# Double optimal transport for differential gene regulatory network inference with unpaired samples

## TL;DR

This paper introduces a new method for comparing gene regulatory networks between conditions using unpaired samples, validated on a gastric cancer dataset.

## Contribution

The novel double optimal transport framework enables efficient differential GRN inference from unpaired samples.

## Key findings

- Double OT outperforms existing methods in efficiency and accuracy across various network scales.
- The method identified MET as a central gene in gastric cancer regulatory networks.
- MET's role in early cancer development supports the biological relevance of the inferred networks.

## Abstract

Inferring differential gene regulatory networks (GRNs) between different conditions from gene expression profiles remains a significant challenge. Current GRN inference approaches are limited by either scalability in large networks or accuracy in high-dimensional scenarios. Furthermore, most existing methods require paired samples for comparative GRN analyses.

To overcome these challenges, we model gene regulation as a distribution transportation problem and propose an efficient and effective method, called double optimal transport (OT), for reconstructing differential GRNs from the perspective of optimal transport theory, applicable to unpaired samples. Double OT is a novel two-level OT framework. It first aligns unpaired samples by solving a partial OT problem at the sample level, and then infers GRNs from the aligned samples by solving a robust OT problem at the gene level. Comprehensive simulation studies demonstrate the superior efficiency and efficacy of double OT in different scales of networks compared to state-of-the-art methods. We also apply the proposed method to a gastric cancer dataset, identifying the proto-oncogene MET as a central node in the gastric cancer GRN. Its crucial role in early oncogenesis and potential as a therapeutic target further validate our approach and enhance our understanding of the regulatory mechanisms of gastric cancer.

A Python library that implements the proposed method is available at https://github.com/Mengyu8042/ot-grn.