Three-way interaction model to trace the mechanisms involved in Alzheimer’s disease transgenic mice

<div><p>Alzheimer's disease (AD) is the most common cause for dementia in human. Currently, more than 46 million people in the world suffer from AD and it is estimated that by 2050 this number increases to more than 131 million. AD is considered as a complex disease. Therefore, understanding the mechanism of AD is a universal challenge. Nowadays, a huge number of disease-related high-throughput “omics” datasets are freely available. Such datasets contain valuable information about disease-related pathways and their corresponding gene interactions. In the present work, a three-way interaction model is used as a novel approach to understand AD-related mechanisms. This model can trace the dynamic nature of co-expression relationship between two genes by introducing their link to a third gene. Apparently, such relationships cannot be traced by the classical two-way interaction model. Liquid association method was applied to capture the statistically significant triplets which are involved in three-way interaction. Subsequently, gene set enrichment analysis (GSEA) and gene regulatory network (GRN) inference were applied to analyze the biological relevance of the statistically significant triplets. The results of this study suggest that the innate immunity processes are important in AD. Specifically, our results suggest that <i>H2-Ob</i> as the switching gene and the gene pair {<i>Csf1r</i>, <i>Milr1</i>} form a statistically significant and biologically relevant triplet, which may play an important role in AD. We propose that the homeostasis-related link between mast cells and microglia is presumably controlled with <i>H2-Ob</i> expression levels as a switching gene.</p></div

Examples of the statistically triplets.

<p>In each case, a considerable change in the correlation of X₁ and X₂ occurs as a result of change in X₃.</p

FDR vs. -log (<i>p</i>-value).

<p>The changes in FDR (BH-corrected <i>p</i>-value) versus -log (<i>p</i>-value) for the first 300000 results of fastLA [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0184697#pone.0184697.ref021" target="_blank">21</a>]. As shown FDR = 0.001 corresponds to -log (<i>p</i>- value) = 6.817.</p

Gene set enrichment analysis.

<p>Enriched terms based on (A) “biological process”; (B) “cellular component”; and (C) “KEGG pathway” for two gene groups, genes in X₃ position and all of the genes involved in the triplets. The common terms in these two groups are shown in red. The high frequency of common terms suggest that the results of liquid association method are consistent with the biological expectation from three-way interactions, that is, the presence of switching and switched genes in the same biological pathway.</p

Regulatory relationships within triplets.

<p>The regulatory relationships of significant triplets obtained from liquid association were traced in the GRN. The more the intensity of the red color, the more the up-regulation of the gene in Alzheimer’ disease. As shown there are regulatory relationships between <i>Milr1</i>, <i>Csf1r</i> and <i>H2-Ob</i> in triplet 72. Additionally, regulatory relationships are observed between <i>Slc14a1</i> and <i>Slamf6</i> in the triplet 97.</p

Biologically relevant triplets.

<p>By tracing statistically significant triplets in the enriched terms, 12 triplets in which X₁ and X₂ are involved in the same biological process or pathway were determined.</p

An example of three-way interaction.

<p>In a three-way interaction with switching mechanism the correlation between two genes, namely X₁ and X₂ is considered. Then, it is assumed that there is a third gene, namely the "switching gene" denoted by X₃, whose expression level affects the co-expression relationship of the two other genes. In other words, based on the expression levels of the third gene (X₃), the expression levels of the two other genes ({X₁, X₂}) are either directly or inversely correlated. Here, the three-way interaction with switching mechanism between <i>H2-Ob</i> (as the switching gene) and {<i>Csf1r</i>, <i>Milr1</i>} (as {X₁, X₂}) is shown. (A) When <i>H2-Ob</i> gene is up-regulated (i.e., its normalized expression level is between 0.37 and 1.84), there is a direct correlation between <i>Milr1</i> and <i>Csf1r</i> expression levels (red); (B) When <i>H2-Ob</i> gene is in the intermediate state (i.e., its normalized expression level is between 0.37 and -0.37), expression levels of <i>Milr1</i> and <i>Csf1r</i> are not correlated (grey); (C) When <i>H2-Ob</i> gene is down-regulated (normalized expression level of it is between -1.84 and -0.37), there is an inverse correlation between <i>Milr1</i> and <i>Csf1r</i> expression levels (green). This triplet will be further explained in the Discussion section.</p