# Genetic Contribution of the Endothelial Constitutive Nitric Oxide Synthase Gene to Plasma Nitric Oxide Levels

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## Abstract

*Abstract *Nitric oxide (NO) has an important physiological role in regulating vascular tone and is also relevant to many pathological processes including hypertension and atherosclerosis. Endothelial constitutive nitric oxide synthase (ecNOS) is the key enzyme in determining basal vascular wall NO production. We used a combination of maximum-likelihood-based statistical genetic methods to explore the contributions of the ecNOS gene and other unmeasured genes to basal NO production measured by its metabolites (NO_{x}: nitrite and nitrate) in 428 members of 108 nuclear families. Our initial quantitative genetic analysis estimated that approximately 30% of the variance in fasting NO_{x} levels is due to genes (χ^{2}_{[1]}=16.04, *P*=.000062). Complex segregation analysis detected the effects of both a single locus and residual polygenes on NO_{x} levels, and measured genotype analysis showed that plasma NO_{x} levels in those homozygous for the rare allele (64.9±7.8 μmol/L) were significantly higher (*P*=.000242) than those homozygous for the common allele (30.2±3.1 μmol/L). The results of the variance component linkage analysis were consistent with linkage of a quantitative trait locus in or near the ecNOS gene to variation in plasma NO_{x} levels (*P*=.0066). While many environmental factors have been shown to alter transiently plasma NO_{x} levels, our study is the first to identify a substantial effect of the ecNOS locus on the variance of plasma NO_{x}, ie basal NO production. This finding may be relevant to atherogenesis and NO-related disorders.

- nitric oxide
- endothelial constitutive nitric oxide synthase
- DNA polymorphism
- quantitative linkage analysis
- major locus effect

- Received December 13, 1996.
- Accepted March 10, 1997.

Nitric oxide is biosynthesized from l-arginine by a family of NOSs in many tissues.^{1} Once generated, NO can interact with a number of molecular targets, and these determine the profile of NO as a major biological mediator, modulator, and effector.^{2} Three NOSs are responsible for NO biosynthesis in various tissues.^{1} Neural constitutive NOS (ncNOS, or NOS1) is expressed in neurons and is responsible for the physiological production of NO in neural tissue. The gene is located on chromosome 12q24.2. ecNOS, or NOS3, is mainly confined to endothelium and produces NO, which contributes to the regulation of vascular tone. The gene is located at 7q35-36. The NO produced by these two constitutive NOSs participates in normal physiology. However, inducible NOS (iNOS, or NOS2, 17 cen-q12) is not normally expressed in most cells but may be induced in pathological processes as seen, for example, during inflammation.^{1}

Circulating NO is mainly produced by ecNOS and has an important role in regulating blood flow, particularly coronary flow.^{3} ^{4} ^{5} ^{6} Reduction in basal NO release may predispose to hypertension, thrombosis, vasospasm, and atherosclerosis.^{3} ^{4} ^{5} ^{6} ^{7} ^{8} ^{9} In animal models, restoration of NO activity can induce regression of preexisting intimal lesions.^{10} On the other hand, high circulating NO levels, which occur with excess iNOS expression under pathological conditions, are generally toxic.^{1} ^{2} There are data indicating that markedly elevated NO levels are associated with endotoxic shock and exaggerated inflammation reactions^{11} and may lead to acute hepatic dysfunction,^{12} as well as contribute to the pathogenesis of glomerulonephritis^{13} and predispose to asthma,^{14} cardiomyopathy,^{15} and a number of other disorders.^{3} The measurement of NO itself is difficult because of its very short half-life, and the stable metabolites of NO (NO_{x}), have been frequently used as a reliable plasma measurement of NO production.^{16} ^{17} ^{18} ^{19} ^{20}

The factors influencing an individual’s continuous basal NO production are not clear.^{1} ^{2} ^{21} More specifically, the association between basal circulating NO levels and genotypic or phenotypic in vivo variations in ecNOS, the key regulator of the basal NO production in vasculature, is not understood. Determinations of in vivo human ecNOS enzymatic activity and its association with plasma NO are difficult because vascular tissue homogenates would be required. As ecNOS genomic DNA can be readily obtained and analyzed from peripheral nucleated blood cells, it is possible to assess the association between plasma NO and ecNOS at the DNA level. The definition of a genetic contribution to basal NO production is important for studies of the potential roles of NO and ecNOS in atherogenesis and hypertension, in both of which there is clustering in families.

