Gene-environment interactions due to quantile-specific heritability of triglyceride and VLDL concentrations

“Quantile-dependent expressivity” is a dependence of genetic effects on whether the phenotype (e.g., triglycerides) is high or low relative to its distribution in the population. Quantile-specific offspring-parent regression slopes (βOP) were estimated by quantile regression for 6227 offspring-parent pairs. Quantile-specific heritability (h2), estimated by 2βOP/(1 + rspouse), decreased 0.0047 ± 0.0007 (P = 2.9 × 10−14) for each one-percent decrement in fasting triglyceride concentrations, i.e., h2 ± SE were: 0.428 ± 0.059, 0.230 ± 0.030, 0.111 ± 0.015, 0.050 ± 0.016, and 0.033 ± 0.010 at the 90th, 75th, 50th, 25th, and 10th percentiles of the triglyceride distribution, respectively. Consistent with quantile-dependent expressivity, 11 drug studies report smaller genotype differences at lower (post-treatment) than higher (pre-treatment) triglyceride concentrations. This meant genotype-specific triglyceride changes could not move in parallel when triglycerides were decreased pharmacologically, so that subtracting pre-treatment from post-treatment triglyceride levels necessarily created a greater triglyceride decrease for the genotype with a higher pre-treatment value (purported precision-medicine genetic markers). In addition, sixty-five purported gene-environment interactions were found to be potentially attributable to triglyceride’s quantile-dependent expressivity, including gene-adiposity (APOA5, APOB, APOE, GCKR, IRS-1, LPL, MTHFR, PCSK9, PNPLA3, PPARγ2), gene-exercise (APOA1, APOA2, LPL), gene-diet (APOA5, APOE, INSIG2, LPL, MYB, NXPH1, PER2, TNFA), gene-alcohol (ALDH2, APOA5, APOC3, CETP, LPL), gene-smoking (APOC3, CYBA, LPL, USF1), gene-pregnancy (LPL), and gene-insulin resistance interactions (APOE, LPL).


Results
There were 3325 Third Generation subjects who had one or more parents in the Offspring Cohort (1089 had one parent, 2236 had both parents). There were 1016 sibships with two or more full siblings in the Offspring Cohort (532 with two, 302 with three, 122 with four, and 60 with ≥five full sibs) and 1171 sibships with two or more full siblings in the Third Generation Cohort (576 with two, 333 with three, 155 with four, and 107 with ≥five full sibs). Unadjusted average triglyceride (SD) for subjects used in the analyses was 2.390 (1.934) mmol/L in the Offspring Cohort and 1.279 (0.914) mmol/L in the Third Generation Cohort. In addition, sibships from the Offspring Cohort had an unadjusted average VLDL-cholesterol concentration of 0.585 (0.294) mmol/L for exams 1-3. Correlational analyses showed spouses were concordantly related for age-and sex-adjusted triglycerides (r spouse = 0.15), log triglycerides (r spouse = 0.31), and VLDL-cholesterol (r spouse = 0.09). Table 1 presents the traditional least squares regression slopes between offspring and parent (β OP ) and offspring and midparent (β OM ) and among full sibs (β FS ). Triglyceride heritability (h 2 ± SE) was significant as traditionally estimated from β OP (0.146 ± 0.013), β OM (0.131 ± 0.012), or β FS (0.456 ± 0.031). Heritability was even stronger for log triglycerides when estimated from β OP (0.360 ± 0.023), β OM (0.380 ± 0.023), or β FS (0.532 ± 0.030). Heritibility of VLDL-cholesterol was 0.343 ± 0.046 when estimated from full sibs (β OP unavailable because parents were not measured). slopes (β OP ) for selected quantiles of the offspring's plasma triglyceride distribution with their associated heritability estimates (h 2 the narrow sense). Heritability became progressively greater with increasing quantiles of the offspring's distribution, and differed significantly between the 10 th and 90 th percentiles (P = 2.2 × 10 −11 ). These selected quantile-specific heritability estimates were included with those of other quantiles to create the quantile-specific heritability function in the lower