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Active Vertex Model for cell-resolution description of epithelial tissue mechanics
Daniel L. Barton, Silke Henkes, Cornelis J. Weijer and 1 more
PLOS Computational Biology · 2017 · CC BY
Abstract
We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.
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- 1.
Ilina O, Friedl P. Mechanisms of collective cell migration at a glance. Journal of cell science. 2009;122(18):3203–3208.
Not in our library10.1242/jcs.036525
- 2.
Weijer CJ. Collective cell migration in development. Journal of cell science. 2009;122(18):3215–3223.
Not in our library10.1242/jcs.036517
- 3.
Forgacs G, Newman SA. Biological physics of the developing embryo. Cambridge University Press; 2005.
Not in our library
- 4.
Martin P. Wound healing–aiming for perfect skin regeneration. Science. 1997;276(5309):75–81.
Not in our library10.1126/science.276.5309.75
- 5.
Brugués A, Anon E, Conte V, Veldhuis JH, Gupta M, Colombelli J, et al Forces driving epithelial wound healing. Nature Physics. 2014;10:683–690.
Not in our library10.1038/nphys3040
- 6.
Wirtz D, Konstantopoulos K, Searson PC. The physics of cancer: the role of physical interactions and mechanical forces in metastasis. Nature Reviews Cancer. 2011;11(7):512–522.
Not in our library10.1038/nrc3080
- 7.
Guillot C, Lecuit T. Mechanics of epithelial tissue homeostasis and morphogenesis. Science. 2013;340(6137):1185–1189.
Not in our library10.1126/science.1235249
- 8.
Schatten GP, Schnell S, Maini P, Newman SA, Newman T. Multiscale modeling of developmental systems. vol. 81 Academic Press; 2007.
Not in our library10.1016/s0070-2153(07)81018-0
- 9.
Lecuit T, Lenne PF, Munro E. Force generation, transmission, and integration during cell and tissue morphogenesis. Annual review of cell and developmental biology. 2011;27:157–184.
Not in our library10.1146/annurev-cellbio-100109-104027
- 10.
Harris AK, Wild P, Stopak D. Silicone rubber substrata: a new wrinkle in the study of cell locomotion. Science. 1980;208(4440):177–179.
Not in our library10.1126/science.6987736
- 11.
Angelini TE, Hannezo E, Trepat X, Marquez M, Fredberg JJ, Weitz DA. Glass-like dynamics of collective cell migration. Proceedings of the National Academy of Sciences. 2011;108(12):4714–4719.
Not in our library10.1073/pnas.1010059108
- 12.
Tambe DT, Hardin CC, Angelini TE, Rajendran K, Park CY, Serra-Picamal X, et al Collective cell guidance by cooperative intercellular forces. Nature materials. 2011;10(6):469–475.
Not in our library10.1038/nmat3025
- 13.
Trepat X, Fredberg JJ. Plithotaxis and emergent dynamics in collective cellular migration. Trends in cell biology. 2011;21(11):638–646.
Not in our library10.1016/j.tcb.2011.06.006
- 14.
Sadati M, Qazvini NT, Krishnan R, Park CY, Fredberg JJ. Collective migration and cell jamming. Differentiation. 2013;86(3):121–125.
Not in our library10.1016/j.diff.2013.02.005
- 15.
Berthier L, Biroli G, Bouchaud JP, Cipelletti L, van Saarloos W. Dynamical heterogeneities in glasses, colloids, and granular media. Oxford University Press; 2011.
Not in our library
- 16.
Bazellières E, Conte V, Elosegui-Artola A, Serra-Picamal X, Bintanel-Morcillo M, Roca-Cusachs P, et al Control of cell–cell forces and collective cell dynamics by the intercellular adhesome. Nature cell biology. 2015;17(4):409–420.
Not in our library10.1038/ncb3135
- 17.
Charras G, Sahai E. Physical influences of the extracellular environment on cell migration. Nature Reviews Molecular Cell Biology. 2014;15(12):813–824.
Not in our library10.1038/nrm3897
- 18.
Discher DE, Janmey P, Wang Yl. Tissue cells feel and respond to the stiffness of their substrate. Science. 2005;310(5751):1139–1143.
