Adalsteinsson,, D., & Sethian,, J. (2003). Transport and diffusion of material quantities on propagating interfaces via level set methods. Journal of Computational Physics, 185(1), 271–288.
Adalsteinsson,, D., & Sethian,, J. A. (1995). A fast level set method for propagating interfaces. Journal of Computational Physics, 118(2), 269–277.
Alias,, M. A., & Buenzli,, P. R. (2020). A level‐set method for the evolution of cells and tissue during curvature‐controlled growth. International Jorunal of Numerical Methods in Biomedical Engineering, 36(1), e3279.
Almendro‐Vedia,, V. G., Monroy,, F., & Cao,, F. J. (2013). Mechanics of constriction during cell division: A variational approach. PLoS One, 8(8), e69750.
Alonso,, S., Stange,, M., & Beta,, C. (2018). Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells. PLoS One, 13(8), e0201977.
Andrews,, S. S. (2012). Spatial and stochastic cellular modeling with the Smoldyn simulator. Methods in Molecular Biology, 804, 519–542.
Arefi,, S. M. A., Tsvirkun,, D., Verdier,, C., & Feng,, J. J. (2020). A biomechanical model for the transendothelial migration of cancer cells. Physical Biology, 17(3), 036004.
Arjunan,, S. N. V., Miyauchi,, A., Iwamoto,, K., & Takahashi,, K. (2020). Pspatiocyte: A high‐performance simulator for intracellular reaction‐diffusion systems. BMC Bioinformatics, 21(1), 33.
Bächer,, C., & Gekle,, S. (2019). Computational modeling of active deformable membranes embedded in three‐dimensional flows. Physical Review E, 99, 062418.
Bansod,, Y. D., Matsumoto,, T., Nagayama,, K., & Bursa,, J. (2018). A finite element bendo‐tensegrity model of eukaryotic cell. Journal of Biomechanical Engineering, 140(10), 101001.
Barrett,, J. W., Garcke,, H., & Nürnberg,, R. (2007). A parametric finite element method for fourth order geometric evolution equations. Journal of Computational Physics, 222(1), 441–467.
Battista,, N. A., Strickland,, W. C., & Miller,, L. A. (2017). Ib2d: A Python and Matlab implementation of the immersed boundary method. Bioinspiration %26 Biomimetics, 12(3), 036003.
Bellas,, E., & Chen,, C. S. (2014). Forms, forces, and stem cell fate. Current Opinion in Cell Biology, 31, 92–97.
Bellotti,, T., & Theillard,, M. (2019). A coupled level‐set and reference map method for interface representation with applications to two‐phase flows simulation. Journal of Computational Physics, 392, 266–290.
Ben Amar,, M., & Wu,, M. (2014). Re‐epithelialization: Advancing epithelium frontier during wound healing. Journal of the Royal Society Interface, 11(93), 20131038.
Berg,, H. C. (1993). Random walks in biology (expanded ed.). Princeton, NJ: Princeton University Press.
Biben,, T., Kassner,, K., & Misbah,, C. (2005). Phase‐field approach to three‐dimensional vesicle dynamics. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 72(4 Pt 1), 041921.
Biben,, T., & Misbah,, C. (2003). Tumbling of vesicles under shear flow within an advected‐field approach. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 67(3 Pt 1), 031908.
Bidhendi,, A. J., & Geitmann,, A. (2018). Finite element modeling of shape changes in plant cells. Plant Physiology, 176(1), 41–56.
Bidone,, T. C., Jung,, W., Maruri,, D., Borau,, C., Kamm,, R. D., & Kim,, T. (2017). Morphological transformation and force generation of active cytoskeletal networks. PLoS Computational Biology, 13(1), e1005277.
Borau,, C., Kim,, T., Bidone,, T., García‐Aznar,, J. M., & Kamm,, R. D. (2012). Dynamic mechanisms of cell rigidity sensing: Insights from a computational model of actomyosin networks. PLoS One, 7(11), e49174.
Bosgraaf,, L., & Van Haastert,, P. J. M. (2009). The ordered extension of pseudopodia by amoeboid cells in the absence of external cues. PLoS One, 4(4), e5253.
Bottino,, D., Mogilner,, A., Roberts,, T., Stewart,, M., & Oster,, G. (2002). How nematode sperm crawl. Journal of Cell Science, 115(Pt 2), 367–384.
Bottino,, D. C. (1998). Modeling viscoelastic networks and cell deformation in the context of the immersed boundary method. Journal of Computational Physics, 147(1), 86–113.
Bottino,, D. C. (2001). Computer simulations of mechanochemical coupling in a deforming domain: Applications to cell motion. In P. K. Maini, & H. G. Othmer, (Eds.), Mathematical models for biological pattern formation (pp. 295–314). New York, NY: Springer New York.
Brakke,, K. A. (1992). The surface evolver. Experimental Mathematics, 1(2), 141–165.
Bresler,, Y., Palmieri,, B., & Grant,, M. (2019). Sharp interface model for elastic motile cells. The European Physical Journal E: Soft Matter, 42(5), 52.
