, Volume 153, Issue 1–2, pp 46–57 | Cite as

Computer simulation of fungal morphogenesis and the mathematical basis for hyphal (tip) growth

  • S. Bartnicki-Garcia
  • F. Hergert
  • G. Gierz


A novel mathematical model is proposed to explain how a tubular shape (e.g., a fungal hypha) is generated by a tip-growing cell. The model derived from a computer simulation of morphogenesis assumes that: i) the cell surface expands from materials discharged by wall-destined vesicles, ii) vesicles are released from a postulated vesicle supply center (VSC), iii) vesicles move from the VSC to the surface in any random direction. The position and movement of the VSC become the critical determinant of morphogenesis: a stationary VSC releases vesicles that reach the cell surface in about equal numbers in all directions, and the cell grows as a sphere. Any displacement of the VSC from its original central position distorts the spherical shape. A sustained linear displacement of the VSC generates the typical cylindroid shape of fungal hyphae. The model yields the equation
$$y = x\cot \frac{{V \cdot x}}{N}$$
which defines both the shape and size (diameter) of a hypha by two parameters, to which physiological significance can be ascribed:N, the amount of wall-destined vesicles released from the VSC per unit time;V, the rate of linear displacement of the VSC. There is a remarkable coincidence between the position of the VSC in the model and the position of the Spitzenkörper in real hyphae. The model affords a simple mechanism to generate a tubular shape from a tip-growing cell; it obviates the need to postulate specific targets for vesicles on the apical cell surface or to invoke gradients in the properties of the apical wall. Other common morphogenetic transitions of fungi and other organisms can be simulated with the same basic model.


Computer simulation Fungal hyphae Mathematical model Morphogenesis Polarity Spitzenkörper Tip growth Vesicles Vesicle supply center Yeast cells 



