Cell-center-based model for simulating three-dimensional monolayer tissue deformation. (English) Zbl 1520.92027
Summary: The shape of the epithelial monolayer can be depicted as a curved tissue in three-dimensional (3D) space, where individual cells are tightly adhered to one another. The 3D morphogenesis of these tissues is governed by cell dynamics, and a variety of mathematical modeling and simulation studies have been conducted to investigate this process. One promising approach is the cell-center model, which can account for the discreteness of cells. The cell nucleus, which is considered to correspond to the cell center, can be observed experimentally. However, there has been a shortage of cell-center models specifically tailored for simulating 3D monolayer tissue deformation. In this study, we developed a mathematical model based on the cell-center model to simulate 3D monolayer tissue deformation. Our model was confirmed by simulating the in-plane deformation, out-of-plane deformation, and invagination due to apical constriction.
MSC:
| 92C37 | Cell biology |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92C15 | Developmental biology, pattern formation |
Keywords:
tissue morphogenesis; multicellular dynamics; cell division; cell rearrangement; apical constrictionReferences:
| [1] | Adachi, H.; Matsuda, K.; Niimi, T.; Inoue, Y.; Kondo, S.; Gotoh, H., Anisotropy of cell division and epithelial sheet bending via apical constriction shape the complex folding pattern of beetle horn primordia, Mech. Dev., 152, June, 32-37 (2018) |
| [2] | Akiyama, M.; Sushida, T.; Ishida, S.; Haga, H., Mathematical model of collective cell migrations based on cell polarity, Dev. Growth Differ., 59, 5, 471-490 (2017), arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/dgd.12381 |
| [3] | Alt, S.; Ganguly, P.; Salbreux, G., Vertex models: from cell mechanics to tissue morphogenesis, Philos. Trans. Biol. Sci., 372, 1720, Article 20150520 pp. (2017) |
| [4] | Antunes, M.; Pereira, T.; Cordeiro, J. V.; Almeida, L.; Jacinto, A., Coordinated waves of actomyosin flow and apical cell constriction immediately after wounding, J. Cell Biol., 202, 2, 365-379 (2013) |
| [5] | Barton, D. L.; Henkes, S.; Weijer, C. J.; Sknepnek, R., Active Vertex Model for cell-resolution description of epithelial tissue mechanics, PLoS Comput. Biol., 13, 6, 1-33 (2017), arXiv:1612.05960 |
| [6] | Belmonte, J. M.; Swat, M. H.; Glazier, J. A., Filopodial-tension model of convergent-extension of tissues, PLoS Comput. Biol., 12, 6, Article e1004952 pp. (2016) |
| [7] | Bi, D.; Yang, X.; Marchetti, M. C.; Manning, M. L., Motility-driven glass and jamming transitions in biological tissues, Phys. Rev. X, 6, 2 (2016), arXiv:1509.06578 |
| [8] | Bonilla, L.L., Carpio, A., Trenado, C., 2020. Tracking Collective Cell Motion By Topological Data Analysis, Vol. 16, (12 December), arXiv:2009.14161, http://dx.doi.org/10.1371/journal.pcbi.1008407. |
| [9] | Brau, F.; Damman, P.; Diamant, H.; Witten, T. A., Wrinkle to fold transition: influence of the substrate response, Soft Matter, 9, 34, 8177-8186 (2013) |
| [10] | Brugués, A.; Anon, E.; Conte, V.; Veldhuis, J. H.; Gupta, M.; Colombelli, J.; Muñoz, J. J.; Brodland, G. W.; Ladoux, B.; Trepat, X., Forces driving epithelial wound healing, Nat. Phys., 10, 9, 683-690 (2014) |
| [11] | Cerda, E.; Mahadevan, L., Geometry and physics of wrinkling, Phys. Rev. Lett., 90, 7, Article 074302 pp. (2003) |
| [12] | Farhadifar, R.; Röper, J.-C.; Aigouy, B.; Eaton, S.; Jülicher, F., The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing, Curr. Biol., 17, 24, 2095-2104 (2007), URL: https://www.sciencedirect.com/science/article/pii/S0960982207023342 |
| [13] | Fletcher, A. G.; Osterfield, M.; Baker, R. E.; Shvartsman, S. Y., Vertex models of epithelial morphogenesis, Biophys. J., 106, 11, 2291-2304 (2014) |
| [14] | Honda, H.; Tanemura, M.; Nagai, T., A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate, J. Theoret. Biol., 226, 4, 439-453 (2004) · Zbl 1439.92074 |
| [15] | Inaki, M.; Hatori, R.; Nakazawa, N.; Okumura, T.; Ishibashi, T.; Kikuta, J.; Ishii, M.; Matsuno, K.; Honda, H., Chiral cell sliding drives left-right asymmetric organ twisting, ELife, 7, Article e32506 pp. (2018) |
| [16] | Inoue, Y.; Suzuki, M.; Watanabe, T.; Yasue, N.; Tateo, I.; Adachi, T.; Ueno, N., Mechanical roles of apical constriction, cell elongation, and cell migration during neural tube formation in xenopus, Biomech. Model. Mechanobiol., 15, 6, 1733-1746 (2016) |
