SEM²: Introducing mechanics in cell and tissue modeling using coarse-grained homogeneous particle dynamics

Modeling multiscale mechanics in shape-shifting engineered tissues, such as organoids and organs-on-chip, is both important and challenging. In fact, it is difficult to model relevant tissue-level large non-linear deformations mediated by discrete cell-level behaviors, such as migration and proliferation. One approach to solve this problem is subcellular element modeling (SEM), where ensembles of coarse-grained particles interacting via empirically defined potentials are used to model individual cells while preserving cell rheology. However, an explicit treatment of multiscale mechanics in SEM was missing. Here, we incorporated analyses and visualizations of particle level stress and strain in the open-source software SEM++ to create a new framework that we call subcellular element modeling and mechanics or SEM². To demonstrate SEM², we provide a detailed mechanics treatment of classical SEM simulations including single-cell creep, migration, and proliferation. We also introduce an additional force to control nuclear positioning during migration and proliferation. Finally, we show how SEM² can be used to model proliferation in engineered cell culture platforms such as organoids and organs-on-chip. For every scenario, we present the analysis of cell emergent behaviors as offered by SEM++ and examples of stress or strain distributions that are possible with SEM². Throughout the study, we only used first-principles literature values or parametric studies, so we left to the Discussion a qualitative comparison of our insights with recently published results. The code for SEM² is available on GitHub at https://github.com/Synthetic-Physiology-Lab/sem2.