Although one large family with hereditary motor and sensory neuropathy (HMSN) type I that showed linkage to the Duffy blood group (FY) on chromosome 1 has previously been reported, we have failed to find evidence for such linkage after examining 14 markers from chromosome 1 in 12 pedigrees. We have excluded linkage between HMSN I and FY up to theta = 0.15 (lod = -3.01) and also between HMSN I and markers flanking FY; amylase (AMY), polymorphic urinary mucin (PUM), serum amyloid protein (APCS), and alpha-spectrin (SPTA). We have excluded HMSN I from 70 cM around this linkage group. Other markers examined were MS1, oncogene L-myc (MYCL), beta-subunit of nerve growth factor (NGFB), oncogene N-ras (NRAS), glucocerebrosidase (GBA), apolipoprotein AII (APOA2), antithrombin III (AT3), renin (REN), and MS32. These cover both the long and the short arms of chromosome 1 in addition to the centromeric region and yielded no evidence of linkage to HMSN I. Two-point lod scores between these markers are also presented. It is possible that there are two or more loci for HMSN I and it will be necessary to obtain significant lod scores from individual families to resolve this issue. This is increasingly possible now that hypervariable genetic markers such as PUM are available.     

Stratification by CARD15 variant genotype in a genome-wide search for inflammatory bowel disease susceptibility loci

Previously we have conducted a genome-wide search for inflammatory bowel disease susceptibility loci in a large European cohort. Results from this study demonstrated suggestive evidence of linkage to loci at chromosomes 1q, 6p, and 10p and replicated linkages on chromosomes 12 and 16. Recently, NOD2/CARD15 on chromosome 16q12 has been found to be strongly associated with Crohn's disease. In order to determine if there are other loci in the genome that interact with the three associated functional variants in CARD15 (R702W, G908R, 1007fs), we have stratified our large inflammatory bowel disease genome scan cohort by dividing pedigrees into two groups stratified by CARD15 variant genotype. The two pedigree groups were analysed using non-parametric allele sharing methods. The group of pedigrees that contained one of the three CARD15 variants had two suggestive linkage results occurring in 6p (lod = 3.06 at D6S197, IBD phenotype) and 10p (lod=2.29 at D10S197, CD phenotype). In addition, at 16q12 where CARD15 is located, the original genome scan had a peak lod score of 2.18 at D16S415 (CD phenotype). The stratified pedigree cohort containing one of three CARD15 variants had a peak lod score of 0.90 at D16S415 (CD phenotype), accounting for approximately less than half of the genetic evidence for linkage at this locus. This result is in agreement with the existence of a substantial number of private variants at the NOD2/CARD15 locus. Interaction with NOD2/CARD15 needs to be considered in future gene identification efforts on chromosomes 6 and 10.     

c-Ha-ras-1 oncogene lies between beta-globin and insulin loci on human chromosome 11p

DNA sequence polymorphisms have been used to determine the linear order and recombinational distances separating the Harvey ras 1 oncogene (c-Ha-ras-1), beta-globin, insulin, and parathyroid hormone genes on the short arm of human chromosome 11. Our results indicate that c-Ha-ras-1 is closely linked to both the beta-globin locus (theta = .08 [8 centimorgans], lod score = 5.11) and the insulin locus (theta = .04 [4 centimorgans], lod score = 3.31). Furthermore, the probable order of these loci on chromosome 11p is centromere-parathyroid hormone-beta globin-c-Ha-ras-1-insulin.     

Linkage of the multiple endocrine neoplasia type 2B gene (MEN2B) to chromosome 10 markers linked to MEN2A

The syndrome of multiple endocrine neoplasia type 2B (MEN 2B) resembles that of MEN 2A in that both include medullary carcinoma of the thyroid, pheochromocytoma, and autosomal dominant inheritance, but is distinct in that MEN 2B patients have neuromas of the mucous membranes. MEN2A has been linked to RBP3, D10S5, FNRB, D10S15, and D10Z1 near the centromere of chromosome 10. We examined linkage between MEN2B and RFLPs on chromosome 10 in all available members in two or three generations of 14 kindreds. The centromere marker D10Z1 was linked to MEN2B with a peak lod score of 5.42 at theta = 0.02. One possible recombinant was observed between D10Z1 and MEN2B. Multipoint analysis of RFLPs at FNRB, D10Z1, RBP3, and D10S15 gave a peak lod score of 7.12 at the midpoint between D10Z1 and RBP3 on the long arm (band q11). The most likely gene order FNRB-D10Z1-MEN2B was 27 times more likely than MEN2B-FNRB-D10Z1 and 31/2 times more likely than FNRB-MEN2B-D10Z1. Additional data will be required to establish the order of these loci with confidence.     

