Presentation Information
[MS08-02]Position-based Dynamics for Multicellular Systems with Adhesion Memory
*Steffen Plunder1 (1. Kyoto University (Japan))
Keywords:
Agent-based model
Position-based dynamics (PBD) is a numerical method particularly suited for handling non-overlap constraints, such as those found in multicellular agent-based models. Though originally developed in computer graphics—where it is known for producing visually plausible yet physically inaccurate collision responses—PBD is explicit, simple to implement, and remarkably stable. In this work, we provide a rigorous numerical analysis of PBD, showing that in the biologically relevant overdamped regime, the method is not only stable but also physically accurate and provably convergent [1].
We present applications of PBD in developmental biology, including simulations of epithelial tissues, epithelial-to-mesenchymal transition (EMT), and cell migration [2,3 In the case of cell migration, detailed models for the cell-matrix adhesion include delayed terms to account for the past extension of the elastic linkages, which leads to an integral equation of Volterra type [4]. We extend both the PBD framework and its numerical analysis to this setting, demonstrating that it offers an efficient and reliable scheme for both the full integral model and its asymptotic limit.
References:
[1] S. Plunder, S. Merino-Aceituno, Convergence proof for first-order position-based dynamics: An efficient scheme for inequality constrained ODEs. (2023) [preprint]
[2] S. Plunder, C. Danesin, B. Glise, M. A. Ferreira, S. Merino-Aceituno, E. Theveneau, Modelling variability and heterogeneity of EMT scenarios highlights nuclear positioning and protrusions as main drivers of extrusion. Nature Communications (2024)
[3] E. Despin-Guitard, V. S. Rosa, S. Plunder, N. Mathiah, K. Van Schoor, E. Nehme, S. Merino-Aceituno, J. Egea, M. N. Shahbazi, E. Theveneau & I. Migeotte Non-apical mitoses contribute to cell delamination during mouse gastrulation. Nature Communications (2024)
[4] V. Milišić, D. Oelz, On the asymptotic regime of a model for friction mediated by transient elastic linkages. Journal de Mathématiques Pures et Appliquées (2011)
We present applications of PBD in developmental biology, including simulations of epithelial tissues, epithelial-to-mesenchymal transition (EMT), and cell migration [2,3 In the case of cell migration, detailed models for the cell-matrix adhesion include delayed terms to account for the past extension of the elastic linkages, which leads to an integral equation of Volterra type [4]. We extend both the PBD framework and its numerical analysis to this setting, demonstrating that it offers an efficient and reliable scheme for both the full integral model and its asymptotic limit.
References:
[1] S. Plunder, S. Merino-Aceituno, Convergence proof for first-order position-based dynamics: An efficient scheme for inequality constrained ODEs. (2023) [preprint]
[2] S. Plunder, C. Danesin, B. Glise, M. A. Ferreira, S. Merino-Aceituno, E. Theveneau, Modelling variability and heterogeneity of EMT scenarios highlights nuclear positioning and protrusions as main drivers of extrusion. Nature Communications (2024)
[3] E. Despin-Guitard, V. S. Rosa, S. Plunder, N. Mathiah, K. Van Schoor, E. Nehme, S. Merino-Aceituno, J. Egea, M. N. Shahbazi, E. Theveneau & I. Migeotte Non-apical mitoses contribute to cell delamination during mouse gastrulation. Nature Communications (2024)
[4] V. Milišić, D. Oelz, On the asymptotic regime of a model for friction mediated by transient elastic linkages. Journal de Mathématiques Pures et Appliquées (2011)