1932

Abstract

The cell is a mechanical machine, and continuum mechanics of the fluid cytoplasm and the viscoelastic deforming cytoskeleton play key roles in cell physiology. We review mathematical models of intracellular fluid mechanics, from cytoplasmic fluid flows, to the flow of a viscous active cytoskeletal gel, to models of two-phase poroviscous flows, to poroelastic models. We discuss application of these models to cell biological phenomena, such as organelle positioning, blebbing, and cell motility. We also discuss challenges of understanding fluid mechanics on the cellular scale.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010816-060238
2018-01-05
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/fluid/50/1/annurev-fluid-010816-060238.html?itemId=/content/journals/10.1146/annurev-fluid-010816-060238&mimeType=html&fmt=ahah

Literature Cited

  1. Alberts B, Johnson A, Lewis J, Morgan D, Raff M. et al. 2014. Molecular Biology of the Cell New York: Garland Sci, 6th ed..
  2. Allen GM, Mogilner A, Theriot JA. 2013. Electrophoresis of cellular membrane components creates the directional cue guiding keratocyte galvanotaxis. Curr. Biol. 23:7560–68 [Google Scholar]
  3. Allen RD, Allen NS. 1978. Cytoplasmic streaming in amoeboid movement. Annu. Rev. Biophys. Bioeng. 7:1469–95 [Google Scholar]
  4. Alt W, Dembo M. 1999. Cytoplasm dynamics and cell motion: two-phase flow models. Math. Biosci. 156:1207–28 [Google Scholar]
  5. Atilgan E, Wirtz D, Sun SX. 2006. Mechanics and dynamics of actin-driven thin membrane protrusions. Biophys. J. 90:165–76 [Google Scholar]
  6. Atzberger PJ, Kramer PR, Peskin CS. 2007. A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. J. Comput. Phys. 224:21255–92 [Google Scholar]
  7. Barnhart E, Lee KC, Allen GM, Theriot JA, Mogilner A. 2015. Balance between cell–substrate adhesion and myosin contraction determines the frequency of motility initiation in fish keratocytes. PNAS 112:165045–50 [Google Scholar]
  8. Bausch AR, Kroy K. 2006. A bottom-up approach to cell mechanics. Nat. Phys. 2:4231–38 [Google Scholar]
  9. Bausch AR, Ziemann F, Boulbitch AA, Jacobson K, Sackmann E. 1998. Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. Biophys. J. 75:42038–49 [Google Scholar]
  10. Bergert M, Chandradoss SD, Desai RA, Paluch E. 2012. Cell mechanics control rapid transitions between blebs and lamellipodia during migration. PNAS 109:3614434–39 [Google Scholar]
  11. Biot MA. 1941. General theory of three‐dimensional consolidation. J. Appl. Phys. 12:2155–64 [Google Scholar]
  12. Bloom M, Evans E, Mouritsen OG. 1991. Physical properties of the fluid lipid-bilayer component of cell membranes: a perspective. Q. Rev. Biophys. 24:3293–397 [Google Scholar]
  13. Bottino DC, Fauci LJ. 1998. A computational model of ameboid deformation and locomotion. Eur. Biophys. J. 27:5532–39 [Google Scholar]
  14. Bretscher MS, Aguado-Velasco C. 1998. Membrane traffic during cell locomotion. Curr. Opin. Cell Biol. 10:4537–41 [Google Scholar]
  15. Brugués J, Nuzzo V, Mazur E, Needleman DJ. 2012. Nucleation and transport organize microtubules in metaphase spindles. Cell 149:3554–64 [Google Scholar]
