Reverse network diffusion to remove indirect noise for better inference of gene regulatory networks

Abstract

Motivation: Gene regulatory networks (GRNs) are vital tools for delineating regulatory relationships between transcription factors and their target genes. The boom in computational biology and various biotechnologies has made inferring GRNs from multi-omics data a hot topic. However, when networks are constructed from gene expression data, they often suffer from false-positive problem due to the transitive effects of correlation. The presence of spurious noise edges obscures the real gene interactions, which makes downstream analyses, such as detecting gene function modules and predicting disease-related genes, difficult and inefficient. Therefore, there is an urgent and compelling need to develop network denoising methods to improve the accuracy of GRN inference.

Results: In this study, we proposed a novel network denoising method named REverse Network Diffusion On Random walks (RENDOR). RENDOR is designed to enhance the accuracy of GRNs afflicted by indirect effects. RENDOR takes noisy networks as input, models higher-order indirect interactions between genes by transitive closure, eliminates false-positive effects using the inverse network diffusion method, and produces refined networks as output. We conducted a comparative assessment of GRN inference accuracy before and after denoising on simulated networks and real GRNs. Our results emphasized that the network derived from RENDOR more accurately and effectively captures gene interactions. This study demonstrates the significance of removing network indirect noise and highlights the effectiveness of the proposed method in enhancing the signal-to-noise ratio of noisy networks.

Availability and implementation: The R package RENDOR is provided at https://github.com/Wu-Lab/RENDOR and other source code and data are available at https://github.com/Wu-Lab/RENDOR-reproduce.

Figure 1.

The framework of RENDOR. RENDOR takes a noisy network as input, which is often affected by indirect effects, and outputs a denoised network containing only direct effects. The core of the RENDOR method lies in employing a reverse network diffusion approach based on random walks.

Figure 2.

The denoising performance of RENDOR on the simulated networks. (a) Six subfigures present the noisy graph with simulated indirect edges, and the denoised graphs obtained by applying five denoising methods. Noisy edges are marked in red. Ture edges are marked in black. (b) The number of FN, TN, TP, and FP edges of the five denoised networks. (c) The AUROC and AUPR scores (y-axis) of applying various denoising methods to the noisy networks under different noise levels (x-axis) generated based on the ER graphs and BA graphs.

Figure 3.

The denoising performance of RENDOR on GRNs that inferred from the DREAM5 dataset. (a) and (b) illustrate the denoising performance of RENDOR on ten GRNs (x-axis) for varying values of RENDOR’s parameter $m$ (y-axis). The heatmap colors represent the degree of improvement in scores after denoising compared to before denoising. The symbol “+” indicates an enhancement in network accuracy after denoising, whereas “-” denotes a reduction. (c) and (d) present the AUPR and AUROC scores for the ten GRNs before denoising (raw) and after denoising using the five methods. The parameter $m$ of RENDOR was set to 4. (e) Boxplot showing the improvement of AURPC and AUPR scores (y-axis) of GRNs derived from various denoising methods (x-axis), as compared to the original GRNs. Each dot corresponds to a GRN.