Loading [Contrib]/a11y/accessibility-menu.js
Special Issues

A Cellular Potts model simulating cell migration on and in matrix environments

  • Cell migration on and through extracellular matrix is fundamental ina wide variety of physiological and pathological phenomena, and isexploited in scaffold-based tissue engineering. Migration isregulated by a number of extracellular matrix- or cell-derivedbiophysical parameters, such as matrix fiber orientation, pore size,and elasticity, or cell deformation, proteolysis, and adhesion. Wehere present an extended Cellular Potts Model (CPM) able toqualitatively and quantitatively describe cell migrationefficiencies and phenotypes both on two-dimensional substrates andwithin three-dimensional matrices, close to experimental evidence.As distinct features of our approach, cells are modeled ascompartmentalized discrete objects, differentiated into nucleusand cytosolic region, while the extracellular matrix iscomposed of a fibrous mesh and a homogeneous fluid. Our modelprovides a strong correlation of the directionality of migrationwith the topological extracellular matrix distribution and abiphasic dependence of migration on the matrix structure, density,adhesion, and stiffness, and, moreover, simulates that celllocomotion in highly constrained fibrillar obstacles requires thedeformation of the cell's nucleus and/or the activity ofcell-derived proteolysis. In conclusion, we here propose amathematical modeling approach that serves to characterize cellmigration as a biological phenomenon in healthy and diseased tissuesand in engineering applications.

    Citation: Marco Scianna, Luigi Preziosi, Katarina Wolf. A Cellular Potts model simulating cell migration on and in matrix environments[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 235-261. doi: 10.3934/mbe.2013.10.235

    Related Papers:

    [1] Colette Calmelet, Diane Sepich . Surface tension and modeling of cellular intercalation during zebrafish gastrulation. Mathematical Biosciences and Engineering, 2010, 7(2): 259-275. doi: 10.3934/mbe.2010.7.259
    [2] Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R. A. Anderson . A spatial model of tumor-host interaction: Application of chemotherapy. Mathematical Biosciences and Engineering, 2009, 6(3): 521-546. doi: 10.3934/mbe.2009.6.521
    [3] Jose E. Zamora Alvarado, Kara E. McCloskey, Ajay Gopinathan . Migration and proliferation drive the emergence of patterns in co-cultures of differentiating vascular progenitor cells. Mathematical Biosciences and Engineering, 2024, 21(8): 6731-6757. doi: 10.3934/mbe.2024295
    [4] Natalia L. Komarova . Spatial stochastic models of cancer: Fitness, migration, invasion. Mathematical Biosciences and Engineering, 2013, 10(3): 761-775. doi: 10.3934/mbe.2013.10.761
    [5] Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut . Modeling of the migration of endothelial cells on bioactive micropatterned polymers. Mathematical Biosciences and Engineering, 2013, 10(4): 997-1015. doi: 10.3934/mbe.2013.10.997
    [6] Akinori Awazu . Input-dependent wave propagations in asymmetric cellular automata: Possible behaviors of feed-forward loop in biological reaction network. Mathematical Biosciences and Engineering, 2008, 5(3): 419-427. doi: 10.3934/mbe.2008.5.419
    [7] Benjamin Steinberg, Yuqing Wang, Huaxiong Huang, Robert M. Miura . Spatial Buffering Mechanism: Mathematical Model and Computer Simulations. Mathematical Biosciences and Engineering, 2005, 2(4): 675-702. doi: 10.3934/mbe.2005.2.675
    [8] Francisco Julian Ariza-Hernandez, Juan Carlos Najera-Tinoco, Martin Patricio Arciga-Alejandre, Eduardo Castañeda-Saucedo, Jorge Sanchez-Ortiz . Bayesian inverse problem for a fractional diffusion model of cell migration. Mathematical Biosciences and Engineering, 2024, 21(4): 5826-5837. doi: 10.3934/mbe.2024257
