Local Ancestry StructLMM for GxG Interactions

Overview

This repository contains a methodology that adapts the StructLMM framework to study Gene-Gene (GxG) interactions instead of Gene-Environment (GxE) interactions. Our approach leverages local ancestry Principal Components (PCs) as a proxy for the "environment" in the StructLMM model. Slides

Methodology

We extend the StructLMM framework by Moore et al. (2018) to detect GxG interactions using the following inputs:

1. A query SNV that has a large effect size for a phenotype
2. A query region of interest to test for interactions (can be cis or trans)
3. The phenotype

The key innovation is using local ancestry Principal Components as the "environment" matrix in the StructLMM model. This allows us to capture interaction effects between the query SNV and genetic variants in the region of interest.

Model

The adapted model is structured as:

$$\mathbf{y} = \mathbf{M}\boldsymbol{\alpha} + g\boldsymbol{\beta_0} + g\circ\boldsymbol{\beta_1} + \mathbf{e} + \boldsymbol{\varepsilon},$$

where:

$$\boldsymbol{\beta_0} \sim \mathcal{N}(\mathbf{0}, r_0 \cdot \rho\mathbf{I}), \quad \boldsymbol{\beta_1} \sim \mathcal{N}(\mathbf{0}, r_0(1-\rho)\mathbf{EE}^\top), \quad \mathbf{e} \sim \mathcal{N}(\mathbf{0}, r_1\mathbf{EE}^\top), \quad \text{and} \quad \boldsymbol{\varepsilon} \sim \mathcal{N}(\mathbf{0}, r_2\mathbf{I}).$$

• y is the phenotype vector
• M contains covariates
• g is the query SNV with large effect size
• E is a matrix representing local ancestry PCs from the query region
• $\rho \in [0, 1]$ dictates the relevance of the interaction effect

Pipeline

We are assuming that the genotypes are in PLINK format split by chromosome and reside in a directory here called "testPlink", click to download the example files (97 files in total), and make sure it's in the testPlink folder

Step 1: Extract Local Ancestry PCs

We extract Principal Components from a specified genomic region to capture local ancestry patterns:

./dataPrepScripts/getPCfromPlinkDirectory.sh testPlink/  chr6:29944513-29945558 output/PCoutput

The script:

1. Extracts variants from the region of interest
2. Performs quality control
3. Calculates PCs that explain up to 90% of variance
4. Outputs PC coordinates and variance explained

Extract the single variant of interest:

./dataPrepScripts/getSingleVariantFromPlinkDirectory.sh testPlink/ chr6:32529369:C:A output/SNVoutput.txt

The query variant can be from any source and can even be an aggregate score over multiple variants.

Step 2: Run StructLMM with Local Ancestry PCs

We then apply the StructLMM framework using:

• The query SNV as the genetic variant
• Local ancestry PCs as the "environment"
• The phenotype of interest

Requirements

• PLINK 2.0
• Python 3.6+
  • numpy
  • pandas
  • scipy
  • StructLMM

Setting up StructLMM Environment via Conda

To install StructLMM and all required dependencies in a clean environment, follow these steps:

# Create a conda environment
conda create --name structlmm_env

# Activate the environment
conda activate structlmm_env

# Install necessary packages
conda install -c conda-forge -c bioconda liknorm-py=1.2.6 glimix-core chi2comb -y

# Install StructLMM
pip install struct-lmm

Usage

Step 1: Extract local ancestry PCs

# Extract PCs from region of interest
./dataPrepScripts/getPCfromPlinkDirectory.sh testPlink/  chr6:29944513-29945558 output/PCoutput

# Extract the variant of interest
./dataPrepScripts/getSingleVariantFromPlinkDirectory.sh testPlink/ chr6:32529369:C:A output/SNVoutput.txt

Step 2: Run GxG analysis

python gxg-structlmm-script.py \
  --pcs output/PCoutput_local_ancestry_pcs.csv \
  --snv output/SNVoutput.txt  \
  --phenotype testPlink/synthetic_small_v1.pheno1 \
  --phenotype-column "Phenotype(binary)" \
  --output results.csv

Reference Implementation

This methodology builds upon the StructLMM framework. The original StructLMM implementation is available at: https://github.com/limix/struct-lmm

Citation

If you use this method in your research, please cite:

Original StructLMM paper:

Moore, R., Casale, F. P., Bonder, M. J., Horta, D., Franke, L., Barroso, I., & Stegle, O. (2018). A linear mixed-model approach to study multivariate gene–environment interactions. Nature Genetics, 50(7), 1167-1174.