panel, i.e., where h 2 (Y-axis) is plotted as a function of the quantile of the offspring's sample distribution (X-axis). Specifically, the Y-axis represents heritability at the 5th quantile, the 6th quantile,…, and the 95th quantiles of the offspring's distribution. The shaded area presents the 95% confidence intervals for the individual slopes at each quantile. The figure shows that h 2 increased from 0.033 ± 0.010 at their 10th percentile (P = 0.0009), 0.050 ± 0.016 at the 25th (P = 0.001), 0.111 ± 0.015 at the 50 th (P = 1.3 × 10 −13 ), 0.230 ± 0.030 at the 75 th (P = 1.7 × 10 −14 ), and 0.428 ± 0.059 at the 90th percentile of the offspring' distribution (P = 6.4 × 10 −13 ). If the heritability was the same for all offspring quantiles as traditionally assumed, then the upper panel would display parallel regression lines, and the lower graph would present a simple horizontal line. In fact, the graph shows that heritability became progressively stronger with increasing quantiles of its offsprings' triglyceride distribution, such that on average each 1-percent increase in the offspring distribution was associated with a 0.0047 ± 0.0007 increase in heritability (P = 2.9 × 10 −14 ). Moreover, the increase in quantile-specific h 2 with increasing offspring's triglyceride concentrations was significantly nonlinear, exhibiting both quadratic (P = 1.7 × 10 −6 ) and cubic (P = 0.0007) effects. With respect to individual quantiles, heritability was statistically significant (P < 0.003) at every percentile between the 5 th and the 95 th percentiles of the offspring' distribution, and was 13-fold greater at the 90th than at the 10th percentile. Figure 2 shows that the full-sib regression slope for triglyceride concentrations (β FS ): 1) was 3.8-fold greater at the 90 th (0.487 ± 0.081) than the 10 th percentile (0.121 ± 0.010) of the sib distribution; and 2) increased 0.0042 ± 0.0007 (P = 1.8 × 10 −9 ) for each percentile increase in the sibs' distribution, and 3) exhibited significant nonlinearity (quadratic: P = 0.0007; cubic: P = 0.003). The full-sib slopes were statistically significant (P < 0.0001) at every percentile between the 5 th and the 95 th percentiles of the offspring' distribution. Figure 2 also shows that siblings exhibited quantile-specific associations that were significantly greater at the 90 th than 10 th percentiles of the VLDL-cholesterol distribution (P = 0.04), and exhibited significant linear increases with each one-percent increment in their VLDL-cholesterol (0.0026 ± 0.0009, P = 0.003).

Discussion
Genome-wide association studies have identified 36 single nucleotide polymorphisms (SNP) associated with triglyceride concentrations 5,6 . The most significant SNPs are associated with the glucokinase regulator (GCKR, P = 2 × 10 −239 ), apolipoprotein A1 (APOA1, P = 7 × 10 −224 ), and lipoprotein lipase genes (LPL, P = 2 × 10 −199 ). Because only about 11% of the triglyceride variance is explained by these 36 loci 5,6 , the current paper investigated www.nature.com/scientificreports www.nature.com/scientificreports/ heritability in the narrow sense (h 2 ) as a more comprehensive, albeit less specific, estimate of genetic transmission. It showed that h 2 increased significantly with increasing percentiles of the triglyceride distribution. This result was replicated for β FS in the Framingham Offspring Cohort and Framingham Third Generation cohort separately. This confirms our previous analyses of fasting plasma triglyceride concentrations vs. GRS TG 2 , and postprandial triglyceride concentrations vs. individual SNPs 3 . The current analyses also demonstrated quantile-dependency for VLDL-cholesterol concentrations in sibs. Quantile dependence was also significant for log-transformed triglyceride concentrations. These analyses were based on simple robust estimates of heritability with nonparametric statistical significance determined from 1000 bootstrap samples.