Not in our library10.1126/science.1116995
- 19.
Elosegui-Artola A, Bazellières E, Allen MD, Andreu I, Oria R, Sunyer R, et al Rigidity sensing and adaptation through regulation of integrin types. Nature materials. 2014;13(6):631–637.
Not in our library10.1038/nmat3960
- 20.
Kim JH, Serra-Picamal X, Tambe DT, Zhou EH, Park CY, Sadati M, et al Propulsion and navigation within the advancing monolayer sheet. Nature materials. 2013;12(9):856–863.
Not in our library10.1038/nmat3689
- 21.
Das T, Safferling K, Rausch S, Grabe N, Boehm H, Spatz JP. A molecular mechanotransduction pathway regulates collective migration of epithelial cells. Nature cell biology. 2015;17(3):276–287.
Not in our library10.1038/ncb3115
- 22.
- 23.
Serra-Picamal X, Conte V, Sunyer R, Muñoz JJ, Trepat X. Mapping forces and kinematics during collective cell migration. Methods in cell biology. 2015;125:309–330.
Not in our library10.1016/bs.mcb.2014.11.003
- 24.
Keller PJ, Schmidt AD, Wittbrodt J, Stelzer EH. Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy. science. 2008;322(5904):1065–1069.
Not in our library10.1126/science.1162493
- 25.
Manning ML, Foty RA, Steinberg MS, Schoetz EM. Coaction of intercellular adhesion and cortical tension specifies tissue surface tension. Proceedings of the National Academy of Sciences. 2010;107(28):12517–12522.
Not in our library10.1073/pnas.1003743107
- 26.
Blanchard GB, Kabla AJ, Schultz NL, Butler LC, Sanson B, Gorfinkiel N, et al Tissue tectonics: morphogenetic strain rates, cell shape change and intercalation. Nature methods. 2009;6(6):458–464.
Not in our library10.1038/nmeth.1327
- 27.
Butler LC, Blanchard GB, Kabla AJ, Lawrence NJ, Welchman DP, Mahadevan L, et al Cell shape changes indicate a role for extrinsic tensile forces in Drosophila germ-band extension. Nature cell biology. 2009;11(7):859–864.
Not in our library10.1038/ncb1894
- 28.
Keller PJ, Schmidt AD, Santella A, Khairy K, Bao Z, Wittbrodt J, et al Fast, high-contrast imaging of animal development with scanned light sheet-based structured-illumination microscopy. Nature methods. 2010;7(8):637–642.
Not in our library10.1038/nmeth.1476
- 29.
Bosveld F, Bonnet I, Guirao B, Tlili S, Wang Z, Petitalot A, et al Mechanical control of morphogenesis by Fat/Dachsous/Four-jointed planar cell polarity pathway. Science. 2012;336(6082):724–727.
Not in our library10.1126/science.1221071
- 30.
Collinet C, Rauzi M, Lenne PF, Lecuit T. Local and tissue-scale forces drive oriented junction growth during tissue extension. Nature cell biology. 2015;.
Not in our library10.1038/ncb3226
- 31.
- 32.
Etournay R, Merkel M, Popović M, Brandl H, Dye NA, Aigouy B, et al TissueMiner: a multiscale analysis toolkit to quantify how cellular processes create tissue dynamics. eLife. 2016;5:e14334
Not in our library10.7554/elife.14334
- 33.
Rozbicki E, Chuai M, Karjalainen AI, Song F, Sang HM, Martin R, et al Myosin-II-mediated cell shape changes and cell intercalation contribute to primitive streak formation. Nature cell biology. 2015;17(4):397–408.
Not in our library10.1038/ncb3138
- 34.
Anderson A, Rejniak K. Single-cell-based models in biology and medicine. Springer Science & Business Media; 2007.
Not in our library
- 35.
Graner F, Glazier JA. Simulation of biological cell sorting using a two-dimensional extended Potts model. Physical review letters. 1992;69(13):2013
Not in our library10.1103/physrevlett.69.2013
- 36.
Glazier JA, Graner F. Simulation of the differential adhesion driven rearrangement of biological cells. Physical Review E. 1993;47(3):2128
Not in our library10.1103/physreve.47.2128
- 37.
