Possible heterogeneity in the phosphoglycolate phosphatase (PGP)-haptoglobin alpha (HPA) linkage.

Previous investigators have reported loose linkage in both sexes for phosphoglycolate phosphatase (PGP) and haptoglobin alpha (HPA). We present results of linkage studies between PGP and HPA in two data sets, one from Houston and the other an update of an earlier report from Los Angeles. Using quadratic interpolation to estimate the male (theta m) and female (theta f) recombination values from bivariate lod tables, we found for the Houston data that theta m = 0.43 and theta f = 0.03 at the maximum lod score of z = 2.23. For the Los Angeles series, we found that theta m = 0.31, theta f = 0.48, and z = 0.27. We invoke heterogeneity in the recombination value in different families as an explanation of our findings. We also recommend that bivariate lod tables should always be generated, even though not reported. This is because the usual assumption of theta m = theta f (and, rarely, theta f = 1.8 theta f) under which lod scores are computed may be invalid in many cases.     

Sensitivity of lod scores to changes in diagnostic status.

This paper investigates effects on lod scores when one individual in a data set changes diagnostic or recombinant status. First we examine the situation in which a single offspring in a nuclear family changes status. The nuclear-family situation, in addition to being of interest in its own right, also has general theoretical importance, since nuclear families are "transparent"; that is, one can track genetic events more precisely in nuclear families than in complex pedigrees. We demonstrate that in nuclear families log10 [(1-theta)/theta] gives an upper limit on the impact that a single offspring's change in status can have on the lod score at that recombination fraction (theta). These limits hold for a fully penetrant dominant condition and fully informative marker, in either phase-known or phase-unknown matings. Moreover, log10 [(1-theta)/theta] (where theta denotes the value of theta at which Zmax occurs) gives an upper limit on the impact of a single offspring's status change on the maximum lod score (Zmax). In extended pedigrees, in contrast to nuclear families, no comparable limit can be set on the impact of a single individual on the lod score. Complex pedigrees are subject to both stabilizing and destabilizing influences, and these are described. Finally, we describe a "sensitivity analysis," in which, after all linkage analysis is completed, every informative individual in the data set is changed, one at a time, to see the effect which each separate change has on the lod scores. The procedure includes identifying "critical individuals," i.e., those who would have the greatest impact on the lod scores, should their diagnostic status in fact change. To illustrate use of the sensitivity analysis, we apply it to the large bipolar pedigree reported by Egeland et al. and Kelsoe et al. We show that the changes in lod scores observed there, on the order of 1.1-1.2 per person, are not unusual. We recommend that investigators include a sensitivity analysis as a standard part of reporting the results of a linkage analysis.     

Recombination rates and gene order for some serum α-protease inhibitors and immunoglobulin heavy-chain allotypes in pigs

Linkage analysis between the genes coding for immunoglobulin heavy-chain allotypes and variants of some serum alpha-protease inhibitors produced lod scores above the significance limit of 3. The maximum likelihood estimate of the recombination fraction (theta) ranged from 0.15 to 0.20. Since this is the second report on this linkage group in pigs, the linkage is confirmed. Data from appropriate matings are consistent with a gene order of Pi1-Po1A-(Po1B)-Pi2-Igh1.     

Linkage analysis of the apolipoprotein C2 gene and myotonic dystrophy on human chromosome 19 reveals linkage disequilibrium in a French-Canadian population.

The gene for human apolipoprotein C2 (APOC2), situated on the proximal long arm of chromosome 19, is closely linked to the gene for the most common form of adult muscular dystrophy, myotonic dystrophy (DM). Six APOC2 RFLPs (TaqI, BglI, BanI, BamHI, NcoI, and AvaII) have been identified to date. We have conducted a comprehensive DM linkage study utilizing all six RFLPs and involving 50 families and 372 individuals. The most informative RFLPs are, in descending order, NcoI (lod = 6.64, theta = 0.05), BglI (lod = 6.12, theta = 0.05), AvaII (lod = 6.02, theta = 0.03), BanI (lod = 5.76, theta = 0.04), TaqI (lod = 4.29, theta = 0.06), and BamHI (lod = 1.75, theta = 0.01). A substantial increase in the lod scores over those seen with the individual RFLPs was obtained when the linkage of the entire APOC2 haplotype (composed of the six RFLPs) was studied (lod = 17.87, theta = 0.04). We have observed significant inter-APOC2 RFLP linkage disequilibrium. Consequently, the three most informative RFLPs have been found to be BanI, TaqI, and either BglI, AvaII, or NcoI polymorphisms. We also demonstrate linkage disequilibrium between DM and APOC2 in our French-Canadian population (standardized disequilibrium constant phi = .22, chi 2 = 5.12, df = 1, P less than 0.04). This represents the first evidence of linkage disequilibrium between APOC2 and the DM locus.     