For example, the histogram in Fig. 4A (insert) shows the reductions in fasting triglyceride levels reported by Lai et al. after three-week fenofibrate treatments 15 . The average decrease was significantly greater in APOA5 56 G carriers than non-carriers (35.8% vs. 27.9% decreases, P = 0.006). An accompanying editorial heralded its potential contribution to personalized medicine 83 . There is, however, an alternative interpretation of Lai et al. 's results from the perspective of quantile-dependent expressivity. Figure 4A shows that average triglyceride levels were higher before (1.58 ± 0.04 mmol/L) than after treatment (1.01 ± 0.02 mmol/L) and that triglyceride difference between genotypes were greater at the higher pre-treatment triglyceride levels (1.99-1.52 = 0.46 mmol/L difference, P = 0.01) than at the lower post-treatment triglyceride levels (1.06-1.00 = 0.06 mmol/L difference, P = 0.22), consistent with quantile-dependent expressivity. The smaller genetic effect size at the lower (post-treatment) than higher (pre-treatment) average triglyceride concentration requires that the trajectories of triglyceride reductions (upper panel) presents the offspring-parent regression slopes (β OP ) for selected quantiles of the offsprings' total triglyceride concentrations, with corresponding estimates of heritability (h 2 = 2β OP /(1 + r spouse )). The slopes became progressively greater (i.e., steeper) with increasing quantiles of the triglyceride distribution. These quantile-specific regression slopes were included with those of other quantiles to create the quantile-specific heritability function in the lower panel. The statistical significance of the linear, quadratic and cubic trends and the 95% confidence intervals (shaded region) were determined by 1000 bootstrap samples. 1 mg/dL = 0.01129 mmol/L. www.nature.com/scientificreports www.nature.com/scientificreports/ cannot move in parallel for different genotypes when triglycerides are decreased pharmacologically. Subtracting the pre-treatment from the post-treatment triglyceride levels will necessarily require a relatively greater triglyceride decrease for the genotype with the higher pre-treatment triglyceride level vis-à-vis the genotype with the lower pre-treatment level.    4 and 5 display additional reports, initially interpreted from the perspective of personalized medicine, that are consistent with quantile-dependent expressivity, i.e., larger pre-treatment genetic effects when average triglycerides are high, followed by smaller post-treatment genetic effects when average triglyceride concentrations are low. Cardona et al. reported that the triglyceride reduction from fenofibrate treatment was over twice as great in TC/CC genotypes than TT homozygotes of the APOA5 -1131T polymorphism (2.34 vs. 1.15 mmol/L decreases, Fig. 4B histogram) 17 . The graph show that there was a greater triglyceride difference between carriers of the C-allele and TT homozygotes before treatment (5.80-3.74 = 2.06 mmol/L) when average triglycerides were high (4.54 mmol/L) than after treatment (3.46-2.60 = 0.86 mmol/L) when average triglycerides were lower (2.93 mmol/L). Perez-Martinez et al 16 . identified three genetic risk groups in hypertriglyceridemic subjects (pre-treatment triglycerides >1.69 mmol/L) derived from the GCKR-APOA5 loci: a protected group, an intermediate group, and a risk group. The histogram in Fig. 4C shows the decreases in plasma triglyceride concentration differed significantly between these groups after three-week fenofibrate treatment (P = 0. Brautbar et al. reported that three SNPs in the ZNF259-APOA5 gene region on chromosome 11 showed substantially smaller genotype differences on fenofibrate/statin combination treatment when average triglyceride levels were low (1.64 mmol/L) compared to pretreatment differences when average levels were higher (3.15 mmol/L) 14 . Specifically, treatment reduced differences between GG, GA, and AA genotypes of rs3741298 from 3.77, 3.20, and 3.04 (P = 3.2 × 10 −5 ) to 1.67, 1.65, and 1.64, respectively (P = 0.79, Fig. 4D), between the CC, CG and GG genotypes of rs964184 from 3.51, 3.41, 3.01 mmol/L (P = 2.3 × 10 −7 ) to 1.77, 1.71, and 1.61 mmol/L, respectively (P = 0.18, Fig. 4E), and between GG, GA, and AA genotypes of rs10750097 from 3.37, 3.26, and 3.05 mmol/L (P = 0.002) to 1.62, 1.66, and 1.63 mmol/L, respectively (P = 0.86). Although the mean triglyceride reductions by genotype did not differ significantly by genotype in Brautbar's paper (0.25 ≤ P ≤ 0.82), one by Aslibekyan et al. did report that the rs964184 polymorphism affected fenofibrate-induced triglyceride change significantly (P < 0.001) 13 .