Izaguirre JA, Chaturvedi R, Huang C, Cickovski T, Coffland J, Thomas G, et al CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics. 2004;20(7):1129–1137.
Not in our library10.1093/bioinformatics/bth050
- 38.
Swat MH, Thomas GL, Belmonte JM, Shirinifard A, Hmeljak D, Glazier JA. Multi-scale modeling of tissues using CompuCell3D. Methods in cell biology. 2012;110:325
Not in our library10.1016/b978-0-12-388403-9.00013-8
- 39.
- 40.
Newman TJ. Modeling Multi-cellular Systems using Sub-cellular Elements. Mathematical Biosciences and Engineering. 2005;2:611–622.
Not in our library10.3934/mbe.2005.2.613
- 41.
Sandersius S, Weijer CJ, Newman TJ. Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes. Physical biology. 2011;8(4):045007
Not in our library10.1088/1478-3975/8/4/045007
- 42.
Drasdo D, Hoehme S, Block M. On the role of physics in the growth and pattern formation of multi-cellular systems: what can we learn from individual-cell based models? Journal of Statistical Physics. 2007;128(1–2):287–345.
Not in our library10.1007/s10955-007-9289-x
- 43.
Meineke FA, Potten CS, Loeffler M. Cell migration and organization in the intestinal crypt using a lattice-free model. Cell proliferation. 2001;34(4):253–266.
Not in our library10.1046/j.0960-7722.2001.00216.x
- 44.
Zimmermann J, Hayes RL, Basan M, Onuchic JN, Rappel WJ, Levine H. Intercellular stress reconstitution from traction force data. Biophysical journal. 2014;107(3):548–554.
Not in our library10.1016/j.bpj.2014.06.036
- 45.
Aland S, Hatzikirou H, Lowengrub J, Voigt A. A mechanistic collective cell model for epithelial colony growth and contact inhibition. Biophysical journal. 2015;109(7):1347–1357.
Not in our library10.1016/j.bpj.2015.08.003
- 46.
Zimmermann J, Camley BA, Rappel WJ, Levine H. Contact inhibition of locomotion determines cell–cell and cell–substrate forces in tissues. Proceedings of the National Academy of Sciences. 2016;113(10):2660–2665.
Not in our library10.1073/pnas.1522330113
- 47.
Honda H, Eguchi G. How much does the cell boundary contract in a monolayered cell sheet? Journal of theoretical biology. 1980;84(3):575–588.
Not in our library10.1016/s0022-5193(80)80021-x
- 48.
Brodland GW. Computational modeling of cell sorting, tissue engulfment, and related phenomena: A review. Applied Mechanics Reviews. 2004;57(1):47–76.
Not in our library10.1115/1.1583758
- 49.
Farhadifar R, Röper JC, Aigouy B, Eaton S, Jülicher F. The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Current Biology. 2007;17(24):2095–2104.
Not in our library10.1016/j.cub.2007.11.049
- 50.
Staple D, Farhadifar R, Röper JC, Aigouy B, Eaton S, Jülicher F. Mechanics and remodelling of cell packings in epithelia. The European Physical Journal E. 2010;33(2):117–127.
Not in our library10.1140/epje/i2010-10677-0
- 51.
Fletcher AG, Osborne JM, Maini PK, Gavaghan DJ. Implementing vertex dynamics models of cell populations in biology within a consistent computational framework. Progress in biophysics and molecular biology. 2013;113(2):299–326.
Not in our library10.1016/j.pbiomolbio.2013.09.003
- 52.
Fletcher AG, Osterfield M, Baker RE, Shvartsman SY. Vertex models of epithelial morphogenesis. Biophysical journal. 2014;106:2291–2304.
Not in our library10.1016/j.bpj.2013.11.4498
- 53.
- 54.
Pathmanathan P, Cooper J, Fletcher A, Mirams G, Murray P, Osborne J, et al A computational study of discrete mechanical tissue models. Physical biology. 2009;6(3):036001
Not in our library10.1088/1478-3975/6/3/036001
- 55.
- 56.
Weliky M, Oster G. The mechanical basis of cell rearrangement. Development. 1990;109(2):373–386.
