Root Hairs pp 103-122 | Cite as

Modeling Tip Growth: Pushing Ahead

  • M. N. de KeijzerEmail author
  • A. M. C. Emons
  • B. M. Mulder
Part of the Plant Cell Monographs book series (CELLMONO, volume 12)


Tip growth, the localized extension of a cell at one of its ends, is a beautiful example of morphogenesis. Because of the highly localized nature of the growth process, it is relatively amenable to analysis. Hence, it has attracted the attention of experimentalists and theorists alike, who over the years, have sought to elucidate the mechanisms underlying this form of development, the latter through explicit mathematical models. This review provides an overview of the modeling of tip-growing cells in general, and that of plant root hairs in particular, as it has developed during the last decades. Two main lines of modeling can be distinguished. In geometrical models, the focus is on the shape of the cells alone, while the aim of biomechanical models is to clarify the underlying physical mechanisms. So far, only a few attempts have been made to combine these two approaches. Yet, the incorporation of the mechanical properties of the nascent cell wall and the forces exerted on it is very likely needed to fully understand and ultimately control tip growth. This synthesis would pave the way to fully predictive models and hence could also guide new experiments to verify them. We provide an outlook on possible routes towards this goal.


Cell Wall Root Hair Actin Filament Cell Boundary Fungal Hypha 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Bartnicki-García (2002) Hyphal tip growth: outstanding questions. In: Osiewacz HD (ed) Molecular biology of fungal development. Dekker, New York pp 29–58Google Scholar
  2. Bartnicki-García S, Hergert F, Gierz G (1989) Computer simulation of fungal morphogenesis and the mathematical basis for hyphal (tip) growth. Protoplasma 153:46–57CrossRefGoogle Scholar
  3. Bartnicki-García S, Bracker CE, Gierz G, López-Franco R, Lu H (2000) Mapping the growth of fungal hyphae: orthogonal cell wall expansion during tip growth and the role of turgor. Biophys J 79:2382–2390PubMedCrossRefGoogle Scholar
  4. Bernal R, Rojas ER, Dumais J (2007) The mechanics of tip growth morphogenesis: what we have learned from rubber balloons. J Mech Mat Struct 2 (6):1157–1168CrossRefGoogle Scholar
  5. Bingham EC (1922) Fluidity and plasticity. Mc-Graw-Hill, New YorkGoogle Scholar
  6. Cosgrove DJ (1998) Cell wall loosening by expansins. Plant Physiol 118:333–339PubMedCrossRefGoogle Scholar
  7. Cosgrove DJ (2000) Loosening of plant cell walls by expansins. Nature 407:321–326PubMedCrossRefGoogle Scholar
  8. de Ruijter NCA, Rook MB, Bisseling T, Emons AMC (1998) Lipochito-oligosaccharides re- initiate root hair tip growth in Vicia sativa with high calcium and spectrin-like antigen at the tip. Plant J 13 (3):341–350CrossRefGoogle Scholar
  9. de Ruijter NCA, Esseling JJ, Emons AMC (2000) “The roles of calcium and the actin cytoskeleton in regulation of root hair tip growth by rhizobial signal molecules”. In: Geitmann A (ed) Cell biology of plant and fungal tip growth. IOS Press, Amsterdam, p 161Google Scholar
  10. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon, OxfordGoogle Scholar
  11. Dumais J, Long SR, Shaw SL (2004) The mechanics of surface expansion anisotropy in Medicago truncatula root hairs. Plant Physiol 136:3266–3275PubMedCrossRefGoogle Scholar
  12. Dumais J, Shaw SL, Steele CR, Long SR, Ray PM (2006) An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth. Int J Dev Biol 50:209–222PubMedCrossRefGoogle Scholar
  13. Emons AMC (1989) Helicoidal microfibril deposition in a tip growing-cell and microtubule alignment during tip morphogenesis: a dry-cleaving and freeze-substitution study. Can J Bot 67:2401–2408Google Scholar
  14. Emons AMC, Mulder BM (1998) The making of architecture of the plant cell wall: How cells exploit geometry. Proc Natl Acad Sci USA 95 (12):7215–7219PubMedCrossRefGoogle Scholar
  15. Esseling JJ, Lhuissier FGP, Emons AMC (2003) Nod factor induced root hair curling: Continuous polar growth towards the point of nod factor application. Plant Phys 132:1982–1988CrossRefGoogle Scholar
