Modeling genetic imprinting effects of DNA sequences with multilocus polymorphism data
 Sheron Wen^{1},
 Chenguang Wang^{1},
 Arthur Berg^{1},
 Yao Li^{1},
 Myron M Chang^{2},
 Roger B Fillingim^{3},
 Margaret R Wallace^{4},
 Roland Staud^{4},
 Lee Kaplan^{4} and
 Rongling Wu^{1, 5, 6}Email author
DOI: 10.1186/17487188411
© Wen et al; licensee BioMed Central Ltd. 2009
Received: 4 February 2009
Accepted: 11 August 2009
Published: 11 August 2009
Abstract
Single nucleotide polymorphisms (SNPs) represent the most widespread type of DNA sequence variation in the human genome and they have recently emerged as valuable genetic markers for revealing the genetic architecture of complex traits in terms of nucleotide combination and sequence. Here, we extend an algorithmic model for the haplotype analysis of SNPs to estimate the effects of genetic imprinting expressed at the DNA sequence level. The model provides a general procedure for identifying the number and types of optimal DNA sequence variants that are expressed differently due to their parental origin. The model is used to analyze a genetic data set collected from a pain genetics project. We find that DNA haplotype GAC from three SNPs, OPRKG36T (with two alleles G and T), OPRKA843G (with alleles A and G), and OPRKC846T (with alleles C and T), at the kappaopioid receptor, triggers a significant effect on pain sensitivity, but with expression significantly depending on the parent from which it is inherited (p = 0.008). With a tremendous advance in SNP identification and automated screening, the model founded on haplotype discovery and statistical inference may provide a useful tool for genetic analysis of any quantitative trait with complex inheritance.
Background
In diploid organisms, there are two copies at every autosomal gene, one inherited from the maternal parent and the other from the paternal parent. Both copies are expressed to affect a trait for a majority of these genes. Yet, there is also a small subset of genes for which one copy from a particular parent is turned off. These genes, whose expression depends on the parent of origin due to the epigenetic or imprinted mark of one copy in either the egg or the sperm, have been thought to play an important role in complex diseases and traits, although imprinted expression can also vary between tissues, developmental stages, and species [1]. Anomalies derived from imprinted genes are often manifested as developmental and neurological disorders during early development and as cancer later in life [2–5].
The mechanisms for genetic imprinting are still incompletely known, but they involve epigenetic modifications that are erased and then reset during the formation of eggs and sperm. Recent research shows that the parentoforigin dependent expression of imprinted genes is related with environmental interactions with the genome [5]. The phenomenon of genomic imprinting is explained from an evolutionary perspective [6]. Genomic imprinting evolves in mammals with the advent of live birth through a parental battle between the sexes to control the maternal expenditure of resources to the offspring [7].
Paternally expressed imprinted genes tend to promote offspring growth by extracting nutrients from the mother during pregnancy while it is suppressed by those genes that are maternally expressed. This genetic battle between the paternal and maternal parents appears to continue even after birth [8, 9].
The genetic mechanisms for imprinting can be made clear if the genomic distribution of imprinted genes and their actions and interactions are studied. Genetic mapping with molecular markers and linkage maps has been used to map quantitative trait loci (QTLs) that show parentoforigin effects [10–12]. Using an outbred strategy appropriate for plants and animals, significant imprinting QTLs were detected for body composition and body weight in pigs [13, 14], chickens [15] and sheep [16]. Cui et al. [12] proposed an F_{2}based strategy to map imprinting QTLs by capitalizing on the difference in the recombination fraction between different sexes. More explorations on the development of imprinting models are given in Cui and others [12, 17]. Liu et al. [18] developed a randomeffect model for estimating the parentdependent genetic variance of complex traits at imprinting QTLs.
We will propose a statistical model for estimating the imprinting effects of DNA sequence variants that encode a complex trait. This model uses widely available single nucleotide polymorphisms (SNPs) that reside within a coding sequence of the human genome. The central idea of this model is to separate maternally and paternallyderived haplotypes (i.e., a linear combination of alleles at different SNPs on a single chromosome) from observed genotypes. By specifying one risk haplotype, i.e., one that operates differently from the rest of haplotypes (called nonrisk haplotypes), Liu et al. [19] proposed a statistical method for detecting risk haplotypes for a complex trait with a random sample drawn from a natural population. Liu et al.'s approach can be used to characterize DNA sequence variants that encode the phenotypic value of a trait. Wu et al. [20] constructed a general multiallelic model in which any number of risk haplotypes can be assumed. The best number and combination of risk haplotypes can be estimated by using the likelihoods and AIC or BIC values. We will derive a computational algorithm for estimating the imprinting effects of SNPconstructed haplotypes with multilocus genetic data based on these previous workings. The new algorithmic model provides a general framework for hypothesis tests on the pattern of genetic imprinting expressed by haplotypes. A real example from a pain genetic study is used to demonstrate the application of the model.
Results
Sexspecific differences observed in haplotype frequencies and higherorder linkage disequilibria estimates
Male  Female  Sexspecific  Sexspecific  