  16. Callan-Jones AC, Jülicher F. 2011. Hydrodynamics of active permeating gels. New J. Phys. 13:9093027 [Google Scholar]
  17. Carlier MF, Romet-Lemonne G, Jegou A. 2014. Actin filament dynamics using microfluidics. Methods Enzymol 540:3–17 [Google Scholar]
  18. Carlsson AE. 2011. Mechanisms of cell propulsion by active stresses. New J. Phys. 13:7073009 [Google Scholar]
  19. Chan CE, Odde DJ. 2008. Traction dynamics of filopodia on compliant substrates. Science 322:59081687–91 [Google Scholar]
  20. Charras GT, Coughlin M, Mitchison TJ, Mahadevan L. 2008. Life and times of a cellular bleb. Biophys. J. 94:51836–53 [Google Scholar]
  21. Charras GT, Mitchison TJ, Mahadevan L. 2009. Animal cell hydraulics. J. Cell Sci. 122:183233–41 [Google Scholar]
  22. Charras GT, Yarrow JC, Horton MA, Mahadevan L, Mitchison TJ. 2005. Non-equilibration of hydrostatic pressure in blebbing cells. Nature 435:7040365–69 [Google Scholar]
  23. Cogan NG, Guy RD. 2010. Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP J 4:111–25 [Google Scholar]
  24. Dai J, Sheetz MP. 1999. Membrane tether formation from blebbing cells. Biophys. J. 77:63363–70 [Google Scholar]
  25. Dembo M. 1989. Mechanics and control of the cytoskeleton in Amoeba proteus. Biophys. J. 55:61053–80 [Google Scholar]
  26. Dembo M, Harlow F. 1986. Cell motion, contractile networks, and the physics of interpenetrating reactive flow. Biophys. J. 50:1109–21 [Google Scholar]
  27. Diz-Muñoz A, Romanczuk P, Yu W, Bergert M, Ivanovitch K. et al. 2016. Steering cell migration by alternating blebs and actin-rich protrusions. BMC Biol 14:174 [Google Scholar]
  28. Drew DA, Segel LA. 1971. Averaged equations for two‐phase flows. Stud. Appl. Math. 50:3205–31 [Google Scholar]
  29. Eloy C, Lauga E. 2012. Kinematics of the most efficient cilium. Phys. Rev. Lett. 109:3038101 [Google Scholar]
  30. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ. 2001. Scaling the microrheology of living cells. Phys. Rev. Lett. 87:14148102 [Google Scholar]
  31. Fogelson B, Mogilner A. 2014. Computational estimates of membrane flow and tension gradient in motile cells. PLOS ONE 9:1e84524 [Google Scholar]
  32. Gabella C, Bertseva E, Bottier C, Piacentini N, Bornert A. et al. 2014. Contact angle at the leading edge controls cell protrusion rate. Curr. Biol. 24:101126–32 [Google Scholar]
  33. Gauthier NC, Masters TA, Sheetz MP. 2012. Mechanical feedback between membrane tension and dynamics. Trends Cell Biol 22:10527–35 [Google Scholar]
  34. Giomi L, DeSimone A. 2014. Spontaneous division and motility in active nematic droplets. Phys. Rev. Lett. 112:14147802 [Google Scholar]
  35. Goldstein RE. 2016. Fluid dynamics at the scale of the cell. J. Fluid Mech. 807:1–39 [Google Scholar]
  36. Goldstein RE, van de Meent JW. 2015. A physical perspective on cytoplasmic streaming. Interface Focus 5:420150030 [Google Scholar]
  37. Gracheva ME, Othmer HG. 2004. A continuum model of motility in ameboid cells. Bull. Math. Biol. 66:1167–93 [Google Scholar]
  38. Gross SP, Welte MA, Block SM, Wieschaus EF. 2000. Dynein-mediated cargo transport in vivo: A switch controls travel distance. J. Cell Biol. 148:5945–56 [Google Scholar]
