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Adapting a plant tissue model to animal development: introducing cell sliding into VirtualLeaf. (English) Zbl 1422.92021

Summary: Cell-based, mathematical modeling of collective cell behavior has become a prominent tool in developmental biology. Cell-based models represent individual cells as single particles or as sets of interconnected particles and predict the collective cell behavior that follows from a set of interaction rules. In particular, vertex-based models are a popular tool for studying the mechanics of confluent, epithelial cell layers. They represent the junctions between three (or sometimes more) cells in confluent tissues as point particles, connected using structural elements that represent the cell boundaries. A disadvantage of these models is that cell-cell interfaces are represented as straight lines. This is a suitable simplification for epithelial tissues, where the interfaces are typically under tension, but this simplification may not be appropriate for mesenchymal tissues or tissues that are under compression, such that the cell-cell boundaries can buckle. In this paper, we introduce a variant of VMs in which this and two other limitations of VMs have been resolved. The new model can also be seen as on off-the-lattice generalization of the cellular Potts model. It is an extension of the open-source package VirtualLeaf, which was initially developed to simulate plant tissue morphogenesis where cells do not move relative to one another. The present extension of VirtualLeaf introduces a new rule for cell-cell shear or sliding, from which cell rearrangement (T1) and cell extrusion (T2) transitions emerge naturally, allowing the application of VirtualLeaf to problems of animal development. We show that the updated VirtualLeaf yields different results than the traditional vertex-based models for differential adhesion-driven cell sorting and for the neighborhood topology of soft cellular networks.

MSC:

92C15 Developmental biology, pattern formation
92C80 Plant biology
92-08 Computational methods for problems pertaining to biology
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[1] Anderson ARA, Chaplain MAJ, Rejniak KA (2007) Single-cell-based models in biology and medicine. In: Mathematics and biosciences in interaction. Birkhaüser, Berlin
[2] Antonelli, PL; Rogers, TD; Willard, MA, Geometry and the exchange principle in cell aggregation kinetics, J Theor Biol, 41, 1-21, (1973)
[3] Atia, L.; Bi, D.; Sharma, Y.; Mitchel, JA; Gweon, B.; Koehler, SA; DeCamp, SJ; Lan, B.; Kim, JH; Hirsch, R.; Pegoraro, AF; Lee, KH; Starr, JR; Weitz, DA; Martin, AC; Park, JA; Butler, JP; Fredberg, JJ, Geometric constraints during epithelial jamming, Nat Phys, 14, 613-620, (2018)
[4] Balter, A.; Merks, RMH; Popławski, NJ; Swat, M.; Glazier, JA; Anderson, ARA (ed.); Rejniak, KA (ed.), The Glazier-Graner-Hogeweg model: extensions, future directions, and opportunities for further study, 151-167, (2007), Basel
[5] Barton, DL; Henkes, S.; Weijer, CJ; Sknepnek, R., Active vertex model for cell-resolution description of epithelial tissue mechanics, PLoS Comput Biol, 13, e1005569, (2017)
[6] Belmonte, JM; Clendenon, SG; Oliveira, GM; Swat, MH; Greene, EV; Jeyaraman, S.; Glazier, JA; Bacallao, RL, Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease, Mol Biol Cell, 27, 3673-3685, (2016)
[7] Bi, D.; Lopez, JH; Schwarz, JM; Manning, ML, A density-independent rigidity transition inbiological tissues, Nat Phys, 11, 1074-1079, (2015) · Zbl 0769.49033
[8] Bi, D.; Yang, X.; Marchetti, MC; Manning, ML, Motility-Driven glass and jamming transitions in biological tissues, Phys Rev X, (2016)