Genetic Parameter  MLE  pvalue  MLE  pvalue  LR  pvalue 
Haplotype Frequency  
GAC  0.780  0.764  
GAT  0.000  0.000  
GGC  0.124  0.081  
GGT  0.011  0.023  
TAC  0.049  0.104  
TAT  0.000  0.000  
TGC  0.008  0.000  
TGT  0.030  0.029  
Allele Frequency and Linkage Disequilibrium  
G (OPRKG36T)  0.914  0.868  6.166  0.0130  
A (OPRKA843G)  0.828  0.868  3.501  0.0613  
A (OPRKC846T)  0.960  0.949  2.943  0.0862  
_{12}  0.034  0.0459  0.045  0.1812  5.771  0.0163 
_{23}  0.026  4.98e^{6}  0.022  3.61e^{6}  42.281  7.91^{e11} 
_{13}  0.023  8.87e^{5}  0.011  0.0089  22.216  2.44e^{6} 
_{123}  0.021  2.53e^{4}  0.018  0.0055  21.088  4.39e^{6} 
A "biallelic" model assuming that there is only one haplotype is used to estimate haplotype effects at the kappaopioid receptor on pain traits.
Haplotype effects are estimated over three pain sensitivity traits
Trait  GAC  GAT  GGC  GGT  TAC  TAT  TGC  TGT 

PreInt49tot  764.663  773.196  771.972  770.903  769.645  773.196  772.842  772.677 
Hpthpent  195.107  199.832  198.640  199.460  193.569  199.832  195.345  199.709 
Hptopent  165.867  170.494  170.468  170.216  157.053  170.494  168.324  170.414 
Additive, dominant, imprinting, and overall effects at three SNPs
Trait  Risk Haplotype  a  d  i  Overall  

