[MS11] Dynamics of Pattern Formation and Morphogenesis in Biological Systems

[MS11-04] Imaging data-based model description tool using optimal transport theory and phase-field method

*Tsubasa Sukekawa¹, Toshiaki Yachimura², Sungrim Seirin-Lee^1,3 (1. Institute for the Advanced Study of Human Biology, Kyoto University Institute for Advanced Study, Kyoto University (Japan), 2. Mathematical Science Center for Co-creative Society, Tohoku University (Japan), 3. Graduate School of Medicine, Kyoto University (Japan))

Keywords:

Optimal transport theory,Phase-field method,Cell shape inference,In silico experiment

Capturing geometrical shapes of cells is an essential issue in understanding many biological phenomena [1], and combining the shape information with mathematical models leads to in silico experiments reflecting the effect of actual cell shapes. Although advances in experimental techniques have enabled live imaging of cells, the time resolution of the imaging is limited due to various factors, such as phototoxicity. This means that the amount of information on cell geometry necessary to understand a phenomenon may not be available. In this study, we develop mathematical tools to infer intermediate cell shapes from time series data of cell shapes to overcome this limitation. Our method is a combination of optimal transport theory (OT) and a phase-field method. OT is a mathematical theory giving distance and optimal matching between probability distributions such as point clouds [4]. OT also provides interpolation and velocity fields between probability distributions. Since we can regard cell shapes as point clouds, we can generate intermediate cell shapes by interpolation, and the velocity field represents the cell's deformation and motion. However, the conventional method of OT may generate unnatural deformation, such as cracks. This property may be due to the fact that interpolation by optimal transport theory does not reflect the physical properties of the cells. To improve this, we combine the velocity field obtained by OT with a phase-field model. Our new method successfully regenerated cell dynamics with smooth and natural cell shapes using live imaging data sets of C. elegans cells and HL-60 cells. Finally, we propose a new bio-chemical modeling method, which combines the realistic cell shapes with previous computational methods [3, 4]. Our research will open new avenues for mathematical modeling approaches to pattern formation phenomena, including cell dynamics based on live imaging data of cells.

[1] S. Seirin-Lee, K. Yamamoto, and A. Kimura, The extra-embryonic space and the local contour are crucial geometric constraints regulating cell arrangement, Development, 149 (9): dev200401, 2022.
[2] G. Peyré, and M. Cuturi, Computational optimal transport: With applications to data science, Foundations and Trends® in Machine Learning, 11(5-6), 355-607, 2019.
[3] J. Kockelkoren, H. Levine, and W.-J. Rappel, Computational approach for modeling intra- and extracellular dynamics, Physical Review E, 68 (2), 037702, 2003.
[4] S. Seirin-Lee, The role of cytoplasmic MEX-5/6 polarity in asymmetric cell division, Bulletin of Mathematical Biology, 83(4), 29, 2021.