Gene-based mediation analysis in epigenetic studies.

Mediation analysis has been a useful tool for investigating the effect of mediators that lie in the path from the independent variable to the outcome. With the increasing dimensionality of mediators such as in (epi)genomics studies, high-dimensional mediation model is needed. In this work, we focus on epigenetic studies with the goal to identify important DNA methylations that act as mediators between an exposure disease outcome. Specifically, we focus on gene-based high-dimensional mediation analysis implemented with kernel principal component analysis to capture potential nonlinear mediation effect. We first review the current high-dimensional mediation models and then propose two gene-based analytical approaches: gene-based high-dimensional mediation analysis based on linearity assumption between mediators and outcome (gHMA-L) and gene-based high-dimensional mediation analysis based on nonlinearity assumption (gHMA-NL). Since the underlying true mediation relationship is unknown in practice, we further propose an omnibus test of gene-based high-dimensional mediation analysis (gHMA-O) by combing gHMA-L and gHMA-NL. Extensive simulation studies show that gHMA-L performs better under the model linear assumption and gHMA-NL does better under the model nonlinear assumption, while gHMA-O is a more powerful and robust method by combining the two. We apply the proposed methods to two datasets to investigate genes whose methylation levels act as important mediators in the relationship: (1) between alcohol consumption and epithelial ovarian cancer risk using data from the Mayo Clinic Ovarian Cancer Case-Control Study and (2) between childhood maltreatment and comorbid post-traumatic stress disorder and depression in adulthood using data from the Gray Trauma Project.

Identifying complex gene-gene interactions: a mixed kernel omnibus testing approach.

Genes do not function independently; rather, they interact with each other to fulfill their joint tasks. Identification of gene-gene interactions has been critically important in elucidating the molecular mechanisms responsible for the variation of a phenotype. Regression models are commonly used to model the interaction between two genes with a linear product term. The interaction effect of two genes can be linear or nonlinear, depending on the true nature of the data. When nonlinear interactions exist, the linear interaction model may not be able to detect such interactions; hence, it suffers from substantial power loss. While the true interaction mechanism (linear or nonlinear) is generally unknown in practice, it is critical to develop statistical methods that can be flexible to capture the underlying interaction mechanism without assuming a specific model assumption. In this study, we develop a mixed kernel function which combines both linear and Gaussian kernels with different weights to capture the linear or nonlinear interaction of two genes. Instead of optimizing the weight function, we propose a grid search strategy and use a Cauchy transformation of the P-values obtained under different weights to aggregate the P-values. We further extend the two-gene interaction model to a high-dimensional setup using a de-biased LASSO algorithm. Extensive simulation studies are conducted to verify the performance of the proposed method. Application to two case studies further demonstrates the utility of the model. Our method provides a flexible and computationally efficient tool for disentangling complex gene-gene interactions associated with complex traits.

Theoretical study of the effects of surface Cu coordination environment on CO2 hydrogenation to CH3OH.

The coordination environment of Cu (the coordination number and arrangement of surface atoms) plays an important role in CO2 hydrogenation to CH3OH. Compared with the extensive studies of the effects of coordination number, the comprehensive effects of coordination number and arrangement of surface atoms were seldom explored in literature. To unravel the effects of surface Cu coordination environment on CO2 hydrogenation to CH3OH, the adsorption and reaction behaviors of H2 and CO2 on Cu(111), (100), (110) and (211) with different coordination numbers and arrangement of surface Cu were systematically calculated by density functional theory (DFT) and kinetic Monte Carlo (kMC) simulation. It was found that the adsorption energies of intermediates in CO2 hydrogenation on Cu surfaces increase with the decrease of coordination number. When the Cu coordination numbers are similar, the charge density on the open surface derived from the different atom arrangement becomes larger and leads to stronger interaction with intermediates than that on the compact one. DFT calculation and kMC simulation indicate that methanol formation pathway follows CO2*→HCOO*→HCOOH*→H2COOH*→H2CO*→CH3O*→CH3OH* on four Cu facets; CO formation is via CO2 direct dissociation on Cu(111), (100) and (110) but COOH* dissociation on (211). The low-coordinated surface Cu with more openness on Cu(211) is the highly active site for CO2 hydrogenation to CH3OH with high turnover of frequency (3.71 × 10-4 s-1) and high selectivity (87.17 %) at 600 K, PCO2 = 7.5 atm and PH2 = 22.5 atm, which is much higher than those on Cu(111), (100) and (110). This work unravels the effects of coordination environment on CO2 hydrogenation at the molecular level and provides an important insight into the design and development of catalysts with high performance in CO2 hydrogenation to CH3OH.

Testing Mediation Effects in High-Dimensional Epigenetic Studies.

Mediation analysis has been a powerful tool to identify factors mediating the association between exposure variables and outcomes. It has been applied to various genomic applications with the hope to gain novel insights into the underlying mechanism of various diseases. Given the high-dimensional nature of epigenetic data, recent effort on epigenetic mediation analysis is to first reduce the data dimension by applying high-dimensional variable selection techniques, then conducting testing in a low dimensional setup. In this paper, we propose to assess the mediation effect by adopting a high-dimensional testing procedure which can produce unbiased estimates of the regression coefficients and can properly handle correlations between variables. When the data dimension is ultra-high, we first reduce the data dimension from ultra-high to high by adopting a sure independence screening (SIS) method. We apply the method to two high-dimensional epigenetic studies: one is to assess how DNA methylations mediate the association between alcohol consumption and epithelial ovarian cancer (EOC) status; the other one is to assess how methylation signatures mediate the association between childhood maltreatment and post-traumatic stress disorder (PTSD) in adulthood. We compare the performance of the method with its counterpart via simulation studies. Our method can be applied to other high-dimensional mediation studies where high-dimensional mediation variables are collected.