Heritability and Preliminary Genome-Wide Linkage Analysis of Arsenic Metabolites in Urine

Background: Arsenic (III) methyltransferase (AS3MT) has been related to urine arsenic metabolites in association studies. Other genes might also play roles in arsenic metabolism and excretion. Objective: We evaluated genetic determinants of urine arsenic metabolites in American Indian adults from the Strong Heart Study (SHS). Methods: We evaluated heritability of urine arsenic metabolites [percent inorganic arsenic (%iAs), percent monomethylarsonate (%MMA), and percent dimethylarsinate (%DMA)] in 2,907 SHS participants with urine arsenic measurements and at least one relative within the cohort. We conducted a preliminary linkage analysis in a subset of 487 participants with available genotypes on approximately 400 short tandem repeat markers using a general pedigree variance component approach for localizing quantitative trait loci (QTL). Results: The medians (interquartile ranges) for %iAs, %MMA, and %DMA were 7.7% (5.4–10.7%), 13.6% (10.5–17.1%), and 78.4% (72.5–83.1%), respectively. The estimated heritability was 53% for %iAs, 50% for %MMA, and 59% for %DMA. After adjustment for sex, age, smoking, body mass index, alcohol consumption, region, and total urine arsenic concentrations, LOD [logarithm (to the base of 10) of the odds] scores indicated suggestive evidence for genetic linkage with QTLs influencing urine arsenic metabolites on chromosomes 5 (LOD = 2.03 for %iAs), 9 (LOD = 2.05 for %iAs and 2.10 for %MMA), and 11 (LOD = 1.94 for %iAs). A peak for %DMA on chromosome 10 within 2 Mb of AS3MT had an LOD of 1.80. Conclusions: This population-based family study in American Indian communities supports a genetic contribution to variation in the distribution of arsenic metabolites in urine and, potentially, the involvement of genes other than AS3MT.

Environmental Health Perspectives doi: 10.1289/ehp.1205305 Statistical Methods, Variance component models for general pedigrees conducted by SOLAR.

Heritability model
We estimated the heritability of urine arsenic metabolites (%iAs, %MMA and %DMA) by using a general pedigree variance-component method as implemented in the software Sequential Oligogenic Linkage Analysis Routines (SOLAR) (Blangero et al. 2013). SOLAR incorporates the information contained in the participants' pedigrees to obtain maximum likelihood estimates for the proportion of unexplained variance due to additive genetic effects from polygenes and the proportion of variance due to unmeasured environmental covariates, measurement error and non-additive genetic effects. The resultant polygenic model is specified as follows: where y i is the observed urine arsenic metabolite (%iAs, %MMA or %DMA) for individual i; μ is the mean when all the covariates in the models are zero; β j is the vector of regression coefficients; x ij is the value of the covariable j in subject i; and g i and e i are the deviations from μ in the individual i which are attributable to additive genetic effects (g i ) and other sources of error (e i ) including unmeasured environmental effects, gene-gene interaction and geneenvironment interaction. We assume that g i and e i are uncorrelated and normally distributed with mean 0 and variances σ 2 g and σ 2 e.
To enable the analysis of arbitrary pedigree structures, the variance in the model is structured as the following covariance matrix: where Φ is the matrix containing the kinship coefficients for all pairs of relatives in the data and I is an identity matrix. Subsequently, the expected mean and covariance matrix for each pedigree are defined, and the likelihood of a pedigree is evaluated using the multivariate normal distribution and summing over all pedigrees. The heritability (h 2 ) is defined as the proportion of unexplained variance in the observed distribution of urine arsenic metabolite that is attributable to additive genetic effects, or h 2 = σ 2 g / (σ 2 g + σ 2 e ). The p-values for h 2 are computed from a likelihood ratio test comparing the likelihood of the model in which the σ 2 g is estimated to a model where σ 2 g is constrained to be 0. These models are more deeply discussed by Hopper JL and Lange K (Hopper and Mathews 1982;Lange and Boehnke 1983).

Quantitative trait locus model
The linkage scan was based on variance component methods as implemented by SOLAR (Almasy and Blangero 1998). The model builds on the model in Equation 1 (see above) adding a term for k quantitative trait loci (QTLs), potentially associated to urine arsenic metabolites variability, where q ik is the normally distributed error term due to the k th QTL in individual i.
The resulting equations for the observed urine arsenic metabolite values including the QTLs and corresponding variance are specified as follows: ], and where Π k is the identity-by-descent (IBD) matrix whose elements provide the probability of sharing genes identical by descent for a given pair of individuals at a given genetic marker locus potentially linked to a QTL, Φ is the kinship matrix and I is the identity matrix, σ qk -refers to genetic variance due to the QTL and σ 2 g -refers to the residual additive genetic variance.
Almasy L. and Blangero have described the variance component model for QTL linkage analysis in general pedigrees in more detail (Almasy and Blangero 1998;Blangero and Almasy 1997). Total arsenic was measured directly using inductively coupled plasma mass spectrometry (ICPMS, see methods section). Table S2. Median (interquartile range) of percentage urine arsenic species in the Strong Heart Study participants with at least one relative within the cohort For BMI we selected 30 kg/m 2 , a cut-off commonly used to classify individuals as obese and non-obese. For education we selected 12 years of education, as at least 12 years of education is consistent with the completion of high school. Total arsenic was measured directly using inductively coupled plasma mass spectrometry (ICPMS, see methods section). Supplemental Material, Figure S1. Correlation matrix Figure S1. Distribution and relationship of total arsenic concentrations (µg/g creatinine) and arsenic metabolites (%iAs, %MMA and %DMA) in urine (n=2,907).

Supplemental Material, Table S2. Urine arsenic metabolites by participant characteristics
The diagonal shows the distribution of the variables in the correlation matrix. The upper diagonal panel shows the Spearman correlation coefficients for the corresponding variables in the correlation matrix. The lower diagonal panel shows the scatterplots and the smoothed relationship for the corresponding variables in the correlation matrix using the lowess command in R software (R-Development Core Team 2012, available at: http://cran.r-project.org/).

Supplemental Material, Table S3. List of short tandem repeat (STR) markers used in the Strong
Heart Family Study. The chromosomal location is based on Haldane centimorgans.