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Originally published In Press as doi:10.1194/jlr.M400136-JLR200 on August 16, 2004

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Journal of Lipid Research, Vol. 45, 2063-2070, November 2004
Copyright © 2004 by American Society for Biochemistry and Molecular Biology

Epistatic interaction between two nonstructural loci on chromosomes 7 and 3 influences hepatic lipase activity in BSB mice

Nengjun Yi*,{dagger}, Sally Chiu§, David B. Allison*,{dagger}, Janis S. Fisler** and Craig H. Warden1,§,{dagger}{dagger}

* Department of Biostatistics, Section on Statistical Genetics, University of Alabama, Birmingham, AL 35294
{dagger} Clinical Nutrition Research Center, University of Alabama, Birmingham, AL 35294
§ Rowe Program in Genetics, University of California, Davis, CA 95616
** Department of Nutrition, University of California, Davis, CA 95616
{dagger}{dagger} Department of Pediatrics and Section of Neurobiology, Physiology, and Behavior, University of California, Davis, CA 95616

Published, JLR Papers in Press, August 16, 2004. DOI 10.1194/jlr.M400136-JLR200

1 To whom correspondence should be addressed. e-mail: chwarden{at}ucdavis.edu


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
BSB mice exhibit a wide range of obesity despite being produced by a backcross of lean C57BL/6J (B) x lean Mus spretus (SPRET/Pt) F1 animals x B. Previous linkage studies identified a quantitative trait locus (QTL) on mouse chromosome 7 with coincident peaks for hepatic lipase activity, obesity, and plasma cholesterol. However, these mice were not analyzed for gene x gene epistasis. Hepatic lipase activity is correlated with obesity and plasma cholesterol levels. In this study, we identified QTLs for plasma hepatic lipase activity with three statistical mapping methods: maximum likelihood interval mapping, Bayesian nonepistatic mapping, and Bayesian epistatic mapping. Bayesian epistatic mapping detected not only the QTL on chromosome 7 but also an additional QTL on chromosome 3, which has a weak main effect but a strong interaction with chromosome 7. SPRET/Pt alleles of the QTL on each chromosome promote hepatic lipase activity.

The proportion of phenotypic variance explained by the epistatic effect is higher than that explained by the main effect of the QTL on chromosome 7.

Abbreviations: cM, centimorgan; HPD, high posterior density; MCMC, Markov chain Monte Carlo; QTL, quantitative trait locus

Supplementary key words gene x gene • mouse • obesity • hepatic lipase • Bayesian • quantitative trait locus


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Hepatic lipase mediates the hydrolysis of triglycerides and phospholipids from large lipoprotein particles, with high hepatic lipase activity resulting in small, dense particles and an atherogenic lipoprotein profile (1–5). Hepatic lipase activity is highly correlated with obesity, particularly abdominal fat mass (6–10), but the mechanism for this effect remains unclear, even though recent studies indicate that the absence of hepatic lipase in knockout mice directly influences obesity (11).

Hepatic lipase is produced in the liver but is also found in the adrenals and circulates in mouse plasma. We performed in vitro assays for hepatic lipase activity from plasma that may be more indicative of hepatic lipase mass than in vivo activity. These assays were used to identify a quantitative trait locus (QTL) where hepatic lipase activity was coincident with QTLs for plasma cholesterol and fat mass on mouse chromosome 7 (12, 13). However, the underlying genes influencing the QTL remain unknown because the QTL does not include the hepatic lipase (Lipc) structural gene located on mouse chromosome 9. Therefore, we applied epistatic analysis to aid in our discovery of gene networks and pathways that may influence hepatic lipase activity and perhaps also plasma cholesterol and obesity.

A mouse model of spontaneous complex obesity was produced by a cross of C57BL/6J x Mus spretus, strains that are both lean on a low-fat diet (14). The lean F1 animals were then backcrossed to C57BL/6J mice, producing BSB mice. Each BSB mouse is genetically related but distinct from every other one. BSB mice exhibit a wide range of obesity and obesity-associated traits (14). Using the traditional interval QTL mapping method, previous studies identified only one QTL on chromosome 7 influencing plasma hepatic lipase activity (12, 13). The fact that sibling mice show a high degree of fat variation, whereas the parental strains do not, suggests that there are multiple genes, and possibly gene interactions, causing the phenotypic differences. However, statistical methods for mapping multiple and epistatic genes were not previously used to analyze these data.

