Inferring the functions of longevity genes with modular subnetwork biomarkers of Caenorhabditis elegans aging

Abstract

A central goal of biogerontology is to identify robust gene-expression biomarkers of aging. Here we develop a method where the biomarkers are networks of genes selected based on age-dependent activity and a graph-theoretic property called modularity. Tested on Caenorhabditis elegans, our algorithm yields better biomarkers than previous methods - they are more conserved across studies and better predictors of age. We apply these modular biomarkers to assign novel aging-related functions to poorly characterized longevity genes.

Figure 1

High-scoring subnetworks fulfill two criteria: they are modular and related to aging. (a) High-scoring subnetworks have high modularity, that is, they are highly interconnected, and sparsely connected to the rest of the network. (b) High-scoring subnetworks have high class relevance, that is, they have activity levels that increase or decrease as a function of worm age.

Figure 2

Identifying modular subnetworks. (a) Start with the largest connected component of the functional interaction network representing all genes whose expression has been measured. (b) Weight every edge of the network with the absolute value of the Spearman correlation between the two genes flanking it. (c) Identify age-related subnetworks by growing subnetworks iteratively out from seed nodes.

Figure 3

Modular subnetworks are highly conserved across studies. Modular subnetworks m1 to m5 are shown in green and regular subnetworks r1 to r5 in blue. Bar height shows the percentage overlap across studies for seed genes of significant modular and regular subnetworks derived from the data in Golden et al. [2] and Budovskaya et al. [21]; this is calculated as the size of the intersection of sets of significant seed genes from both studies, divided by the union. P-values above each bar show the significance of the overlap calculated using the hypergeometric test.

Figure 4

Predicting worm age using machine learning. The activities of genes or subnetworks (subnetwork activity is calculated as the mean activity of its member genes) are used by support vector regression (SVR) algorithms to predict age on the basis of gene expression. Performance is typically measured using both the mean-squared error (MSE) of the difference between true and predicted ages, and the squared correlation coefficient between true and predicted ages.

Figure 5

Subnetworks and genes predict the age of fer-15 worms. Modular subnetworks are shown in green, regular subnetworks in blue, and gene sets in gray. This figure shows the best-performing type of modular subnetworks, regular subnetworks, and genes at each feature level. For modular subnetworks, this is type m3 at every feature level; for regular subnetworks, type r3 at 5 and 10 features, r2 at 25 features, and r4 at 50 features; for genes, g2 at all feature levels. Support vector regression algorithms using 5, 10, 25, or 50 features were trained to predict age on the data from Golden et al. [2] and tested on Budovskaya et al. [21]. For each size of feature set, 1,000 different support vector regression learners were computed; curves show their median performance (quantified using the squared correlation coefficient (SCC) between true and predicted age in the bottom panel), and error bars indicate the 95% confidence intervals for the medians (calculated using a bootstrap estimate).

Figure 6

Modular subnetwork biomarkers of aging predict the age of individual wild-type worms. (a) Machine learners built from modular subnetworks or genes, predicting worm age in a cross-validation task on the data from Golden et al. [2] using 5, 10, 25, or 50 features. For each size of feature set, 1,000 different support vector regression learners were computed; curves show their median performance (quantified using mean-squared error (MSE) in the top panel, and the squared correlation coefficient (SCC) between true and predicted age in the bottom panel), and error bars indicate the 95% confidence intervals for the medians (calculated using a bootstrap estimate). (b) The performance of a typical support vector regression learner built using 50 modular subnetworks as features; true worm age is shown on the x-axis, and predicted age on the y-axis.

Figure 7

Some examples of significant longevity subnetworks. (a-g) Examples of significant modular subnetworks from Golden et al. [2] containing multiple known longevity genes (from L2; see Materials and methods). Edge width is proportional to gene-gene co-expression, node size is proportional to the Spearman correlation between gene expression and age, and known longevity genes are indicated by green circles.