The histogram in Fig. 5A shows substantially greater triglyceride reductions due to fenofibrate treatment in 44 carriers of LPL P207L mutation than in 247 non-carriers who were hypertriglyceridemic (13.3 vs. 4.5 mmol/L average reductions). Brisson et al. attributed the difference to the mutation's modulating effect on the fenofibrate response 19 . Alternatively, quantile-dependent expressivity would attribute the difference to the greater genetic effect size of the mutation (18.93-7.38 = 11.5 mmol/L difference) when average triglycerides were elevated before treatment (9.13 mmol/L) compared to post-treatment genetic effect size (5.60-2.88 = 2.72 mmol/L difference) when average triglycerides were much lower (3.29 mmol/L).
A non-pharmacological example is provided by Balakrishnan et al. who reported that triglyceride concentrations were significantly reduced, from 1.87 to 1.50 mmol/L, in 93 patients who received pancreas transplants (P = 0.002) 24 . The triglyceride difference between APOE ε4-carriers and ε3ε3 homozygotes went from being significant (0.45 mmol/L as estimated from their Fig. 2, P = 0.04) to nonsignificant (0.08 mmol/L) after the transplant, consistent with quantile-dependent expressivity (Fig. 5E).
Hypertriglyceridemia is the most common reason for discontinuing bexarotene, a drug used for treating cutaneous T-cell lymphomas 84 . Cabello et al. proposed that carriers of the APOA5 -1131T > C or APOC3 c.40 C > G mutations were the best candidates for bexarotene treatment because of their smaller triglyceride response 25 . Figure 5F presents the triglyceride differences between genotypes before and after oral bexarotene therapy while receiving prophylactic hypolipidemic therapy and 50 μg/d of levothyroxine sodium. From the perspective of personalized medicine, carriers of either minor allele experienced smaller triglyceride increases than non-carriers (1.25 vs. 2.39 mmol/L), whereas quantile dependent-expressivity would ascribe some of the effect to the smaller genetic difference between carriers and non-carriers before treatment (effect size: + 0.12 mmol/L) when average triglyceride concentrations were lower (1.59 mmol/L) than after treatment (effect size: −1.01 mmol/L, P = 0.02) when average triglyceride concentrations were higher (3.53 mmol/L).
To summarize, whereas other papers advocate individualized drug prescriptions using genetic markers to target patients (e.g., the histograms of Figs. 4 and 5), quantile-dependent expressivity postulates that these genetic markers follow different trajectories due to smaller genetic effects at lower triglyceride concentrations. It is unnecessary to hypothesize pharmacologic interactions of these genetic markers with treatment, rather APOA5, GCKR, APOA1, and APOE are simply among the brightest genetic signals tracking the reduced heritability.
Body mass index and waist circumference. Meta-analyses suggest that plasma triglyceride concentrations decrease 0.015 mmol/L per kg of weight loss 85 . BMI and waist circumference are associated with higher triglyceride concentrations due, at least in part, to the release of free fatty acids from visceral depots causing greater hepatic synthesis of VLDL 86 . Most reports of gene-weight interactions appear to be at least partially attributable to quantile-dependent expressivity, including six studies based on genetic risk scores (GRS TG ) 26 Klimentidis et al. 28 . report that increasing tertiles of waist-to-hip ratio were associated with progressive increases in the GRS TG effect size (estimated β 1st tertile = 0.16, β 2nd = 0.18, and β 3rd = 0.22, P Interaction = 3.9 × 10 −8 ). This, however, was in the context of highly significant increases in average triglyceride concentrations with increasing waist circumference (P = 1.3 × 10 −56 ). Zubair et al. reported that the triglyceride difference between a high and low GRS TG score was greater in overweight/obese women than leaner women (0.49 vs. 0.29 mmol/L, P interaction = 0.03) and greater in broad-waisted than slim-waisted women (0.54 vs. 0.27 mmol/L, P interaction = 0.02) 29 . Again, these differences are consistent with quantile-dependent expressivity given that average triglycerides concentrations were greater in overweight/obese than leaner women (1. www.nature.com/scientificreports www.nature.com/scientificreports/ x GRS TG interactions (Inter99: P = 0.0001; Health 2006: P = 0.05; combined; P = 2.0 × 10 −5 ), with a larger genetic effect among individuals who were obese. However, average triglyceride levels for normal weight, overweight, and obese increased from 0.92, to 1.23 to 1.55 mmol/L in the Inter99 cohort, respectively, and from 0.94 to 1.23 to 1.54 mmol/L in the Health2006 cohort. Similarly, average triglyceride levels for normal, centrally overweight, and centrally obese subjects increased from 0.96 to 1.26 to 1.49 mmol/L in the Inter99 cohort and from 0.95 to 1.18 to 1.41 mmol/L in the Health2006 cohort. From the perspective of quantile-dependent expressivity, greater adiposity was an indicator of higher average triglyceride concentrations and its larger genetic effect.