Discrete combinations of alleles of genes, or gene products, may interact with each other in markedly different ways to influence complex diseases (15, 16). These epistatic interactions likely influence many complex diseases, with obesity as a clear example (17–19). Evidence that epistasis is common in obesity has been derived from statistical analyses (20), but it is also apparent from the almost universal observation that obesity phenotypes of knockout and spontaneous mutant mice are dependent on the background mouse strain on which the mutations are placed (21–24). That is, different alleles of genes other than the knockout or mutant gene present in different mouse strains interact with (are epistatic with) the knockout or mutation to produce the phenotype.

A practical implication of epistasis for experimental work is that some QTLs may have no independent effects but may significantly influence the trait if combined with a specific allele of another gene. Thus, epistatic analysis may aid in the identification of underlying loci. Potential candidate genes for epistatically interacting loci that accelerate mammary tumor formation were identified by a combined bioinformatics and genomics strategy (25). A search of the literature identified molecular pathways containing genes from candidate intervals. Among the genes identified were the cell cycle-associated genes Cdc25A and c-Myc, both of which have been implicated in breast cancer. Sequence analysis identified functional polymorphisms of both genes (25). Thus, identification of epistasis may speed the discovery of underlying genes.

The most widely used statistical methods for QTL mapping of experimental crosses were developed under single-QTL models, in which only one QTL is fitted to the model and the marginal effect is detected (26). To evaluate epistatic interactions, the marginal effects and epistatic effects must be modeled simultaneously. Recently, Yi and Xu (27) and Yi, Xu, and Allison (28) proposed a Bayesian model and variable selection for identifying multiple QTLs with complex epistatic patterns in experimental designs. In the present study, we used this Bayesian method to map epistatic QTLs for hepatic lipase activity in the BSB mouse model. The aim is to unravel the genetic architecture of hepatic lipase activity by jointly estimating the number of QTLs, their genomic positions, main effects, and epistatic effects. We also compared our Bayesian epistatic mapping with traditional interval mapping and Bayesian nonepistatic analysis.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Genetic cross and data acquisition
The experimental design and data acquisition methods were described previously in detail (12, 13). Briefly, inbred Mus musculus domesticus (C57BL/6J) female mice were crossed with noninbred Mus spretus (SPRET/Pt) male mice to produce F1 progeny. These breeding pairs were obtained from The Jackson Laboratory (Bar Harbor, ME) and Dr. Michael Potter (National Institutes of Health, Bethesda, MD), respectively. A backcross was performed by crossing F1 females with C57BL/6J males, producing 203 progeny. For any locus, we here denote the heterozygous genotype as BS and the homozygous genotype as BB.

At ~5 months of age, BSB mice were fasted overnight and bled from the retro-orbital plexus under isoflurane anesthesia ~3 h after the beginning of the light cycle. Blood was collected in separator tubes, placed on ice, and centrifuged to prepare plasma. Plasma hepatic lipase activity was measured as previously described (13). Kidneys, liver, brain, and gastrocnemius muscle were dissected and frozen for DNA isolation and other analyses reported elsewhere.

Genomic DNA was extracted from mouse kidney (QIAamp Blood and Tissue kit; Qiagen, Inc., Valencia, CA). A total of 148 simple sequence length polymorphism markers polymorphic between C57BL/6J and SPRET/Pt and located on every chromosome were genotyped as previously described (12, 13). The marker linkage map is estimated to cover >90% of the genome with an average spacing of ~10 centimorgan (cM) between markers. Because we detected evidence of QTLs for hepatic lipase activity only on chromosomes 7 and 3 in this study, here we show only the marker linkage maps for these two chromosomes (Table 1).


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  		TABLE 1. Markers on chromosomes 3 and 7 and their locations

 
Statistical analyses
To detect QTLs for hepatic lipase activity, we analyzed genome-wide scans with three statistical mapping methods: 1) maximum likelihood interval mapping; 2) Bayesian analysis not incorporating epistatic effects; and 3) Bayesian analysis incorporating epistatic effects. The interval-mapping method is built on a single-QTL model in which one QTL is fitted to the model at a time and only marginal (main) QTL effects are detected (26). This method evaluates the association between the trait values and the expected genotype of a hypothetical QTL at multiple analysis points between each pair of adjacent marker loci. The analysis point that yields the most significant association may be taken as the location of a putative QTL.