Recently, we have reported an association between the ecNOS gene and an increased risk of coronary artery disease using a DNA polymorphism at intron 4 of the gene as a molecular marker.^{22} In the present study, we used this polymorphic marker to test the specific hypothesis that variation at the ecNOS locus contributes to quantitative phenotypic variation in circulating plasma NO levels, as estimated by NO_{x} levels. Our results indicate that there is a significant genetic contribution to plasma NO_{x} levels.

## Methods

### Nuclear Families in the Study

We collected blood samples from 428 members of 108 nuclear families. These families were healthy volunteers recruited from our ongoing Heart Health Education Program for family-based primary coronary prevention. They were selected for the current study on the basis that all were white of European origin, and residing in Sydney; none were current smokers. They were advised to remain on their usual diet before the blood collection and all were healthy at the time of study. Written consent was obtained from every parent. The study was approved by the Ethics Committee of the University of New South Wales.

A 4-mL venous blood sample was drawn into an EDTA sample tube after an overnight fast (12 to 14 hours). The blood sample was centrifuged within 2 hours and plasma stored at −70°C in aliquots until analysis. DNA was extracted from the frozen cellular blood component by a salting-out method.^{22} The extracted DNA was stored at 4°C until analysis.

### Genotyping of the 27-bp Repeat Polymorphism in Intron 4 of the ecNOS Gene

A polymerase chain reaction method was used for the genotyping of the repeat polymorphism as described previously.^{22} We used oligonucleotide primers that flank the region of the 27-bp direct repeat in intron 4 of the ecNOS gene. The PCR products were electrophoresed on 8% polyacrylamide gels and visualized by silver staining. There are two alleles differing by one repeat, ie, 27 bp in size. We have denoted these two alleles as ecNOS4a for four repeats and ecNOS4b for five repeats; ecNOS4b is the common allele.^{22}

### Determination of Plasma NO_{x} Levels

Since NO is unstable and quickly oxidized to nitrate and nitrite after production, to estimate plasma NO levels, circulating NO_{x} levels were determined using a modified method described by Moshage et al.^{16} Nitrate was measured as nitrite after enzymatic conversion by nitrate reductase and nitrite was measured after deproteinization using the Griess color reaction,^{18} which was read at a wavelength of 540 nm. Values obtained by this procedure represent the sum of nitrite and nitrate derived from NO. The detection limit of the assay and the recovery rates for nitrate and nitrite were similar to those described by Moshage et al.^{16} The precision profile of the assay was assessed by the intra-assay and interassay coefficients of variation, and they were 2.1% and 4.3%, respectively, in our laboratory.

### Statistical Genetic Analysis

There were two principal objectives of the statistical genetic analysis of circulating NO_{x} levels in these 108 human nuclear families. The first objective included the detection and characterization of genetic contributions to the phenotypic variance in circulating levels of NO_{x}. To achieve this objective, we employed quantitative genetic analysis and complex segregation analysis. The second objective was to test the specific hypothesis that variation at the ecNOS4 locus contributes to phenotypic variation in circulating NO_{x} levels. To achieve this objective, we employed a variance component linkage analysis and measured genotype analysis (see “Appendix” for details of the analysis).

## Results

There were 428 members of 108 nuclear families included in the current study. The average number of children was 2.3±1.5 with a range of 1 to 4 in each family. The ages (mean±SD) for fathers, mothers, boys, and girls were 43.5±6.1, 39.8±4.6, 11.1±3.2, and 11.0±3.2 years, respectively. Creatinine levels were within the normal range for all subjects in the study. The mean±SD fasting plasma NO_{x} levels were not different between fathers, mothers, boys, and girls and were, respectively, 36.9±17.8, 33.6±19.4, 33.4±17.0, and 29.6±14.2 μmol/L.

### Quantitative Genetic Analysis

The maximum-likelihood parameter estimates and their SEs for the more general additive genetic (often referred to as “polygenic”) model and the restricted sporadic model are presented in Table 1⇓. In the former, the phenotypic variance is attributable to the effects of additive genes, selected covariates, and random environmental factors; in the latter, it is attributable to the covariates and random environmental factors only. The results of the likelihood ratio tests comparing these two models indicate that a significant proportion of the residual phenotypic variance in plasma NO_{x} levels, approximately 30%, is due to the additive effects of genes (χ^{2}_{[1]}=16.04, *P*=.000062). Inclusion of sex and the age-by-sex terms as covariates does not contribute significantly to the likelihood of this polygenic model (*P*>.10).