PreInt49tot  Effect  GAC  13.47  6.22  19.02  
pvalue  0.005  0.237  0.008  0.004  
Hpthpent  Effect  TAC  3.06  3.08  0.26  
pvalue  0.002  0.003  0.089  0.023  
Hptopent  Effect  TAC  2.15  2.33  0.28  
pvalue  0.003  0.003  0.621  0.025 
The statistical properties of the imprinting model are investigated through simulation studies. The first simulation mimics the data structure of the real example (with 237 subjects) above based on its estimates of sexspecific allele frequencies and linkage disequilibria among three SNPs (Table 1) and of the additive, dominant, and imprinting effects arising from different haplotypes (for PreInt49tot, Table 3). The second simulation includes sample size from 237 to 400, 800, and 2000, keeping the other parameters unchanged. Each simulation scheme is repeated for 1000 runs.
 (1)
Population genetic parameters including threeSNP haplotype frequencies, allele frequencies, and linkage disequilibria of different orders can be precisely estimated even when a smaller sample size (237) is used. As expected, the estimation precision can be improved consistently when the sample size increases from 237 to 2000.
 (2)
Quantitative genetic parameters can also be well estimated, but the better estimation of the dominant and imprinting effects needs a larger sample size (400 or more). With a sample size of 2000, the precision of all parameter estimates are remarkably high, with sampling errors of each estimate being low than 10% of the estimate.
 (3)
The power to detect imprinting effects reaches 75% for a sample size of 237, but it can increase dramatically when increasing the sample size to 400.
 (4)
The type I error rate of detecting the imprinting effect, i.e, a probability for a false positive discovery of that effect, is quite low (< 10%) for a small sample size and can be lowered when sample size increases.
The simulation for testing the type I error rate in (4) was based on the same parameters as used in (1)–(3), except that no imprinting effect is assumed. Because we have derived a series of closed forms for the estimation of parameters within the EM framework, parameter estimation is very efficient. For a single simulation run, it will take a few dozen of seconds to obtain all estimates on a PC laptop. Also, estimates do not depend heavily on initial values of parameters, showing that the estimates achieve a global maxima for the likelihood.
Discussion
Although a traditional view assumes that the maternally and paternally derived alleles of each gene are expressed simultaneously at a similar level, there are many exceptions where alleles are expressed from only one of the two parental chromosomes [1, 23]. This socalled genetic imprinting or parentoforigin effect has been thought to play a pivotal role in regulating the phenotypic variation of a complex trait [24–27]. With the discovery of more imprinting genes involved in trait control through molecular and bioinformatics approaches, we will be in a position to elucidate the genetic architecture of quantitative variation for various organisms including humans. Genetic mapping in controlled crosses has opened up a great opportunity for a genomewide search of imprinting effects by identifying imprinted quantitative trait loci (iQTLs). This approach has successfully detected iQTLs that are responsible for body mass and diseases [10, 11, 14, 19, 28, 29]. Cloning of these iQTLs will require highresolution mapping of genes, which is hardly met for traditional linkage analysis based on the production of recombinants in experimental crosses. Single nucleotide polymorphisms (SNPs) are powerful markers that can explain interindividual differences. Multiple adjacent SNPs are especially useful to associate phenotypic variability with haplotypes [30–34]. The quantitative effect of haplotypes on a complex trait was modeled by Liu et al. [19] and subsequently refined by Wu et al. [20].
In this article, we incorporate genetic imprinting into Wu et al.'s [20] multiallelic model to estimate the number and combination of multiple functional haplotypes that are expressed differently depending on the parental origin of these haplotypes. Because of the modeling of any possible distinct haplotypes, the multiallelic model will have more power for detecting significant haplotypes and their imprinting effects than biallelic models. The imprinting model was shown to work well in a wide range of parameter space for a modest sample size. However, a considerably large sample size is needed if there are multiple risk haplotypes that contribute to trait variation. By analyzing a real example for pain genetics, the new model detects significant haplotypes composed of three SNPs within the kappaopioid receptor, which may play an important role in affecting pain sensitivity to heat.