Brill‐Karniely,, Y., Nisenholz,, N., Rajendran,, K., Dang,, Q., Krishnan,, R., & Zemel,, A. (2014). Dynamics of cell area and force during spreading. Biophysical Journal, 107(12), L37–L40.
Cahn,, J. W., & Hilliard,, J. E. (1958). Free energy of a nonuniform system. I. Interfacial free energy. Journal of Chemical Physics, 258(2), 258–267.
Camley,, B. A., & Rappel,, W.‐J. (2017). Cell‐to‐cell variation sets a tissue‐rheology‐dependent bound on collective gradient sensing. Proceedings of the National Academy of Sciences of the United States of America, 114(47), E10074–E10082.
Camley,, B. A., Zhang,, Y., Zhao,, Y., Li,, B., Ben‐Jacob,, E., Levine,, H., & Rappel,, W.‐J. (2014). Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns. Proceedings of the National Academy of Sciences of the United States of America, 111(41), 14770–14775.
Camley,, B. A., Zimmermann,, J., Levine,, H., & Rappel,, W.‐J. (2016). Collective signal processing in cluster chemotaxis: Roles of adaptation, amplification, and co‐attraction in collective guidance. PLoS Computational Biology, 12(7), e1005008.
Campbell,, E. J., & Bagchi,, P. (2017). A computational model of amoeboid cell swimming. Physics of Fluids, 29(10), 101902.
Campbell,, E. J., & Bagchi,, P. (2018). A computational model of amoeboid cell motility in the presence of obstacles. Soft Matter, 14(28), 5741–5763.
Cao,, Y., Ghabache,, E., Miao,, Y., Niman,, C., Hakozaki,, H., Reck‐Peterson,, S. L., … Rappel,, W.‐J. (2019). A minimal computational model for three‐dimensional cell migration. Journal of Royal Society Interface, 16(161), 20190619.
Chanet,, S., Miller,, C. J., Vaishnav,, E. D., Ermentrout,, B., Davidson,, L. A., & Martin,, A. C. (2017). Actomyosin meshwork mechanosensing enables tissue shape to orient cell force. Nature Communications, 8, 15014.
Cortes,, D. B., Gordon,, M., Nédélec,, F., & Maddox,, A. S. (2020). Bond type and discretization of nonmuscle myosin II are critical for simulated contractile dynamics. Biophysical Journal, 118(11), 2703–2717.
Cowan,, A. E., Moraru,, I. I., Schaff,, J. C., Slepchenko,, B. M., & Loew,, L. M. (2012). Spatial modeling of cell signaling networks. Methods in Cell Biology, 110, 195–221.
Cross,, S. E., Jin,, Y.‐S., Rao,, J., & Gimzewski,, J. K. (2007). Nanomechanical analysis of cells from cancer patients. Nature Nanotechnology, 2(12), 780–783.
Devreotes,, P. N., Bhattacharya,, S., Edwards,, M., Iglesias,, P. A., Lampert,, T., & Miao,, Y. (2017). Excitable signal transduction networks in directed cell migration. Annual Review of Cell and Developmental Biology, 33, 103–125.
Dhatt,, G., Touzot,, G., & Lefrançois,, E. (2012). Finite element method. In Numerical methods series. London: ISTE.
Dillon,, R., & Othmer,, H. G. (1999). A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud. Journal of Theoretical Biology, 197(3), 295–330.
Drawert,, B., Engblom,, S., & Hellander,, A. (2012). Urdme: A modular framework for stochastic simulation of reaction‐transport processes in complex geometries. BMC Systems Biology, 6(1), 76.
Du,, Q., Liu,, C., & Wang,, X. (2004). A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. Journal of Computational Physics, 198(2), 450–468.
DuChez,, B. J., Doyle,, A. D., Dimitriadis,, E. K., & Yamada,, K. M. (2019). Durotaxis by human cancer cells. Biophysical Journal, 116(4), 670–683.
Effler,, J. C., Kee,, Y.‐S., Berk,, J. M., Tran,, M. N., Iglesias,, P. A., & Robinson,, D. N. (2006). Mitosis‐specific mechanosensing and contractile‐protein redistribution control cell shape. Current Biology, 16(19), 1962–1967.
Elgeti,, S., & Sauerland,, H. (2016). Deforming fluid domains within the finite element method: Five mesh‐based tracking methods in comparison. Archives of Computational Methods in Engineering, 23(2), 323–361.
Elliott,, C. M., Stinner,, B., & Venkataraman,, C. (2012). Modelling cell motility and chemotaxis with evolving surface finite elements. Journal of Royal Society Interface, 9(76), 3027–3044.
Engelich,, G., Wright,, D. G., & Hartshorn,, K. L. (2001). Acquired disorders of phagocyte function complicating medical and surgical illnesses. Clinical Infectious Diseases, 33(12), 2040–2048.
Escribano,, J., Sunyer,, R., Sánchez,, M. T., Trepat,, X., Roca‐Cusachs,, P., & García‐Aznar,, J. M. (2018). A hybrid computational model for collective cell durotaxis. Biomechanics and Modeling in Mechanobiology, 17(4), 1037–1052.
