Transferring entropy to the realm of GxG interactions

Revealing third-order interactions through the integration of machine learning and entropy methods in genomic studies

BACKGROUND

Non-linear relationships at the genotype level are essential in understanding the genetic interactions of complex disease traits. Genome-wide association Studies (GWAS) have revealed statistical association of the SNPs in many complex diseases. As GWAS results could not thoroughly reveal the genetic background of these disorders, Genome-Wide Interaction Studies have started to gain importance. In recent years, various statistical approaches, such as entropy-based methods, have been suggested for revealing these non-additive interactions between variants. This study presents a novel prioritization workflow integrating two-step Random Forest (RF) modeling and entropy analysis after PLINK filtering. PLINK-RF-RF workflow is followed by an entropy-based 3-way interaction information (3WII) method to capture the hidden patterns resulting from non-linear relationships between genotypes in Late-Onset Alzheimer Disease to discover early and differential diagnosis markers.

RESULTS

Three models from different datasets are developed by integrating PLINK-RF-RF analysis and entropy-based three-way interaction information (3WII) calculation method, which enables the detection of the third-order interactions, which are not primarily considered in epistatic interaction studies. A reduced SNP set is selected for all three datasets by 3WII analysis by PLINK filtering and prioritization of SNP with RF-RF modeling, promising as a model minimization approach. Among SNPs revealed by 3WII, 4 SNPs out of 19 from GenADA, 1 SNP out of 27 from ADNI, and 4 SNPs out of 106 from NCRAD are mapped to genes directly associated with Alzheimer Disease. Additionally, several SNPs are associated with other neurological disorders. Also, the genes the variants mapped to in all datasets are significantly enriched in calcium ion binding, extracellular matrix, external encapsulating structure, and RUNX1 regulates estrogen receptor-mediated transcription pathways. Therefore, these functional pathways are proposed for further examination for a possible LOAD association. Besides, all 3WII variants are proposed as candidate biomarkers for the genotyping-based LOAD diagnosis.

CONCLUSION

The entropy approach performed in this study reveals the complex genetic interactions that significantly contribute to LOAD risk. We benefited from the entropy-based 3WII as a model minimization step and determined the significant 3-way interactions between the prioritized SNPs by PLINK-RF-RF. This framework is a promising approach for disease association studies, which can also be modified by integrating other machine learning and entropy-based interaction methods.

Detecting gene-gene interactions from GWAS using diffusion kernel principal components

Genes and gene products do not function in isolation but as components of complex networks of macromolecules through physical or biochemical interactions. Dependencies of gene mutations on genetic background (i.e., epistasis) are believed to play a role in understanding molecular underpinnings of complex diseases such as inflammatory bowel disease (IBD). However, the process of identifying such interactions is complex due to for instance the curse of high dimensionality, dependencies in the data and non-linearity. Here, we propose a novel approach for robust and computationally efficient epistasis detection. We do so by first reducing dimensionality, per gene via diffusion kernel principal components (kpc). Subsequently, kpc gene summaries are used for downstream analysis including the construction of a gene-based epistasis network. We show that our approach is not only able to recover known IBD associated genes but also additional genes of interest linked to this difficult gastrointestinal disease.

Optimized permutation testing for information theoretic measures of multi-gene interactions

Background

Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large.

Results

In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 10³ for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples.

Conclusions

The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

Genome-wide association analysis of pulse wave velocity traits provide new insights into the causal relationship between arterial stiffness and blood pressure

Background

The pathophysiology of arterial stiffness is not completely understood. Pulse wave velocity (PWV) is an established marker for arterial stiffness. We compare genetics of three PWV modes, namely carotid-femoral PWV (cfPWV), brachial-ankle (baPWV) and brachial-femoral (bfPWV), reflecting different vascular segments to analyse association with genetic variants, heritability and genetic correlation with other biological traits. Furthermore we searched for shared genetic architecture concerning PWV, blood pressure (BP) and coronary artery disease (CAD) and examined the causal relationship between PWV and BP.

Methods and results

We performed a genome-wide association study (GWAS) for cfPWV, baPWV and bfPWV in LIFE-Adult (N = 3,643–6,734). We analysed the overlap of detected genetic loci with those of BP and CAD and performed genetic correlation analyses. By bidirectional Mendelian Randomization, we assessed the causal relationships between PWV and BP. For cfPWV we identified a new locus with genome-wide significance near SLC4A7 on cytoband 3p24.1 (lead SNP rs939834: p = 2.05x10^-8). We replicated a known PWV locus on cytoband 14q32.2 near RP11-61O1.1 (lead SNPs: rs17773233, p = 1.38x10^-4; rs1381289, p = 1.91x10^-4) For baPWV we estimated a heritability of 28% and significant genetic correlation with hypertension (rg = 0.27, p = 6.65x10^-8). We showed a positive causal effect of systolic blood pressure on PWV modes (cfPWV: p = 1.51x10^-4; bfPWV: p = 1.45x10^-3; baPWV: p = 6.82x10^-15).

Conclusions

We identified a new locus for arterial stiffness and successfully replicated an earlier proposed locus. PWV shares common genetic architecture with BP and CAD. BP causally affects PWV. Larger studies are required to further unravel the genetic determinants and effects of PWV.

Information Theory in Computational Biology: Where We Stand Today

"A Mathematical Theory of Communication" was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then, the concepts and ideas developed in Shannon's work have formed the basis of information theory, a cornerstone of statistical learning and inference, and has been playing a key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In this article we review the basic information theory based concepts and describe their key applications in multiple major areas of research in computational biology-gene expression and transcriptomics, alignment-free sequence comparison, sequencing and error correction, genome-wide disease-gene association mapping, metabolic networks and metabolomics, and protein sequence, structure and interaction analysis.

Modified entropy-based procedure detects gene-gene-interactions in unconventional genetic models

BACKGROUND

Since it is assumed that genetic interactions play an important role in understanding the mechanisms of complex diseases, different statistical approaches have been suggested in recent years for this task. One interesting approach is the entropy-based IGENT method by Kwon et al. that promises an efficient detection of main effects and interaction effects simultaneously. However, a modification is required if the aim is to only detect interaction effects.

METHODS

Based on the IGENT method, we present a modification that leads to a conditional mutual information based approach under the condition of linkage equilibrium. The modified estimator is investigated in a comprehensive simulation based on five genetic interaction models and applied to real data from the genome-wide association study by the North American Rheumatoid Arthritis Consortium (NARAC).

RESULTS

The presented modification of IGENT controls the type I error in all simulated constellations. Furthermore, it provides high power for detecting pure interactions specifically on unconventional genetic models both in simulation and real data.

CONCLUSIONS

The proposed method uses the IGENT software, which is free available, simple and fast, and detects pure interactions on unconventional genetic models. Our results demonstrate that this modification is an attractive complement to established analysis methods.