Two multiple QTL models, a nonepistatic model and an epistatic model, were used to analyze the data. The multiple QTL models fit all putative QTLs simultaneously and jointly estimate the number, genomic positions, and genetic effects of the QTLs (27, 28). Under the nonepistatic model, the epistatic effects are not included in the model and thus the multiple putative QTLs are chosen based only on their significant main effects. Assuming that hepatic lipase activity is affected by l QTL, the nonepistatic model can be expressed as follows:

where n is the number of animals, yi is the observed phenotypic value of the ith mouse, µ is the overall mean, and xiq is the indicator variable denoting the genotype of putative QTL q for animal i and is defined by 0.5 or –0.5 for the two genotypes, BS and BB. aq represents the main effect of putative QTL q, quantifying the difference between genotypic values of BS and BB. ei is the residual error assumed to follow N. Under the epistatic model, the interaction effects among the putative QTLs are included in the model and thus the multiple putative QTL are chosen based not only on their main effects but also on their epistatic effects. The epistatic model can be expressed as follows:

where bq1q2 is the epistatic effect between QTLs q1 and q2, {gamma}q is a binary indicator variable for the main effect of putative QTL q, taking the value 1 if QTL q has a main effect and 0 otherwise, and {gamma}q1q2 is a binary indicator variable for the epistatic effect between QTLs q1 and q2, taking the value 1 if QTLs q1 and q2 interact and 0 otherwise. Hereafter, we call these binary indicator variables effect indicators. Each QTL included in model 2 has at least one nonzero effect indicator.

The multiple QTL models were analyzed using Bayesian methods. In a Bayesian framework, the QTL mapping problem is not formulated in a sequential hypothesis-testing framework, as in traditional interval mapping. The Bayesian statistical inference is based on the joint posterior distribution of all unknowns in a model given the observed data. The observed data include the phenotypic values and the marker genotypes. The unknowns include the number of QTLs, the genomic locations of the QTLs, effect indicators, main effects, epistatic effects, overall mean, residual variance, genotypes of missing markers, and genotypic indicators of putative QTLs. Calculation of the joint posterior distributions is analytically intractable, and thus a Markov chain Monte Carlo (MCMC) approach is used to obtain posterior samples from the joint posterior distribution. We used the Bayesian method and MCMC algorithm developed by Yi , Xu, and Allison (28) to generate posterior samples from the joint posterior distribution and then estimate the number, locations, main effects, and epistatic effects of QTLs simultaneously using the posterior samples. Briefly, the MCMC algorithm consisted of the following steps: a) update the model parameters (main effects, epistatic effects, overall mean, and residual variance); b) update the genotypic indicators of QTLs and the genotypes of missing markers; c) update the locations of the QTLs; d) update the effect indicator by adding or deleting a main or epistatic effect; and e) update the number of QTLs. Two different steps were used to update the number of QTLs: 1) add a QTL with main effects or epistatic effects between existing QTLs or delete an existing QTL; and 2) add two new QTLs with only epistatic effects between themselves or delete two existing QTLs. The detailed algorithms for each of these steps were described by Yi and Xu (27) and Yi , Xu, and Allison (28).

The phenotypic value was standardized using (yi – )/s where is the mean and s is the standard deviation of y. The standardized record was subjected to the Bayesian analysis. For both nonepistatic and epistatic analyses, the MCMC was started with no QTLs in the model. The prior for the overall mean was N(0, 10). The residual variance took Uniform(0, 1), where the upper bound is the variance of the standardized record. The priors for all main and epistatic effects were chosen to be N(0, 1). The prior distribution for the number of QTLs was taken as Uniform(0, 10). The prior for each effect indicator was taken as uniform at two states of 0 and 1. The tuning parameter of proposals in the random-walk Metropolis-Hastings algorithm for updating QTL positions was chosen to be 2 cM. The prior of the QTL position was uniform over the genome region. We also tried to take Poisson distribution with different means as the prior for the number of QTLs and several different prior variances for genetic effects, and the results were essentially the same. Therefore, we report only the results for the prior specifications described above.

Bayesian QTL analyses were executed with a C program (29). In each analysis, the MCMC sampler was run for 4 x 105 cycles after discarding the first 2,000 cycles for the burn-in period. The chain was thinned (one iteration was saved in every 20 cycles) to reduce serial correlation in the stored samples so that the total number of samples kept in the post-Bayesian analysis was 2 x 104. The stored samples are called posterior samples.