Fais,, S., & Overholtzer,, M. (2018). Cell‐in‐cell phenomena in cancer. Nature Reviews. Cancer, 18(12), 758–766.
Flemming,, S., Font,, F., Alonso,, S., & Beta,, C. (2020). How cortical waves drive fission of motile cells. Proceedings of the National Academy of Sciences of the United States of America, 117(12), 6330–6338.
Fougeron,, N., Rohan,, P.‐Y., Haering,, D., Rose,, J.‐L., Bonnet,, X., & Pillet,, H. (2020). Combining freehand ultrasound‐based indentation and inverse finite element modelling for the identification of hyperelastic material properties of thigh soft tissues. Journal of Biomechanical Engineering, 142(9), 091004.
Friedl,, P., & Gilmour,, D. (2009). Collective cell migration in morphogenesis, regeneration and cancer. Nature Reviews. Molecular Cell Biology, 10(7), 445–457.
Gallinato,, O., Ohta,, M., Poignard,, C., & Suzuki,, T. (2017). Free boundary problem for cell protrusion formations: Theoretical and numerical aspects. Journal of Mathematical Biology, 75(2), 263–307.
Ganesh,, T., Laughrey,, L. E., Niroobakhsh,, M., & Lara‐Castillo,, N. (2020). Multiscale finite element modeling of mechanical strains and fluid flow in osteocyte lacunocanalicular system. Bone, 137, 115328.
Gardel,, M. L., Shin,, J. H., MacKintosh,, F. C., Mahadevan,, L., Matsudaira,, P., & Weitz,, D. A. (2004). Elastic behavior of cross‐linked and bundled actin networks. Science, 304(5675), 1301–1305.
Gomez,, H., Bures,, M., & Moure,, A. (2019). A review on computational modelling of phase‐transition problems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 377(2143), 20180203.
Griffith,, B. E. (2020). An adaptive and distributed‐memory parallel implementation of the immersed boundary (IB) method. https://github.com/IBAMR/IBAMR
Guckenberger,, A., & Gekle,, S. (2017). Theory and algorithms to compute Helfrich bending forces: A review. Journal of Physics. Condensed Matter, 29(20), 203001.
Guyot,, Y., Luyten,, F. P., Schrooten,, J., Papantoniou,, I., & Geris,, L. (2015). A three‐dimensional computational fluid dynamics model of shear stress distribution during neotissue growth in a perfusion bioreactor. Biotechnology and Bioengineering, 112(12), 2591–2600.
Guyot,, Y., Papantoniou,, I., Chai,, Y. C., Van Bael,, S., Schrooten,, J., & Geris,, L. (2014). A computational model for cell/ECM growth on 3d surfaces using the level set method: A bone tissue engineering case study. Biomechanics and Modeling in Mechanobiology, 13(6), 1361–1371.
Guyot,, Y., Papantoniou,, I., Luyten,, F. P., & Geris,, L. (2016). Coupling curvature‐dependent and shear stress‐stimulated neotissue growth in dynamic bioreactor cultures: A 3D computational model of a complete scaffold. Biomechanics and Modeling in Mechanobiology, 15(1), 169–180.
Hannabuss,, J., Lera‐Ramirez,, M., Cade,, N. I., Fourniol,, F. J., Nédélec,, F., & Surrey,, T. (2019). Self‐organization of minimal anaphase spindle midzone bundles. Current Biology, 29(13), 2120–2130.e7.
Hannezo,, E., & Heisenberg,, C.‐P. (2019). Mechanochemical feedback loops in development and disease. Cell, 178(1), 12–25.
Hayashi,, A., Yavas,, A., McIntyre,, C. A., Ho,, Y.‐J., Erakky,, A., Wong,, W., … Iacobuzio‐Donahue,, C. A. (2020). Genetic and clinical correlates of entosis in pancreatic ductal adenocarcinoma. Modern Pathology, 33(9), 1822–1831.
Hecht,, I., Kessler,, D. A., & Levine,, H. (2010). Transient localized patterns in noise‐driven reaction‐diffusion systems. Physical Review Letters, 104(15), 158301.
Hecht,, I., Skoge,, M. L., Charest,, P. G., Ben‐Jacob,, E., Firtel,, R. A., Loomis,, W. F., … Rappel,, W.‐J. (2011). Activated membrane patches guide chemotactic cell motility. PLoS Computational Biology, 7(6), e1002044.
Heck,, T., Vargas,, D. A., Smeets,, B., Ramon,, H., Van Liedekerke,, P., & Van Oosterwyck,, H. (2020). The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model. PLoS Computational Biology, 16(1), e1007250.
Helfrich,, W. (1973). Elastic properties of lipid bilayers: Theory and possible experiments. Zeitschrift für Naturforschung. Section C, 28(11), 693–703.
Herant,, M., Heinrich,, V., & Dembo,, M. (2005). Mechanics of neutrophil phagocytosis: Behavior of the cortical tension. Journal of Cell Science, 118(Pt 9), 1789–1797.
Herant,, M., Heinrich,, V., & Dembo,, M. (2006). Mechanics of neutrophil phagocytosis: Experiments and quantitative models. Journal of Cell Science, 119(Pt 9), 1903–1913.
