Biomechanics and Modeling in Mechanobiology

, Volume 12, Issue 5, pp 987–996 | Cite as

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

  • Satoru Okuda
  • Yasuhiro Inoue
  • Mototsugu Eiraku
  • Yoshiki Sasai
  • Taiji AdachiEmail author
Original Paper


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.


Tissue morphogenesis Cell proliferation Cell division Multicellular dynamics Three-dimensional vertex model Reversible network reconnection model Computational biomechanics Developmental biomechanics 



This work was partially supported by the Funding Program for Next Generation World-Leading Researchers (LR017) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan. Satoru Okuda was supported by the Japan Society for the Promotion of Science (JSPS) as a JSPS fellow. Yasuhiro Inoue was supported by “Morphologic” Grant-in-Aid for Scientific Research on Innovative Areas (23127506) from the MEXT in Japan.

Supplementary material

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  1. Baena-López LA, Baonza A et al (2005) The orientation of cell divisions determines the shape of Drosophila organs. Curr Biol 15(18):1640–1644CrossRefGoogle Scholar
  2. Davies JA (2005) Mechanisms of morphogenesis: the creation of biological form. Elsevier, BurlingtoGoogle Scholar
  3. Eiraku M, Adachi T et al (2012) Relaxation-expansion model for self-driven retinal morphogenesis. Bioessays 34(1):17–25CrossRefGoogle Scholar
  4. Eiraku M, Takata N et al (2011) Self-organizing optic-cup morphogenesis in three-dimensional culture. Nature 472(7341):51–56CrossRefGoogle Scholar
  5. Farhadifar R, Röper JC et al (2007) The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr Biol 17(24):2095–2104CrossRefGoogle Scholar
  6. Friedlander DR, Mège RM et al (1989) Cell sorting-out is modulated by both the specificity and amount of different cell-adhesion molecules (CAMs) expressed on cell-surfaces. Proc Natl Acad Sci USA 86(18):7043–7047CrossRefGoogle Scholar
  7. Gibson WT, Veldhuis JH et al (2011) Control of the mitotic cleavage plane by local epithelial topology. Cell 144(3):427–438CrossRefGoogle Scholar
  8. Gong Y, Fraser C, Mo SE (2004) Planar cell polarity signalling controls cell division orientation during zebrafish gastrulation. Nature 430:689–693CrossRefGoogle Scholar
  9. Heisenberg CP, Tada M et al (2000) Silberblick/Wnt11 mediates convergent extension movements during zebrafish gastrulation. Nature 405:76–81CrossRefGoogle Scholar
  10. Honda H, Yamanaka H (1984) A computer simulation of geometrical configurations during cell division. J Theor Biol 106(3):423–435CrossRefGoogle Scholar
  11. Honda H, Motosugi N et al (2008) Computer simulation of emerging asymmetry in the mouse blastocyst. Development 135(8):1407–1414 Google Scholar
  12. Honda H, Nagai T et al (2008) Two different mechanisms of planar cell intercalation leading to tissue elongation. Dev Dyn 237(7):1826–1836Google Scholar
  13. Honda H, Tanemura M et al (2004) A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate. J Theor Biol 226(4):439–453MathSciNetCrossRefGoogle Scholar
  14. Ingber DE, Mammoto T (2010) Mechanical control of tissue and organ development. Development 137(9):1407–1420CrossRefGoogle Scholar
  15. Lechler T, Fuchs E (2005) Asymmetric cell divisions promote stratification and differentiation of mammalian skin. Nature 437(7056):275–280CrossRefGoogle Scholar
  16. Lecuit T, Lenne PF (2007) Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nat Rev Mol Cell Biol 8(8):633–644CrossRefGoogle Scholar
  17. Lecuit T, Rauzi M et al (2008) Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nat Cell Biol 10(12): 1401–1410Google Scholar
  18. Lecuit T, Rauzi M et al (2010) Planar polarized actomyosin contractile flows control epithelial junction remodelling. Nature 468(7327):1110–1114CrossRefGoogle Scholar
  19. Noguchi H, Gompper G (2005) Dynamics of fluid vesicles in shear flow: effect of membrane viscosity and thermal fluctuations. Phys Rev E 72(1):11901–11914CrossRefGoogle Scholar
  20. Okuda S, Inoue Y et al. (2012) Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis. Biomech Model Mechanobiol. doi: 10.1007/s10237-012-0430-7
  21. Rauzi M, Verant P et al (2008) Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nat Cell Biol 10(12):1401–1410CrossRefGoogle Scholar
  22. Reddy GV, Heisler MG et al (2004) Real-time lineage analysis reveals oriented cell divisions associated with morphogenesis at the shoot apex of Arabidopsis thaliana. Development 131:4225–4237CrossRefGoogle Scholar
  23. Staple DB, Farhadifar R et al (2010) Mechanics and remodelling of cell packings in epithelia. Eur Phys J E Soft Matter 33(2):117–127CrossRefGoogle Scholar
  24. Ujihara Y, Nakamura M et al (2005) Proposed spring network cell model based on a minimum energy concept. Ann Biomed Eng 38(4):1530–1538CrossRefGoogle Scholar
  25. Poulson ND, Lechler T (2010) Robust control of mitotic spindle orientation in the developing epidermis. J Cell Biol 191(5):915–922CrossRefGoogle Scholar
  26. Shraiman BI (2005) Mechanical feedback as a possible regulator of tissue growth. Proc Natl Acad Sci USA 102(9):3318–3323CrossRefGoogle Scholar
  27. Siller KH, Cabernard C et al (2006) The NuMA-related Mud protein binds Pins and regulates spindle orientation in Drosophila neuroblasts. Nat Cell Biol 8(6):594–600CrossRefGoogle Scholar
  28. Taniguchi K, Maeda R et al (2011) Chirality in planar cell shape contributes to left-right asymmetric epithelial morphogenesis. Science 333(6040):339–341CrossRefGoogle Scholar
  29. Weliky M, Oster G (1990) The mechanical basis of cell rearrangement. 1. Epithelial morphogenesis during fundulus epiboly. Development 109(2):373–386Google Scholar
  30. Woolner S, Papalopulu N (2012) Spindle position in symmetric cell divisions during epiboly is controlled by opposing and dynamic apicobasal forces. Dev Cell 22(4):775–787CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Satoru Okuda
    • 1
  • Yasuhiro Inoue
    • 1
  • Mototsugu Eiraku
    • 2
  • Yoshiki Sasai
    • 3
  • Taiji Adachi
    • 1
    Email author
  1. 1.Department of Biomechanics, Institute for Frontier Medical SciencesKyoto UniversitySakyo-ku, KyotoJapan
  2. 2.Four-Dimensional Tissue Analysis UnitCenter for Developmental Biology, RIKENKobeJapan
  3. 3.Organogenesis and Neurogenesis GroupCenter for Developmental Biology, RIKENKobeJapan

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