# The signed two-space proximity model for learning representations in protein–protein interaction networks

## TL;DR

This paper introduces a new model for predicting protein–protein interactions that considers both activating and inhibitory relationships, improving accuracy and biological insight.

## Contribution

The novel Signed Two-Space Proximity Model (S2-SPM) captures both positive and negative interactions in signed PPI networks using dual latent spaces.

## Key findings

- S2-SPM outperforms baseline methods in predicting signed PPI interactions.
- Archetypes identified by S2-SPM are biologically relevant, as shown by Gene Ontology enrichment analysis.
- The model's reliability is confirmed through statistical significance and robustness metrics like BNMI.

## Abstract

Accurately predicting complex protein–protein interactions (PPIs) is crucial for decoding biological processes, from cellular functioning to disease mechanisms. However, experimental methods for determining PPIs are computationally expensive. Thus, attention has been recently drawn to machine learning approaches. Furthermore, insufficient effort has been made toward analyzing signed PPI networks, which capture both activating (positive) and inhibitory (negative) interactions. To accurately represent biological relationships, we present the Signed Two-Space Proximity Model (S2-SPM) for signed PPI networks, which explicitly incorporates both types of interactions, reflecting the complex regulatory mechanisms within biological systems. This is achieved by leveraging two independent latent spaces to differentiate between positive and negative interactions while representing protein similarity through proximity in these spaces. Our approach also enables the identification of archetypes representing extreme protein profiles.

S2-SPM’s superior performance in predicting the presence and sign of interactions in SPPI networks is demonstrated in link prediction tasks against relevant baseline methods. Additionally, the biological prevalence of the identified archetypes is confirmed by an enrichment analysis of Gene Ontology (GO) terms, which reveals that distinct biological tasks are associated with archetypal groups formed by both interactions. This study is also validated regarding statistical significance and sensitivity analysis, providing insights into the functional roles of different interaction types. Finally, the robustness and consistency of the extracted archetype structures are confirmed using the Bayesian Normalized Mutual Information (BNMI) metric, proving the model’s reliability in capturing meaningful SPPI patterns.

S2-SPM is implemented and freely available under the MIT license at https://github.com/Nicknakis/S2SPM.