[9] Boas, SEM; Merks, RMH, Synergy of cell-cell repulsion and vacuolation in a computational model of lumen formation, J R Soc Interface, 11, 20131049-20131049, (2014)
[10] Boas, SEM; Navarro, JMI; Merks, RMH; Blom, JG, A global sensitivity analysis approach for morphogenesis models, BMC Syst Biol, 9, 85, (2015)
[11] Brodland, GW, The differential interfacial tension hypothesis (DITH): a comprehensive theory for the self-rearrangement of embryonic cells and tissues, J Biomech Eng Trans ASME, 124, 188, (2002)
[12] Brodland, GW; Veldhuis, JH; Kim, S.; Perrone, M.; Mashburn, D.; Hutson, MS, CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries, PLoS One, 9, e99116, (2014)
[13] Carmona-Fontaine, C.; Matthews, HK; Kuriyama, S.; Moreno, M.; Dunn, GA; Parsons, M.; Stern, CD; Mayor, R., Contact inhibition of locomotion in vivo controls neural crest directional migration, Nature, 456, 957-961, (2008)
[14] Carter, R.; Sánchez-Corrales, YE; Hartley, M.; Grieneisen, VA; Marée, AFM, Pavement cells and the topology puzzle, Development (Cambridge, England), 144, 4386-4397, (2017)
[15] Vos, D.; Dzhurakhalov, A.; Stijven, S.; Klosiewicz, P.; Beemster, GTS; Broeckhove, J., Virtual plant tissue: building blocks for next-generation plant growth simulation, Front Plant Sci, 8, 686, (2017)
[16] Dupuy, L.; Mackenzie, J.; Rudge, T.; Haseloff, J., A system for modelling cell-cell interactions during plant morphogenesis, Ann Bot, 101, 1255-1265, (2008)
[17] Farhadifar, R.; Röper, JC; Aigouy, B.; Eaton, S.; Jülicher, F., The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing, Curr Biol, 17, 2095-2104, (2007)
[18] Feroze, R.; Shawky, JH; Dassow, M.; Davidson, LA, Mechanics of blastopore closure during amphibian gastrulation, Dev Biol, 398, 57-67, (2015)
[19] Fletcher, AG; Cooper, F.; Baker, RE, Mechanocellular models of epithelial morphogenesis, Philos Trans R Soc B Biol Sci, 372, 20150519, (2017)
[20] Fu, Y.; Gu, Y.; Zheng, Z.; Wasteneys, G.; Yang, Z., Arabidopsis interdigitating cell growth requires two antagonistic pathways with opposing action on cell morphogenesis, Cell, 120, 687-700, (2005)
[21] Ghaffarizadeh, A.; Heiland, R.; Friedman, SH; Mumenthaler, SM; Macklin, P., PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems, PLoS Comput Biol, 14, e1005991, (2018)
[22] Gibson, MC; Patel, AB; Nagpal, R.; Perrimon, N., The emergence of geometric order in proliferating metazoan epithelia, Nature, 442, 1038-1041, (2006)
[23] Glazier, JA; Graner, F., Simulation of the differential adhesion driven rearrangement of biological cells, Phys Rev E, 47, 2128-2154, (1993)
[24] Graner, F.; Glazier, JA, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys Rev Lett, 69, 2013-2016, (1992)
[25] Graner, F.; Sawada, Y., Can surface adhesion drive cell rearrangement?, J Theor Biol, 164, 477-506, (1993)
[26] Harris, AK, Is cell sorting caused by differences in the work of intercellular adhesion? A critique of the Steinberg hypothesis, J Theor Biol, 61, 267-285, (1976)
[27] Hester, SD; Belmonte, JM; Gens, JS; Clendenon, SG; Glazier, JA, A multi-cell, multi-scale model of vertebrate segmentation and somite formation, PLoS Comput Biol, 7, e1002155, (2011)
[28] Honda, H.; Dan-Sohkawa, M.; Watanabe, K., Geometrical analysis of cells becoming organized into a tensile sheet, the blastular wall, in the starfish, Differentiation, 25, 16-22, (1983)
[29] Hutson, MS; Brodland, GW; Yang, J.; Viens, D., Cell sorting in three dimensions: topology, fluctuations, and fluidlike instabilities, Phys Rev Lett, 101, 4, (2008)
[30] Ishimoto, Y.; Morishita, Y., Bubbly vertex dynamics: a dynamical and geometrical model for epithelial tissues with curved cell shapes, Phys Rev E, 90, 052711, (2014)