    [9] Floriane Lignet, Vincent Calvez, Emmanuel Grenier, Benjamin Ribba . A structural model of the VEGF signalling pathway: Emergence of robustness and redundancy properties. Mathematical Biosciences and Engineering, 2013, 10(1): 167-184. doi: 10.3934/mbe.2013.10.167
    [10] N. H. AlShamrani, A. M. Elaiw . Stability of an adaptive immunity viral infection model with multi-stages of infected cells and two routes of infection. Mathematical Biosciences and Engineering, 2020, 17(1): 575-605. doi: 10.3934/mbe.2020030
  • Cell migration on and through extracellular matrix is fundamental ina wide variety of physiological and pathological phenomena, and isexploited in scaffold-based tissue engineering. Migration isregulated by a number of extracellular matrix- or cell-derivedbiophysical parameters, such as matrix fiber orientation, pore size,and elasticity, or cell deformation, proteolysis, and adhesion. Wehere present an extended Cellular Potts Model (CPM) able toqualitatively and quantitatively describe cell migrationefficiencies and phenotypes both on two-dimensional substrates andwithin three-dimensional matrices, close to experimental evidence.As distinct features of our approach, cells are modeled ascompartmentalized discrete objects, differentiated into nucleusand cytosolic region, while the extracellular matrix iscomposed of a fibrous mesh and a homogeneous fluid. Our modelprovides a strong correlation of the directionality of migrationwith the topological extracellular matrix distribution and abiphasic dependence of migration on the matrix structure, density,adhesion, and stiffness, and, moreover, simulates that celllocomotion in highly constrained fibrillar obstacles requires thedeformation of the cell's nucleus and/or the activity ofcell-derived proteolysis. In conclusion, we here propose amathematical modeling approach that serves to characterize cellmigration as a biological phenomenon in healthy and diseased tissuesand in engineering applications.


    [1] $3^{rd}$ edition, Garland Science, 1994.
    [2] Nano Lett., 8 (2008), 2063-2069.
    [3] Immunity, 25 (2006), 989-1001.
    [4] in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions" (eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 157-167.
    [5] Biophys. J., 92 (2007), 3105-3121.
    [6] Mol. Biol. Cell., 19 (2008), 3357-3368.
    [7] Odontology, 96 (2008), 1-11.
    [8] Biopolymers, 54 (2000), 222-234.
    [9] Langmuir, 19 (2003), 1611-1617.
    [10] Ann. Biomed. Eng., 28 (2003), 110-118.
    [11] IEEE Eng. Med. Biol. Mag., 22 (2003), 42-50.
    [12] Biophys. J., 92 (2007), 2964-2974.
    [13] Nat. Rev. Cancer, 3 (2003), 921-930.
    [14] Am. J. Pathol., 178 (2011), 1221-1232.
    [15] Ann. Biomed. Eng., 22 (1994), 342-356.
    [16] J. Cell. Biol., 122 (1993), 729-737.
    [17] J. Cell. Biol., 184 (2009), 481-490.
    [18] Biomaterials, 22 (2001), 1065-1075.
    [19] Exp. Cell. Res., 111 (1978), 475-479.
    [20] Agents Actions Suppl., 12 (1983), 14-33.
    [21] Biophys. J., 86 (2004), 617-628.
    [22] Eur. J. Immunol., 28 (1998), 2331-2343.
    [23] Cell. Mol. Life Sci., 57 (2000), 41-64.
    [24] Nat. Rev. Cancer, 3 (2003), 362-374.
    [25] Cancer Res., 57 (1997), 2061-2070.
    [26] Curr. Opin. Cell. Biol., 23 (2011), 253.
    [27] Nat. Immunol., 9 (2008), 960-969.
    [28] J. Cell. Biol., 188 (2009), 11-19.
    [29] Nat. Rev. Mol. Cell. Biol., 10 (2009), 445-457.
    [30] Biophys. J., 85 (2003), 3329-3335.
    [31] Trends Cell. Biol., 21 (2011), 6-11.
    [32] Math. Model. Nat. Phenom., 5 (2010), 203-223.
    [33] in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions" (eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 79-106.
    [34] Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 47 (1993), 2128-2154.
    [35] J. Cell. Biol., 109 (1989), 799-809.
    [36] Phys. Rev. Lett., 69 (1992), 2013-2016.