Linkage of cystic fibrosis to two tightly linked DNA markers: Joint report from a collaborative study

A collaborative study involving seven research groups provided an opportunity to investigate the linkage relationships between cystic fibrosis and two DNA marker loci, MET and pJ3.11 (D7S8), on an extended sample of 211 tested families. The maximum lod scores, recombination estimates, and confidence upper bounds (in parentheses) were 91.0 at theta = .004 (.012) for CF and MET, 71.3 at theta = .003 (.011) for CF and D7S8, and 69.3 at theta = .018 (.036) for MET and D7S8. Three-locus analyses yielded best support for the order MET-CF-D7S8, with odds against the alternate orders CF-MET-D7S8 and CF-D7S8-MET of 9:1 and 161:1, respectively. However, the number of observed recombinants was small and only one of the recombinants was jointly informative for all three markers. Significant allelic association was found between CF and both MET and D7S8. Weaker association between the latter two loci is consistent with the order MET-CF-D7S8.     

Linkage of human narcolepsy with HLA association to chromosome 4p13-q21

Although narcolepsy is highly associated with human leukocyte antigen (HLA) DQ6/DQB1*0602 and/or DR2/DRB1*1501, most individuals with the HLA haplotype are free of narcolepsy. This indicates that HLA alone makes a relatively small contribution to the development of narcolepsy and that a non-HLA gene(s) can contribute to the genetic predisposition even in narcoleptic cases with HLA association. We conducted a genome-wide linkage search for narcolepsy in eight Japanese families with 21 DR2-positive patients (14 narcoleptic cases with cataplexy and 7 cases with an incomplete form of narcolepsy). A lod score of 3.09 suggested linkage to chromosome 4p13-q21. A lod score of 1.53 was obtained at the HLA-DRB1 locus, though this lod score may be biased since all the affected patients and many of the family members were DR2-positive. No other loci including hypocretin, hypocretin receptor 1, and hypocretin receptor 2 had lod scores greater than 1.0. The present study suggests that chromosome 4p13-q21 contains a second locus for HLA-associated human narcolepsy.     

Monte Carlo comparison of preliminary methods for ordering multiple genetic loci.

We carried out a simulation study to compare the power of eight methods for preliminary ordering of multiple genetic loci. Using linkage groups of six loci and a simple pedigree structure, we considered the effects on method performance of locus informativity, interlocus spacing, total distance along the chromosome, and sample size. Method performance was assessed using the mean rank of the true order, the proportion of replicates in which the true order was the best order, and the number of orders that needed to be considered for subsequent multipoint linkage analysis in order to include the true order with high probability. A new method which maximizes the sum of adjacent two-point maximum lod scores divided by the equivalent number of informative meioses and the previously described method which minimizes the sum of adjacent recombination fraction estimates were found to be the best overall locus-ordering methods for the situations considered, although several other methods also performed well.     

Duplicate marker loci can result in incorrect locus orders on linkage maps

Genetic linkage maps, constructed from multi-locus recombination data, are the basis for many applications of molecular markers. For the successful employment of a linkage map, it is essential that the linear order of loci on a chromosome is correct. The objectives of this theoretical study were to (1) investigate the occurrence of incorrect locus orders caused by duplicate marker loci, (2) develop a statistical test for the detection of duplicate markers, and (3) discuss the implications for practical applications of linkage maps. We derived conditions, under which incorrect locus orders do or do not occur with duplicate marker loci for the general case of n markers on a chromosome in a BC₁ mapping population. We further illustrated these conditions numerically for the special case of four markers. On the basis of the extent of segregation distortion, an exact test for the presence of duplicate marker loci was suggested and its power was investigated numerically. Incorrect locus orders caused by duplicate marker loci can (1) negatively affect the assignment of target genes to chromosome regions in a map-based cloning experiment, (2) hinder indirect selection for a favorable allele at a quantitative trait locus, and (3) decrease the efficiency of reducing the length of the chromosome segment attached to a target gene in marker-assisted backcrossing.Communicated by G. WenzelM. Frisch and M. Quint contributed equally to this article.     