HLODs, trait models, and ascertainment: implications of admixture for parameter estimation and linkage detection

Maximizing the homogeneity lod is known to be an appropriate procedure for estimating parameters of the trait model in an approximately 'ascertainment assumption free' (AAF) manner. We have investigated whether this same property also holds for the heterogeneity lod (HLOD). We show that, when the genetic models at linked and unlinked loci differ, HLODs are not AAF, and maximizing the HLOD yields parameter estimates that are for all practical purposes meaningless; indeed, the admixture parameter alpha does not even measure the proportion of linked families within the sample, as is commonly supposed. In spite of this, our results confirm a large body of evidence supporting the use of HLODs as robust tools for linkage detection, and suggest further that maximizing the HLOD over both alpha and parameters of the trait model can improve accuracy in estimation of the recombination fraction theta;. These findings have important implications for the optimal handling of nuisance parameters in linkage analysis, particularly when evaluating the evidence for or against linkage based on multiple independent heterogeneous sets of data.     

Genetic analysis of multiply-affected families of insulin-dependent diabetes mellitus (IDDM) probands

The present study combines segregation and linkage information on 30 families ascertained through a proband and a first degree relative affected with insulin-dependent diabetes mellitus (IDDM). An autosomal dominant model with incomplete penetrance was much more likely to fit the family data than a recessive model, whether or not linkage to HLA was assumed. The lod scores for linkage to HLA were 2.46 at theta M = theta F = 0.00 for dominant and 1.45 at theta M = theta F = 0.22 for a recessive model. The results are discussed in light of heterogeneity in likelihood and lod scores when the families are grouped by familial types, which indicate that the increase in likelihood of a dominant hypothesis can be attributed to the parent-child families and not the sib-sib families.     

Using lod scores to detect sex differences in male-female recombination fractions

Human recombination fraction (RF) can differ between males and females, but investigators do not always know which disease genes are located in genomic areas of large RF sex differences. Knowledge of RF sex differences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprinting. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex differences and answered the following questions, in both phase-known and phase-unknown matings: (1) How large a sample size is needed to detect a RF sex difference? (2) What are "optimal" proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally informative matings lead to ascertainment bias? Our results were as follows: (1) We calculated expected lod scores (ELODs) under two different conditions: "unconstrained," allowing sex-specific RF parameters (theta(female), theta(male)); and "constrained," requiring theta(female) = theta(male). We then examined the DeltaELOD (identical with difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant DeltaELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statistical significance. We give general sample size guidelines for detecting RF differences in informative phase-known and phase-unknown matings. (2) We defined p as the proportion of paternally informative matings in the dataset; and the optimal proportion p(circ) as that value of p that maximizes DeltaELOD. We determined that, surprisingly, p(circ) does not necessarily equal (1/2), although it does fall between approximately 0.4 and 0.6 in most situations. (3) We showed that if p in a sample deviates from its optimal value, no bias is introduced (asymptotically) to the maximum likelihood estimates of theta(female) and theta(male), even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the proportions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differences in recombination fraction.     

Heterogeneity in X-linked recessive Charcot-Marie-Tooth neuropathy.

Three families presenting with X-linked recessive Charcot-Marie-Tooth neuropathies (CMT) were studied both clinically and genetically. The disease phenotype in family 1 was typical of CMT type 1, except for an infantile onset; two of five affected individuals were mentally retarded, and obligate-carrier females were unaffected. Families 2 and 3 showed distal atrophy with weakness, juvenile onset, and normal intelligence. Motor-nerve conduction velocities were significantly slowed, and electromyography data were consistent with denervation in affected CMT males in all three families. Thirty X-linked RFLPs were tested for linkage studies against the CMT disease loci. Family 1 showed tight linkage (recombination fraction [theta] = 0) to Xp22.2 markers DXS16, DXS143, and DXS43, with peak lod scores of 1.75, 1.78, and 2.04, respectively. A maximum lod score of 3.48 at DXS16 (theta = 0) was obtained by multipoint linkage analysis of the map DXS143-DXS16-DXS43. In families 2 and 3 there was suggestion of tight linkage (theta = 0) to Xq26 markers DXS86, DXS144, and DXS105, with peak lod scores of 2.29, 1.33, and 2.32, respectively. The combined maximum multipoint lod score of 1.81 at DXS144 (theta = 0) for these two families occurred in the map DXS10-DXS144-DXS51-DXS105-DXS15-DXS52++ +. A joint homogeneity analysis including both regions (Xp22.2 and Xq26-28) provided evidence against homogeneity (chi 2 = 9.12, P less than .005). No linkage to Xp11.12-q22 markers was observed, as was reported for X-linked dominant CMT and the Cowchock CMT variant. Also, the chromosomes 1 and 17 CMT loci were excluded by pairwise linkage analysis in all three families.     