    [37] Biophys. J., 95 (2008), 4013-4024.
    [38] Cells Tissues Organs, 176 (2008), 153-165.
    [39] J. Cell Sci., 122 (2009), 3203-3208.
    [40] Z. Physik., 31 (1925), 253.
    [41] Biophys. J., 72 (1997), 1472-1480.
    [42] Birth Defects Res. C. Embryo Today, 84 (2008), 102-122.
    [43] Eur. Cell. Mater., 9 (2010), 329-343.
    [44] Oxford University Press, London, 1996.
    [45] Cell, 84 (1996), 359-369.
    [46] J. Cell. Sci., 117 (2004), 41-52.
    [47] Proc. Natl. Acad. Sci. U. S. A., 100 (2003), 5413-5418.
    [48] Mol. Biol. Cell., 10 (1999), 3067-3079.
    [49] in "IEEE conference on Computational Intelligence in Bioinformatics and Bioengineering," (2008), 233-240.
    [50] in "Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions" (eds. A. R. A. Anderson, M. A. J. Chaplain and K. A. Rejniak), Birkhaüser, (2007), 107-136.
    [51] PLoS Comput. Biol., 4 (2008), e1000163, 16 pp.
    [52] J. Chem. Phys., 21 (1953), 1087-1092.
    [53] Current Biology, 13 (2003), R721-733.
    [54] Biomaterials, 25 (2004), 1077-1086.
    [55] J. Mater. Sci. Mater. Med., 6 (1995), 460-472.
    [56] J. Biomed. Mater. Res. A, 68 (2004), 756-762.
    [57] Nature, 385 (1997), 537-540.
    [58] Dev. Biol., 313 (2008), 545-555.
    [59] J. Cell. Physiol., 204 (2005), 198-209.
    [60] Cell, 112 (2003), 453-465.
    [61] Proc. Camb. Phil. Soc., 48 (1952), 106-109.
    [62] Biophys. J., 89 (2005), 1374-1388.
    [63] Biophys. J., 92 (2007), 2212-2222.
    [64] Science, 302 (2003), 1704-1709.
    [65] J. Biomech. Eng., 124 (2002), 214-222.
    [66] PLoS ONE, 5 (2010), e8726.
    [67] Biophys. J., 95 (2006), 5661-5680.
    [68] J. Cell. Biol., 185 (2009), 11-19.
    [69] Nat. Rev. Cancer, 7 (2007), 737-749.
    [70] Bull. Math. Biol., 76 (2011), 1253-1291.
    [71] Multiscale Model. Simul., 10 (2012), 342-382.
    [72] Biomaterials, 22 (2001), 1713-1719.
    [73] Cell. Tissue Res., 339 (2010), 83-92.
    [74] J. Biol. Chem., 251 (1976), 5786-5792.
    [75] Conf. Proc. IEEE Eng. Med. Biol. Soc., 2010 (2010), 843-846.
    [76] Science, 141 (1963), 401-408.
    [77] J. Exp. Zool., 171 (1970), 395-433.
    [78] Oncology, 21 (2007), 6-12.
    [79] Cancer Res., 69 (2009), 4167-4174.
    [80] Cell. Transplant., 3 (1994), 339-343.
    [81] Nat. Cell. Biol., 9 (2007), 893-904.
    [82] Semin. Cell. Dev. Biol., 20 (2009), 931-941.
    [83] Trends Cell. Biol., 21 (2011), 736-744.
    [84] J. Cell. Biol., 160 (2003), 267-277.
    [85] Biophys. J., 96 (2009), 1566-1585.
    [86] Proc. Natl. Acad. Sci. U. S. A., 86 (1989), 933-937.
    [87] Ann. Biomed. Eng., 35 (2007), 91-100.
    [88] Proc. Natl. Acad. Sci. USA, 103 (2006), 10889-10894.