Herant,, M., Lee,, C.‐Y., Dembo,, M., & Heinrich,, V. (2011). Protrusive push versus enveloping embrace: Computational model of phagocytosis predicts key regulatory role of cytoskeletal membrane anchors. PLoS Computational Biology, 7(1), e1001068.
Hou,, J. C., Maas,, S. A., Weiss,, J. A., & Ateshian,, G. A. (2018). Finite element formulation of multiphasic shell elements for cell mechanics analyses in FEBio. Journal of Biomechanical Engineering, 140(12), 121009.
Iglesias,, P. A., & Devreotes,, P. N. (2008). Navigating through models of chemotaxis. Current Opinion in Cell Biology, 20(1), 35–40.
Ii,, K., Mashimo,, K., Ozeki,, M., Yamada,, T. G., Hiroi,, N., & Funahashi,, A. (2019). Xitosbml: A modeling tool for creating spatial systems biology markup language models from microscopic images. Frontiers in Genetics, 10, 1027.
Janmey,, P. A., Fletcher,, D. A., & Reinhart‐King,, C. A. (2020). Stiffness sensing by cells. Physiological Reviews, 100(2), 695–724.
Katti,, D. R., & Katti,, K. S. (2017). Cancer cell mechanics with altered cytoskeletal behavior and substrate effects: A 3d finite element modeling study. Journal of the Mechanical Behavior of Biomedical Materials, 76, 125–134.
Keating,, S. M., Waltemath,, D., König,, M., Zhang,, F., Dräger,, A., Chaouiya,, C., … SBML Level 3 Community members. (2020). SBML Level 3: An extensible format for the exchange and reuse of biological models. Molecular Systems Biology, 16(8), e9110.
Kennaway,, R., & Coen,, E. (2019). Volumetric finite‐element modelling of biological growth. Open Biology, 9(5), 190057.
Kim,, M.‐C., Silberberg,, Y. R., Abeyaratne,, R., Kamm,, R. D., & Asada,, H. H. (2018). Computational modeling of three‐dimensional ECM‐rigidity sensing to guide directed cell migration. Proceedings of the National Academy of Sciences of the United States of America, 115(3), E390–E399.
Kothari,, P., Johnson,, C., Sandone,, C., Iglesias,, P. A., & Robinson,, D. N. (2019). How the mechanobiome drives cell behavior, viewed through the lens of control theory. Journal of Cell Science, 132(17), jcs234476.
Kouwer,, P. H. J., Koepf,, M., Le Sage,, V. A. A., Jaspers,, M., van Buul,, A. M., Eksteen‐Akeroyd,, Z. H., … Rowan,, A. E. (2013). Responsive biomimetic networks from polyisocyanopeptide hydrogels. Nature, 493(7434), 651–655.
Kulawiak,, D. A., Camley,, B. A., & Rappel,, W.‐J. (2016). Modeling contact inhibition of locomotion of colliding cells migrating on micropatterned substrates. PLoS Computational Biology, 12(12), e1005239.
Langtangen,, H. P. (2012). A FEniCS tutorial. In A. Logg,, K.‐A. Mardal,, & G. Wells, (Eds.), Automated solution of differential equations by the finite element method: The FEniCS book (pp. 1–73). Berlin: Springer.
Lee,, S. (2018). Mathematical model of contractile ring‐driven cytokinesis in a three‐dimensional domain. Bulletin of Mathematical Biology, 80(3), 583–597.
Levchenko,, A., & Iglesias,, P. A. (2002). Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils. Biophysical Journal, 82(1 Pt 1), 50–63.
Li,, Y., & Kim,, J. (2016). Three‐dimensional simulations of the cell growth and cytokinesis using the immersed boundary method. Mathematical Biosciences, 271, 118–127.
Lo,, C. M., Wang,, H. B., Dembo,, M., & Wang,, Y. L. (2000). Cell movement is guided by the rigidity of the substrate. Biophysical Journal, 79(1), 144–152.
Löber,, J., Ziebert,, F., & Aranson,, I. S. (2015). Collisions of deformable cells lead to collective migration. Scientific Reports, 5, 9172.
Ma,, L., Janetopoulos,, C., Yang,, L., Devreotes,, P. N., & Iglesias,, P. A. (2004). Two complementary, local excitation, global inhibition mechanisms acting in parallel can explain the chemoattractant‐induced regulation of pi(3,4,5)p3 response in dictyostelium cells. Biophysical Journal, 87(6), 3764–3774.
Maas,, S. A., Ellis,, B. J., Ateshian,, G. A., & Weiss,, J. A. (2012). FEBio: Finite elements for biomechanics. Journal of Biomechanical Engineering, 134(1), 011005.
Maas,, S. A., LaBelle,, S. A., Ateshian,, G. A., & Weiss,, J. A. (2018). A plugin framework for extending the simulation capabilities of FEBio. Biophysical Journal, 115(9), 1630–1637.
Mackenzie,, J. A., Nolan,, M., Rowlatt,, C. F., & Insall,, R. H. (2019). An adaptive moving mesh method for forced curve shortening flow. SIAM Journal on Scientific Computing, 41(2), A1170–A1200.