Ahmad et al. reported that each unit increase in their 40-SNP GRS TG produced a significantly stronger effect on triglycerides in overweight and obese (1.013% triglyceride increase) than healthy weight women (1.011%, P interaction = 0.004), and a significantly stronger effect in centrally overweight and obese (1.012%) than centrally healthy weight women (1.010%, P interaction = 0.005) 31 . These results are consistent with quantile-dependent expressivity and the higher triglyceride concentrations of the overweight and obese vs. healthy weight women (1.8 vs. 1.3 mmol/L, P < 0.0001), and the centrally overweight and obese vs. centrally normal weight women (1.7 vs. 1.2 mmol/L, P < 0.0001).
The APOA5 gene is the strongest genetic determinant of plasma triglyceride concentrations 87 . Four studies report interactions between BMI and APOA5 polymorphisms that are consistent with quantile-dependent expressivity. Wu et al. reported that the effect size for the Gly185Cys polymorphism at APOA5 rs3741297 was accentuated in Filipinos with a higher waist circumference 32 34 . The fourth study, by Cole et al. 26 ., reported a significantly greater effect size for APOA5 rs964184 in obese than lean subjects (β = 0.159 ± 0.03 vs. 0.140 ± 0.03 mmol/L per G allele, P interaction = 0.009) whose average triglycerides differed by >0.5 mmol/L.
The LPL enzyme hydrolyzes triglycerides, and it participates in hepatic triglyceride-rich lipoprotein (TRL) clearance via the LDL receptor-related protein 1 . Multiple studies suggest that purported interactions between LPL polymorphisms and BMI on triglycerides are consistent with quantile-dependent expressivity, in that greater adiposity is associated with higher average triglyceride concentrations. Fisher et al. first reported a significant interaction between LPL S291 and BMI on triglycerides (P interaction = 0.02) 35 . Compared to those with a BMI < 25, their Fig. 2 showed heavier men had a greater triglyceride difference between genotypes (heavier vs. leaner: 0.42 vs. −0.17 mmol/L difference) corresponding to their higher average triglyceride (1.94 vs. 1.54 mmol/L) in the Northwich Park Heart Study II project 35 . The European Atherosclerosis Research Studies reported that S291-carriers had greater increases in plasma triglycerides with increasing BMI than non-carriers (P < 0.01) 36 . Correspondingly, the genotype differences and average triglyceride concentrations were −0.08 and 0.89 mmol/L in the lowest BMI tertile, respectively, 0.18 and 1.00 mmol/L in the intermediate BMI tertile, respectively, and 0.18 and 1.13 mmol/L in the highest BMI tertile, respectively. Mailly et al. reported a marginally greater triglyceride difference for carriers vs. non-carriers of the N9 mutation in overweight men (0.53 ± 0.27 mmol/L difference) with higher average triglycerides (1.86 ± 0.05 mmol/L) than in leaner men (0.02 ± 0.26 mmol/L difference) with lower average triglycerides (1.51 ± 0.05 mmol/L) 37 , as did Gerdes et al. for the highest BMI tertile (0.25 mmol/L genotype difference) with higher average triglycerides (1.12 mmol/L) vis-à-vis leaner men (0.10 mmol/L genotype difference) with lower average triglycerides (0.93 mmol/L) 36 , although neither reached statistical significance. Figure 6A presents Jemaa et al. 's findings for a 10 week restricted calorie diet by the LPL HindIII polymorphism 38 . From a precision medicine perspective, the histogram (insert) shows plasma triglyceride concentration decreased significantly more in H2H2 homozygotes than H1-carriers (0.27 vs. 0.04 mmol/L decreases, P = 0.03). Consistent with quantile-dependent expressivity, the difference between genotypes was greater at baseline than after weight loss (0.32 ± 0.13 vs. 0.09 ± 0.11 mmol/L) in accordance with the higher average triglycerides at baseline (1.23 ± 0.07 vs. 1.08 ± 0.05 mmol/L). Again, the smaller genetic effect size at the lower (post-treatment) than higher (pre-treatment) triglyceride concentrations require that the effects of the genotypes do not move in parallel when triglycerides are decreased by weight loss. Subtracting the pre-treatment from the post-treatment triglyceride levels will necessarily create a relatively greater triglyceride decrease for the genotype with the higher pre-treatment triglyceride level vis-à-vis the genotype with the lower pre-treatment level. Figure 6B  www.nature.com/scientificreports www.nature.com/scientificreports/ www.nature.com/scientificreports www.nature.com/scientificreports/ loss than before (CC vs. TT difference ± SE: 0.19 ± 0.12 after vs. 0.43 ± 0.19 mmol/L before) due to the lower average triglyceride concentrations after weight loss (1.27 ± 0.04 vs. 1.55 ± 0.05 mmol/L).