  16. Esseling JJ, Lhuissier FGP, Emons AMC (2004) A nonsymbiotic root hair tip growth phenotype in NORK-mutated legumes: implications for nodulation factor-induced signaling and formation of a multifaceted root hair pocket for bacteria. Plant Cell 16 (4):933–944PubMedCrossRefGoogle Scholar
  17. Evans EA, Skalak R (1980) Mechanics and thermodynamics of biomembranes. CRC Press, Boca RatonGoogle Scholar
  18. Foreman J, Dolan L (2001) Root hairs as a model system for studying plant cell growth. Ann Bot 88: 1–7CrossRefGoogle Scholar
  19. Gierz G, Bartnicki-García S (2001) A three-dimensional model of fungal morphogenesis based on the vesicle supply center concept. J Theor Biol 208:151–164PubMedCrossRefGoogle Scholar
  20. Gollnick F, Meyer R, Stockem W (1991) Visualization and measurement of calcium transients in Amoeba proteus by fura-2 fluorescence. Eur J Cell Biol 55:262–271PubMedGoogle Scholar
  21. Goodwin BC, Trainor LEH (1985) Tip and whorl morphogenesis in Acetabularia by calcium- regulated strain fields. J Theor Biol 117:79–106CrossRefGoogle Scholar
  22. Goriely A, Tabor M (2003a) Biomechanical models of hyphal growth in Actinomycetes. J Theor Biol 222:211–218PubMedCrossRefGoogle Scholar
  23. Goriely A, Tabor M (2003b) “Self-similar tip growth in filamentary organisms.” Phys Rev Lett 90 (10):108101:1– 108101:4CrossRefGoogle Scholar
  24. Goriely A, Károlyi G, Tabor M (2005) Growth induced curve dynamics for filamentary micro-organisms. J Math Biol 51:355–366PubMedCrossRefGoogle Scholar
  25. Green PB, Erickson RO, Richmond PA (1970) On the physical basis of cell morphogenesis. Ann NY Acad Sci 175(Article 2):712–731CrossRefGoogle Scholar
  26. Harold FM (1997) How hyphae grow: morphogenesis explained? Protoplasma 197:137–147CrossRefGoogle Scholar
  27. Heath IB, van Rensburg EJJ (1996) Critical evaluation of the VSC model for tip growth. Mycoscience 37:71–80CrossRefGoogle Scholar
  28. Hejnowicz Z, Heinemann B, Sievers A (1977) Tip growth: patterns of growth rate and stress in the Chara rhizoid. J Plant Phys 81:409–424Google Scholar
  29. Hill R (1950) The mathematical theory of plasticity. Oxford University Press, OxfordGoogle Scholar
  30. Hyde GJ, Heath IB (1997) Ca2+ gradients in hyphae and branches of Saprolegnia ferax. Exp Mycol 13:1–12Google Scholar
  31. Ketelaar T, Faivre-Moskalenko C, Esseling JJ, de Ruijter NCA, Grierson CS, Dogterom M, Emons AMC (2002) Positioning of nuclei in Arabidopsis root hairs: An actin-regulated process of tip growth. Plant Cell 14(11):2941–2955PubMedCrossRefGoogle Scholar
  32. Ketelaar T, Galway M, Mulder BM, Emons AMC (in press) A study into exocytosis and endocytosis rates in Arabidopsis root hairs and pollen tubes. J MicroscGoogle Scholar
  33. Koch AL (1982) The shape of the hyphal tips of fungi. J Gen Microbiol 128: 947Google Scholar
  34. Koch AL (1994) The problem of hyphal growth in streptomycetes and fungi. J Theor Biol 171:137–150CrossRefGoogle Scholar
  35. 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 Soft Matter 16(1):5–16PubMedCrossRefGoogle Scholar
  36. Landau LD, Lifschitz EM (1986) “heory of elasticity Pergamon, New YorkGoogle Scholar
  37. Lockhart JA (1965) An analysis of irreversible plant cell elongation. Bot Rev 6:515–574Google Scholar
  38. Miller DD, de Ruijter NCA, Bisseling T, Emons AMC (1999) The role of actin in root hair morphogenesis: studies with lipochito-oligosaccharide as a growth stimulator and cytochalasin as an actin perturbing drug. Plant J 17:141–154CrossRefGoogle Scholar
  39. Miller DJ, Leferink-ten Klooster HB, Emons AMC (2000) Lipochito-oligosaccharide nodulation factors stimulate cytoplasmic polarity with longidunal Endoplasmic Reticulum and vesicles at the tip in vetch root hairs. MPMI 13(12):1385–1390PubMedCrossRefGoogle Scholar
  40. Money NP (1997) Wishful thinking of turgor revisited: the mechanics of fungal growth. Fungal Genet Biol 21:173–187CrossRefGoogle Scholar
  41. Money NP (2001) Functions and evolutionary origin of hyphal turgor pressure. In: Geitmann A (ed) Cell biology of plant and fungal tip growth. IOS Press, Amsterdam, p 161Google Scholar
  42. Money NP, Harold FM (1992)“Extension growth of the water mold Achlya: interplay of turgor and wall strength. Proc Natl Acad Sci USA 89:4245–4249PubMedCrossRefGoogle Scholar
  43. Mulder BM, Emons AMC (2001) A dynamic model for plant cell wall architecture formation. J Mat Biol 42:261–289CrossRefGoogle Scholar