Marzban,, B., Kang,, J., Li,, N., Sun,, Y., & Yuan,, H. (2019). A contraction–reaction–diffusion model: Integrating biomechanics and biochemistry in cell migration. Extreme Mechanics Letters, 32, 100566.
Meinhardt,, H. (1999). Orientation of chemotactic cells and growth cones: Models and mechanisms. Journal of Cell Science, 112, 2867–2874.
Meyers,, J., Craig,, J., & Odde,, D. J. (2006). Potential for control of signaling pathways via cell size and shape. Current Biology, 16(17), 1685–1693.
Miao,, Y., Bhattacharya,, S., Banerjee,, T., Abubaker‐Sharif,, B., Long,, Y., Inoue,, T., … Devreotes,, P. N. (2019). Wave patterns organize cellular protrusions and control cortical dynamics. Molecular Systems Biology, 15(3), e8585.
Miao,, Y., Bhattacharya,, S., Edwards,, M., Cai,, H., Inoue,, T., Iglesias,, P. A., & Devreotes,, P. N. (2017). Altering the threshold of an excitable signal transduction network changes cell migratory modes. Nature Cell Biology, 19(4), 329–340.
Mietke,, A., Jülicher,, F., & Sbalzarini,, I. F. (2019). Self‐organized shape dynamics of active surfaces. Proceedings of the National Academy of Sciences of the United States of America, 116(1), 29–34.
Mihai,, L. A., & Goriely,, A. (2017). How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2207), 20170607.
Minc,, N., Burgess,, D., & Chang,, F. (2011). Influence of cell geometry on division‐plane positioning. Cell, 144(3), 414–426.
Mirams,, G. R., Arthurs,, C. J., Bernabeu,, M. O., Bordas,, R., Cooper,, J., Corrias,, A., … Gavaghan,, D. J. (2013). Chaste: An open source C++ library for computational physiology and biology. PLoS Computational Biology, 9(3), e1002970.
Mitchell,, I. M. (2008). The flexible, extensible and efficient toolbox of level set methods. Journal of Scientific Computing, 35(2), 300–329.
Mogilner,, A., & Manhart,, A. (2016). Agent‐based modeling: Case study in cleavage furrow models. Molecular Biology of the Cell, 27(22), 3379–3384.
Mohammadi,, H., & Sahai,, E. (2018). Mechanisms and impact of altered tumour mechanics. Nature Cell Biology, 20(7), 766–774.
Molina,, J. J., & Yamamoto,, R. (2019). Modeling the mechanosensitivity of fast‐crawling cells on cyclically stretched substrates. Soft Matter, 15(4), 683–698.
Moure,, A., & Gomez,, H. (2018). Three‐dimensional simulation of obstacle‐mediated chemotaxis. Biomechanics and Modeling in Mechanobiology, 17(5), 1243–1268.
Moure,, A., & Gomez,, H. (2019). Phase‐field modeling of individual and collective cell migration. Archives of Computational Methods in Engineering. https://doi.org/10.1007/s11831-019-09377-1
Moure,, A., & Gomez,, H. (2020a). Dual role of the nucleus in cell migration on planar substrates. Biomechanics and Modeling in Mechanobiology, 19, 1491–1508.
Moure,, A., & Gomez,, H. (2020b). Influence of myosin activity and mechanical impact on keratocyte polarization. Soft Matter, 16(22), 5177–5194.
Mukherjee,, S., Nazemi,, M., Jonkers,, I., & Geris,, L. (2020). Use of computational modeling to study joint degeneration: A review. Frontiers in Bioengineering and Biotechnology, 8, 93.
Müller,, R., & Rüegsegger,, P. (1995). Three‐dimensional finite element modelling of non‐invasively assessed trabecular bone structures. Medical Engineering %26 Physics, 17(2), 126–133.
Najem,, S., & Grant,, M. (2016). Phase‐field model for collective cell migration. Physical Review E, 93(5), 052405.
Nakamura,, M., Bessho,, S., & Wada,, S. (2013). Spring‐network‐based model of a red blood cell for simulating mesoscopic blood flow. International Journal of Numerical Methods in Biomedical Engineering, 29(1), 114–128.
Neilson,, M. P., Mackenzie,, J. A., Webb,, S. D., & Insall,, R. H. (2010). Use of the parameterised finite element method to robustly and efficiently evolve the edge of a moving cell. Integrative Biology (Cambridge), 2(11–12), 687–695.
Neilson,, M. P., Veltman,, D. M., van Haastert,, P. J. M., Webb,, S. D., Mackenzie,, J. A., & Insall,, R. H. (2011). Chemotaxis: A feedback‐based computational model robustly predicts multiple aspects of real cell behaviour. PLoS Biology, 9(5), e1000618.
Nguyen,, A. V., Nyberg,, K. D., Scott,, M. B., Welsh,, A. M., Nguyen,, A. H., Wu,, N., … Rowat,, A. C. (2016). Stiffness of pancreatic cancer cells is associated with increased invasive potential. Integrative Biology (Cambridge), 8(12), 1232–1245.