The posterior samples were used to obtain inferences about the parameters of interest. The posterior probability distribution of the number of QTLs, p(l = x|y,M) (x = 0, 1, 2 ... ), was obtained by counting the number of samples in which the number of QTLs is l, divided by the total of number of samples. The posterior probability that a chromosomal region contains at least one QTL was calculated as the number of samples with at least one QTL in this region over the total number of samples. QTL locations were estimated using the posterior QTL intensity function (30). The posterior QTL intensity was depicted by plotting the frequency of hits by the QTL in a short interval against the genome location of the interval. The regions frequently hit by the QTL are candidate locations of the QTL. The location-wise estimates for main effect and proportion of variance explained by the main effect were obtained by calculating the mean of the estimates for these parameters in each short interval. The main effect and proportion of variance explained by the main effect at a chromosomal region were obtained similarly. Inference for the epistatic effects and the proportion of phenotypic variance explained by each epistatic effect were obtained conditioned on the estimated loci falling into the corresponding regions. The posterior probability that each epistatic effect is included in the model was calculated as the number of samples containing this epistatic effect over the total number of samples.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Maximum likelihood interval mapping
In the maximum likelihood analysis, the model only includes a single QTL. So the entire genome was searched from one position to another with an increment of 1 cM. Most chromosomes show very flat logarithm of the odds (LOD) score profiles (data not shown). The only chromosome that shows evidence of a QTL for hepatic lipase activity is chromosome 7 (Fig. 1). Although we did not provide a separate name for this QTL in previous work, we now name this QTL LIPChrom7BSB. As will be seen in Bayesian analysis of the epistatic model, we detected an additional QTL on chromosome 3; thus, for comparison, the LOD score profile on this chromosome is also depicted in Fig. 1. One peak appears at position 64 cM in the profile of chromosome 7, which is close to D7Mit187 (64 cM), D7Ucla1 (64.4 cM), and D7Mit12 (66 cM). This peak has a LOD score of 4.8, which is greater than the threshold of 3.2 for statistically significant linkage (31). The profiles of the LIPChrom7BSB QTL main effects and the proportion of the total variance explained by the QTL are also depicted in Fig. 1. The main effect at 64 cM of chromosome 7 was 0.6527, which accounts for 10.67% of the phenotypic variance.



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  		Fig. 1. Maximum likelihood interval mapping for hepatic lipase activity. Profiles of logarithm of odds score, main effects, and heritability explained by the main effects on chromosomes 7 and 3. Tick marks on the x axes represent marker chromosome distances as given in Table 1.

 
Bayesian analysis of the nonepistatic model
The posterior probability distribution of the number of QTLs for hepatic lipase activity is shown in Fig. 2. Under the nonepistatic model, the posterior mode and the posterior expectation of the number of QTLs were estimated to be 1 and 1.29, respectively. The Bayes factor B(1,2)

comparing a model with one QTL against a model with two QTLs was 3.2. There is most likely one QTL influencing the variation of hepatic lipase activity when ignoring epistasis. The profile of the posterior QTL intensity on the whole genome is fairly similar to the profile of LOD scores in the analysis of interval mapping (not shown here); only chromosome 7 shows evidence of QTLs, and the profiles on other chromosomes are very flat. The posterior QTL intensity profiles on chromosomes 7 and 3 are depicted in Fig. 3. The peak on chromosome 7 overlaps that identified by the maximum likelihood method. The high posterior density (HPD) region of QTL locations was ~48–66 cM on chromosome 7. The posterior probability that this HPD region includes one QTL was 93%. However, the posterior probabilities for other chromosomes were close to 0, showing that only one QTL was detected when ignoring epistasis. The profiles of the QTL main effects and the proportion of the total variance explained by the QTL are depicted in Fig. 3. In the HPD region, the estimated main effect was 0.5437, which accounts for 6.54% of the phenotypic variance (Table 2).



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  		Fig. 2. Posterior probability distribution of the number of quantitative trait loci (QTLs) in Bayesian analyses of the nonepistatic and epistatic models for hepatic lipase activity.

 


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  		Fig. 3. Profiles of posterior QTL intensity, location-wise main effects, and heritability explained by the main effects on chromosomes 7 and 3 in Bayesian analyses of the nonepistatic (broken lines) and epistatic (solid lines) models for hepatic lipase activity. Tick marks on the x axes represent marker chromosome distances as given in Table 1.

