A discussion of gene-gene and gene-environment interactions and longitudinal genetic analysis of complex traits

Interaction analyses based on growth parameters of GWAS between Escherichia coli and Staphylococcus aureus

To accurately explore the interaction mechanism between Escherichia coli and Staphylococcus aureus, we designed an ecological experiment to monoculture and co-culture E. coli and S. aureus. We co-cultured 45 strains of E. coli and S. aureus, as well as each species individually to measure growth over 36 h. We implemented a genome wide association study (GWAS) based on growth parameters (λ, R, A and s) to identify significant single nucleotide polymorphisms (SNPs) of the bacteria. Three commonly used growth regression equations, Logistic, Gompertz, and Richards, were used to fit the bacteria growth data of each strain. Then each equation's Akaike's information criterion (AIC) value was calculated as a commonly used information criterion. We used the optimal growth equation to estimate the four parameters above for strains in co-culture. By plotting the estimates for each parameter across two strains, we can visualize how growth parameters respond ecologically to environment stimuli. We verified that different genotypes of bacteria had different growth trajectories, although they were the same species. We reported 85 and 52 significant SNPs that were associated with interaction in E. coli and S. aureus, respectively. Many significant genes might play key roles in interaction, such as yjjW, dnaK, aceE, tatD, ftsA, rclR, ftsK, fepA in E. coli, and scdA, trpD, sdrD, SAOUHSC_01219 in S. aureus. Our study illustrated that there were multiple genes working together to affect bacterial interaction, and laid a solid foundation for the later study of more complex inter-bacterial interaction mechanisms.

Integrating High-Throughput Phenotyping and Statistical Genomic Methods to Genetically Improve Longitudinal Traits in Crops

The rapid development of remote sensing in agronomic research allows the dynamic nature of longitudinal traits to be adequately described, which may enhance the genetic improvement of crop efficiency. For traits such as light interception, biomass accumulation, and responses to stressors, the data generated by the various high-throughput phenotyping (HTP) methods requires adequate statistical techniques to evaluate phenotypic records throughout time. As a consequence, information about plant functioning and activation of genes, as well as the interaction of gene networks at different stages of plant development and in response to environmental stimulus can be exploited. In this review, we outline the current analytical approaches in quantitative genetics that are applied to longitudinal traits in crops throughout development, describe the advantages and pitfalls of each approach, and indicate future research directions and opportunities.

Longitudinal linear combination test for gene set analysis

Background

Although microarray studies have greatly contributed to recent genetic advances, lack of replication has been a continuing concern in this area. Complex study designs have the potential to address this concern, though they remain undervalued by investigators due to the lack of proper analysis methods. The primary challenge in the analysis of complex microarray study data is handling the correlation structure within data while also dealing with the combination of large number of genetic measurements and small number of subjects that are ubiquitous even in standard microarray studies. Motivated by the lack of available methods for analysis of repeatedly measured phenotypic or transcriptomic data, herein we develop a longitudinal linear combination test (LLCT).

Results

LLCT is a two-step method to analyze multiple longitudinal phenotypes when there is high dimensionality in response and/or explanatory variables. Alternating between calculating within-subjects and between-subjects variations in two steps, LLCT examines if the maximum possible correlation between a linear combination of the time trends and a linear combination of the predictors given by the gene expressions is statistically significant. A generalization of this method can handle family-based study designs when the subjects are not independent. This method is also applicable to time-course microarray, with the ability to identify gene sets that exhibit significantly different expression patterns over time. Based on the results from a simulation study, LLCT outperformed its alternative: pathway analysis via regression. LLCT was shown to be very powerful in the analysis of large gene sets even when the sample size is small.

Conclusions

This self-contained pathway analysis method is applicable to a wide range of longitudinal genomics, proteomics, metabolomics (OMICS) data, allows adjusting for potentially time-dependent covariates and works well with unbalanced and incomplete data. An important potential application of this method could be time-course linkage of OMICS, an attractive possibility for future genetic researchers.

Availability: R package of LLCT is available at: https://github.com/its-likeli-jeff/LLCT

Conditional Inference Tree for Multiple Gene-Environment Interactions on Myocardial Infarction

BACKGROUND AND AIMS

Identifying gene-environment interaction in the context of multiple environmental factors has been a challenging task. We aimed to use conditional inference tree (CTREE) to strata myocardial infarction (MI) risk synthesizing information from both genetic and environmental factors.

METHODS

We conducted a case-control study including 1440 Chinese men (730 MI patients and 710 controls). We first calculated a weighted genetic risk score (GRS) by combining 25 single nucleotide polymorphisms (SNPs) that had been identified to be associated with coronary artery diseases in previous genome wide association studies. We then developed a CTREE model to interpret the gene-environment interaction network in predicting MI.