Nguyen,, L. T. S., & Robinson,, D. N. (2020). The unusual suspects in cytokinesis: Fitting the pieces together. Frontiers in Cell and Development Biology, 8, 441.
Nickaeen,, M., Novak,, I. L., Pulford,, S., Rumack,, A., Brandon,, J., Slepchenko,, B. M., & Mogilner,, A. (2017). A free‐boundary model of a motile cell explains turning behavior. PLoS Computational Biology, 13(11), e1005862.
Niculescu,, I., Textor,, J., & de Boer,, R. J. (2015). Crawling and gliding: A computational model for shape‐driven cell migration. PLoS Computational Biology, 11(10), e1004280.
Nishimura,, S. I., Ueda,, M., & Sasai,, M. (2009). Cortical factor feedback model for cellular locomotion and cytofission. PLoS Computational Biology, 5(3), e1000310.
Nonomura,, M. (2012). Study on multicellular systems using a phase field model. PLoS One, 7(4), e33501.
Oakes,, P. W., Bidone,, T. C., Beckham,, Y., Skeeters,, A. V., Ramirez‐San Juan,, G. R., Winter,, S. P., … Gardel,, M. L. (2018). Lamellipodium is a myosin‐independent mechanosensor. Proceedings of the National Academy of Sciences of the United States of America, 115(11), 2646–2651.
Osher,, S., & Fedkiw,, R. P. (2003). Level set methods and dynamic implicit surfaces. In Applied mathematical sciences (Vol. 153). New York: Springer.
Osher,, S., & Sethian,, J. A. (1988). Fronts propagating with curvature‐dependent speed: Algorithms based on Hamilton–Jacobi formulations. Journal of Computational Physics, 79(1), 12–49.
Overholtzer,, M., Mailleux,, A. A., Mouneimne,, G., Normand,, G., Schnitt,, S. J., King,, R. W., … Brugge,, J. S. (2007). A nonapoptotic cell death process, entosis, that occurs by cell‐in‐cell invasion. Cell, 131(5), 966–979.
Parent,, C. A., & Devreotes,, P. N. (1999). A cell`s sense of direction. Science, 284(5415), 765–770.
Peskin,, C. S. (1972). Flow patterns around heart valves: A numerical method. Journal of Computational Physics, 10(2), 252–271.
Peskin,, C. S. (2002). The immersed boundary method. Acta Numerica, 11, 479–517.
Poirier,, C. C., Ng,, W. P., Robinson,, D. N., & Iglesias,, P. A. (2012). Deconvolution of the cellular force‐generating subsystems that govern cytokinesis furrow ingression. PLoS Computational Biology, 8(4), e1002467.
Pollard,, T. D., & O`Shaughnessy,, B. (2019). Molecular mechanism of cytokinesis. Annual Review of Biochemistry, 88, 661–689.
Pons,, J.‐P., Hermosillo,, G., Keriven,, R., & Faugeras,, O. (2006). Maintaining the point correspondence in the level set framework. Journal of Computational Physics, 220(1), 339–354.
Rangamani,, P., Lipshtat,, A., Azeloglu,, E. U., Calizo,, R. C., Hu,, M., Ghassemi,, S., … Iyengar,, R. (2013). Decoding information in cell shape. Cell, 154(6), 1356–1369.
Rappel,, W.‐J., & Edelstein‐Keshet,, L. (2017). Mechanisms of cell polarization. Current Opinion in Systems Biology, 3, 43–53.
Reichl,, E. M., Ren,, Y., Morphew,, M. K., Delannoy,, M., Effler,, J. C., Girard,, K. D., … Robinson,, D. N. (2008). Interactions between myosin and actin crosslinkers control cytokinesis contractility dynamics and mechanics. Current Biology, 18(7), 471–480.
Remmerbach,, T. W., Wottawah,, F., Dietrich,, J., Lincoln,, B., Wittekind,, C., & Guck,, J. (2009). Oral cancer diagnosis by mechanical phenotyping. Cancer Research, 69(5), 1728–1732.
Rens,, E. G., & Edelstein‐Keshet,, L. (2019). From energy to cellular forces in the cellular Potts model: An algorithmic approach. PLoS Computational Biology, 15(12), e1007459.
Resasco,, D. C., Gao,, F., Morgan,, F., Novak,, I. L., Schaff,, J. C., & Slepchenko,, B. M. (2012). Virtual cell: Computational tools for modeling in cell biology. WIREs: Systems Biology and Medicine, 4(2), 129–140.
Robinson,, D. N., & Iglesias,, P. A. (2012). Bringing the physical sciences into your cell biology research. Molecular Biology of the Cell, 23(21), 4167–4170.
Roca‐Cusachs,, P., Sunyer,, R., & Trepat,, X. (2013). Mechanical guidance of cell migration: Lessons from chemotaxis. Current Opinion in Cell Biology, 25(5), 543–549.
Rodrigues,, M., Kosaric,, N., Bonham,, C. A., & Gurtner,, G. C. (2019). Wound healing: A cellular perspective. Physiological Reviews, 99(1), 665–706.