Multipoint linkage analysis in Menkes disease.

Linkage analyses were performed in 11 families with X-linked Menkes disease. In each family more than one affected patient had been diagnosed. Forty informative meioses were tested using 11 polymorphic DNA markers. From two-point linkage analyses high lod scores are seen for DXS146 (pTAK-8; maximal lod score 3.16 at recombination fraction [theta] = .0), for DXS1 (p-8; maximal lod score 3.44 at theta = .0), for PGK1 (maximal lod score 2.48 at theta = .0), and for DXS3 (p19-2; maximal lod score 2.90 at theta = .0). This indicates linkage to the pericentromeric region. Multilocus linkage analyses of the same data revealed a peak for the location score between DXS146(pTAK-8) and DXYS1X(pDP34). The most likely location is between DXS159 (cpX289) and DXYS1X(pDP34). Odds for this location relative to the second-best-supported region, between DXS146(pTAK-8) and DXS159 (cpX289), are better than 74:1. Visualization of individual recombinant X chromosomes in two of the Menkes families showed the Menkes locus to be situated between DXS159(cpX289) and DXS94(pXG-12). Combination of the present results with the reported absence of Menkes symptoms in male patients with deletions in Xq21 leads to the conclusion that the Menkes locus is proximal to DXSY1X(pDP34) and located in the region Xq12 to Xq13.3.     

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.     

Alström syndrome: further evidence for linkage to human chromosome 2p13

Alstr?m syndrome is a rare autosomal recessive disorder characterized by retinal degeneration, sensorineural hearing loss, early-onset obesity, and non-insulin-dependent diabetes mellitus. The gene for Alstr?m syndrome (ALMS1) has been previously localized to human chromosome 2p13 by homozygosity mapping in two distinct isolated populations - French Acadian and North African. Pair-wise analyses resulted in maximum lod (logarithm of the odds ratio) scores of 3.84 and 2.9, respectively. To confirm these findings, a large linkage study was performed in twelve additional families segregating for Alstr?m syndrome. A maximum two-point lod score of 7.13 (theta = 0.00) for marker D2S2110 and a maximum cumulative multipoint lod score of 9.16 for marker D2S2110 were observed, further supporting linkage to chromosome 2p13. No evidence of genetic heterogeneity was observed in these families. Meiotic recombination events have localized the critical region containing ALMS1 to a 6.1-cM interval flanked by markers D2S327 and D2S286. A fine resolution radiation hybrid map of 31 genes and markers has been constructed.     

Linkage mapping reveals sex-dimorphic map distances in a passerine bird

Linkage maps are lacking for many highly influential model organisms in evolutionary research, including all passerine birds. Consequently, their full potential as research models is severely hampered. Here, we provide a partial linkage map and give novel estimates of sex-specific recombination rates in a passerine bird, the great reed warbler (Acrocephalus arundinaceus). Linkage analysis of genotypic data at 51 autosomal microsatellites and seven markers on the Z-chromosome (one of the sex chromosomes) from an extended pedigree resulted in 12 linkage groups with 2-8 loci. A striking feature of the map was the pronounced sex-dimorphism: males had a substantially lower recombination rate than females, which resulted in a suppressed autosomal map in males (sum of linkage groups: 110.2 cM) compared to females (237.2 cM; female/male map ratio: 2.15). The sex-specific recombination rates will facilitate the building of a denser linkage map and cast light on hypotheses about sex-specific recombination rates.     

Genetic heterogeneity in X-linked amelogenesis imperfecta.