 

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  		TABLE 2. HPD regions of QTL locations, posterior modes of QTL locations, main and epistatic effects and heritability explained by each effect, and the posterior probabilities that the main and epistatic effects are included in the Bayesian model

 
Bayesian analysis of the epistatic model
The posterior probability distribution of the number of QTLs is shown in Fig. 2. Under the epistatic model, the posterior mode and the posterior expectation of the number of QTLs were estimated to be 2 and 2.37, respectively. The Bayes factor B(2,1) comparing a model with two QTLs against a model with one QTL was 5. The epistatic model analysis showed that hepatic lipase activity was most likely affected by two loci, demonstrating that there was a posterior prediction of one additional QTL when allowing for epistasis. The profile of the posterior QTL intensity on the whole genome shows that only chromosomes 7 and 3 have QTL activity (not shown here). The posterior QTL intensity profiles on chromosomes 7 and 3 are depicted in Fig. 3. The epistatic analysis detected the same region on chromosome 7 as did the nonepistatic analysis. The HPD region of QTL locations was ~60–70 cM on chromosome 7, which has posterior probability of 95% to include one QTL (Table 2). The profiles of the location-wise main effect and the heritability explained by the main effect are depicted in Fig. 3. In the HPD region, the estimated main effect of the QTL on chromosome 7 was 0.5612, explaining 6.78% of the phenotypic variance (Table 2).

Chromosome 3 had a weak main effect on hepatic lipase activity and thus was not detected in the nonepistatic analysis. However, the epistatic analysis found strong evidence of an epistatic QTL at ~66.4 cM on chromosome 3. We name this QTL LIPChrom3epiBSB. The HPD region for this QTL was ~46.6–74.6 cM, which has a posterior probability of 78% to include one QTL (Table 2). Chromosome 3 was found to strongly interact with the LIPChrom 7BSB QTL on chromosome 7. The epistatic effect between these two QTLs was estimated to be –1.0889 and explained 7.03% of the phenotypic variance. Obviously, the epistatic genetic variance was even larger than the genetic variance explained by the main effect of chromosome 7, showing that epistasis plays an important role in controlling the genetic variation of hepatic lipase activity.

In all three analyses, the main effects of QTL on chromosome 7 were estimated to be positive; thus, the SPRET/Pt allele acts to promote hepatic lipase activity. As seen in Table 3, mice with the BS genotype at each of the markers D7Mit187, D7Ucla1, and D7Mit12 have a higher hepatic lipase activity than mice with the BB genotype. The SPRET/Pt allele of the QTL on chromosome 3 also promotes hepatic lipase activity, although the difference between the genotypic values of BS and BB at chromosome 3 is not large enough to be detected in the nonepistatic analyses. As shown in Table 2, the estimated interaction effect between chromosomes 7 and 3 is negative. This indicates that an animal with the SPRET/Pt allele at the two interacting peak markers, D3Mit18 on chromosome 3 and D7Mit187, D7Ucla1, and D7Mit12 on chromosome 7, will have (on average) greater hepatic lipase activity than that expected from the combined additive effects of the SPRET/Pt allele at each marker individually. This is in fact the case, as shown in Table 4, which gives average values of hepatic lipase activity within genotype classes.


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  		TABLE 3. Average hepatic lipase activity within single-marker genotype classes for the original phenotype and the standardized phenotype

 

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  		TABLE 4. Average hepatic lipase activity within two-marker genotype classes for the original phenotype and the standardized phenotype

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
In this study, we adopted a Bayesian model selection method recently developed by Yi, Xu, and Allison (28) to evaluate potential epistatic interactions in the BSB backcross for hepatic lipase activity. We now report a significant main effect on chromosome 7 and a gene x gene epistasis involving chromosome 3 for plasma hepatic lipase activity. The statistical approach used here models multiple QTLs, their main effects, and epistatic effects simultaneously. With this statistical method, we can jointly infer the genetic architecture of a complex trait and estimate the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTLs as well as the genetic variance and heritability explained by each genetic effect. Therefore, this Bayesian mapping method can detect multiple QTLs with any combination of main and epistatic effects.

A variety of other statistical methods for mapping epistatic QTLs have been developed. The simplest method is to fit two QTLs at a time and then a two-dimensional search along the genome is used to detect QTLs and estimate two-locus interactions (32). The two-dimensional search requires many statistical tests; hence, a high statistical threshold must be adopted to avoid false-positives among those tests. A high threshold would drastically reduce the power of detecting QTLs and finding significant epistasis. Non-Bayesian (or frequentist) model selection methods have been recently applied to map multiple and epistatic QTLs (33). The common aim of these non-Bayesian methods is to find a single "optimal" model, regarded as the number, locations, and effects of QTLs, and then to make inferences as if the selected model were the true model. However, this ignores uncertainty about the model itself. As a consequence, these methods result in overly optimistic beliefs concerning the accuracy of parameter estimates.

