Wasserstein FLOW Learning for multi-Omics

Introduction

Single cell molecular profiling allows mapping cellular development at an unprecedented level of detail. Optimal transport (OT) enables the analysis of this dynamical process as a trajectory inference problem, using OT flows. These flows treat cells as particles evolving on an energy landscape over an "omics" space (such as transcriptomic, epigenomic, proteomic, and location).

Challenges in Learning Models

Learning this model from large scale omics datasets poses formidable mathematical and computational challenges, which will be tackled by WOLF.

Joint Learning of Gene Embedding Space

The first challenge is the joint learning of both the gene embedding space and the energy landscape. Existing approaches use ad-hoc Euclidean embeddings, ignoring biological relationships between genes. WOLF will develop a new type of non-Euclidean OT flows, which takes into account complex genetic relations.

Fusion of Multiple Omics Datasets

The second challenge is the fusion of multiple omics datasets (for instance, transcriptomics, proteomics, and spatial data) without having access to an explicit pairing between the cells across the omics. Multi-omics is the next frontier in developmental analysis, and the corresponding trajectories cannot be captured with existing OT flows.

WOLF will develop a new class of multi-linear OT flows where interaction terms couple particles together across different omics.

Computational Integration

These advances will be integrated into an efficient computational package where the parameters of the models are learned using parallelizable OT flow solvers.

Leveraging Deep Learning

Leveraging the connection between OT flows and attention mechanisms in deep learning, these methods will be approximated using transformer architectures and optimized using implicit differentiation.

Conclusion

These theoretical and numerical contributions will work hand in hand to offer the first comprehensive framework for multi-omics trajectory inference. This will unlock biological findings for the characterization of developmental molecular pathways and the understanding of disease mechanisms.