  39. Guy RD, Nakagaki T, Wright GB. 2011. Flow-induced channel formation in the cytoplasm of motile cells. Phys. Rev. E 84:1016310 [Google Scholar]
  40. He X, Dembo M. 1997. On the mechanics of the first cleavage division of the sea urchin egg. Exp. Cell Res. 233:2252–73 [Google Scholar]
  41. Hecht I, Rappel WJ, Levine H. 2009. Determining the scale of the Bicoid morphogen gradient. PNAS 106:61710–15 [Google Scholar]
  42. Herant M, Dembo M. 2010. Form and function in cell motility: from fibroblasts to keratocytes. Biophys. J. 98:81408–17 [Google Scholar]
  43. Herant M, Marganski WA, Dembo M. 2003. The mechanics of neutrophils: synthetic modeling of three experiments. Biophys. J. 84:53389–413 [Google Scholar]
  44. Holmes WR, Edelstein-Keshet L. 2012. A comparison of computational models for eukaryotic cell shape and motility. PLOS Comput. Biol. 8:12e1002793 [Google Scholar]
  45. Hu J, Verkman AS. 2006. Increased migration and metastatic potential of tumor cells expressing aquaporin water channels. FASEB J 20:111892–94 [Google Scholar]
  46. Iglesias PA, Devreotes PN. 2012. Biased excitable networks: how cells direct motion in response to gradients. Curr. Opin. Cell Biol. 24:2245–53 [Google Scholar]
  47. Iskratsch T, Wolfenson H, Sheetz MP. 2014. Appreciating force and shape—the rise of mechanotransduction in cell biology. Nat. Rev. Mol. Cell Biol. 15:12825–33 [Google Scholar]
  48. Jaeger M, Carin M, Medale M, Tryggvason G. 1999. The osmotic migration of cells in a solute gradient. Biophys. J. 77:31257–67 [Google Scholar]
  49. Janmey PA, Slochower DR, Wang YH, Wen Q, Cēbers A. 2014. Polyelectrolyte properties of filamentous biopolymers and their consequences in biological fluids. Soft Matter 10:101439–49 [Google Scholar]
  50. Joanny JF, Prost J. 2009. Active gels as a description of the actin‐myosin cytoskeleton. HFSP J 3:294–104 [Google Scholar]
  51. Kamm RD. 2002. Cellular fluid mechanics. Annu. Rev. Fluid Mech. 34:1211–32 [Google Scholar]
  52. Keener JP, Sircar S, Fogelson AL. 2011. Kinetics of swelling gels. SIAM J. Appl. Math. 71:3854–75 [Google Scholar]
  53. Keren K, Yam PT, Kinkhabwala A, Mogilner A, Theriot JA. 2009. Intracellular fluid flow in rapidly moving cells. Nat. Cell Biol. 11:101219–24 [Google Scholar]
  54. Khismatullin DB, Truskey GA. 2012. Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity. Biophys. J. 102:81757–66 [Google Scholar]
  55. Kimpton LS, Whiteley JP, Waters SL, King JR, Oliver JM. 2013. Multiple travelling-wave solutions in a minimal model for cell motility. Math. Med. Biol. 30:3241–72 [Google Scholar]
  56. Kimpton LS, Whiteley JP, Waters SL, Oliver JM. 2015. On a poroviscoelastic model for cell crawling. J. Math. Biol. 70:1–2133–71 [Google Scholar]
  57. Kole TP, Tseng Y, Jiang I, Katz JL, Wirtz D. 2005. Intracellular mechanics of migrating fibroblasts. Mol. Biol. Cell 16:1328–38 [Google Scholar]
  58. Kozlov MM, Mogilner A. 2007. Model of polarization and bistability of cell fragments. Biophys. J. 93:113811–19 [Google Scholar]
  59. Kruse K, Joanny JF, Jülicher F, Prost J. 2006. Contractility and retrograde flow in lamellipodium motion. Phys. Biol. 3:2130 [Google Scholar]