Rubinstein,, B., Fournier,, M. F., Jacobson,, K., Verkhovsky,, A. B., & Mogilner,, A. (2009). Actin‐myosin viscoelastic flow in the keratocyte lamellipod. Biophysical Journal, 97(7), 1853–1863.
Satulovsky,, J., Lui,, R., & Wang,, Y.‐L. (2008). Exploring the control circuit of cell migration by mathematical modeling. Biophysical Journal, 94(9), 3671–3683.
Schaff,, J. C., Gao,, F., Li,, Y., Novak,, I. L., & Slepchenko,, B. M. (2016). Numerical approach to spatial deterministic‐stochastic models arising in cell biology. PLoS Computational Biology, 12(12), e1005236.
Schneider,, I. C., & Haugh,, J. M. (2005). Quantitative elucidation of a distinct spatial gradient‐sensing mechanism in fibroblasts. The Journal of Cell Biology, 171(5), 883–892.
Sethian,, J. A. (1999). Level set methods and fast marching methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science (2nd ed.). Cambridge, England: Cambridge University Press.
Shao,, D., Levine,, H., & Rappel,, W.‐J. (2012). Coupling actin flow, adhesion, and morphology in a computational cell motility model. Proceedings of the National Academy of Sciences of the United States of America, 109(18), 6851–6856.
Shao,, D., Rappel,, W.‐J., & Levine,, H. (2010). Computational model for cell morphodynamics. Physical Review Letters, 105(10), 108104.
Shi,, C., Huang,, C.‐H., Devreotes,, P. N., & Iglesias,, P. A. (2013). Interaction of motility, directional sensing, and polarity modules recreates the behaviors of chemotaxing cells. PLoS Computational Biology, 9(7), e1003122.
Shlomovitz,, R., & Gov,, N. S. (2008). Physical model of contractile ring initiation in dividing cells. Biophysical Journal, 94(4), 1155–1168.
Storm,, C., Pastore,, J. J., MacKintosh,, F. C., Lubensky,, T. C., & Janmey,, P. A. (2005). Nonlinear elasticity in biological gels. Nature, 435(7039), 191–194.
Strychalski,, W., Adalsteinsson,, D., & Elston,, T. C. (2010). Simulating biochemical signaling networks in complex moving geometries. SIAM Journal on Scientific Computing, 32(5), 3039–3070.
Sun,, Q., Luo,, T., Ren,, Y., Florey,, O., Shirasawa,, S., Sasazuki,, T., … Overholtzer,, M. (2014). Competition between human cells by entosis. Cell Research, 24(11), 1299–1310.
Surcel,, A., & Robinson,, D. N. (2019). Meddling with myosin`s mechanobiology in cancer. Proceedings of the National Academy of Sciences of the United States of America, 116(31), 15322–15323.
Surcel,, A., Schiffhauer,, E. S., Thomas,, D. G., Zhu,, Q., DiNapoli,, K. T., Herbig,, M., … Robinson,, D. N. (2019). Targeting mechanoresponsive proteins in pancreatic cancer: 4‐Hydroxyacetophenone blocks dissemination and invasion by activating MYH14. Cancer Research, 79(18), 4665–4678.
Swaminathan,, V., Mythreye,, K., O`Brien,, E. T., Berchuck,, A., Blobe,, G. C., & Superfine,, R. (2011). Mechanical stiffness grades metastatic potential in patient tumor cells and in cancer cell lines. Cancer Research, 71(15), 5075–5080.
Swat,, M. H., Thomas,, G. L., Belmonte,, J. M., Shirinifard,, A., Hmeljak,, D., & Glazier,, J. A. (2012). Multi‐scale modeling of tissues using CompuCell3D. Methods in Cell Biology, 110, 325–366.
Tang,, G., Galluzzi,, M., Zhang,, B., Shen,, Y.‐L., & Stadler,, F. J. (2019). Biomechanical heterogeneity of living cells: Comparison between atomic force microscopy and finite element simulation. Langmuir, 35(23), 7578–7587.
Tao,, K., Wang,, J., Kuang,, X., Wang,, W., Liu,, F., & Zhang,, L. (2020). Tuning cell motility via cell tension with a mechanochemical cell migration model. Biophysical Journal, 118(12), 2894–2904.
Teo,, S.‐K., Goryachev,, A. B., Parker,, K. H., & Chiam,, K.‐H. (2010). Cellular deformation and intracellular stress propagation during optical stretching. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 81(5 Pt 1), 051924.
Thompson,, D. W. (1917). On growth and form. Cambridge: Cambridge University Press.
Thüroff,, F., Goychuk,, A., Reiter,, M., & Frey,, E. (2019). Bridging the gap between single‐cell migration and collective dynamics. eLife, 8, e46842.
Tollis,, S., Dart,, A. E., Tzircotis,, G., & Endres,, R. G. (2010). The zipper mechanism in phagocytosis: Energetic requirements and variability in phagocytic cup shape. BMC Systems Biology, 4, 149.
Ujihara,, Y., Nakamura,, M., Miyazaki,, H., & Wada,, S. (2010). Proposed spring network cell model based on a minimum energy concept. Annals of Biomedical Engineering, 38(4), 1530–1538.