Huang et al. reported that the triglyceride difference between SS and SX/XX genotypes of the LPL S447X polymorphism was greater in centrally obese than nonobese twins (0.24 vs. 0.06 mmol/L differences, P = 0.16), corresponding to the greater average triglycerides in centrally obese than nonobese twins (1. Physical activity. Aerobic physical activity decreases triglyceride concentrations by facilitating triglyceride hydrolysis and use by skeletal muscles 88 . Meta-analyses suggest that triglyceride concentrations average 0.11 mmol/L less for those who walked ≥6000 vs. <2000 steps/day, and 0.23 mmol/L less for those who exercised at 50% of VO 2 max for three 30-minute sessions per week compared to less active subjects 89 . Our analyses of Senti et al.'s data 53 showed that the each dose of the H+ allele of the LPL HindIII polymorphism was associated with a triglyceride increase of 0.148 mmol/L in the least active men (expending ≤291 kcal/d), 0.135 mmol/L in men expending 292-525 kcal/d, and 0.105 mmol/L in the most active men (>525 kcal/d) in an apparent gene-environment interaction. However, average triglyceride concentrations decreased with increasing physical activity: from 1.432, 1.250, to 1.106 mmol/L, respectively, suggesting an effect size for the H+ allele consistent with quantile-dependent expressivity.
Ruaño et al. reported that 6 months of supervised aerobic exercise training produced significantly greater percent reductions in triglyceride concentration in A-carriers of the APOA1 -75G > A polymorphism than in GG homozygotes (P = 0.05) 57 . Figure 6D shows that average triglyceride concentrations were lower after training than before (1.30 vs. 1.49 mmol/L) corresponding to smaller genotypic differences after training than before (0.38 vs. 0.72 mmol/L).

Smoking.
Smokers are insulin resistant and exhibit impaired lipid metabolism, including impaired triglyceride clearance after a mixed meal 90 . Meta-analyses suggest that triglyceride concentrations of smokers average 9.1% higher than nonsmokers, and show a dose-dependent relationship from light (10.7%), moderate (11.5%) to heavy smokers (18%) 91 . Quantile-dependent expressivity would predict greater genetic effects on triglycerides in smokers than nonsmokers because of the smokers' higher triglyceride concentrations. Czerwinski et al. in fact reported that the heritability of plasma triglyceride concentrations was higher in smokers (h 2 = 0.70, average triglycerides 1.68 ± 0.06) than nonsmokers (h 2 = 0.42, average triglycerides 1.58 ± 0.03) 58 . With respect to individual loci, smoking is reported to modify the effects on triglycerides of the upstream stimulatory factor 1 (USF1) gene polymorphism rs2516839 59  Niemiec et al. reported that the USF1 rs2516839 polymorphism modified the triglyceride response to smoking, however, triglyceride differences between the CC, CT and TT genotypes were greater in smokers (2.27 ± 0.26, 1.80 ± 0.09, 1.53 ± 0.10 mmol/L, respectively) in accordance with their higher average triglycerides (1.79 ± 0.07 mmol/L) than in nonsmokers (1.49 ± 0.11, 1.46 ± 0.06, 1.57 ± 0.08, respectively) in accordance with their lower concentrations (1.51 ± 0.05 mmol/L) 59  Smokers did not have higher triglycerides than nonsmokers in the 41,000 subjects of the Population Architecture Using Genomics and Epidemiology (PAGE) study (mean ± SE: 1.476 ± 0.010 vs. 1.486 ± 0.005 mmol/L) 92 . Consistent with quantile-dependent expressivity, their meta-analysis did not show any significant SNP by smoking interactions.