  60. Kruse K, Joanny JF, Jülicher F, Prost J, Sekimoto K. 2004. Asters, vortices, and rotating spirals in active gels of polar filaments. Phys. Rev. Lett. 92:7078101 [Google Scholar]
  61. Kruse K, Joanny JF, Jülicher F, Prost J, Sekimoto K. 2005. Generic theory of active polar gels: a paradigm for cytoskeletal dynamics. Eur. Phys. J. E 16:15–16 [Google Scholar]
  62. Kuusela E, Alt W. 2009. Continuum model of cell adhesion and migration. J. Math. Biol. 58:1–2135–61 [Google Scholar]
  63. Larripa K, Mogilner A. 2006. Transport of a 1D viscoelastic actin–myosin strip of gel as a model of a crawling cell. Physica A 372:1113–23 [Google Scholar]
  64. Lee P, Wolgemuth CW. 2011. Crawling cells can close wounds without purse strings or signaling. PLOS Comput. Biol. 7:3e1002007 [Google Scholar]
  65. Lewis OL, Guy RD, Allard JF. 2014. Actin-myosin spatial patterns from a simplified isotropic viscoelastic model. Biophys. J. 107:4863–70 [Google Scholar]
  66. Lewis OL, Zhang S, Guy RD, del Álamo JC. 2015. Coordination of contractility, adhesion and flow in migrating Physarum amoebae. J. R. Soc. Interface 12:10620141359 [Google Scholar]
  67. Li Y, Mori Y, Sun SX. 2015. Flow-driven cell migration under external electric fields. Phys. Rev. Lett. 115:26268101 [Google Scholar]
  68. Lieber AD, Schweitzer Y, Kozlov MM, Keren K. 2015. Front-to-rear membrane tension gradient in rapidly moving cells. Biophys. J. 108:71599–603 [Google Scholar]
  69. Lim FY, Chiam KH, Mahadevan L. 2012. The size, shape, and dynamics of cellular blebs. Europhys. Lett. 100:228004 [Google Scholar]
  70. Lim FY, Koon YL, Chiam KH. 2013. A computational model of amoeboid cell migration. Comput. Methods Biomech. Biomed. Eng. 16:101085–95 [Google Scholar]
  71. Liu AS, Wang H, Copeland CR, Chen CS, Shenoy VB, Reich DH. 2016. Matrix viscoplasticity and its shielding by active mechanics in microtissue models: experiments and mathematical modeling. Sci. Rep. 6:33919 [Google Scholar]
  72. Loitto VM, Forslund T, Sundqvist T, Magnusson KE, Gustafsson M. 2002. Neutrophil leukocyte motility requires directed water influx. J. Leukoc. Biol. 71:2212–22 [Google Scholar]
  73. Luby-Phelps K. 1999. Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area. Int. Rev. Cytol. 192:189–221 [Google Scholar]
  74. Luby-Phelps K. 2013. The physical chemistry of cytoplasm and its influence on cell function: an update. Mol. Biol. Cell 24:172593–96 [Google Scholar]
  75. MacKintosh FC, Schmidt CF. 2010. Active cellular materials. Curr. Opin. Cell Biol. 22:129–35 [Google Scholar]
  76. Marée AF, Jilkine A, Dawes A, Grieneisen VA, Edelstein-Keshet L. 2006. Polarization and movement of keratocytes: a multiscale modelling approach. Bull. Math. Biol. 68:51169–211 [Google Scholar]
  77. Marquez JP, Genin GM, Zahalak GI, Elson EL. 2005. The relationship between cell and tissue strain in three-dimensional bio-artificial tissues. Biophys. J. 88:2778–89 [Google Scholar]
  78. Mitchison TJ, Charras GT, Mahadevan L. 2008. Implications of a poroelastic cytoplasm for the dynamics of animal cell shape. Semin. Cell Dev. Biol. 19:3215–23 [Google Scholar]