### Complex Segregation Analysis

Likelihood ratio test screens of the five potential covariates detected significant effects on variation in NO_{x} levels for creatinine and apolipoprotein A-I levels only. Inclusion of both these covariates in the maximum-likelihood models reduced the sample size from 428 individuals in 108 pedigrees to 291 individuals in 88 pedigrees.

The results of the complex segregation analysis, summarized in Table 2⇓, are consistent with the detection of the effect of a single locus on quantitative variation in plasma NO_{x} levels in this population. With the exception of the genetic (Mendelian) mixture model, the ln likelihoods of all restricted alternate models tested were significantly worse than that of the unrestricted general model. Given their SEs, the maximum-likelihood estimates of the transmission probabilities in the general model (τ_{AA}=0.95±0.10, τ_{Aa}=0.52±0.11, and τ_{aa,}=0.24±0.27) correspond to those expected under Mendelian segregation (ie, 1.0, 0.5, and 0). The best-fitting model was a codominant mixture model. The common allele segregating at this locus (designated *A* in this analysis) produces lower NO_{x} levels and has a relative frequency of p_{A}=0.64. Given the estimated genotypic means, this allele appears to be dominant to the higher NO_{x} allele (*a*) in this model. Assuming Hardy-Weinberg equilibrium, the approximate expected genotypic proportions are 0.41 (*AA*), 0.46 (*Aa*), 0.13(*aa*).

### Measured Genotype Analysis

Table 3⇓ shows the maximum-likelihood estimates of the parameters of the measured genotype model. The effects of sex and the age-by-sex terms on the likelihood of the measured genotype model were not significant (*P*>.10). Likelihood ratio tests reveal a significant measured gene effect on plasma NO_{x} levels (χ^{2}_{[3]}=19.25, *P*=.000242). The pattern of genotypic means of NO_{x} levels is consistent with the ecNOS4a/a homozygote exhibiting significantly higher levels of circulating plasma NO_{x} than the other two genotypes, which have similar values (Table 3⇓ and the Figure⇓). In this sample of nuclear families, the measured gene accounts for 25% of the total phenotypic variance in plasma NO_{x} levels; residual additive genes and environmental factors account for approximately 7% and 68%, respectively.

### Variance Component Linkage Analysis

The results of the variance components genetic analysis of plasma NO_{x} levels are summarized in Table 4⇓. Sex, age-by-sex, and age^{2}-by-sex exerted no significant effects on the likelihoods of either the restricted or general models and consequently were removed prior to a second maximization series, and this is summarized in the table. Maximization of the restricted model on the nuclear family data clearly identifies a significant heritable component to quantitative variation in plasma NO_{x} levels. The proportion of the phenotypic variance attributable to the additive effects of genes is 31.5% (Λ=16.338, *P*=.000053). As disclosed by the likelihood ratio test comparing the general model and restricted models, a significant proportion of the phenotypic variance, 25.3%, is attributable to variation at the ecNOS4 locus. Approximately 10% and 64% of the phenotypic variance is attributable, respectively, to residual additive genetic effects and to random environmental effects.

## Discussion

Our study is the first to detect the effect of genes on quantitative variation in plasma NO_{x} levels in healthy human subjects who were randomly ascertained with respect to the NO_{x} phenotype and to identify a specific quantitative trait locus responsible for a significant portion of that effect. The results of our quantitative genetic analysis indicate that a moderate but significant proportion of the phenotypic variance in circulating plasma NO_{x} levels in this population is attributable to the additive effects of genes. This conclusion is supported and expanded by the results of our subsequent complex segregation analysis, conducted on a subsample of the subject population, that also detects these additive genetic effects plus the influence of a single locus, with apparent dominance effects, on variation in plasma NO_{x} levels.

The measured genotype analysis provides initial evidence for the involvement of the ecNOS locus in the regulation of plasma levels of NO_{x} in these families. The location in a noncoding region of the candidate gene minimizes the likelihood of a functional association between the polymorphic marker itself and plasma NO_{x} levels in this study. The 25% contribution of this marker to the phenotypic variance in the study, estimated in the measured genotype analysis, represents a minimum estimate of the variance in plasma NO_{x} levels attributable to the associated quantitative trait locus.