| [17] | Inoue, Y.; Tateo, I.; Adachi, T., Epithelial tissue folding pattern in confined geometry, Biomech. Model. Mechanobiol., 19, 3, 815-822 (2020) |
| [18] | Inoue, Y.; Watanabe, T.; Okuda, S.; Adachi, T., Mechanical role of the spatial patterns of contractile cells in invagination of growing epithelial tissue, Dev. Growth Differ., 59, 5, 444-454 (2017) |
| [19] | Keller, R.; Shih, J.; Sater, A., The cellular basis of the convergence and extension of the Xenopus neural plate, Dev. Dyn., 193, 3, 199-217 (1992) |
| [20] | Lee, J.-Y.; Harland, R. M., Actomyosin contractility and microtubules drive apical constriction in Xenopus bottle cells, Dev. Biol., 311, 1, 40-52 (2007) |
| [21] | Li, B.; Sun, S. X., Coherent motions in confluent cell monolayer sheets, Biophys. J., 107, 7, 1532-1541 (2014) |
| [22] | Lomas, A., Cellular forms: An artistic exploration of morphogenesis, (ACM SIGGRAPH 2014 Studio, SIGGRAPH 2014 (2014)) |
| [23] | Lowery, L. A.; Sive, H., Strategies of vertebrate neurulation and a re-evaluation of teleost neural tube formation, Mech. Dev., 121, 10, 1189-1197 (2004) |
| [24] | Martin, A. C.; Goldstein, B., Apical constriction: themes and variations on a cellular mechanism driving morphogenesis, Development (Cambridge), 141, 10, 1987-1998 (2014) |
| [25] | Meineke, F. A.; Potten, C. S.; Loeffler, M., Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif., 34, 4, 253-266 (2001) |
| [26] | Metzcar, J.; Wang, Y.; Heiland, R.; Macklin, P., A review of cell-based computational modeling in cancer biology, JCO Clin. Cancer Inform., 3, 1-13 (2019) |
| [27] | Murphy, S. V.; Atala, A., 3D bioprinting of tissues and organs, Nature Biotechnol., 32, 8, 773-785 (2014) |
| [28] | Nishimura, T.; Honda, H.; Takeichi, M., Planar cell polarity links axes of spatial dynamics in neural-tube closure, Cell, 149, 5, 1084-1097 (2012) |
| [29] | Okuda, S.; Inoue, Y.; Eiraku, M.; Sasai, Y.; Adachi, T., Modeling cell proliferation for simulating three-dimensional tissue morphogenesis based on a reversible network reconnection framework, Biomech. Model. Mechanobiol., 12, 5, 987-996 (2013) |
| [30] | Okuda, S.; Inoue, Y.; Eiraku, M.; Sasai, Y.; Adachi, T., Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis, Biomech. Model. Mechanobiol., 12, 4, 627-644 (2013) |
| [31] | Osborne, J. M.; Walter, A.; Kershaw, S. K.; Mirams, G. R.; Fletcher, A. G.; Pathmanathan, P.; Gavaghan, D.; Jensen, O. E.; Maini, P. K.; Byrne, H. M., A hybrid approach to multi-scale modelling of cancer, Phil. Trans. R. Soc. A, 368, 1930, 5013-5028 (2010) · Zbl 1211.37113 |
| [32] | Pathmanathan, P.; Cooper, J.; Fletcher, A.; Mirams, G.; Murray, P.; Osborne, J.; Pitt-Francis, J.; Walter, A.; Chapman, S. J., A computational study of discrete mechanical tissue models, Phys. Biol., 6, 3 (2009) |
| [33] | Romanazzo, S.; Nemec, S.; Roohani, I., iPSC bioprinting: Where are we at?, Materials, 12, 15, 2453 (2019) |
| [34] | Saye, R. I.; Sethian, J. A.; Lawrence Berkeley National Lab. (LBNL), C. U.S., Voronoi Implicit Interface Method for computing multiphase physics, Proc. Natl. Acad. Sci. - PNAS, 108, 49, 19498-19503 (2011) · Zbl 1256.65082 |
| [35] | Shindo, A.; Inoue, Y.; Kinoshita, M.; Wallingford, J. B., PCP-dependent transcellular regulation of actomyosin oscillation facilitates convergent extension of vertebrate tissue, Dev. Biol., 446, 2, 159-167 (2019) |
| [36] | Smith, A. M.; Baker, R. E.; Kay, D.; Maini, P. K., Incorporating chemical signalling factors into cell-based models of growing epithelial tissues, J. Math. Biol., 65, 3, 441-463 (2012) · Zbl 1303.92017 |
| [37] | Soumya, S. S.; Gupta, A.; Cugno, A.; Deseri, L.; Dayal, K.; Das, D.; Sen, S.; Inamdar, M. M., Coherent motion of monolayer sheets under confinement and its pathological implications, PLoS Comput. Biol., 11, 12 (2015), arXiv:1507.06481 |
| [38] | Staple, D. B.; Farhadifar, R.; Röper, J..; Aigouy, B.; Eaton, S.; Jülicher, F., Mechanics and remodelling of cell packings in epithelia, Eur. Phys. J. E Soft Matter Biol. Phys., 33, 2, 117-127 (2010) |
| [39] | Szabó, B.; Szöllösi, G. J.; Gönci, B.; Jurányi, Z.; Selmeczi, D.; Vicsek, T., Phase transition in the collective migration of tissue cells: Experiment and model, Phys. Rev. E, 74, 6, Article 061908 pp. (2006) |
| [40] | Tada, M.; Heisenberg, C. P., Convergent extension: Using collective cell migration and cell intercalation to shape embryos, Development (Cambridge), 139, 21, 3897-3904 (2012) |
| [41] | Vicsek, T.; Czirók, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75, 1226-1229 (1995), URL: https://link.aps.org/doi/10.1103/PhysRevLett.75.1226 |
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