  79. Moeendarbary E, Valon L, Fritzsche M, Harris AR, Moulding DA. et al. 2013. The cytoplasm of living cells behaves as a poroelastic material. Nat. Mater. 12:3253–61 [Google Scholar]
  80. Monteith CE, Brunner ME, Djagaeva I, Bielecki AM, Deutsch JM, Saxton WM. 2016. A mechanism for cytoplasmic streaming: kinesin-driven alignment of microtubules and fast fluid flows. Biophys. J. 110:92053–65 [Google Scholar]
  81. Nishimura SI, Sasai M. 2007. Modulation of the reaction rate of regulating protein induces large morphological and motional change of amoebic cell. J. Theor. Biol. 245:2230–37 [Google Scholar]
  82. Oakes PW, Banerjee S, Marchetti MC, Gardel ML. 2014. Geometry regulates traction stresses in adherent cells. Biophys. J. 107:4825–33 [Google Scholar]
  83. Oliver JM, King JR, McKinlay KJ, Brown PD, Grant DM. et al. 2005. Thin-film theories for two-phase reactive flow models of active cell motion. Math. Med. Biol. 22:153–59 [Google Scholar]
  84. Oster GF, Perelson AS. 1987. The physics of cell motility. J. Cell Sci. 1987:Suppl. 835–54 [Google Scholar]
  85. Paluch EK, Raz E. 2013. The role and regulation of blebs in cell migration. Curr. Opin. Cell Biol. 25:5582–90 [Google Scholar]
  86. Peskin CS, McQueen DM. 1995. A general method for the computer simulation of biological systems interacting with fluids. Symp. Soc. Exp. Biol. 49:265–76 [Google Scholar]
  87. Petrie RJ, Koo H, Yamada KM. 2014. Generation of compartmentalized pressure by a nuclear piston governs cell motility in a 3D matrix. Science 345:62001062–65 [Google Scholar]
  88. Phillips R, Kondev J, Theriot J, Garcia HG. 2013. Physical Biology of the Cell New York: Garland Sci, 2nd ed..
  89. Pollack GH. 2001. Cells, Gels and the Engines of Life: A New, Unifying Approach to Cell Function Seattle: Ebner
  90. Prass M, Jacobson K, Mogilner A, Radmacher M. 2006. Direct measurement of the lamellipodial protrusive force in a migrating cell. J. Cell Biol. 174:6767–72 [Google Scholar]
  91. Quinlan ME. 2016. Cytoplasmic streaming in the Drosophila oocyte. Annu. Rev. Cell Dev. Biol. 32:173–95 [Google Scholar]
  92. Recho P, Putelat T, Truskinovsky L. 2013. Contraction-driven cell motility. Phys. Rev. Lett. 111:10108102 [Google Scholar]
  93. Robinson DN, Spudich JA. 2004. Mechanics and regulation of cytokinesis. Curr. Opin. Cell Biol. 16:2182–88 [Google Scholar]
  94. Rosenbluth MJ, Crow A, Shaevitz JW, Fletcher DA. 2008. Slow stress propagation in adherent cells. Biophys. J. 95:126052–59 [Google Scholar]
  95. Rotsch C, Jacobson K, Radmacher M. 1999. Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy. PNAS 96:3921–26 [Google Scholar]
  96. Rubinstein B, Fournier MF, Jacobson K, Verkhovsky AB, Mogilner A. 2009. Actin-myosin viscoelastic flow in the keratocyte lamellipod. Biophys. J. 97:71853–63 [Google Scholar]
  97. Rubinstein B, Jacobson K, Mogilner A. 2005. Multiscale two-dimensional modeling of a motile simple-shaped cell. Multiscale Model. Simul. 3:2413–39 [Google Scholar]
  98. Sabass B, Gardel ML, Waterman CM, Schwarz US. 2008. High resolution traction force microscopy based on experimental and computational advances. Biophys. J. 94:1207–20 [Google Scholar]
  99. Schwarz US. 2015. Physical constraints for pathogen movement. Semin. Cell Dev. Biol. 46:82–90 [Google Scholar]
