Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework.

Tissue morphogenesis in multicellular organisms is accompanied by proliferative cell behaviors: cell division (increase in cell number after each cell cycle) and cell growth (increase in cell volume during each cell cycle). These proliferative cell behaviors can be regulated by multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze multicellular dynamics, a reversible network reconnection (RNR) model has been suggested, in which each cell shape is expressed by a single polyhedron. In this study, to apply the RNR model to simulate tissue morphogenesis involving proliferative cell behaviors, we model cell proliferation based on a RNR model framework. In this model, cell division was expressed by dividing a polyhedron at a planar surface for which cell division behaviors were characterized by three quantities: timing, intracellular position, and normal direction of the dividing plane. In addition, cell growth was expressed by volume growth as a function of individual cell times within their respective cell cycles. Numerical simulations using the proposed model showed that tissues grew during successive cell divisions with several cell cycle times. During these processes, the cell number in tissues increased while maintaining individual cell size and shape. Furthermore, tissue morphology dramatically changed based on different regulations of cell division directions. Thus, the proposed model successfully provided a basis for expressing proliferative cell behaviors during morphogenesis based on a RNR model framework.