  • This article has been cited by:

    1. Benjamin Michael Yeoman, Parag Katira, Wenguo Cui, A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments, 2018, 13, 1932-6203, e0207216, 10.1371/journal.pone.0207216
    2. Shoubin Dong, Zetao Huang, Liqun Tang, Xiaoyang Zhang, Yongrou Zhang, Yi Jiang, A three-dimensional collagen-fiber network model of the extracellular matrix for the simulation of the mechanical behaviors and micro structures, 2017, 20, 1025-5842, 991, 10.1080/10255842.2017.1321113
    3. Marco Scianna, Luigi Preziosi, A Cellular Potts Model for Analyzing Cell Migration across Constraining Pillar Arrays, 2021, 10, 2075-1680, 32, 10.3390/axioms10010032
    4. Gabriel Shatkin, Benjamin Yeoman, Katherine Birmingham, Parag Katira, Adam J. Engler, Computational models of migration modes improve our understanding of metastasis, 2020, 4, 2473-2877, 041505, 10.1063/5.0023748
    5. Satoru Okuda, Takashi Miura, Yasuhiro Inoue, Taiji Adachi, Mototsugu Eiraku, Combining Turing and 3D vertex models reproduces autonomous multicellular morphogenesis with undulation, tubulation, and branching, 2018, 8, 2045-2322, 10.1038/s41598-018-20678-6
    6. Maarten van der Sande, Yulia Kraus, Evelyn Houliston, Jaap Kaandorp, A cell-based boundary model of gastrulation by unipolar ingression in the hydrozoan cnidarian Clytia hemisphaerica, 2020, 460, 00121606, 176, 10.1016/j.ydbio.2019.12.012
    7. Veronika te Boekhorst, Luigi Preziosi, Peter Friedl, Plasticity of Cell Migration In Vivo and In Silico, 2016, 32, 1081-0706, 491, 10.1146/annurev-cellbio-111315-125201
    8. R. Allena, M. Scianna, L. Preziosi, A Cellular Potts Model of single cell migration in presence of durotaxis, 2016, 275, 00255564, 57, 10.1016/j.mbs.2016.02.011
    9. Marco Scianna, An extended Cellular Potts Model analyzing a wound healing assay, 2015, 62, 00104825, 33, 10.1016/j.compbiomed.2015.04.009
    10. Chiara Giverso, Luigi Preziosi, 2014, Chapter 5, 978-3-319-02656-5, 59, 10.1007/978-3-319-02657-2_5
    11. Vincent E. Debets, Liesbeth M.C. Janssen, Cornelis Storm, Enhanced persistence and collective migration in cooperatively aligning cell clusters, 2021, 00063495, 10.1016/j.bpj.2021.02.014
    12. Nadia Loy, Luigi Preziosi, Modelling physical limits of migration by a kinetic model with non-local sensing, 2020, 80, 0303-6812, 1759, 10.1007/s00285-020-01479-w
    13. David Lepzelter, Muhammad H. Zaman, Modeling Persistence in Mesenchymal Cell Motility Using Explicit Fibers, 2014, 30, 0743-7463, 5506, 10.1021/la404832t
    14. L. Preziosi, M. Scianna, 2016, Chapter 3, 978-3-319-42678-5, 131, 10.1007/978-3-319-42679-2_3
    15. Ondrej Maxian, Alex Mogilner, Wanda Strychalski, Christopher V. Rao, Computational estimates of mechanical constraints on cell migration through the extracellular matrix, 2020, 16, 1553-7358, e1008160, 10.1371/journal.pcbi.1008160
    16. Marina A. Ferreira, Evangeline Despin-Guitard, Fernando Duarte, Pierre Degond, Eric Theveneau, Philip K. Maini, Interkinetic nuclear movements promote apical expansion in pseudostratified epithelia at the expense of apicobasal elongation, 2019, 15, 1553-7358, e1007171, 10.1371/journal.pcbi.1007171
    17. Hamid Bolouri, Network dynamics in the tumor microenvironment, 2015, 30, 1044579X, 52, 10.1016/j.semcancer.2014.02.007