  100. Schweitzer Y, Lieber AD, Keren K, Kozlov MM. 2014. Theoretical analysis of membrane tension in moving cells. Biophys. J. 106:184–92 [Google Scholar]
  101. Shao D, Rappel WJ, Levine H. 2010. Computational model for cell morphodynamics. Phys. Rev. Lett. 105:10108104 [Google Scholar]
  102. Sheetz MP, Sable JE, Döbereiner HG. 2006. Continuous membrane-cytoskeleton adhesion requires continuous accommodation to lipid and cytoskeleton dynamics. Annu. Rev. Biophys. Biomol. Struct. 35:417–34 [Google Scholar]
  103. Shinar T, Mana M, Piano F, Shelley MJ. 2011. A model of cytoplasmically driven microtubule-based motion in the single-celled Caenorhabditis elegans embryo. PNAS 108:2610508–13 [Google Scholar]
  104. Shivashankar GV. 2011. Mechanosignaling to the cell nucleus and gene regulation. Annu. Rev. Biophys. 40:361–78 [Google Scholar]
  105. Sigurdsson JK, Atzberger PJ. 2016. Hydrodynamic coupling of particle inclusions embedded in curved lipid bilayer membranes. Soft Matter 12:326685–707 [Google Scholar]
  106. Stroka KM, Jiang H, Chen SH, Tong Z, Wirtz D. et al. 2014. Water permeation drives tumor cell migration in confined microenvironments. Cell 157:3611–23 [Google Scholar]
  107. Strychalski W, Copos CA, Lewis OL, Guy RD. 2015. A poroelastic immersed boundary method with applications to cell biology. J. Comput. Phys. 282:77–97 [Google Scholar]
  108. Strychalski W, Guy RD. 2012. A computational model of bleb formation. Math. Med. Biol. 30:2115–30 [Google Scholar]
  109. Strychalski W, Guy RD. 2016. Intracellular pressure dynamics in blebbing cells. Biophys. J. 110:51168–79 [Google Scholar]
  110. Tanaka T, Fillmore DJ. 1979. Kinetics of swelling of gels. J. Chem. Phys. 70:31214–18 [Google Scholar]
  111. Tao J, Li Y, Vig DK, Sun SX. 2017. Cell mechanics: a dialogue. Rep. Prog. Phys. 80:3036601 [Google Scholar]
  112. Terasaki M, Shemesh T, Kasthuri N, Klemm RW, Schalek R. et al. 2013. Stacked endoplasmic reticulum sheets are connected by helicoidal membrane motifs. Cell 154:2285–96 [Google Scholar]
  113. Tinevez JY, Schulze U, Salbreux G, Roensch J, Joanny JF, Paluch E. 2009. Role of cortical tension in bleb growth. PNAS 106:4418581–86 [Google Scholar]
  114. Tjhung E, Tiribocchi A, Marenduzzo D, Cates ME. 2015. A minimal physical model captures the shapes of crawling cells. Nat. Commun. 6:5420 [Google Scholar]
  115. Tozluoğlu M, Tournier AL, Jenkins RP, Hooper S, Bates PA, Sahai E. 2013. Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions. Nat. Cell Biol. 15:7751–62 [Google Scholar]
  116. Trong PK, Doerflinger H, Dunkel J, St. Johnston D, Goldstein RE. 2015. Cortical microtubule nucleation can organise the cytoskeleton of Drosophila oocytes to define the anteroposterior axis. eLife 4:e06088 [Google Scholar]
  117. Vanderlei B, Feng JJ, Edelstein-Keshet L. 2011. A computational model of cell polarization and motility coupling mechanics and biochemistry. Multiscale Model. Simul. 9:41420–43 [Google Scholar]
  118. Weirich KL, Banerjee S, Dasbiswas K, Witten TA, Vaikuntanathan S, Gardel ML. 2017. Liquid behavior of cross-linked actin bundles. PNAS 114:92131–36 [Google Scholar]
