Simulation for tubular and spherical structure formation via self- organization of vascular mesenchymal cells in three dimensions

Cellular self-organization in extracellular matrix (ECM) is a complex process highly related to ECM proteins, cytokines, growth factors, cell-cell contacts, and mechanical stimuli, and study on the underlying mechanism is vital for rationally tuning the self-organization of cells. Here, we investigate the 3D pattern formation process of vascular mesenchymal cells (VMCs) at the interfaces between hydrogels with different components in a mathematical model. A reaction-diffusion model based on Turing's instability is derived and utilized to simulate the self-organized VMC patterns according to the biochemical interactions of activator, inhibitor and cells. The simulation results show that 3D hollow tubular and spherical structures with large lumen diameters generated around interfacial regions between different hydrogels, which are not observed in a two-dimensional study. The multicellular morphology changes from the branched tubes to the short-length tubes with the variation of parameter values. The short-length tubes also can evolve to hollow sphere-like structures in specific parameter ranges. The hollow structure which emerges is mainly because of the concentration gradients of proteins and cells across the hydrogel interfaces. This study provides flexible predictions, which may be useful for engineering 3D artificial tissue that highly dynamic and variable in terms of their 3D structure, mechanical properties and biochemical microenvironment.