The results of the variance component linkage analysis indicate that the marker is most likely physically linked to the quantitative trait locus. They also indicate that the marker is most likely physically linked to the quantitative trait locus and provide a more valid estimate of the proportion of the variance attributable to the quantitative trait locus in these families. Our results indicate that the quantitative trait locus is linked to the ecNOS4 polymorphism. Given that many environmental factors have been shown to alter transiently plasma NO_{x} levels,^{1} ^{2} ^{3} the effect of the detected locus, accounting for over 25% of the phenotypic variation in this trait, is substantial and is likely to have relevance to the pathogenesis of NO related disorders such as atherosclerosis.

Perhaps of importance to the biology of mechanisms involved in the regulation of plasma NO_{x} levels is the detection of a minor residual additive genetic component to the phenotypic variance. This indicates the possible action of additional genes that directly influence quantitative variation in plasma levels of NO_{x}. Such genes may be many with very small additive effects or this residual additive genetic component may subsume the effect of one or more loci with modest influence on plasma NO_{x} levels. Increased family size, particularly by means of extending pedigrees, additional markers in the functional gene itself, and a better characterization of the interactions between this locus and relevant biological and environmental factors would improve our resolution of the contributions of the other quantitative trait loci in addition to that detected in this study.

Due to the radical nature of NO, which quickly oxidizes to NO_{x} in vivo and in vitro, direct determination from plasma is difficult.^{16} ^{17} ^{18} ^{19} ^{20} However, studies have shown that measurement of NO_{x} in blood collected after an overnight (12 to 14 hours) fast can reliably reflect basal (endogenous) NO production.^{20} ^{23} ^{24} Dietary nitrite/nitrate content could be a potential confounding factor for the plasma estimation, but we reduced the likelihood of the measurement’s being affected significantly by the diet of previous days by collecting the blood after an overnight fast.^{20} ^{24} While Jungersten et al^{25} suggested that oral intake of nitrate should be restricted for at least 48 hours, others indicated that dietary nitrates are eliminated from the blood by urinary excretion after approximately 12 to 16 hours.^{20} ^{24} It should also be pointed out that a restricted diet may create an artificial condition and not reflect the normal physiological condition, which is more relevant to atherogenesis, a chronic process that may start from early life and last for decades. Although a low nitrite/nitrate diet was not employed for the present study, identification and modeling of dietary factors that actually influence variation in plasma NO_{x} levels would only explain a greater proportion of the residual phenotypic variance and/or decrease the random environmental contribution to the variance in the phenotype. This would increase the relative signal of the quantitative trait locus effect detected in this family study and facilitate the detection and characterization of the genes that contribute to the residual additive genetic component of the variance in plasma NO_{x} levels.

In conclusion, we report a major gene effect on plasma NO_{x} levels, ie, NO production. The measured ecNOS4 polymorphism accounts for over 25% of the basal plasma NO production, indicating that the gene may contribute significantly to mechanisms mediating atherogenesis and other conditions.

## Selected Abbreviations and Acronyms

ecNOS | = | endothelial constitutive NOS |

IBD | = | identical by descent |

NO | = | nitric oxide |

NOS | = | NO synthase |

NO_{x} | = | nitrite and nitrate |

## Appendix A1

### Statistical Analysis

#### Quantitative Genetic Analysis

According to classic quantitative genetic theory,^{26} the total phenotypic variance in a trait, ς^{2}_{P} can be decomposed into the variance due to the effects of genes, ς^{2}_{G}, and the variance due to the environmental effects, ς^{2}_{E}. These effects are additive, such that The heritability, or the proportion of the total phenotypic variance attributable to the additive effects of genes, *h*^{2}, is obtainedas ς^{2}_{G}/ς^{2}_{P}. For the initial detection of the effects of genes on phenotypic variation in circulating NO_{x} levels, we modeled the NO_{x} phenotype as where y is the n×1 vector of phenotypes, μ is the grand mean of the phenotype in the population, X is an n×k matrix of k covariates, 1_{n}, is a vector of n ones, s′ is the transposed vector of baseline covariates (eg, 0 and X for discontinuous and continuous covariates in which X denotes the mean value of each covariate, respectively), β is k×1 vector of regression coefficients, and g, d, and e are the vectors of additive genetic values, dominance genetic effects, and random environmental effects, respectively. For such a model, the expected variance-covariance matrix for y is obtained as Where Φ is the n×n matrix of kinship coefficients, Δ is a matrix in which the *ij*th element is the probability that the *i*th and *j*th individuals share two genes IBD at any given locus, and I_{n} is an identity matrix of order n. The variance terms in equation 3 include the additive genetic variance, the variance attributable to dominance effects, and the random environmental variance. If multivariate normality is assumed, the likelihood of the pedigree is easily calculated and numerical optimization routines can be employed for the estimation of parameter values.