    18. Xiaofeng Liu, Diego A. Vargas, Dongyuan Lü, Yan Zhang, Muhammad H. Zaman, Mian Long, Computational Modeling of Stem Cell Migration: A Mini Review, 2014, 7, 1865-5025, 196, 10.1007/s12195-014-0330-2
    19. Katrin Talkenberger, Elisabetta Ada Cavalcanti-Adam, Anja Voss-Böhme, Andreas Deutsch, Amoeboid-mesenchymal migration plasticity promotes invasion only in complex heterogeneous microenvironments, 2017, 7, 2045-2322, 10.1038/s41598-017-09300-3
    20. Adrian Moure, Hector Gomez, Phase-Field Modeling of Individual and Collective Cell Migration, 2021, 28, 1134-3060, 311, 10.1007/s11831-019-09377-1
    21. Nicola Mulberry, Leah Edelstein-Keshet, Self-organized multicellular structures from simple cell signaling: a computational model, 2020, 17, 1478-3975, 066003, 10.1088/1478-3975/abb2dc
    22. G. Wayne Brodland, How computational models can help unlock biological systems, 2015, 47-48, 10849521, 62, 10.1016/j.semcdb.2015.07.001
    23. Sonja E. M. Boas, Roeland M. H. Merks, Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation, 2014, 11, 1742-5689, 20131049, 10.1098/rsif.2013.1049
    24. Fleur Jeanquartier, Claire Jean-Quartier, David Cemernek, Andreas Holzinger, In silico modeling for tumor growth visualization, 2016, 10, 1752-0509, 10.1186/s12918-016-0318-8
    25. Sjoerd van Helvert, Cornelis Storm, Peter Friedl, Mechanoreciprocity in cell migration, 2018, 20, 1465-7392, 8, 10.1038/s41556-017-0012-0
    26. Nadia Loy, Luigi Preziosi, Kinetic models with non-local sensing determining cell polarization and speed according to independent cues, 2020, 80, 0303-6812, 373, 10.1007/s00285-019-01411-x
    27. MA Al-Mamun, W. Srisukkham, C. Fall, R. Bass, A. Hossain, D.M. Farid, 2014, A cellular automaton model for hypoxia effects on tumour growth dynamics, 978-1-4799-6399-7, 1, 10.1109/SKIMA.2014.7083562
    28. N. E. Muzzio, M. A. Pasquale, M. A. C. Huergo, A. E. Bolzán, P. H. González, A. J. Arvia, Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media, 2016, 42, 0092-0606, 477, 10.1007/s10867-016-9418-3
    29. Elies Fuster-Garcia, Juan Miguel García-Gómez, Elena De Angelis, Arthur Sraum, Arthur Molnar, Sabine Van Huffel, Georgios Stamatakos, 2017, Chapter 16, 978-3-319-43502-2, 181, 10.1007/978-3-319-43504-6_16
    30. M. Scianna, C.G. Bell, L. Preziosi, A review of mathematical models for the formation of vascular networks, 2013, 333, 00225193, 174, 10.1016/j.jtbi.2013.04.037
    31. Francisco Merino-Casallo, Maria J. Gomez-Benito, Yago Juste-Lanas, Ruben Martinez-Cantin, Jose M. Garcia-Aznar, Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration, 2018, 9, 1664-042X, 10.3389/fphys.2018.01246
    32. Francisco Serrano-Alcalde, José Manuel García-Aznar, María José Gómez-Benito, The role of nuclear mechanics in cell deformation under creeping flows, 2017, 432, 00225193, 25, 10.1016/j.jtbi.2017.07.028
    33. Joao Carvalho, Valeria Lopes, Rui Travasso, Tumor cell invasiveness in the initial stages of bladder cancer development ‐ A computational study, 2021, 37, 2040-7939, 10.1002/cnm.3417
    34. Yony Bresler, Benoit Palmieri, Martin Grant, Sharp interface model for elastic motile cells, 2019, 42, 1292-8941, 10.1140/epje/i2019-11815-x
    35. Sandeep Kumar, Aastha Kapoor, Sejal Desai, Mandar M. Inamdar, Shamik Sen, Proteolytic and non-proteolytic regulation of collective cell invasion: tuning by ECM density and organization, 2016, 6, 2045-2322, 10.1038/srep19905