Haplotype GAC derived from this gene appears to be imprinted for PreInt49tot, a pain sensitivity trait to heat stimuli at 49°C before drug administration, leading to different levels of pain sensitivity between the patients when they inherit this haplotype from maternal and paternal parents. In this example, no imprinting was detected for Hpthpent and Hptopent, two pain sensitivity traits measured after the patients were administrated with pentazocine. This result should be, however, explained with caution. First, the risk haplotype, TAC, detected for Hpthpent and Hptopent is a rare haplotype in the admixed population studied, although it is quite common in African Americans and Hispanics. The significance of this rare haplotype detected could be a sample size artifact, or it could be indicating a powerful haplotype effect. Second, in a different analysis, no significant genetic association was detected for the same heat pain test at heat stimuli at 52°C (data not shown). Nonetheless, the method provides a powerful tool for detecting possible associations and imprinting effects, which provide a starting point for future work to pursue the positive results with larger sample sizes and family studies. There have not been any previous reports suggesting an imprinting effect at an opioid receptor locus, or related to pain measures.
In practice, although the human genome contains millions of SNPs, it is not possible and also not necessary to model and analyze these SNPs simultaneously. These SNPs are often distributed in different haplotype blocks [35], within each of which a particular (small) number of representative SNPs or htSNPs can uniquely explain most of the haplotype variation. A minimal subset of htSNPs, identified by several computing algorithms, can be implemented into our imprinting model to detect their imprinting effects at the haplotype level. In addition, our model can be extended to model imprinting effects in a network of interactive architecture, including haplotypehaplotype interactions from different genomic regions, haplotypeenvironment interactions, and haplotype effects regulating pharmacodynamic reactions of drugs. It can be expected that all extensions will require expensive computation, but this computing can be made possible if combinatorial mathematics, graphical models, and machine learning are incorporated into closed forms of parameter estimation.
This imprinting model assumes that if the SNPs constituting haplotypes are tightly linked, haplotype frequencies estimated from the current generation can be used to approximate haplotype frequencies in the parental generation. To relax this assumption, a strategy of sampling a panel of random families from a population is required, in which a known family structure allows the tracing and estimation of maternally and paternallyderived haplotypes. Such a strategy will help to precisely estimate and test imprinting effects of haplotypes, providing a new gateway for studying the genetic architecture of complex traits.
Methods
Imprinting Model
Consider a set of three ordered SNPs, each with two alleles 1 and 0, genotyped from a candidate gene. These three SNPs form eight haplotypes, 111, 110, 101, 100, 011, 010, 001, and 000. A risk haplotype group is defined as a set of haplotypes that are in manner distinct from the other haplotypes in affecting a complex trait. For example, if a risk haplotype group only consists of the haplotype 111, the remaining seven haplotypes form the nonrisk haplotype group; this means that the diplotypes composed of 111 will have different genotypic values from those composed of 110, 101, 100, 011, 010, 001, or 000. There may be multiple risk haplotype groups, and we let R_{ k }denote any risk haplotype from the k^{th} risk haplotype group (k = 1,...,K; K < 8, where K is the number of risk haplotype groups) and R_{0} denote any of the remaining nonrisk haplotypes in the nonrisk haplotype group. The combinations between the risk and nonrisk haplotypes are called the composite diplotypes, including R_{ k }R_{ k' }(k ≤ k' = 1,...,K), R_{ k }R_{0} and R_{0}R_{0} (any two nonrisk haplotypes). Here we do not distinguish between R_{ k }R_{ k' }and R_{ k' }R_{ k }as we do not know parental origin of the haplotypes, however genetic imprinting implies that the same composite diplotype may function differently, depending on the parental origin of its underlying haplotypes. To reflect the parental origin of haplotypes in the composite diplotype, the following notation is used: R_{ k }R_{ k' }(k, k' = 1,....,K), R_{ k }R_{0}, R_{0}R_{ k }, and R_{0}R_{0}, where the vertical lines are used to separate the haplotypes derived from the maternal parent (left) and paternal parent (right).