Using the interval-mapping method (26), two previous studies searched for QTLs in BSB mice (12, 13). In those BSB crosses, the central region of chromosome 7 was significant for coincident QTLs for percentage body fat, total cholesterol, and hepatic lipase activity. These QTLs were all named Mob-1 for multigenic obesity-1. These results were followed by subsequent publications reporting studies using other independent models that also identified QTLs for linkage of mouse chromosome 7 to obesity (13, 34, 35). A chromosome 12 QTL for percentage body fat was present in a BSB cross using noninbred SPRET/Pt (12) but was absent in a later cross using inbred SPRET/Ei (13). QTLs were previously identified for femoral and mesenteric fat depots, but not for percentage body fat, on chromosomes 6 and 15, respectively.

We recently found that epistasis plays an important role in controlling the obesity traits in BSB mice (29). The epistatic interaction, estimated to be negative and thus promoting leanness, between chromosomes 2 and 12 had significant effects on all measured obesity traits. For percentage body fat, chromosome 12 also interacts with chromosome 15, and this epistatic effect resulted in the detection of chromosome 15 in the epistatic model analysis. Except for the interaction between chromosomes 2 and 12, which are shared for all obesity traits, different epistatic interactions were detected for different traits, indicating largely separate genetic control for these aspects of obesity. We also found that total cholesterol was influenced only by chromosomes 6 and 12 (29). Thus, a different genetic architecture was discovered for the obesity traits and total cholesterol. The main effects of these two chromosomes were estimated to be positive; thus, the SPRET/Pt allele led to higher phenotypes on both chromosomes. There was a strong negative epistatic effect between chromosomes 6 and 12 that led to lower total cholesterol. The proportion of the phenotypic variance explained by this epistatic interaction was actually higher than those explained by the main effects.

Mapping gene x gene QTL (epistasis QTL) is not only useful because epistasis influences a significant fraction of the variance of many complex traits but also because identification of underlying genes may be simpler for epistatic than for nonepistatic QTLs. Several methods have already been developed that have been, or could be, used to identify quantitative trait genes that exhibit epistatic interactions. Investigators used epistasis to identify candidate genes based on their participation in a single pathway (25). Thus, the presence of epistasis can be used to facilitate gene identification using a network analysis. The major limitation of this approach is that it assumes that some information is already available about the functions of both genes, which is not always the case. Other investigators demonstrated epistasis in congenic strains by breeding together complementary strains (36, 37). This is an important step because one can then use recombination in the two congenic strains to reduce the number of candidate genes and thus focus attention on the few best positional candidates. These discoveries emphasize the importance of identifying epistatic QTLs when analyzing F2 or N2 data, as is done in the present study, so that the underlying loci can be isolated as congenic strains, regardless of their independent main effects. We have observed that it is possible to isolate congenic strains with phenotypes even when the QTL peak has both epistatic and nonepistatic main effects (38). There are other conceivable methods to isolate genes that participate in epistasis. For instance, it may be possible to use haplotypes that are naturally present in outbred strains, as was done for a skin cancer QTL (39). We already demonstrated that SPRET/Pt haplotypes have very different effects on plasma leptin levels (40). Thus, studies of haplotypes may provide a general approach to high-resolution positional mapping. Overall, epistasis aids in the discovery of some quantitative trait genes and may complicate the discovery of others, but epistasis is not a general block to all gene discovery.


   ACKNOWLEDGMENTS
 
N.Y. and D.B.A. are supported by National Institutes of Health Grants RO1 ES-09912, RO1 DK-056366, and P30 DK-056336 and by an Obesity-Related Pilot/Feasibility Studies grant at the University of Alabama (528176). S.C., J.S.F., and C.H.W. are supported by National Institutes of Health Grant R01 DK-52581, by National Institutes of Health Training Grant PHS DK-07355, and by the University of California Davis Clinical Nutrition Research Unit (National Institutes of Health Grant DK-35747). The authors thank Dr. Howard Wong for the hepatic lipase assays and are grateful to Susan Bennett and Noreene Shibata for the breeding and care of animals.

Manuscript received April 8, 2004 and in revised form July 30, 2004.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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N. Yi, B. S. Yandell, G. A. Churchill, D. B. Allison, E. J. Eisen, and D. Pomp
Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis
Genetics, July 1, 2005; 170(3): 1333 - 1344.
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