[31] Keller, EF; Segel, LA, Initiation of slime mold aggregation viewed as an instability, J Theor Biol, 26, 399-415, (1970) · Zbl 1170.92306
[32] Keller, EF; Segel, LA, Model for chemotaxis, J Theor Biol, 30, 225-234, (1971) · Zbl 1170.92307
[33] Kim, S.; Cai, M.; Hilgenfeldt, S., Lewis’ law revisited: the role of anisotropy in size-topology correlations, New J Phys, 16, 015024, (2014)
[34] Krieg, MM; Arboleda-Estudillo, YY; Puech, PHP; Käfer, JJ; Graner, FF; Müller, DJD; Heisenberg, CPC, Tensile forces govern germ-layer organization in zebrafish, Nat Cell Biol, 10, 429-436, (2008)
[35] Kudryashova, N.; Tsvelaya, V.; Agladze, K.; Panfilov, A., Virtual cardiac monolayers for electrical wave propagation, Sci Rep, 7, 7887, (2017)
[36] Lander, AD, Morpheus unbound: reimagining the morphogen gradient, Cell, 128, 245-256, (2007)
[37] Lewis, FT, The effect of cell division on the shape and size of hexagonal cells, Anat Rec, 33, 331-355, (1926)
[38] Liedekerke, P.; Palm, MM; Jagiella, N.; Drasdo, D., Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results, Comput Part Mech, 2, 401-444, (2015)
[39] Magno, R.; Grieneisen, VA; Marée, AF, The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics, BMC Biophys, 8, 2038, (2015)
[40] Maree, A.; Hogeweg, P., Modelling dictyostelium discoideum morphogenesis: the culmination, Bull Math Biol, 64, 327-353, (2002) · Zbl 1334.92040
[41] Merkel, M.; Manning, ML, Using cell deformation and motion to predict forces and collective behavior in morphogenesis, Semin Cell Dev Biol, 67, 161-169, (2017)
[42] Merks, R.; Engquist, B. (ed.), Cell-based modeling, 195-201, (2015), Berlin
[43] Merks, RMH; Brodsky, SV; Goligorksy, MS; Newman, SA; Glazier, JA, Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling, Dev Biol, 289, 44-54, (2006)
[44] Merks, RMH; Glazier, JA, A cell-centered approach to developmental biology, Physica A, 352, 113-130, (2005)
[45] Merks, RMH; Guravage, M.; Inzé, D.; Beemster, GTS, VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development, Plant Phys, 155, 656-666, (2011)
[46] Merks, RMH; Guravage, M.; Inze, D.; Beemster, GTS, VirtualLeaf: an open-source framework for cell-based modeling of plant tissue growth and development, Plant Physiol, 155, 656-666, (2011)
[47] Merks, RMH; Guravage, MA; Smet, I. (ed.), Building simulation models of developing plant organs using VirtualLeaf, 333-352, (2012), New York
[48] Newman, T., Modeling multicellular systems using subcellular elements, Math Biosci Eng, 2, 613-624, (2005) · Zbl 1079.92025
[49] Odell, GM; Oster, G.; Alberch, P.; Burnside, B., The mechanical basis of morphogenesis. I. Epithelial folding and invagination, Dev Biol, 85, 446-462, (1981)
[50] Osborne, JM; Fletcher, AG; Pitt-Francis, JM; Maini, PK; Gavaghan, DJ, Comparing individual-based approaches to modelling the self-organization of multicellular tissues, PLoS Comput Biol, 13, e1005387, (2017)
[51] Painter, KJ; Bloomfield, JM; Sherratt, JA; Gerisch, A., A nonlocal model for contact attraction and repulsion in heterogeneous cell populations, Bull Math Biol, 77, 1132-1165, (2015) · Zbl 1335.92026
[52] Palachanis, D.; Szabó, A.; Merks, RMH, Particle-based simulation of ellipse-shaped particle aggregation as a model for vascular network formation, Comput Part Mech, 2, 371-379, (2015)
[53] Palm, MM; Dallinga, MG; Dijk, E.; Klaassen, I.; Schlingemann, RO; Merks, RMH, Computational screening of tip and stalk cell behavior proposes a role for apelin signaling in sprout progression, PLoS One, 11, e0159478, (2016)
[54] Perrone, MC; Veldhuis, JH; Brodland, GW, Non-straight cell edges are important to invasion and engulfment as demonstrated by cell mechanics model, Biomech Model Mechanobiol, 15, 405-418, (2016)