    36. Janaina de Andréa Dernowsek, Rodrigo Alvarenga Rezende, Jorge Vicente Lopes da Silva, The role of information technology in the future of 3D biofabrication, 2017, 1, 2059-4755, 63, 10.2217/3dp-2016-0005
    37. Tullio Genova, Guillaume P. Grolez, Chiara Camillo, Michela Bernardini, Alexandre Bokhobza, Elodie Richard, Marco Scianna, Loic Lemonnier, Donatella Valdembri, Luca Munaron, Mark R. Philips, Virginie Mattot, Guido Serini, Natalia Prevarskaya, Dimitra Gkika, Alessandra Fiorio Pla, TRPM8 inhibits endothelial cell migration via a non-channel function by trapping the small GTPase Rap1, 2017, 216, 0021-9525, 2107, 10.1083/jcb.201506024
    38. Catalina-Paula Spatarelu, Hao Zhang, Dung Trung Nguyen, Xinyue Han, Ruchuan Liu, Qiaohang Guo, Jacob Notbohm, Jing Fan, Liyu Liu, Zi Chen, Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods, 2019, 5, 2373-9878, 3766, 10.1021/acsbiomaterials.8b01428
    39. D. Aubry, H. Thiam, M. Piel, R. Allena, A computational mechanics approach to assess the link between cell morphology and forces during confined migration, 2015, 14, 1617-7959, 143, 10.1007/s10237-014-0595-3
    40. A. Arduino, L. Preziosi, A multiphase model of tumour segregation in situ by a heterogeneous extracellular matrix, 2015, 75, 00207462, 22, 10.1016/j.ijnonlinmec.2015.04.007
    41. Paola Masuzzo, Marleen Van Troys, Christophe Ampe, Lennart Martens, Taking Aim at Moving Targets in Computational Cell Migration, 2016, 26, 09628924, 88, 10.1016/j.tcb.2015.09.003
    42. Guillermo Vilanova, Ignasi Colominas, Hector Gomez, Coupling of discrete random walks and continuous modeling for three-dimensional tumor-induced angiogenesis, 2014, 53, 0178-7675, 449, 10.1007/s00466-013-0958-0
    43. Mélina L. Heuzé, Pablo Vargas, Mélanie Chabaud, Maël Le Berre, Yan-Jun Liu, Olivier Collin, Paola Solanes, Raphaël Voituriez, Matthieu Piel, Ana-Maria Lennon-Duménil, Migration of dendritic cells: physical principles, molecular mechanisms, and functional implications, 2013, 256, 01052896, 240, 10.1111/imr.12108
    44. Terri Applewhite-Grosso, Nancy Davis Griffeth, Elisa Lannon, Uchenna Unachukwu, Stephen Redenti, Naralys Batista, 2015, A multi-scale, physics engine-based simulation of cellular migration, 978-1-4673-9743-8, 1230, 10.1109/WSC.2015.7408248
    45. Annachiara Colombi, Marco Scianna, Andrea Tosin, Differentiated cell behavior: a multiscale approach using measure theory, 2015, 71, 0303-6812, 1049, 10.1007/s00285-014-0846-z
    46. Maurício Moreira-Soares, Susana P Cunha, José Rafael Bordin, Rui D M Travasso, Adhesion modulates cell morphology and migration within dense fibrous networks, 2020, 32, 0953-8984, 314001, 10.1088/1361-648X/ab7c17
    47. SHOUBIN DONG, ZHOU LONG, LIQUN TANG, YI JIANG, YANNAN YAN, SIMULATION OF GROWTH AND DIVISION OF 3D CELLS BASED ON FINITE ELEMENT METHOD, 2014, 06, 1758-8251, 1450041, 10.1142/S1758825114500410
    48. Yue Liu, Elisabeth G. Rens, Leah Edelstein-Keshet, Spots, stripes, and spiral waves in models for static and motile cells, 2021, 82, 0303-6812, 10.1007/s00285-021-01550-0
    49. Sonja E. M. Boas, Joao Carvalho, Marloes van den Broek, Ester M. Weijers, Marie-José Goumans, Pieter Koolwijk, Roeland M. H. Merks, Qing Nie, A local uPAR-plasmin-TGFβ1 positive feedback loop in a qualitative computational model of angiogenic sprouting explains the in vitro effect of fibrinogen variants, 2018, 14, 1553-7358, e1006239, 10.1371/journal.pcbi.1006239