  44. Pelcé P (2004) New visions of form and growth. Fingered, growth, dendrites and flames. Oxford University Press, OxfordGoogle Scholar
  45. Pelcé P, Pocheau A (1992) Geometrical approach to the morphogenesis of unicellular algae. J Theor Biol 156:197–214CrossRefGoogle Scholar
  46. Popper KR (1935) Logik der Forschung. Springer, Berlin Heidelberg New YorkGoogle Scholar
  47. Proseus TE, Boyer JS (2006) Periplasm turgor pressure controls wall deposition and assembly in growing Chara corallina cells. Ann Bot 98:93–105PubMedCrossRefGoogle Scholar
  48. Prager MW (1937) Mécanique des solides isotropes au delà du domaine élastique. Mem Sci Math 87:1–66Google Scholar
  49. Read ND, Allan WTG, Knight H, Knight MR, Malho R, Russel A, Shacklock PS, Trewavas A (1992) Imaging and measurement of cytosolic free calcium in plant and fungal cells. J Miscrosc 166:57–86Google Scholar
  50. Regalado CM (1998) Roles of calcium gradients in hyphal tip growth: a mathematical model. Microbiology 144:2771–2782PubMedCrossRefGoogle Scholar
  51. Reinhardt MO (1892) Das wachstum der pilzhyphen. Jahrb Wissenschaft Bot 23:479–566Google Scholar
  52. Roberson RW, Fuller MS (1988) Ultrastructural aspects of the hyphal tip of Sclerotium rolfsii preserved by freeze substitution. Protoplasma 146:143–149CrossRefGoogle Scholar
  53. Skalak R, Tozeren A, Zarda RP, Chien S (1973) Strain energy function of red blood cell membranes. Biophys J 13:245–264PubMedCrossRefGoogle Scholar
  54. Sieberer BJ, Ketelaar T, Esseling JJ, Emons AMC (2005a) Microtubules guide root hair tip growth. New Phytol 167 (3):711–719PubMedCrossRefGoogle Scholar
  55. Sieberer BJ, Timmers AC, Emons AMC (2005b) Nod factors alter the microtubule cytoskeleton in Medicago truncatula root hairs to allow root hair reorientation. Mol Plant Microbe Interact 18(11):1195–1204PubMedCrossRefGoogle Scholar
  56. Sietsma JH, Wessels JGH (1990) The occurrence of glucosaminoglycan in the wall of Schizosaccharomyces pombe. J Gen Microbiol 136 (11):2261–2265PubMedGoogle Scholar
  57. Sietsma JH, Wösten HAB, Wessels JGH (1995) Cell-wall growth and protein secretion in fungi. Can J Bot 73:388–395CrossRefGoogle Scholar
  58. Sugden KEP, Evans MR, Poon WCK, Read ND (2007):Model of hyphal tip growth involving microtubule-based transport. Phys Rev E 75:031909:1– 031909:5Google Scholar
  59. Sugimoto K, Williamson RE, Wasteneys GO (2000) New techniques enable comparative analysis of microtubule orientation, wall texture, and growth rate in intact roots of Arabidopsis. Plant Physiol 124(4):1493–1506PubMedCrossRefGoogle Scholar
  60. Surrey T, Nedelec F, Leibler S, Karsenti E (2001) Physical properties determining self-organization of motors and microtubules. Science 292 (5519):1167–1171PubMedCrossRefGoogle Scholar
  61. Taiz L (1994) Expansins: proteins that promote cell wall loosening in plants. Proc Natl Acad Sci USA 91 (16):7387–7389PubMedCrossRefGoogle Scholar
  62. Timmers ACJ, Vallotton P, Heym C, Menzel D (2007) Microtubule dynamics in root hairs of Medicago truncatula. Eur JCell Biol 86: 69–83CrossRefGoogle Scholar
  63. Tindemans SH, Kern N, Mulder BM (2006) The diffusive vesicle supply center model for tip growth in fungal hyphae. J Theor Biol 238 (4):937–948PubMedCrossRefGoogle Scholar
  64. Todd PH (1986) Intrinsic geometry of biological surface growth. Springer Lecture Notes in Biomathematics 67Google Scholar
  65. Van Batenburg FHD, Jonker R, Kijne JW (1986) Rhizobium induces marked root hair curling by redirection of tip growth: a computer simulation. Physiol Plant 66:476–480CrossRefGoogle Scholar
  66. Veytsman BA, Cosgrove DJ (1998) A model of cell wall expansion based on thermodynamics of polymer networks. Biophys J 75:2240–2250PubMedCrossRefGoogle Scholar
  67. Wymer C, Bibikova T, Gilroy S (1997) Calcium distributions in growing root hairs of Arabidopsis thaliana. Plant J 12:427–439PubMedCrossRefGoogle Scholar
  68. Yin HL, Zaner KS, Stossel TP (1980) Ca2+ control of actin gelation. Interaction of gelsolin with actin filaments and regulation of actin gelation. J Biol Chem 255: 9494–9500PubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. N. de Keijzer
    • 1
    Email author
  • A. M. C. Emons
  • B. M. Mulder
  1. 1.FOM Institute AMOLFAmsterdamThe Netherlands

Personalised recommendations