RESULTS

We detected high-order interactions between dyslipidemia, GRS, smoking status, age and diabetes. Of all the variables examined, high density lipoprotein cholesterol (HDL-C) of 1.25 mmlo/L was identified as the key discriminator. The subsequent splits of MI were low density lipoprotein cholesterol (LDL-C) of 4.01 mmol/L and GRS of 20.9. We found that individuals with HDL-C ≤1.25 mmol/L, GRS >20.9 and lipoprotein (a) > 0.09 g/L had a higher risk of MI than those who at the lowest risk group (OR: 5.89, 95% CI: 3.99-8.69). This magnitude of MI risk was similar to the combination of HDL-C ≤1.25 mmol/L, GRS ≤20.9, smoking and lipoprotein (a) > 0.15 g/L (OR: 5.49, 95% CI: 3.51-8.58).

CONCLUSIONS

The multiple interactions between genetic and environmental factors can be visually present via the CTREE approach. The tree diagram also simplifies the decision making procedure by answering a sequence of questions along the branches.

Classification and Clustering Methods for Multiple Environmental Factors in Gene-Environment Interaction: Application to the Multi-Ethnic Study of Atherosclerosis

There has been an increased interest in identifying gene-environment interaction (G × E) in the context of multiple environmental exposures. Most G × E studies analyze one exposure at a time, but we are exposed to multiple exposures in reality. Efficient analysis strategies for complex G × E with multiple environmental factors in a single model are still lacking. Using the data from the Multiethnic Study of Atherosclerosis, we illustrate a two-step approach for modeling G × E with multiple environmental factors. First, we utilize common clustering and classification strategies (e.g., k-means, latent class analysis, classification and regression trees, Bayesian clustering using Dirichlet Process) to define subgroups corresponding to distinct environmental exposure profiles. Second, we illustrate the use of an additive main effects and multiplicative interaction model, instead of the conventional saturated interaction model using product terms of factors, to study G × E with the data-driven exposure subgroups defined in the first step. We demonstrate useful analytical approaches to translate multiple environmental exposures into one summary class. These tools not only allow researchers to consider several environmental exposures in G × E analysis but also provide some insight into how genes modify the effect of a comprehensive exposure profile instead of examining effect modification for each exposure in isolation.

Novel likelihood ratio tests for screening gene-gene and gene-environment interactions with unbalanced repeated-measures data

There has been extensive literature on modeling gene-gene interaction (GGI) and gene-environment interaction (GEI) in case-control studies with limited literature on statistical methods for GGI and GEI in longitudinal cohort studies. We borrow ideas from the classical two-way analysis of variance literature to address the issue of robust modeling of interactions in repeated-measures studies. While classical interaction models proposed by Tukey and Mandel have interaction structures as a function of main effects, a newer class of models, additive main effects and multiplicative interaction (AMMI) models, do not have similar restrictive assumptions on the interaction structure. AMMI entails a singular value decomposition of the cell residual matrix after fitting the additive main effects and has been shown to perform well across various interaction structures. We consider these models for testing GGI and GEI from two perspectives: likelihood ratio test based on cell means and a regression-based approach using individual observations. Simulation results indicate that both approaches for AMMI models lead to valid tests in terms of maintaining the type I error rate, with the regression approach having better power properties. The performance of these models was evaluated across different interaction structures and 12 common epistasis patterns. In summary, AMMI model is robust with respect to misspecified interaction structure and is a useful screening tool for interaction even in the absence of main effects. We use the proposed methods to examine the interplay between the hemochromatosis gene and cumulative lead exposure on pulse pressure in the Normative Aging Study.

Longitudinal association analysis of quantitative traits

Longitudinal genetic studies provide a valuable resource for exploring key genetic and environmental factors that affect complex traits over time. Genetic analysis of longitudinal data that incorporate temporal variations is important for understanding genetic architecture and biological variations of common complex diseases. Although they are important, there is a paucity of statistical methods to analyze longitudinal human genetic data. In this article, longitudinal methods are developed for temporal association mapping to analyze population longitudinal data. Both parametric and nonparametric models are proposed. The models can be applied to multiple diallelic genetic markers such as single-nucleotide polymorphisms and multiallelic markers such as microsatellites. By analytical formulae, we show that the models take both the linkage disequilibrium and temporal trends into account simultaneously. Variance-covariance structure is constructed to model the single measurement variation and multiple measurement correlations of an individual based on the theory of stochastic processes. Novel penalized spline models are used to estimate the time-dependent mean functions and regression coefficients. The methods were applied to analyze Framingham Heart Study data of Genetic Analysis Workshop (GAW) 13 and GAW 16. The temporal trends and genetic effects of the systolic blood pressure are successfully detected by the proposed approaches. Simulation studies were performed to find out that the nonparametric penalized linear model is the best choice in fitting real data. The research sheds light on the important area of longitudinal genetic analysis, and it provides a basis for future methodological investigations and practical applications.