Valero,, C., Navarro,, B., Navajas,, D., & García‐Aznar,, J. M. (2016). Finite element simulation for the mechanical characterization of soft biological materials by atomic force microscopy. Journal of the Mechanical Behavior of Biomedical Materials, 62, 222–235.
Vanderlei,, B., Feng,, J. J., & Edelstein‐Keshet,, L. (2011). A computational model of cell polarization and motility coupling mechanics and biochemistry. Multiscale Modeling and Simulation, 9(4), 1420–1443.
Varennes,, J., Han,, B., & Mugler,, A. (2016). Collective chemotaxis through noisy multicellular gradient sensing. Biophysical Journal, 111(3), 640–649.
Vavylonis,, D., Wu,, J.‐Q., Hao,, S., O`Shaughnessy,, B., & Pollard,, T. D. (2008). Assembly mechanism of the contractile ring for cytokinesis by fission yeast. Science, 319(5859), 97–100.
Walker,, C., Mojares,, E., & Del Río Hernández,, A. (2018). Role of extracellular matrix in development and cancer progression. International Journal of Molecular Sciences, 19(10), 3028.
Wolgemuth,, C. W., & Zajac,, M. (2010). The moving boundary node method: A level set‐based, finite volume algorithm with applications to cell motility. Journal of Computational Physics, 229(19), 7287–7308.
Xin,, Y., Chen,, X., Tang,, X., Li,, K., Yang,, M., Tai,, W. C.‐S., … Tan,, Y. (2019). Mechanics and actomyosin‐dependent survival/chemoresistance of suspended tumor cells in shear flow. Biophysical Journal, 116(10), 1803–1814.
Xiong,, Y., Kabacoff,, C., Franca‐Koh,, J., Devreotes,, P. N., Robinson,, D. N., & Iglesias,, P. A. (2010). Automated characterization of cell shape changes during amoeboid motility by skeletonization. BMC Systems Biology, 4, 33.
Yang,, L., Effler,, J. C., Kutscher,, B. L., Sullivan,, S. E., Robinson,, D. N., & Iglesias,, P. A. (2008). Modeling cellular deformations using the level set formalism. BMC Systems Biology, 2, 68.
Yang,, Y., Jolly,, M. K., & Levine,, H. (2019). Computational modeling of collective cell migration: Mechanical and biochemical aspects. Advances in Experimental Medicine and Biology, 1146, 1–11.
Yang,, Y., & Levine,, H. (2018). Role of the supracellular actomyosin cable during epithelial wound healing. Soft Matter, 14, 4866–4873.
Zhan,, H., Bhattacharya,, S., Cai,, H., Iglesias,, P. A., Huang,, C.‐H., & Devreotes,, P. N. (2020). An excitable Ras/PI3K/ERK signaling network controls migration and oncogenic transformation in epithelial cells. Developmental Cell, 54(5), 608–623.e5.
Zhang,, W., & Robinson,, D. N. (2005). Balance of actively generated contractile and resistive forces controls cytokinesis dynamics. Proceedings of the National Academy of Sciences of the United States of America, 102(20), 7186–7191.
Zhang,, Z., Rosakis,, P., Hou,, T. Y., & Ravichandran,, G. (2020). A minimal mechanosensing model predicts keratocyte evolution on flexible substrates. Journal of the Royal Society Interface, 17(166), 20200175.
Zhao,, H.‐K., Chan,, T., Merriman,, B., & Osher,, S. (1996). A variational level set approach to multiphase motion. Journal of Computational Physics, 127(1), 179–195.
Zhao,, J., & Wang,, Q. (2016a). A 3D multi‐phase hydrodynamic model for cytokinesis of eukaryotic cells. Communications in Computational Physics, 19(3), 663–681.
Zhao,, J., & Wang,, Q. (2016b). Modeling cytokinesis of eukaryotic cells driven by the actomyosin contractile ring. International Journal of Numerical Methods in Biomedical Engineering, 32(12), e02774.
Zhou,, E. H., Xu,, F., Quek,, S. T., & Lim,, C. T. (2012). A power‐law rheology‐based finite element model for single cell deformation. Biomechanics and Modeling in Mechanobiology, 11(7), 1075–1084.
Zhu,, J., & Mogilner,, A. (2016). Comparison of cell migration mechanical strategies in three‐dimensional matrices: A computational study. Interface Focus, 6(5), 20160040.
Ziebert,, F., & Aranson,, I. S. (2013). Effects of adhesion dynamics and substrate compliance on the shape and motility of crawling cells. PLoS One, 8(5), e64511.
Zienkiewicz,, O. C., & Taylor,, R. L. (2000). The finite element method (5th ed.). Butterworth‐Heinemann: Oxford.
Zimmermann,, J., Camley,, B. A., Rappel,, W.‐J., & Levine,, H. (2016). Contact inhibition of locomotion determines cell–cell and cell–substrate forces in tissues. Proceedings of the National Academy of Sciences of the United States of America, 113(10), 2660–2665.
Zmurchok,, C., & Holmes,, W. R. (2020). Simple Rho GTPase dynamics generate a complex regulatory landscape associated with cell shape. Biophysical Journal, 118(6), 1438–1454.