Not in our library10.1242/dev.109.2.373
- 57.
Nagai T, Honda H. A dynamic cell model for the formation of epithelial tissues. Philosophical Magazine B. 2001;81(7):699–719.
Not in our library10.1080/13642810108205772
- 58.
Spencer MA, Jabeen Z, Lubensky DK. Vertex stability and topological transitions in vertex models of foams and epithelia. The European Physical Journal E. 2017;40:2
Not in our library10.1140/epje/i2017-11489-4
- 59.
Bi D, Yang X, Marchetti MC, Manning ML. Motility-driven glass and jamming transitions in biological tissues. Physical Review X. 2016;6(2):021011
Not in our library10.1103/physrevx.6.021011
- 60.
Marchetti M, Joanny J, Ramaswamy S, Liverpool T, Prost J, Rao M, et al Hydrodynamics of soft active matter. Reviews of Modern Physics. 2013;85(3):1143
Not in our library10.1103/revmodphys.85.1143
- 61.
Soft Active Matter on Surfaces (SAMoS);. Available from: https://github.com/sknepneklab/SAMoS.
Not in our library
- 62.
Weaire DL, Hutzler S. The physics of foams. Oxford University Press; 2001.
Not in our library
- 63.
Ishimoto Y, Morishita Y. Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapes. Physical Review E. 2014;90(5):052711
Not in our library10.1103/physreve.90.052711
- 64.
Perrone MC, Veldhuis JH, Brodland GW. Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model. Biomechanics and modeling in mechanobiology. 2016;15(2):405–418.
Not in our library10.1007/s10237-015-0697-6
- 65.
Chaikin PM, Lubensky TC. Principles of condensed matter physics. vol. 1 Cambridge Univ Press; 2000.
Not in our library
- 66.
Sánchez-Gutiérrez D, Tozluoglu M, Barry JD, Pascual A, Mao Y, Escudero LM. Fundamental physical cellular constraints drive self-organization of tissues. The EMBO journal. 2016;35(1):77–88.
Not in our library10.15252/embj.201592374
- 67.
Bock M, Tyagi AK, Kreft JU, Alt W. Generalized voronoi tessellation as a model of two-dimensional cell tissue dynamics. Bulletin of mathematical biology. 2010;72(7):1696–1731.
Not in our library10.1007/s11538-009-9498-3
- 68.
Delaunay B. Sur la sphere vide. Izv Akad Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk. 1934;7(793–800):1–2.
Not in our library
- 69.
Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford university press; 1989.
Not in our library
- 70.
Asnacios A, Hamant O. The mechanics behind cell polarity. Trends in cell biology. 2012;22(11):584–591.
Not in our library10.1016/j.tcb.2012.08.005
- 71.
Chaté H, Ginelli F, Grégoire G, Peruani F, Raynaud F. Modeling collective motion: variations on the Vicsek model. The European Physical Journal B. 2008;64(3–4):451–456.
Not in our library
- 72.
Zallen JA. Planar polarity and tissue morphogenesis. Cell. 2007;129(6):1051–1063.
Not in our library10.1016/j.cell.2007.05.050
- 73.
Wallingford JB. Planar cell polarity and the developmental control of cell behavior in vertebrate embryos. Annual review of cell and developmental biology. 2012;28:627–653.
Not in our library10.1146/annurev-cellbio-092910-154208
- 74.
Szabo B, Szöllösi G, Gönci B, Jurányi Z, Selmeczi D, Vicsek T. Phase transition in the collective migration of tissue cells: experiment and model. Physical Review E. 2006;74(6):061908
Not in our library10.1103/physreve.74.061908
- 75.
Henkes S, Fily Y, Marchetti MC. Active jamming: Self-propelled soft particles at high density. Physical Review E. 2011;84(4):040301
Not in our library10.1103/physreve.84.040301
- 76.
Aubouy M, Jiang Y, Glazier JA, Graner F. A texture tensor to quantify deformations. Granular Matter. 2003;5(2):67–70.
Not in our library10.1007/s10035-003-0126-x
- 77.
Wyatt TP, Harris AR, Lam M, Cheng Q, Bellis J, Dimitracopoulos A, et al Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis. Proceedings of the National Academy of Sciences. 2015;112(18):5726–5731.
