Deciphering cell cycle from single-cell gene expression data using TDA and optimal transport

Mentors:
Lead: Zixuan Cang (Mathematics, NC State)
Collaborator: Nicholas Buchler (Molecular and Biomedical Sciences, NC State)

Intellectual merit and significance:
Cells grow and replicate through the cell cycle process, which is crucial to maintaining homeostasis, repair, and regeneration. Recent single-cell gene expression data enables the investigation of cellular processes with great resolution. Yet, extracting cell cycle mechanisms remains challenging due to a lack of prior knowledge and high dimensionality [1]. DRUMS students will explore the innovative integration of applied topology [2] and optimal transport [3] to learn the cell cycle structures from single-cell data and reconstruct the spatiotemporal dynamics of cell cycles.

Objectives:
(i) Learning cyclic embeddings of data representing cell cycles using persistent (co)homology. (ii) Model cell cycle dynamics on the learned manifold using optimal transport. (iii) Identify cell cycle driving genes through the reconstructed spatiotemporal dynamics.

Outcomes:
Computational method and software package for the new analysis of cell cycle dynamics from single-cell gene expression data.

References:

1. Guo, X. and L. Chen. From G1 to M: a comparative study of methods for identifying cell cycle phases. Brief Bioinf, 2024. 25.2: p. bbad517.

2. De Silva, V. and M. Johansson. Persistent cohomology and circular coordinates. in Proceedings of the twenty-fifth annual symposium on Computational geometry. 2009.

3. Benamou, J.-D. and Y. Brenier, A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer Mathematik, 2000. 84: p. 375-393.