Stochastic modeling of topological defects in arbitrary confined geometries for quantifying nematic order of cell populations

Recently, analyses of spatiotemporal nematic order around a topological defect have been applied to the estimation of physical parameters in active nematics of biological cells [1, 2], which is a promising method for quantifying cell behaviors based on physical aspects. However, existing studies have considered only full-integer topological defects and circular domains for simplicity in theoretical analyses, whereas half-integer defects are often observed in actual cell culture experiments. To analyze the defect dynamics in more generalized situations and consider the stochasticity of cell alignment in experiments, this presentation presents a new stochastic model of topological defects of nematic cells in arbitrary confined geometries. To this end, we apply our residue calculus theory [3] for the expression of deterministic defect dynamics and construct Langevin dynamics for modeling the stochastic behaviors of defects. We verified that the proposed model could reproduce th equilibrium defect distributions in confined myoblast cells by estimating model parameters from experiments[4]. Since the parameters of the proposed model are small in number, the estimated model parameters would be reliable for quantifying the cell activity.



[1] C. Blanch-Mercader et al., Physical Review Letters, 126, 028101 (2021).

[2] Z. Zhao et al., Nature Communications, 16, 2452 (2025).

[3] H. Miyazako et al., Soft Matter, 21, 5947-5956 (2025).

[4] H. Miyazako et al., npj Biological Physics and Mechanics, 1, 1 (2024).