On the basis of maximum-likelihood estimation theory, this approach permits hypothesis testing as well as parameter estimation. This is accomplished by comparing a general model, in which all parameters are estimated, to one or more restricted models in which the parameter estimate is constrained to zero or some other value. Likelihood ratio test statistics are used to reject less adequate models in comparisons between each restricted model and the general model. The hypothesis to be tested is the null hypothesis of no additive genetic variance for the NO_{x} phenotype (ie, h^{2}=0). The likelihood ratio test statistic. Λ, is obtained as When the comparison is between the restricted model in which the value of a single parameter like the heritability is fixed at a boundary (ie, 0) and a more general model in which it is estimated, the likelihood ratio test statistic is distributed asymptotically approximately as a 50:50 mixture of χ^{2} with a point mass at zero.^{27} In all other comparisons, the likelihood ratio test statistic is distributed asymptotically approximately as a χ^{2} variate with degrees of freedom equal to the difference in the number of parameters estimated in the two models.

We first conducted a univariate, quantitative genetic analysis of circulating NO_{x} levels in which maximum-likelihood methods were used to simultaneously estimate the phenotypic mean (μ), phenotypic standard deviation (ς_{p}), h^{2}, and the effects of sex, age-by-sex, and age^{2}-by-sex. Using our modified version of PAP,^{28} we maximized the likelihood of this model, in which all the genetic variance was attributable to additive effects of genes, on the data from 428 individuals from 108 pedigrees. We then maximized the likelihood of an alternate, nested model in which h^{2} was constrained to equal zero. Comparison of the likelihoods of these two models was made by means of a likelihood ratio test. Tests of the significance of the sex and age terms in this model were conducted by means of likelihood ratio tests as well.

#### Complex Segregation Analysis

To characterize further the genetic contribution to the variance in plasma NO_{x} levels we employed complex segregation analysis^{29} to detect and measure the contribution of a single locus (although not necessarily the only locus) to plasma NO_{x} using data from the families described above. This approach entails the statistical comparison of the likelihoods for alternate models (a nested subset of more restricted nongenetic and genetic models, each representing different transmission hypotheses for plasma concentrations of NO_{x}) with that of an unrestricted general model. The general transmission model^{30} assumes a mixture of three normal phenotypic distributions with a common SD and residual additive genetic contribution to the phenotypic variance. The three phenotypic distributions are referred to as “ousiotypes”^{31} and, in the case of a segregating major locus, are interpreted to reflect unobservable genotypes. Ousiotypes are a result of influence from two discrete factors, *A* and/or *a*. In ousiotype notation, upper-case letters indicate factors associated with lower levels of the trait and lower-case letters indicate higher levels. The expected relative frequencies of the three possible ousiotypes (*AA*, *Aa*, and *aa*) are assumed to conform to the classic Hardy-Weinberg proportions such that, given a single parameter p_{A}=p, the ousiotype relative frequencies are predicted by p^{2}:2p(1-p):(1-p)^{2}.

Under the mixed model for complex segregation analysis, which includes a major factor and a residual additive genetic component, the phenotype of the *j*th individual with ousiotype *i* is with where *o* is the ousiotype, μ_{i} (i=AA, Aa, aa) is the mean associated with the *i*th ousiotype, and X_{j} is the *j*th individual’s vector of covariates (ie, the *j*th row of X is equation 2 above). The genetic component, ς^{2}_{g}, of the conditional variance, given immediately above, represents the residual additive genetic variance. The unconditional variance of y has an additional variance component attributable to the effect of the major factor and is given by: Associated with each of the three ousiotypes is an arbitrary probability of transmitting a factor (A) from parent to offspring dependent on the parental ousiotype (denoted τ_{AA}, τ_{Aa}, and τ_{aa,}). The parameters estimated in the simplest of the general models for plasma levels of NO_{x} in this study were the frequency of the factor, or allele in a genetic model, producing lower plasma NO_{x} levels; the mean of the three phenotypic distributions (μ_{AA}, μ_{Aa}, and μ_{AA}); an additive genetic residual heritability (h^{2}); a common phenotypic SD (ς), assumed to be the same for each distribution; three transmission probabilities (τ_{AA}, τ_{Aa}, and τ_{aa,}); plus the effects of sex and the linear and quadratic age-by-sex terms (βsex, βage_{males}, βage_{females}, βage^{2} _{males}, and βage^{2}_{females}).

