Modeling cell apoptosis for simulating three-dimensional multicellular morphogenesis based on a reversible network reconnection framework

Abstract

Morphogenesis in multicellular organisms is accompanied by apoptotic cell behaviors: cell shrinkage and cell disappearance. The mechanical effects of these behaviors are spatiotemporally regulated within multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze 3D multicellular dynamics, 3D vertex models have been suggested, in which a reversible network reconnection (RNR) model has successfully expressed 3D cell rearrangements during large deformations. To analyze the effects of apoptotic cell behaviors on 3D multicellular morphogenesis, we modeled cell apoptosis based on the RNR model framework. Cell shrinkage was modeled by the potential energy as a function of individual cell times during the apoptotic phase. Cell disappearance was modeled by merging neighboring polyhedrons at their boundary surface according to the topological rules of the RNR model. To establish that the apoptotic cell behaviors could be expressed as modeled, we simulated morphogenesis driven by cell apoptosis in two types of tissue topology: 3D monolayer cell sheet and 3D compacted cell aggregate. In both types of tissue topology, the numerical simulations successfully illustrated that cell aggregates gradually shrank because of successive cell apoptosis. During tissue shrinkage, the number of cells in aggregates decreased while maintaining individual cell size and shape. Moreover, in case of localizing apoptotic cells within a part of the 3D monolayer cell aggregate, the cell apoptosis caused the global tissue bending by pulling on surrounding cells. In case of localizing apoptotic cells on the surface of the 3D compacted cell aggregate, the cell apoptosis caused successive, directional cell rearrangements from the inside to the surface. Thus, the proposed model successfully provided a basis for expressing apoptotic cell behaviors during 3D multicellular morphogenesis based on an RNR model framework.

Combining Turing and 3D vertex models reproduces autonomous multicellular morphogenesis with undulation, tubulation, and branching

“…Mathematical models have been well used for understanding multicellular dynamics 15 – 22 and have been improved to analyze their 3D dynamics 23 – 28 . We have developed a full 3D vertex model that expresses 3D multicellular dynamics compacted in a monolayer sheet as well as a multilayer aggregate, involving cell rearrangements 29 , division 30 , apoptosis 31 , and viscoelastic behaviors 32 . The models have succeeded in reproducing basic epithelial deformations 33 , 34 as well as reproducing several developmental phenomena, such as blastocyst formation 35 .…”

Three-dimensional deformation mode of multicellular epithelial tube under tension and compression tests

“…Moreover, cells involve various mechanical behaviors such as viscoelastic property, cell division, and cell apoptosis, which may also contribute to their macroscopic mechanical characteristics. These cell behaviors can be taken into account in the 3D vertex model (Okuda et al 2013c(Okuda et al , 2016. Such stress environments and cell behaviors are challenging topics as the future work.…”

Design Principles for Engineering of Tissues from Human Pluripotent Stem Cells

“…For example, developing epithelial sheets maintain smooth curvature on both the apical and basal surfaces despite cellular changes, such as proliferation, that could cause a disruption in force balance. To compensate for these local force changes in cell sheets, one model predicts that a tangential contractile force is maintained along the apical surface that reduces the impact of any irregular local force changes [66–68]. Computational predictions of cell behaviors during tissue organization not only provide insight into developmental morphogenesis, but also describe tissue-level changes that occur during disease.…”