[Paper Review] Prediction and verification of indirect interactions in densely interconnected regulatory networks

Koon‐Kiu Yan, Sergei Maslov+2 more|ArXiv.org|Oct 3, 2007

Gene Regulatory Network Analysis10 references3 citations

TL;DR

This paper presents a matrix-based algorithm that predicts and verifies indirect regulatory interactions in large, densely interconnected gene and protein networks by leveraging path length discounting and sign consistency across multiple cascades. The method achieves high reliability in predicting unknown indirect regulations and inferring their activation/repression signs, with optimal performance at λ = 0.025 for positive and λ = 0.030 for negative interactions in human networks, validated via ROC curve analysis and gold-standard datasets.

ABSTRACT

We develop a matrix-based approach to predict and verify indirect interactions in gene and protein regulatory networks. It is based on the approximate transitivity of indirect regulations (e.g. A regulates B and B regulates C often implies that A regulates C) and optimally takes into account the length of a cascade and signs of intermediate interactions. Our method is at its most powerful when applied to large and densely interconnected networks. It successfully predicts both the yet unknown indirect regulations, as well as the sign (activation or repression) of already known ones. The reliability of sign predictions was calibrated using the gold-standard sets of positive and negative interactions. We fine-tuned the parameters of our algorithm by maximizing the area under the Receiver Operating Characteristic (ROC) curve. We then applied the optimized algorithm to large literature-derived networks of all direct and indirect regulatory interactions in several model organisms (Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster).

Motivation & Objective

• To develop a reliable computational method for predicting and verifying indirect regulatory interactions in large, densely connected biological networks.
• To infer the sign (activation or repression) of indirect regulations when unknown, using known direct interactions and network topology.
• To distinguish between direct and indirect regulatory links when such information is missing, especially in microarray-based data.
• To optimize the algorithm’s performance using ROC curve analysis and gold-standard interaction sets.
• To enable systematic reconstruction of functional regulatory networks from literature-derived data.

Proposed method

• The method models indirect regulations as weighted paths in a directed, signed network, where each path contributes to the likelihood of an indirect interaction between source and target proteins.
• Pathways are discounted exponentially by length using a decay parameter λ, with longer cascades contributing less to the predicted interaction strength.
• The sign of an indirect regulation is determined by the product of signs along a path, and consistent signs across multiple paths increase confidence in the prediction.
• A matrix formulation computes the total influence between all protein pairs, aggregating contributions from all paths of all lengths.
• The algorithm uses a gold-standard set of high-frequency literature-reported interactions to calibrate prediction reliability via ROC curve analysis.
• Optimal λ values are selected by maximizing the area under the ROC curve from 0 to a cutoff of 0.1, defined as θ, to prioritize highly reliable predictions.

Experimental results

Research questions

• RQ1 Can indirect regulatory interactions in large, densely interconnected networks be reliably predicted using path-based inference with sign consistency?
• RQ2 How does path length affect the reliability of indirect regulation predictions, and what optimal decay parameter λ minimizes error?
• RQ3 To what extent can the algorithm infer the sign of indirect regulations when it is unknown?
• RQ4 How does the algorithm perform in distinguishing direct from indirect interactions in the absence of explicit annotation?
• RQ5 What is the optimal balance between sensitivity and precision in predicting indirect interactions using literature-derived networks?

Key findings

• The algorithm achieves optimal performance at λ = 0.025 for positive and λ = 0.030 for negative indirect regulation predictions in the human regulatory network.
• The area under the ROC curve from 0 to 0.1, used as a performance metric θ, was maximized at these λ values, indicating high reliability in top predictions.
• The method successfully predicted both unknown indirect interactions and the correct sign of known indirect regulations, with performance validated against gold-standard sets of high-frequency literature-reported interactions.
• The approach outperforms simple path counting by incorporating both path length discounting and sign consistency, reducing false positives from conflicting or long cascades.
• The algorithm was applied to large, literature-derived networks in Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana, and Drosophila melanogaster, demonstrating broad applicability.
• The use of a cutoff at x = 0.1 in the ROC curve analysis ensures focus on the most reliable predictions, improving interpretability and reducing noise from low-confidence results.