[55] Rudge, T.; Haseloff, J., A computational model of cellular morphogenesis in plants, Lect Notes Comput Sci, 3630, 78-87, (2005)
[56] Sahlin, P.; Jönsson, H., A modeling study on how cell division affects properties of epithelial tissues under isotropic growth, PLoS One, 5, e11750, (2010)
[57] Salbreux, G.; Charras, G.; Paluch, E., Actin cortex mechanics and cellular morphogenesis, Trends Cell Biol, 22, 536-545, (2012)
[58] Sapala, A.; Runions, A.; Routier-Kierzkowska, AL; Das Gupta, M.; Hong, L.; Hofhuis, H.; Verger, S.; Mosca, G.; Li, CB; Hay, A.; Hamant, O.; Roeder, AH; Tsiantis, M.; Prusinkiewicz, P.; Smith, RS, Why plants make puzzle cells, and how their shape emerges, eLife, 7, e32794, (2018)
[59] Scianna, M.; Preziosi, L., A node-based version of the cellular Potts model, Comput Biol Med, 76, 94-112, (2016)
[60] Sluka, JP; Fu, X.; Maaciej, S.; Belmonte, JM; Cosmanescu, A.; Clendenon, SG; Wambaugh, JF; Glazier, JA, A liver-centric multiscale modeling framework for xenobiotics, PLoS One, 11, e0162428, (2016)
[61] Smeets, B.; Alert, R.; Pešek, J.; Pagonabarraga, I.; Ramon, H.; Vincent, R., Emergent structures and dynamics of cell colonies by contact inhibition of locomotion, Proc Natl Acad Sci USA, 113, 14621-14626, (2016)
[62] Solon, J.; Kaya-Copur, A.; Colombelli, J.; Brunner, D., Pulsed forces timed by a ratchet-like mechanism drive directed tissue movement during dorsal closure, Cell, 137, 1331-1342, (2009)
[63] Sozinova, O.; Jiang, Y.; Kaiser, D.; Alber, M., A three-dimensional model of myxobacterial fruiting-body formation, Proc Natl Acad Sci USA, 103, 17255-17259, (2006)
[64] Staple, DB; Farhadifar, R.; Röper, JC; Aigouy, B.; Eaton, S.; Jülicher, F., Mechanics and remodelling of cell packings in epithelia, Eur Phys J E, 33, 117-127, (2010) · Zbl 1007.52008
[65] Steinberg, M., Reconstruction of tissues by dissociated cells, Science (New York, NY), 141, 401-408, (1963)
[66] Steinberg, MS, Adhesion in development: an historical overview, Dev Biol, 180, 377-388, (1996)
[67] Steinberg, MS, Differential adhesion in morphogenesis: a modern view, Curr Opin Genet Dev, 17, 281-286, (2007)
[68] Sulsky, D.; Childress, S.; Percus, JK, A model of cell sorting, J Theor Biol, 106, 275-301, (1984)
[69] Tamulonis, C.; Postma, M.; Marlow, HQ; Magie, CR; Jong, J.; Kaandorp, J., A cell-based model of Nematostella vectensis gastrulation including bottle cell formation, invagination and zippering, Dev Biol, 351, 217-228, (2010)
[70] Tanaka, S.; Sichau, D.; Iber, D., LBIBCell: a cell-based simulation environment for morphogenetic problems, Bioinformatics (Oxford, England), 31, 2340-2347, (2015)
[71] Tlili, S.; Gauquelin, E.; Li, B.; Cardoso, O.; Ladoux, B.; Delanoë-Ayari, H.; Graner, F., Collective cell migration without proliferation: density determines cell velocity and wave velocity, R Soc Open Sci, 5, 172421, (2018)
[72] Toyama, Y.; Peralta, XG; Wells, AR; Kiehart, DP; Edwards, GS, Apoptotic force and tissue dynamics during Drosophila embryogenesis, Science (New York, NY), 321, 1683-1686, (2008)
[73] Voss-Böhme, A.; Deutsch, A., The cellular basis of cell sorting kinetics, J Theor Biol, 263, 419-436, (2010) · Zbl 1406.92066
[74] Weliky, M.; Oster, G., The mechanical basis of cell rearrangement. I. Epithelial morphogenesis during Fundulus epiboly, Development (Cambridge, England), 109, 373-386, (1990)
[75] Woods, ML; Carmona-Fontaine, C.; Barnes, CP; Couzin, ID; Mayor, R.; Page, KM, Directional collective cell migration emerges as a property of cell interactions, PLoS One, 9, e104969, (2014)
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