Not in our library10.1073/pnas.1420585112
- 78.
Du Roure O, Saez A, Buguin A, Austin RH, Chavrier P, Siberzan P, et al Force mapping in epithelial cell migration. Proceedings of the National Academy of Sciences of the United States of America. 2005;102(7):2390–2395.
Not in our library10.1073/pnas.0408482102
- 79.
Binamé F, Pawlak G, Roux P, Hibner U. What makes cells move: requirements and obstacles for spontaneous cell motility. Molecular BioSystems. 2010;6(4):648–661.
Not in our library10.1039/b915591k
- 80.
Sknepnek R, Henkes S. Active swarms on a sphere. Physical Review E. 2015;91(2):022306
Not in our library10.1103/physreve.91.022306
- 81.
Aegerter-Wilmsen T, Smith AC, Christen AJ, Aegerter CM, Hafen E, Basler K. Exploring the effects of mechanical feedback on epithelial topology. Development. 2010;137(3):499–506.
Not in our library10.1242/dev.041731
- 82.
Bell GI, Anderson EC. Cell growth and division: I. a mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophysical journal. 1967;7(4):329
Not in our library10.1016/s0006-3495(67)86592-5
- 83.
Smith J, Martin L. Do cells cycle? Proceedings of the National Academy of Sciences. 1973;70(4):1263–1267.
Not in our library10.1073/pnas.70.4.1263
- 84.
Brakke KA. The surface evolver. Experimental mathematics. 1992;1(2):141–165.
Not in our library10.1080/10586458.1992.10504253
- 85.
Coburn L, Lopez H, Caldwell BJ, Moussa E, Yap C, Priya R, et al Contact inhibition of locomotion and mechanical cross-talk between cell–cell and cell–substrate adhesion determine the pattern of junctional tension in epithelial cell aggregates. Molecular Biology of the Cell. 2016;27(22):3436–3448.
Not in our library10.1091/mbc.e16-04-0226
- 86.
Bi D, Lopez JH, Schwarz J, Manning ML. Energy barriers and cell migration in densely packed tissues. Soft Matter. 2014;10(12):1885–1890.
Not in our library10.1039/c3sm52893f
- 87.
Hébraud P, Lequeux F, Munch J, Pine D. Yielding and rearrangements in disordered emulsions. Physical Review Letters. 1997;78(24):4657
Not in our library10.1103/physrevlett.78.4657
- 88.
Park JA, Kim JH, Bi D, Mitchel JA, Qazvini NT, Tantisira K, et al Unjamming and cell shape in the asthmatic airway epithelium. Nature materials. 2015;14(10):1040–1048.
Not in our library10.1038/nmat4357
- 89.
Harding MJ, McGraw HF, Nechiporuk A. The roles and regulation of multicellular rosette structures during morphogenesis. Development. 2014;141(13):2549–2558.
Not in our library10.1242/dev.101444
- 90.
Poujade M, Grasland-Mongrain E, Hertzog A, Jouanneau J, Chavrier P, Ladoux B, et al Collective migration of an epithelial monolayer in response to a model wound. Proceedings of the National Academy of Sciences. 2007;104(41):15988–15993.
Not in our library10.1073/pnas.0705062104
- 91.
Petitjean L, Reffay M, Grasland-Mongrain E, Poujade M, Ladoux B, Buguin A, et al Velocity fields in a collectively migrating epithelium. Biophysical journal. 2010;98(9):1790–1800.
Not in our library10.1016/j.bpj.2010.01.030
- 92.
- 93.
Tarle V, Ravasio A, Hakim V, Gov NS. Modeling the finger instability in an expanding cell monolayer. Integr Biol. 2015;7:1218–1227.
Not in our library10.1039/c5ib00092k
- 94.
- 95.
Köpf MH, Pismen LM. A continuum model of epithelial spreading. Soft Matter. 2013;9(14):3727–3734.
Not in our library10.1039/c3sm26955h
- 96.
Admal NC, Tadmor EB. A unified interpretation of stress in molecular systems. Journal of elasticity. 2010;100(1–2):63–143.
Not in our library10.1007/s10659-010-9249-6
- 97.
Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, et al Physical forces during collective cell migration. Nature physics. 2009;5(6):426–430.
Not in our library10.1038/nphys1269
- 98.
Delarue M, Joanny JF, Jülicher F, Prost J. Stress distributions and cell flows in a growing cell aggregate. Interface focus. 2014;4(6):20140033
Not in our library10.1098/rsfs.2014.0033
- 99.
Shraiman BI. Mechanical feedback as a possible regulator of tissue growth. Proceedings of the National Academy of Sciences of the United States of America. 2005;102(9):3318–3323.
Not in our library10.1073/pnas.0404782102
- 100.
Gibson MC, Patel AB, Nagpal R, Perrimon N. The emergence of geometric order in proliferating metazoan epithelia. Nature. 2006;442(7106):1038–1041.
Not in our library10.1038/nature05014
- 101.
Sandersius SA, Chuai M, Weijer CJ, Newman TJ. Correlating cell behavior with tissue topology in embryonic epithelia. PLoS One. 2011;6(4):e18081–e18081.
Not in our library10.1371/journal.pone.0018081
- 102.
Graner F, Sawada Y. Can surface adhesion drive cell rearrangement? Part II: a geometrical model. Journal of theoretical biology. 1993;164(4):477–506.
Not in our library
- 103.
Foty RA, Steinberg MS. The differential adhesion hypothesis: a direct evaluation. Developmental biology. 2005;278(1):255–263.
Not in our library10.1016/j.ydbio.2004.11.012
- 104.
Serra-Picamal X, Conte V, Vincent R, Anon E, Tambe DT, Bazellieres E, et al Mechanical waves during tissue expansion. Nature Physics. 2012;8(8):628–634.
Not in our library10.1038/nphys2355
- 105.
Deforet M, Hakim V, Yevick H, Duclos G, Silberzan P. Emergence of collective modes and tri-dimensional structures from epithelial confinement. Nature communications. 2014;5
Not in our library10.1038/ncomms4747
- 106.
Delarue M, Hartung J, Schreck C, Gniewek P, Hu L, Herminghaus S, et al Self-driven jamming in growing microbial populations. Nature Physics. 2016;.
Not in our library10.1038/nphys3741
- 107.
Honda H, Tanemura M, Nagai T. A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate. Journal of Theoretical Biology. 2004;226(4):439–453.
Not in our library10.1016/j.jtbi.2003.10.001
- 108.
Osterfield M, Du X, Schüpbach T, Wieschaus E, Shvartsman SY. Three-dimensional epithelial morphogenesis in the developing Drosophila egg. Developmental cell. 2013;24(4):400–410.
Not in our library10.1016/j.devcel.2013.01.017
- 109.
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. Biomechanics and modeling in mechanobiology. 2013;12(5):987–996.
Not in our library10.1007/s10237-012-0458-8
- 110.
Okuda S, Inoue Y, Eiraku M, Sasai Y, Adachi T. Reversible network reconnection model for simulating large deformation in dynamic tissue morphogenesis. Biomechanics and modeling in mechanobiology. 2013; p. 1–18.
Not in our library10.1007/s10237-012-0430-7
- 111.
Okuda S, Inoue Y, Adachi T. Three-dimensional vertex model for simulating multicellular morphogenesis. Biophysics and Physicobiology. 2015;12:13–20.
Not in our library10.2142/biophysico.12.0_13
- 112.
- 113.
- 114.
Buske P, Przybilla J, Loeffler M, Sachs N, Sato T, Clevers H, et al On the biomechanics of stem cell niche formation in the gut–modelling growing organoids. FEBS Journal. 2012;279(18):3475–3487.
Not in our library10.1111/j.1742-4658.2012.08646.x
- 115.
Clevers H. The intestinal crypt, a prototype stem cell compartment. Cell. 2013;154(2):274–284.
Not in our library10.1016/j.cell.2013.07.004
- 116.
Dunn SJ, Osborne J, Appleton P, Näthke I. Combined changes in Wnt signaling response and contact inhibition induce altered proliferation in radiation-treated intestinal crypts. Molecular biology of the cell. 2016;27(11):1863–1874.
Not in our library10.1091/mbc.e15-12-0854
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