    50. Luigi Preziosi, Marco Scianna, V. Volpert, J. Clairambault, Relevance of Cell-ECM Interactions: From a Biological Perspective to the Mathematical Modeling, 2015, 5, 2271-2097, 00004, 10.1051/itmconf/20150500004
    51. Marina Krause, Katarina Wolf, Cancer cell migration in 3D tissue: Negotiating space by proteolysis and nuclear deformability, 2015, 9, 1933-6918, 357, 10.1080/19336918.2015.1061173
    52. Linnea C. Franssen, Tommaso Lorenzi, Andrew E. F. Burgess, Mark A. J. Chaplain, A Mathematical Framework for Modelling the Metastatic Spread of Cancer, 2019, 81, 0092-8240, 1965, 10.1007/s11538-019-00597-x
    53. Jonathan F. Li, John Lowengrub, The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the Cellular Potts Model, 2014, 343, 00225193, 79, 10.1016/j.jtbi.2013.10.008
    54. Marco Scianna, Luigi Preziosi, A cellular Potts model for the MMP-dependent and -independent cancer cell migration in matrix microtracks of different dimensions, 2014, 53, 0178-7675, 485, 10.1007/s00466-013-0944-6
    55. N. Sfakianakis, A. Brunk, Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM, 2018, 80, 0092-8240, 2789, 10.1007/s11538-018-0460-0
    56. P. Van Liedekerke, M. M. Palm, N. Jagiella, D. Drasdo, Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results, 2015, 2, 2196-4378, 401, 10.1007/s40571-015-0082-3
    57. Raphaël Conradin, Christophe Coreixas, Jonas Latt, Bastien Chopard, PalaCell2D: A framework for detailed tissue morphogenesis, 2021, 18777503, 101353, 10.1016/j.jocs.2021.101353
    58. Antara Pal, Pegi Haliti, Bhushan Dharmadhikari, Wu Qi, Prabir Patra, Manipulating Extracellular Matrix Organizations and Parameters to Control Local Cancer Invasion, 2021, 18, 1545-5963, 2566, 10.1109/TCBB.2020.2989223
    59. D. Pramanik, M.K. Jolly, R. Bhat, Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales, 2021, 524, 00225193, 110733, 10.1016/j.jtbi.2021.110733
    60. Na Fan, Gangfei Feng, Yanwei Tan, Jie Zou, Bei Peng, 2022, Chapter 191, 978-981-19-1308-2, 2042, 10.1007/978-981-19-1309-9_191
    61. Alejandro Torres-Sánchez, Max Kerr Winter, Guillaume Salbreux, Saúl Ares, Interacting active surfaces: A model for three-dimensional cell aggregates, 2022, 18, 1553-7358, e1010762, 10.1371/journal.pcbi.1010762
    62. N. LOY, T. HILLEN, K. J. PAINTER, Direction-dependent turning leads to anisotropic diffusion and persistence, 2022, 33, 0956-7925, 729, 10.1017/S0956792521000206
    63. Nasibeh Rady Raz, Mohammad-R. Akbarzadeh-T, Target Convergence Analysis of Cancer-Inspired Swarms for Early Disease Diagnosis and Targeted Collective Therapy, 2022, 33, 2162-237X, 2132, 10.1109/TNNLS.2021.3130207
    64. Martina Conte, Nadia Loy, Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis, 2022, 84, 0092-8240, 10.1007/s11538-021-00978-1
    65. Thomas Thenard, Anita Catapano, Michel Mesnard, Rachele Allena, A Cellular Potts energy-based approach to analyse the influence of the surface topography on single cell motility, 2021, 509, 00225193, 110487, 10.1016/j.jtbi.2020.110487
    66. Luigi Preziosi, Marco Scianna, 2021, Chapter 8, 978-981-16-4865-6, 124, 10.1007/978-981-16-4866-3_8
    67. R. Eftimie, A. Mavrodin, S.P.A. Bordas, 2022, 00652156, 10.1016/bs.aams.2022.09.001