where μ is the overall mean, a_{ k }is the additive effect due to the substitution of risk haplotype k by the nonrisk haplotype, d_{ kk' }is the dominance effect due to the interaction between risk haplotypes k and k'(d_{ kk' }= d_{k'k}), d_{k 0}is the dominance effect due to the interaction between risk haplotypes k and the nonrisk haplotype (d_{k 0}= d_{0k}), i_{ kk' }is the imprinting effects due to different parental origins of risk haplotypes k and k'(i_{ kk' }= i_{ k'k }), and i_{k 0}is the imprinting effect due to different parental origins of risk haplotype k and the nonrisk haplotype (i_{k 0}= i_{0k}). The sizes and signs of i_{ kk' }and i_{k 0}determine the extent and direction of imprinting effects at the haplotype level.
Estimating Model
Genetic Structure
Suppose the three SNPs are genotyped from a natural human population at HardyWeinberg equilibrium (HWE). Let and denote the frequencies of two alternative alleles r_{ l }(r_{ l }= 1 or 0) at SNP l in the population of sex s (s = M for females and P for males). Sexspecific frequencies of eight haplotypes produced by the three SNPs are generally expressed as . For each sex s, genotypes consisting of three SNPs are denoted as , totaling 27 distinct genotypes. Let denote the observation of a threeSNP genotype for sex s, which sums over the two sexes to . Some genotypes are consistent with diplotypes, whereas those that are heterozygous at two or more SNPs are not. Each double heterozygote contains two different diplotypes, and the triple heterozygote, i.e., 10/10/10, contains four different diplotypes: 111000 (with probability for sex s), 110001 (with probability for sex s), 101010 (with probability for sex s), and 100011 (with probability for sex s). Note that slashes are used to separate genotypes at different SNPs and vertical lines are used to separate haplotypes derived from the maternal parent (left) and paternal parent (right). The observed genotypes, the underlying diplotypes, and diplotype frequencies are provided in Additional file 1. From the HWE assumption, diplotype frequencies are simply expressed as the products of the underlyinghaplotype frequencies derived from different parents.
Because the three SNPs are genotyped from the same region of a candidate gene, their recombination fractions should be very small and can be thought to be close to zero. Thus, the frequencies of maternally and paternallyderived haplotypes can be approximated by the estimates of these haplotype frequencies in the female and male populations of current generation, respectively.
Likelihoods
With a random sample from a natural population, in which each genotyped subject is measured for a phenotypic trait of interest, we will develop a model to estimate population genetic parameters, including the eight maternallyderived haplotype frequencies , the eight paternallyderived haplotype frequencies , and the quantitative genetic parameters (Ω_{ q }) that include haplotype effects ( ) and the residual variance of the trait (σ^{2}). The haplotype effects are derived uniquely from genotypic values of composite diplotypes ( ) as provided in equations (2)–(6).
Thus, maximizing the likelihood in (1) is equivalent to individually maximizing the three terms on the right hand side of (1).
The EM algorithm is derived to estimate quantitative genetic parameters with a detailed procedure given in Additional file 2. The estimated genotypic values of composite diplotypes are used to estimate the additive, dominant and imprinting effects of haplotypes using equations (2)–(6).
Model Selection
Number of choices for serveral multiallelic models with likelihood and model selection notation
Risk Haplotype  Loglikelihood  AIC/BIC  

Model  No.  Choice 
 
Biallelic  1 



Triallelic  2  28 


Quadriallelic  3  56 


Pentaallelic  4  170 


Hexaallelic  5  56 


Septemallelic  6  24 


Octoallelic  7  8 


Hypothesis Tests
H_{1} : At least one of equality in H_{0} does not hold The loglikelihood ratio (LR) is then calculated by plugging the estimated parameters into the likelihood under the H_{0} and H_{1}, respectively. The LR can be viewed as being asymptotically χ^{2}distributed with (k + 1)^{2}  1 degrees of freedom.
In practice, it is also interesting to test each of the additive genetic effects, each of the dominance effects and each of the imprinting effects for the triand quadriallelic models. The estimates of the parameters under the null hypotheses can be obtained with the same EM algorithm derived for the alternative hypotheses but with a constraint of the tested effect equal to zero. The loglikelihood ratio test statistics for each hypothesis is thought to asymptotically follow a χ^{2}distributed with the degree of freedom equal to the difference of the numbers of the parameters being tested under the null and alternative hypotheses.
Declarations
Acknowledgements
This work is supported by Joint grant DMS/NIGMS0540745 and NIH RO1 grant NS41670.
Authors’ Affiliations
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