Diet. Each 1% isoenergetic replacement of carbohydrates with fat is expected to decrease plasma triglyceride concentrations by an average of 0.021 mmol/L if saturated, 0.019 if monounsaturated, and 0.026 mmol/L if polyunsaturated 93 . Adherence to a Mediterranean diet decreases plasma triglyceride concentrations by an average of 0.069 mmol/L 94 . Quantile-dependent expressivity would predict larger genetic effects on low-fat high-carbohydrate diets than high-fat low-carbohydrate diets, and larger genetic effects on Western than Mediterranean diets, in accordance with the expected higher triglycerides of the former. www.nature.com/scientificreports www.nature.com/scientificreports/ Gomez-Delgado et al. reported that decreases in plasma triglyceride due to adopting a Mediterranean diet were significantly greater in 203 GG homozygotes of the tumor necrosis factor alpha gene (TNFA, rs1800629) than in 48 carriers of the A-allele, i.e. approximately 0.31 vs. 0.12 mmol/L, respectively (P = 0.005) 64 . However, plasma triglyceride concentrations averaged approximately 1.80 mmol/L at baseline and 1.52 mmol/L on the diet, and correspondingly, the differences between the GG and GA/AA genotypes were 0.38 vs. 0.19 mmol/L, respectively. A quantile-dependent interpretation of these results is that the Mediterranean diet decreased plasma triglyceride concentrations, which in turn produced a smaller difference between genotypes.
Garcia-Rios et al. reported significant interactions between plasma concentrations of n-6 polyunsaturated fatty acids and LPL rs238 (P interaction = 0.05) and LPL rs1059611 (P interaction = 0.04) 65 . Below median n-6 PUFA concentrations, the rs1059611 triglyceride difference between AA homozygotes and carriers of the G allele was 0.33 mmol/L and the average triglyceride concentration across genotypes was 2.14 mmol/L. Above the median, the genotype difference was smaller (−0.09 mmol/L) in accordance with lower average triglyceride concentrations (1.37 mmol/L), consistent with quantile-dependent expressivity. Nearly identical results were reported for rs238, which was in strong linkage disequilibrium with rs1059611.
Garcia-Rios et al. also reported a significant interaction between plasma saturated fatty acids concentrations and the circadian clock gene Period 2 (PER2) rs2304672 on plasma triglyceride concentrations (P interaction = 0.004) 66 67 . Figure 6E presents Lin et al. 's report of a two-fold greater triglyceride increase in C-carriers of the APOA5 -1131T > C polymorphism vs. TT homozygotes in going from a 54% carbohydrate/31% fat diet to a 70% carbohydrate/15% fat diet 68 . Consistent with quantile-dependent expressivity, the genotype difference went from 0.13 ± 0.10 to 0.22 ± 0.10 mmol/L while average triglycerides increased from 0.83 ± 0.08 to 0.94 ± 0.05 mmol/L. Figure 6F displays the significantly greater triglyceride decreases in LPL Hindlll H-carriers than H+ homozygotes when switching from a high saturated fat to a high polyunsaturated fat diet (0.35 vs. 0.10 mmol/L decreases, P = 0.05) reported by Humphries et al. 69 However, the high polyunsaturated fat diet produced smaller differences between H-and H+ genotypes than the high saturated fat diet (0.31 vs. 0.56 mmol/L) in accordance with its lower average triglyceride concentrations (2.15 vs. 2.29 mmol/L). Figure 7A presents Carvalho-Wells et al. 's finding that switching from a low-fat diet to a high-fat diet containing 3.45 g/d DHA produced significantly greater triglyceride reductions in APOE ε3ε4 heterozygotes (−0.48 ± 0.11 mmol/L) than ε3ε3 homozygotes (−0.22 ± 0.06 mmol/L, P interaction = 0.03). Average triglyceride concentrations were higher on the low-fat than high-fat diet (1.43 vs. 1.08 mmol/L), and the difference between genotypes was correspondingly greater on the low-fat than the high fat diet (0.33 vs. 0.06 mmol/l difference) 70 . Figure 7B presents Kang et al. 's report of significantly greater triglyceride increases from a refined rice diet in carriers of C-allele than TT homozygotes of the APOA5 -1131 T > C polymorphism (0.53 vs. −0.01 mmol/L, P = 0.02) 71 . Again, the difference between genotypes was greater after the diet than before (0.92 ± 0.04 vs. 0.38 ± 0.03 mmol/L difference) when average triglycerides were higher (2.03 ± 0.02 vs. 1.75 ± 0.01 mmol/L).
