Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 4, pp 805–816 | Cite as

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

  • Satoru OkudaEmail author
  • Yasuhiro Inoue
  • Mototsugu Eiraku
  • Taiji Adachi
  • Yoshiki Sasai
Original Paper


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.


Multicellular morphogenesis Cell apoptosis Apoptotic force Three-dimensional vertex model Reversible network reconnection model Computational biomechanics 



We appreciate Dr. Erina Kuranaga from RIKEN Center for Developmental Biology for her valuable comments. This work was supported by JSPS KAKENHI Grant Number 15K14534.

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Satoru Okuda
    • 1
    • 2
    Email author
  • Yasuhiro Inoue
    • 3
  • Mototsugu Eiraku
    • 1
  • Taiji Adachi
    • 3
  • Yoshiki Sasai
    • 2
  1. 1.Laboratory for in vitro Histogenesis, Center for Developmental Biology (CDB)RIKENChuo-ku, KobeJapan
  2. 2.Laboratory for Organogenesis and Neurogenesis, Center for Developmental Biology (CDB)RIKENKobeJapan
  3. 3.Department of Biomechanics, Institute for Frontier Medical SciencesKyoto UniversityKyotoJapan

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