Multilocus Analysis for Gene-Centromere Mapping Using First Polar Bodies and Secondary Oocytes

Polar body and oocyte typing is a new technique for gene-centromere mapping and for generating female linkage maps. A maximum likelihood approach is presented for ordering multiple markers relative to the centromere and for estimating recombination frequencies between markers and between the centromere and marker loci. Three marker-centromere orders are possible for each pair of markers: two orders when the centromere flanks the two markers and one order when the centromere is flanked by the two markers. For each possible order, the likelihood was expressed as a function of recombination frequencies for two adjacent intervals. LOD score for recombination frequency between markers or between the centromere and a marker locus was derived based on the likelihood for each gene-centromere order. The methods developed herein provide a general solution to the problem of multilocus genecentromere mapping that involves all theoretical crossover possibilities, including four-strand double crossovers.     

Twenty-seven protein polymorphisms by two-dimensional electrophoresis of serum, erythrocytes, and fibroblasts in two pedigrees

Twenty-seven independent polymorphic loci were detected by two-dimensional electrophoresis (2DE) of serum, erythrocytes, and fibroblasts in two large families and analyzed for linkage to classical genetic markers. We detected seven serum, four erythrocyte, and 17 fibroblast protein loci that exhibited charge variation in these two families and in a sample of unrelated individuals. The genetic basis of protein variants was confirmed by quantitative gene-dosage dependence and by conformance to Mendelian transmission in the two families, except for four rare variants for which transmission analysis was not possible. Linkage analysis demonstrated that each of the variants represent products of independent loci, with the exception of erythrocyte locus (RBC4), which we also detected in fibroblasts (NC27). Two allozyme polymorphisms, glyoxalase-1 (GLO1) and phosphoglucomutase-3 (PGM3) were specifically identified here based on genotypic concordance and molecular mass. Unknown fibroblast protein (NC22) may be linked to apolipoprotein E (lod score = 2.8 at theta m = theta f = 0), while a serum protein locus (SER1) may be linked to alpha-haptoglobin (lod score = 2.54 at theta m = .20, theta f = .01). Six of seven polymorphic serum loci were previously located on two-dimensional gels: alpha-1 antitrypsin (PI), Gc-globulin (GC), alpha-2 HS glycoprotein (HSGA), alpha-haptoglobin (HP), and two apolipoproteins (APOE and APOA4). Six of 17 polymorphisms detected in fibroblasts were positionally identical to polymorphic loci seen in lymphocytes. These studies indicate a minimum level of average protein charge heterozygosity of approximately 2.2% for the most predominant human cellular proteins and of 5.6% for the most predominant proteins of serum.     

Two-locus models of disease: comparison of likelihood and nonparametric linkage methods.

The power to detect linkage for likelihood and nonparametric (Haseman-Elston, affected-sib-pair, and affected-pedigree-member) methods is compared for the case of a common, dichotomous trait resulting from the segregation of two loci. Pedigree data for several two-locus epistatic and heterogeneity models have been simulated, with one of the loci linked to a marker locus. Replicate samples of 20 three-generation pedigrees (16 individuals/pedigree) were simulated and then ascertained for having at least 6 affected individuals. The power of linkage detection calculated under the correct two-locus model is only slightly higher than that under a single locus model with reduced penetrance. As expected, the nonparametric linkage methods have somewhat lower power than does the lod-score method, the difference depending on the mode of transmission of the linked locus. Thus, for many pedigree linkage studies, the lod-score method will have the best power. However, this conclusion depends on how many times the lod score will be calculated for a given marker. The Haseman-Elston method would likely be preferable to calculating lod scores under a large number of genetic models (i.e., varying both the mode of transmission and the penetrances), since such an analysis requires an increase in the critical value of the lod criterion. The power of the affected-pedigree-member method is lower than the other methods, which can be shown to be largely due to the fact that marker genotypes for unaffected individuals are not used.