A minimal mechanically consistent model of smoothly dividing disk-shaped cells

Replication through cell division is one of the fundamental processes of life and a major driver of dynamics in systems ranging from bacterial colonies to embryogenesis, tissues and tumors. While regulation also shapes self-organization, many biologically relevant behaviors arise from a limited number of physical ingredients, and particle-based models have become a popular platform to investigate these emergent dynamics. However, incorporating division into such models often produces aberrant mechanical fluctuations that hinder meaningful analysis. Here, we introduce a minimal model ensuring mechanical consistency during cell division. Cells consist of two nodes, overlapping disks which separate during division, forming transient dumbbell shapes. Internal degrees of freedom, cell-cell interactions and equations of motion guarantee force continuity at all times, including during division, both for the dividing cell and its interaction partners, while allowing arbitrary anisotropic mobilities. As a benchmark, we also translate an established model of proliferating spherocylinders with similar dynamics into our theoretical framework. Numerical simulations demonstrate force continuity of the new disk cell model, quantify the improvements, and show agreement in terms of collective behaviors such as alignment and orientational order. We also demonstrate force extraction and a Voronoi-based interpretation in a confluent-tissue context-with a three-dimensional generalization in embryonic-like confinement. A reference implementation of the model in two and three dimensions is freely available as a Julia package based on InPartS.jl. Our model provides a framework for analyzing mechanical observables such as velocities and stresses, and can be readily extended with additional biological features.