  119. Wolgemuth CW, Stajic J, Mogilner A. 2011. Redundant mechanisms for stable cell locomotion revealed by minimal models. Biophys. J. 101:3545–53 [Google Scholar]
  120. Wolke U, Jezuit EA, Priess JR. 2007. Actin-dependent cytoplasmic streaming in C. elegans oogenesis. Development 134:122227–36 [Google Scholar]
  121. Wollman R, Civelekoglu‐Scholey G, Scholey JM, Mogilner A. 2008. Reverse engineering of force integration during mitosis in the Drosophila embryo. Mol. Syst. Biol. 4:1195 [Google Scholar]
  122. Woodhouse FG, Goldstein RE. 2012. Shear-driven circulation patterns in lipid membrane vesicles. J. Fluid Mech. 705:165–75 [Google Scholar]
  123. Woolley TE, Gaffney EA, Oliver JM, Baker RE, Waters SL, Goriely A. 2014. Cellular blebs: pressure-driven, axisymmetric, membrane protrusions. Biomech. Model. Mechanobiol. 13:2463–76 [Google Scholar]
  124. Xie J, Hu GH. 2016. Hydrodynamic modeling of Bicoid morphogen gradient formation in Drosophila embryo. Biomech. Model. Mechanobiol. 15:61765–73 [Google Scholar]
  125. Yi K, Unruh JR, Deng M, Slaughter BD, Rubinstein B, Li R. 2011. Dynamic maintenance of asymmetric meiotic spindle position through Arp2/3-complex-driven cytoplasmic streaming in mouse oocytes. Nat. Cell Biol. 13:101252–58 [Google Scholar]
  126. Young J, Mitran S. 2010. A numerical model of cellular blebbing: a volume-conserving, fluid–structure interaction model of the entire cell. J. Biomech. 43:2210–20 [Google Scholar]
  127. Zajac M, Dacanay B, Mohler WA, Wolgemuth CW. 2008. Depolymerization-driven flow in nematode spermatozoa relates crawling speed to size and shape. Biophys. J. 94:103810–23 [Google Scholar]
  128. Zhao J, Wang Q. 2016. A 3D multi-phase hydrodynamic model for cytokinesis of eukaryotic cells. Commun. Comput. Phys. 19:03663–81 [Google Scholar]
  129. Zheng F, Basciano C, Li J, Kuznetsov AV. 2007. Fluid dynamics of cell cytokinesis—numerical analysis of intracellular flow during cell division. Int. Commun. Heat Mass Transf. 34:11–7 [Google Scholar]
  130. Zhu CH, Skalak RI. 1988. A continuum model of protrusion of pseudopod in leukocytes. Biophys. J. 54:61115–37 [Google Scholar]
  131. Zhu J, Mogilner A. 2016. Comparison of cell migration mechanical strategies in three-dimensional matrices: a computational study. Interface Focus 6:520160040 [Google Scholar]
  132. Zicha D, Dobbie IM, Holt MR, Monypenny J, Soong DY. et al. 2003. Rapid actin transport during cell protrusion. Science 300:5616142–45 [Google Scholar]
  133. Ziebert F, Aranson IS. 2013. Effects of adhesion dynamics and substrate compliance on the shape and motility of crawling cells. PLOS ONE 8:5e64511 [Google Scholar]
  134. Ziebert F, Swaminathan S, Aranson IS. 2011. Model for self-polarization and motility of keratocyte fragments. J. R. Soc. Interface 9:701084–92 [Google Scholar]
  135. Zumdieck A, Voituriez R, Prost J, Joanny JF. 2008. Spontaneous flow of active polar gels in undulated channels. Faraday Discuss 139:369–75 [Google Scholar]
/content/journals/10.1146/annurev-fluid-010816-060238
Loading
/content/journals/10.1146/annurev-fluid-010816-060238
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error