Pregnancy. There is a two-fold increase in circulating triglyceride levels during the third trimester due to enhanced VLDL-production and LPL supression 86 . Ma et al. reported that the effect of LPL deficiency had a much greater effect during pregnancy, when triglycerides are normally two-to three-fold higher, than when not pregnant, i.e., the LPL deficient women's triglyceride were 20. Limitations. An important limitation of the analysis of the Framingham data its reliance on the simple formula h 2 = 2β OP /(1 + r spouse ) and h 2 = [(1 + 8r spouse β FS ) 0.5 − 1]/(2r spouse) to estimate heritability 12 . These formula are unlikely to embody the true complexity of triglyceride inheritance. With respect to the published examples cited, we wish to emphasize that consistency with quantile-dependent expressivity does not disprove gene-environment interactions, rather, it provides an alternative interpretation. The examples presented are those originally interpreted from the perspective of precision medicine and biological interactions that might be more easily explained by quantile-dependent expressivity. It is not our contention that all triglyceride gene-environment interactions are explained by quantile-dependent expressivity. For example, Wojczynski et al. 's report of the significant effect (P < 0.0001) of the APOB rs676210 variant on the triglyceride response to fenofibrate would not be attributable to the quantile-dependent expressivity of Fig. 1 due to their being larger genotype differences post-treatment when triglycerides were low than pretreatment when triglycerides were high 95 . Some gene-environmental interactions may arise because triglycerides and environmental factors may be coregulated by shared genes or genes in strong linkage equilibrium. For that reason, the examples presented in Figs. 4-7 may be particularly informative for testing whether the genetic effect size is affected by average triglyceride concentrations because they represent intervention affecting triglyceride concentrations directly. Among the various genetic variants discovered to date, the proportion of the total triglyceride heritability explained by any specific SNP is too small to noticeably affect h 25,6 . Thus quantile-dependence of triglyceride heritability estimated from parent and offspring phenotypes does not necessarily describe the interactions between any particular genetic variant and its environment. Many published reports do not provide the information required to evaluate their consistency with quantile-dependent expressivity, namely unadjusted triglyceride concentrations by genotype and condition.
In conclusion, assuming Falconer and Mackay's formula apply 12 , these analyses suggest that triglyceride heritability is strongly dependent upon whether an individual is high or low relative to the triglyceride distribution in the population. Alternatively, quantile-dependent shared environmental effects could also give rise to the increase in β OP and β FS with increasing average triglyceride concentrations, however our previous findings showing increasing genetic effect size for GRS TG 2 and during post-prandial triglyceride increases 3 , and the studies cited herein 13-79 support a genetic interpretation. Quantile-dependent expressivity potentially provides a common principle underlying a plethora of published gene-drug and gene-environment interactions. Specifically, rather than attributing these interactions on the basis of triglyceride metabolism, gene functionality, and the specific metabolic effect of adiposity, physical activity, insulin resistance, diet, smoking, alcohol, and pregnancy, quantile-dependent expressivity postulates that the impaired functionalities of these genetic variants are simply triglyceride concentration dependent.