We tested four classes of restricted models against the most general model using the unified approach of Lalouel et al.^{30} The simplest alternate model to be considered was the sporadic model, which allows only random environmental effects and no genetic transmission (h^{2}=0). The second alternate model, the polygenic model, assumes a single distribution to which the genetic contribution is entirely due to the additive effects of genes. The third class of alternate models, the Mendelian models, assumes the segregation of a major locus effect and incorporates transmission probabilities fixed at classical Mendelian expectations (ie, τ_{AA}=1, τ_{Aa}=0.5, τ_{aa,}=0). Additionally, Mendelian mixture models allow for residual polygenic background. The fourth model class tested, the environmental transmission model, assumes random environmental effects for major factors with the transmission probabilities constrained to equal p_{A}. Environmental mixture models permit the additional estimation of residual polygenic inheritance.

Data on five additional variables (levels of apolipoprotein AI, apolipoprotein B, creatinine, HDL cholesterol, and total cholesterol), each of which were viewed as a potential covariate in our analyses, were also available. We used likelihood ratio tests to screen these five potential covariates in the following manner. The likelihoods of two nested models, the polygenic and codominant mixture models, that included a potential covariate were compared by likelihood ratio test with those of the same two nested models in which the regression parameter for that covariate was fixed at 0. The tested covariate was retained for estimation in the subsequent segregation analyses if the likelihood ratio test statistic was significant at the α=0.10 level. It is analytically possible to simultaneously estimate the effects of all five potential covariates in all the nested models. However, because our statistical genetic approach uses only individuals with complete data on all variables included in the maximized models, and complete data on all five covariates were not available for all individuals in our sample, we tested the significance of each covariate singly in an attempt to retain the largest possible proportion of the original 428 family members in the subsequent segregation analysis.

### Measured Genotype Approach

We used the “measured genotype” approach^{27} ^{32} to assess the effects of specific alleles on variation in plasma NO_{x} levels. In this method, the mean effect of each allele is computed as the difference in phenotype value between the population mean and individuals carrying the allele. The contribution of the locus to quantitative variation in the phenotype is the ratio of the variance among the mean phenotype values for the separate genotypes to the total phenotypic variance. When a polymorphic marker identifies a functional mutation in a locus, this ratio is a reasonable estimate of the contribution of that locus to variation in the trait of interest. In the present case, where the marker is located in intron 4 of the ecNOS4 gene, this contribution generally will be less than the contribution of the associated quantitative trait locus and reflective of gametic or linkage disequilibrium with the functional locus.^{33}

Using maximum-likelihood estimation techniques implemented in our modified version of the computer program *PAP*, v3.0,^{28} we conducted a measured genotype analysis of plasma NO_{x} levels in the members of this sample who were genotyped at the ecNOS4 maker locus. The parameters estimated in this analysis included the frequency of the “low” plasma NOS allele (designated p_{A}), three genotypic means (μ_{AA}, μ_{Aa}, μ_{aa}), the residual phenotypic standard deviation (ς), the residual additive genetic heritability (h^{2}), and the mean effects of sex (βsex), age-by-sex (βage_{females}; βage_{males}), and age^{2}-by-sex (βage^{2}_{females}; βage^{2} _{males}). The hypothesis of no measured gene effect was tested by means of a likelihood ratio test in which the likelihood of a more general model in which three genotypic means were estimated was compared with that of a restricted model in which the genotypic means were constrained to be equal. The likelihood ratio test statistic, Λ, is usually obtained as two times the difference in the ln likelihoods of the two models and is distributed approximately asymptotically as a χ^{2} variate with degrees of freedom equal to the difference in the number of parameters estimated in the two models.^{34} If a measured gene effect is found to be significant, the total phenotypic covariance matrix can be partitioned into its component covariance matrices due to the measured gene, residual additive genes, and residual environments^{35} to calculate the proportions of the total covariance attributable to each.