The AMELX gene located at Xp22.1-p22.3 encodes for the enamel protein amelogenin and has been implicated as the gene responsible for the inherited dental abnormality X-linked amelogenesis imperfecta (XAI). Three families with XAI have been investigated using polymorphic DNA markers flanking the position of AMELX. Using two-point linkage analysis, linkage was established between XAI and several of these markers in two families, with a combined lod score of 6.05 for DXS16 at theta = 0.04. This supports the involvement of AMELX, located close to DXS16, in the XAI disease process (AIH1) in those families. Using multipoint linkage analysis, the combined maximum lod score for these two families was 7.30 for a location of AIH1 at 2 cM distal to DXS16. The support interval around this location extended about 8 cM proximal to DXS92, and the AIH1 location could not be precisely defined by multipoint mapping. Study of recombination events indicated that AIH1 lies in the interval between DXS143 and DXS85. There was significant evidence against linkage to this region in the third family, indicating locus heterogeneity in XAI. Further analysis with markers on the long arm of the X chromosome showed evidence of linkage to DXS144E and F9 with no recombination with either of these markers. Two-point analysis gave a peak lod score at DXS144E with a maximum lod score of 2.83 at theta = 0, with a peak lod score in multipoint linkage analysis of 2.84 at theta = 0. The support interval extended 9 cM proximal to DXS144E and 14 cM distal to F9.(ABSTRACT TRUNCATED AT 250 WORDS)     

The problem of ascertainment for linkage analysis.

It is generally believed that ascertainment corrections are unnecessary in linkage analysis, provided individuals are selected for study solely on the basis of trait phenotype and not on the basis of marker genotype. The theoretical rationale for this is that standard linkage analytic methods involve conditioning likelihoods on all the trait data, which may be viewed as an application of the ascertainment assumption-free (AAF) method of Ewens and Shute. In this paper, we show that when the observed pedigree structure depends on which relatives within a pedigree happen to have been the probands (proband-dependent, or PD, sampling) conditioning on all the trait data is not a valid application of the AAF method and will result in asymptotically biased estimates of genetic parameters (except under single ascertainment). Furthermore, this result holds even if the recombination fraction R is the only parameter of interest. Since the lod score is proportional to the likelihood of the marker data conditional on all the trait data, this means that when data are obtained under PD sampling the lod score will yield asymptotically biased estimates of R, and that so-called mod scores (i.e., lod scores maximized over both R and parameters theta of the trait distribution) will yield asymptotically biased estimates of R and theta. Furthermore, the problem appears to be intractable, in the sense that it is not possible to formulate the correct likelihood conditional on observed pedigree structure. In this paper we do not investigate the numerical magnitude of the bias, which may be small in many situations. On the other hand, virtually all linkage data sets are collected under PD sampling. Thus, the existence of this bias will be the rule rather than the exception in the usual applications.     

No evidence for linkage between the loci for coagulation factor XIII-A and HLA

Summary The linkage analysis between the locus for coagulation factor XIII-A (F13A) and HLA region genes (HLA-A,-C,-B) was performed. In males, the maximum of lod scores between F13A and HLA was 0.33 at =0.30, and in females lod scores were negative at all values of . The results provided no evidence for close linkage between F13A and HLA genes.     

Linkage of cystic fibrosis locus and polymorphic DNA markers in 14 families

Linkage relationships between the cystic fibrosis (CF) locus and three polymorphic DNA markers were examined in 14 families, five of which were of Hispanic origin. Tight linkage was found between the CF locus and MET (maximum lod score = 7.16 at theta = .001), and between CF and pJ3.11 (maximum lod score = 3.87 at theta = .001). We observed two recombinations between CF and collagen, yielding a maximum lod score of 0.359 at theta = .125, and one recombination in the cluster CF-MET-pJ3.11. Analysis by the seriation method indicates the order COL-pJ3.11-CF-MET.     

Autosomal dominant macrothrombocytopenia with leukocyte inclusions (May-Hegglin anomaly) is linked to chromosome 22q12-13

Macrothrombocytopenia with leukocyte inclusions (May-Hegglin anomaly) is a rare autosomal dominant disorder characterized by thrombocytopenia, giant platelets, and D?hle body-like inclusions in leukocytes. To determine the genetic basis of this disorder, we performed a genome-wide screen for linkage in three families with May-Hegglin anomaly. For the pooled analysis of the three families, three markers on chromosome 22 had two-point logarithm-of-difference (lod) scores greater than 3, with a maximum lod score of 3.91 at a recombination fraction (theta) of 0.076 for marker D22S683. Within the largest family (MHA-1), the maximum lod score was 5.36 at theta=0 at marker D22S445. Fine mapping of recombination events using eight adjacent markers indicated that the minimal disease region of family MHA-1 alone is in the approximately 26 cM region from D22S683 to the telomere. The maximum lod score for the three families combined was 5.84 at theta=0 for marker IL2RB. With the assumption of locus homogeneity, haplotype analysis of family MHA-4 indicated the disease region is centromeric to marker D22S1045. These data best support a minimal disease region from D22S683 to D22S1045, a span of about 1 Mb of DNA that contains 17 known genes and 4 predicted genes. Further analysis of this region will identify the genetic basis of May-Hegglin anomaly, facilitating subsequent characterization of the biochemical role of the disease gene in platelet formation.     