    68. Joseph Ackermann, Martine Ben Amar, Jean-François Joanny, Multi-cellular aggregates, a model for living matter, 2021, 927, 03701573, 1, 10.1016/j.physrep.2021.05.001
    69. Zahra Allahyari, Thomas R. Gaborski, Engineering cell–substrate interactions on porous membranes for microphysiological systems, 2022, 22, 1473-0197, 2080, 10.1039/D2LC00114D
    70. Rabea Link, Ulrich S. Schwarz, 2023, Chapter 22, 978-1-0716-2850-8, 323, 10.1007/978-1-0716-2851-5_22
    71. R. Allena, D. Aubry, Implicit implementation of the cell-micropillars interaction during cell drop under gravity, 2023, 130, 00936413, 104129, 10.1016/j.mechrescom.2023.104129
    72. Takuya Kato, Robert P Jenkins, Stefanie Derzsi, Melda Tozluoglu, Antonio Rullan, Steven Hooper, Raphaël AG Chaleil, Holly Joyce, Xiao Fu, Selvam Thavaraj, Paul A Bates, Erik Sahai, Interplay of adherens junctions and matrix proteolysis determines the invasive pattern and growth of squamous cell carcinoma, 2023, 12, 2050-084X, 10.7554/eLife.76520
    73. Rabea Link, Kai Weißenbruch, Motomu Tanaka, Martin Bastmeyer, Ulrich S. Schwarz, Cell Shape and Forces in Elastic and Structured Environments: From Single Cells to Organoids, 2023, 1616-301X, 10.1002/adfm.202302145
    74. Erika Tsingos, Bente Hilde Bakker, Koen A.E. Keijzer, Hermen Jan Hupkes, Roeland M.H. Merks, Hybrid cellular Potts and bead-spring modeling of cells in fibrous extracellular matrix, 2023, 00063495, 10.1016/j.bpj.2023.05.013
    75. Chiara Giverso, Gaspard Jankowiak, Luigi Preziosi, Christian Schmeiser, The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments, 2023, 85, 0092-8240, 10.1007/s11538-023-01187-8
    76. Martina Conte, Nadia Loy, A Non-Local Kinetic Model for Cell Migration: A Study of the Interplay Between Contact Guidance and Steric Hindrance, 2023, 0036-1399, S429, 10.1137/22M1506389
    77. Ye Fan, Lifang Yu, Qianyi Chen, Tao Yu, Zhixuan Ma, Yahong Yang, Mechanisms of partial denitrification in an integrated fixed-film activated sludge (IFAS) system: From progressive startup to stabilization, 2024, 63, 22147144, 105437, 10.1016/j.jwpe.2024.105437
    78. Rebecca M. Crossley, Samuel Johnson, Erika Tsingos, Zoe Bell, Massimiliano Berardi, Margherita Botticelli, Quirine J. S. Braat, John Metzcar, Marco Ruscone, Yuan Yin, Robyn Shuttleworth, Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist, 2024, 12, 2296-634X, 10.3389/fcell.2024.1354132
    79. R. Belousov, S. Savino, P. Moghe, T. Hiiragi, L. Rondoni, A. Erzberger, Poissonian Cellular Potts Models Reveal Nonequilibrium Kinetics of Cell Sorting, 2024, 132, 0031-9007, 10.1103/PhysRevLett.132.248401
    80. Steffen Lange, Jannik Schmied, Paul Willam, Anja Voss-Böhme, Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth, 2024, 00225193, 111882, 10.1016/j.jtbi.2024.111882
    81. Tien Comlekoglu, Bette J. Dzamba, Gustavo G. Pacheco, David R. Shook, T. J. Sego, James A. Glazier, Shayn M. Peirce, Douglas W. DeSimone, Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm, 2024, 13, 2046-6390, 10.1242/bio.060615
    82. Quirine J. S. Braat, Cornelis Storm, Liesbeth M. C. Janssen, Formation of motile cell clusters in heterogeneous model tumors: The role of cell-cell alignment, 2024, 110, 2470-0045, 10.1103/PhysRevE.110.064401
  • Reader Comments
  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4364) PDF downloads(858) Cited by(82)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog