A minimal model of smoothly dividing disk-shaped cells

Replication through cell division is one of the most fundamental processes of life and a major driver of dynamics in systems ranging from bacterial colonies to embryogenesis, tissues and tumors. While regulation often plays a role in shaping self-organization, mounting evidence suggests that many biologically relevant behaviors exploit principles based on a limited number of physical ingredients, and particle-based models have become a popular platform to reconstitute and investigate these emergent dynamics. However, incorporating division into such models often leads to aberrant mechanical fluctuations that hamper physically meaningful analysis. Here, we present a minimal model focusing on mechanical consistency during division. Cells are comprised of two nodes, overlapping disks which separate from each other during cell division, resulting in transient dumbbell shapes. Internal degrees of freedom, cell-cell interactions and equations of motion are designed to ensure force continuity at all times, including through division, both for the dividing cell itself as well as interaction partners, while retaining the freedom to define arbitrary anisotropic mobilities. As a benchmark, we also translate an established model of proliferating spherocylinders with similar dynamics into our theoretical framework. Numerical simulations of both models demonstrate force continuity of the new disk cell model and quantify our improvements. We also investigate some basic collective behaviors related to alignment and orientational order and find consistency both between the models and with the literature. A reference implementation of the model is freely available as a package in the Julia programming language based on $\mathit{InPartS}$. Our model is ideally suited for the investigation of mechanical observables such as velocities and stresses, and is easily extensible with additional features.