Genetic linkage analysis of prostate cancer families to Xq27-28

OBJECTIVES: A recent linkage analysis of 360 families at high risk for prostate cancer identified the q27-28 region on chromosome X as the potential location of a gene involved in prostate cancer susceptibility. Here we report on linkage analysis at this putative HPCX locus in an independent set of 186 prostate cancer families participating in the Prostate Cancer Genetic Research Study (PROGRESS). METHODS: DNA samples from these families were genotyped at 8 polymorphic markers spanning 14.3 cM of the HPCX region. RESULTS: Two-point parametric analysis of the total data set resulted in positive lod scores at only two markers, DXS984 and DXS1193, with scores of 0.628 at a recombination fraction (theta) of 0.36 and 0.012 at theta = 0.48, respectively. The stratification of pedigrees according to the assumed mode of transmission increased the evidence of linkage at DXS984 in 81 families with no evidence of male-to-male transmission (lod = 1.062 at theta = 0.28). CONCLUSIONS: Although this analysis did not show statistically significant evidence for the linkage of prostate cancer susceptibility to Xq27-28, the results are consistent with a small percentage of families being linked to this region. The analysis further highlights difficulties in replicating linkage results in an etiologically heterogeneous, complexly inherited disease.     

Replication of genetic linkage by follow-up of previously studied pedigrees.

Independent replication of linkage in previously studied pedigrees is desirable when genetic heterogeneity is suspected or when the illness is very rare. When the likelihood of the new data in this type of replication study is computed as conditional on the previously reported linkage results, it can be considered independent. We describe a simulation method using the SLINK program in which the initial data are fixed and newly genotyped individuals are simulated under theta = .01 and theta = .50. These give appropriate lod score criteria for rejection and acceptance of linkage in the follow-up study, which take into account the original marker genotypes in the data. An estimate of the power to detect linkage in the follow-up data is also generated.     

Genetic linkage heterogeneity in the fragile X syndrome

Summary Genetic linkage between a factor IX DNA restriction fragment length polymorphism (RFLP) and the fragile X chromosome marker was analyzed in eight fragile X pedigrees and compared to eight previously reported pedigrees. A large pedigree with apparently full penetrance in all male members showed a high frequency of recombination. A lod score of-7.39 at =0 and a maximum score of 0.26 at =0.32 were calculated. A second large pedigree with a non-penetrant male showed tight linkage with a maximum lod score of 3.13 at =0, a result similar to one large pedigree with a nonpenetrant male previously reported. The differences in lod scores seen in these large pedigrees suggested there was genetic heterogeneity in linkage between families which appeared to relate to the presence of nonpenetrant males. The combined lod score for the three pedigrees with nonpenetrant males was 6.84 at 0=0. For the 13 other pedigrees without nonpenetrant males the combined lod score was-21.81 at =0, with a peak of 0.98 at =0.28. When lod scores from all 16 families were combined, the value was-15.14 at =0 and the overall maximum was 5.13 at =0.17.To determine whether genetic heterogeneity was present, three statistical tests for heterogeneity were employed. First, a predivided-sample test was used. The 16 pedigrees were divided into two classes, NP and P, based upon whether or not any nonpenetrant males were detected in the pedigree. This test gave evidence for significant genetic heterogencity whether the three large pedigrees with seven or more informative males (P<0.005), the eight pedigrees with three informative males (P<0.001), or all 16 pedigrees (P<0.001) were included in the analysis. Second, Morton's large sample test was employed. Significant heterogeneity was present when the analysis was restricted to the three large pedigrees (P<0.025), or to the eight pedigrees with informative males (P<0.05) but not when smaller, less informative pedigrees were also included. Third, an admixture test for heterogeneity was employed which tests for linkage versus no linkage. A trend toward significance was seen (0.05<P<0.10) which increased when the analysis was restricted to the larger, more informative pedigrees.The pedigrees where nonpenetrant males are detected appear to constitute one class (NP) where tight linkage to factor IX is predicted. The pedigrees where full penetrance is present appear to consitute a second class (P) where loose linkage to factor IX is predicted. Either the chromosomal location of the mutation or suppression of recombination to nearby genes may be different in the two classes of pedigrees. In the NP class of fra X pedigrees, information from DNA analysis should be useful for carrier detection, prenatal diagnosis, and genetic counseling.