Computational modeling of hormone- and cytokine-dependent proliferation of endometrial cells in 3D co-culture

The endometrium and menstrual disorders, such as endometriosis and adenomyosis, are difficult to study, partly because menstruation depends on interactions between multiple cell types through complex molecular mechanisms. To help understand this system, researchers need humanized experimental and computational models that can interrogate how endometrial cell populations impact each other in both physiological and pathological conditions. Here, we use ordinary differential equations (ODEs) to model changes in the rates of endometrial cell proliferation and death in response to hormones, cytokines, and the specific cell types present. To calibrate this computational model, we used previously-published experimental datasets from a 3D co-culture platform supporting primary human endometrial epithelial organoids and endometrial stromal cells. Our ODE-based model can simulate the size of endometrial epithelial organoids and the density of stromal cells over time under multiple hormone/cytokine conditions in mono- and co-cultures. We further created a second, partial differential equation (PDE)-based model that simulates the diffusion of molecules added to these 3D cultures and their uptake by proliferating endometrial cells using the predicted cell densities from the ODE model as inputs to the PDE simulations. We show that the exposure to hormones and cytokines used in the experiments is reasonably homogenous throughout the 3D culture and identify conditions where this would not be true. Altogether we use these models to quantify the influence of stromal cells on epithelial cell proliferation and vice versa , to identify differences across cells from different donors, and to provide a quantitative assessment of experimental designs.