### Variance Component Linkage Analysis

To test for linkage between the ecNOS4 polymorphism and a quantitative trait locus influencing variation in the plasma NO_{x} phenotype, we employed a general variance-components linkage analysis developed by Blangero^{36} and Blangero and Almasy.^{38} This method is an extension of the strategy developed by Amos^{39} to estimate the genetic variance attributable to the region around a specific marker locus. The approach entails specifying the expected genetic covariances between arbitrary relatives as a function of IBD relationships at a given marker locus that is assumed to be in tight linkage with a quantitative trait locus. The variance component method is more powerful than the widely used sibpair test of Haseman and Elston^{40} because it can use information on all types of relatives and provide an estimate of the relative variance of a trait that is determined by an underlying major locus while allowing for the simultaneous estimation of residual genetic effects, covariate effects, and random environmental effects.^{36}

For the current application of the variance-component linkage method, the sampling unit is the nuclear family, and the covariance matrix for a given nuclear family is given by: where Π is a matrix with elements (π_{mij}) that are estimates of the proportion of genes that individuals *i* and *j* shared IBD at marker locus m that is linked to a quantitative trait locus; ς^{2}_{m} is the additive genetic variance attributable to the marker locus; Φ is the n×n matrix kinship coefficients; ς^{2}_{g} and ς^{2}_{e}, respectively, are the proportions of the residual phenotypic variance attributable to, respectively, additive genetic and random environmental effects; and I_{n} is an identity matrix of order n.

Variance components and covariate effects were estimated simultaneously by maximum-likelihood techniques. A likelihood function assuming a multivariate normal density was numerically maximized to obtain parameter estimates. In the most general model, the following parameters were estimated: the phenotypic mean (μ); the effects of (ie, regression coefficients for) sex (βsex), age-by-sex (βage_{females}; βage_{males}), and age^{2}-by-sex (βage^{2}_{females}; βage^{2} _{males}); the phenotypic standard deviation (ς); and the proportions of the residual phenotypic variance attributable to the effects of residual additive genes (h^{2}), the marker locus that is linked to the quantitative trait locus (h^{2}_{m}), and random environmental effects (e^{2}).

The hypothesis of no linkage is tested also by likelihood ratio tests that compare the likelihood of the general model in which h^{2}_{m} is estimated with that of an alternate, restricted model in which h^{2}_{m} was constrained to equal zero

Pedigree, phenotype, and genotype data for the statistical genetic analyses are managed and prepared for statistical genetic analysis using the computer program package PEDSYS.^{41} The variance-component linkage method itself is implemented by us using the computer program FISHER.^{42} This method requires an accurate estimate of the probability that alleles at the marker are IBD for pairs of relatives (in this analysis, nuclear family members). We employed the programs FSP and SIBPAL (SAGE 1994)^{43} to obtain maximum-likelihood estimates of the proportion of marker alleles at the ecNOS4 locus that are IBD for each relative pair.

## Acknowledgments

This work was supported by a grant from NH&MRC (940521) and an International Atherosclerosis Society Visiting Fellowship for X.L. Wang and D.E.L. Wilcken, and a grant from the US NIH (HL45522) for M.C. Mahaney, J. Blangero, and L. Almasy. We would like to thank Judy Lynch and the team members of the Heart Health Education Program for recruiting families in this study. Some of the results of the research reported in this manuscript were obtained using the program package SAGE, which is supported by a US Public Health Service Research source grant (1 P41 RR03655) from the Division of Research Resources.

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- Genetic Contribution of the Endothelial Constitutive Nitric Oxide Synthase Gene to Plasma Nitric Oxide LevelsXing L. Wang, Michael C. Mahaney, Ah Siew. Sim, Jun Wang, Jian Wang, John Blangero, Laura Almasy, Renee B. Badenhop and David E. L. WilckenArteriosclerosis, Thrombosis, and Vascular Biology. 1997;17:3147-3153, originally published November 1, 1997https://doi.org/10.1161/01.ATV.17.11.3147
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- Genetic Contribution of the Endothelial Constitutive Nitric Oxide Synthase Gene to Plasma Nitric Oxide LevelsXing L. Wang, Michael C. Mahaney, Ah Siew. Sim, Jun Wang, Jian Wang, John Blangero, Laura Almasy, Renee B. Badenhop and David E. L. WilckenArteriosclerosis, Thrombosis, and Vascular Biology. 1997;17:3147-3153, originally published November 1, 1997https://doi.org/10.1161/01.ATV.17.11.3147