vesicle supply center


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams AEM, Pringle JR (1984) Relationship of actin and tubulin distribution to bud growth in wild-type and morphogenetic-mutantSaccharomyces cerevisiae. J Cell Biol 98: 934–945Google Scholar
  2. Anderson JM, Soll DR (1986) Differences in actin localization during bud and hypha formation in the yeastCandida albicans. J Gen Microbiol 132: 2035–2047Google Scholar
  3. Barstow WE, Lovett JS (1974) Apical vesicles and microtubules in rhizoids ofBlastocladiella emersonii: effects of actinomycin D and cycloheximide on development during germination. Protoplasma 82: 103–117Google Scholar
  4. Bartnicki-Garcia S (1973) Fundamental aspects of hyphal morphogensis. In: Ashworth JM, Smith JE (eds) Microbial differentiation. Cambridge University Press, Cambridge, UK, pp 245–267Google Scholar
  5. — (1981) Cell wall construction during spore germination in Phycomycetes. In: Turian G, Hohl HR (eds) The fungal spore: morphogenetic controls. Academic Press, London, pp 533–556Google Scholar
  6. — (1987) Chitosomes and chitin biogenesis. Food Hydrocolloids 1: 353–358Google Scholar
  7. —, Lippman E (1969) Fungal morphogenesis: cell wall construction inMucor rouxii. Science 165: 302–304Google Scholar
  8. — (1977) Polarization of cell wall synthesis during spore germination ofMucor rouxii. Exp Mycol 1: 230–240Google Scholar
  9. —, Hergert F, Gierz G (1989) A novel computer model for generating cell shape: application to fungal morphogenesis. In: Kuhn P et al (eds) Biochemistry of cell walls and membranes of fungi. Springer, Berlin Heidelberg New York Tokyo Hong Kong pp 43–60Google Scholar
  10. Betina V, Micekova D, Nemec P (1972) Antimicrobial properties of cytochalasins and their alteration of fungal morphology. J Gen Microbiol 71: 343–349Google Scholar
  11. Brunswik H (1924) Untersuchungen über Geschlechts- und Kernverhältnisse bei der HymenomyzetengattungCoprinus. In: Goebel K (eds) Botanische Abhandlungen. Gustav Fischer, Jena, pp 1–152Google Scholar
  12. Castle ES (1953) Problems of oriented growth and structure inPhycomyces. Q Rev Biol 28: 364–372Google Scholar
  13. — (1958) The topography of tip growth in a plant cell. J Gen Physiol 41: 913–926Google Scholar
  14. Collinge AJ, Trinci APJ (1974) Hyphal tips of wild type and spreading colonial mutants ofNeurospora crassa. Arch Microbiol 99: 353–368Google Scholar
  15. da Riva Ricci D, Kendrick B (1972) Computer modelling of hyphal tip growth in fungi. Can J Bot 50: 2455–2462Google Scholar
  16. Girbardt M (1957) Der Spitzenkörper vonPolystictus versicolor. Planta 50: 47–59Google Scholar
  17. — (1969) Die Ultrastruktur der Apikairegion von Pilzhyphen. Protoplasma 67: 413–441Google Scholar
  18. Gooday GW (1971) An autoradiographic study of hyphal growth of some fungi. J Gen Microbiol 67: 125–133Google Scholar
  19. —, Trinci APJ (1980) Wall structure and biosynthesis in fungi. In: Gooday GW, Lloyd D, Trinci APJ (eds) The eukaryotic microbial cell. 30th Symposium of the Society for General Microbiology. Cambridge University Press, Cambridge, UK, pp 207–251Google Scholar
  20. Green PB (1965) Pathways of cellular morphogenesis: a diversity inNitella. J Cell Biol 27: 343–363Google Scholar
  21. — (1969) Cell morphogenesis. Annu Rev Plant Physiol 20: 365–394Google Scholar
  22. —, King A (1966) A mechanism for the origin of specifically oriented textures in development with special reference toNitella wall texture. Aust J Biol Sci 19: 421–437Google Scholar
  23. Grove SN, Bracker CE (1970) Protoplasmic organization of hyphal tips among fungi: vesicles and Spitzenkörper. J Bacteriol 104: 989–1009Google Scholar
  24. —, Sweigard JA (1980) Cytochalasin A inhibits spore germination and hyphal tip growth inGilbertella persicaria. Exp Mycol 4: 239–250Google Scholar
  25. Heath IB (1987) Preservation of a labile cortical array of actin filaments in growing hyphal tips of the fungusSaprolegnia ferax. Eur J Cell Biol 44: 10–16Google Scholar
  26. —, Gay JL, Greenwood AD (1971) Cell wall formation in the saprolegniales: cytoplasmic vesicles underlying developing walls. J Gen Microbiol 65: 225–232Google Scholar
  27. Hoch HC, Staples RC (1985) The microtubule cytoskeleton in hyphae ofUromyces phaseoli germlings: its relationship to the region of nucleation and to the F-actin cytoskeleton. Protoplasma 124: 112–122Google Scholar
  28. Howard RJ (1981) Ultrastructural analysis of hyphal tip cell growth in fungi: Spitzenkörper, cytoskeleton and endomembranes after freeze-substitution. J Cell Sci 48: 89–103Google Scholar
  29. —, Aist JR (1977) Effects of MBC on hyphal tip organization, growth and mitosis ofFusarium acuminatum, and their antagonism by D2O. Protoplasma 92: 195–210Google Scholar
  30. — — (1979) Hyphal tip cell ultrastructure of the fungusFusarium: improved preservation by freeze substitution. J Ultrastruct Res 66: 224–234Google Scholar
  31. Jaffe LF (1968) Localization in the developingFucus egg and the general role of localizing currents. Adv Morphogenesis 7: 295–328Google Scholar
  32. Koch AL (1982) The shape of the hyphal tips of fungi. J Gen Microbiol 128: 947–951Google Scholar
  33. McClure WK, Park D, Robinson PM (1968) Apical organization in the somatic hyphae of fungi. J Gen Microbiol 50: 177–182Google Scholar
  34. McGillviray AM, Gow NAR (1987) The transhyphal electrical current ofNeurospora crassa is carried principally by protons. J Gen Microbiol 133: 2875–2881Google Scholar
  35. McKerracher LJ, Heath IB (1987) Cytoplasmic migration and intracellular organelle movements during tip growth of fungal hyphae. Exp Mycol 11: 79–100Google Scholar
  36. Prosser JI (1979) Mathematical modelling of mycelial growth. In: Burnett JH, Trinci APJ (eds) Fungal walls and hyphal growth. Cambridge University Press, Cambridge, UK, pp 359–384Google Scholar
  37. —, Trinci APJ (1979) A model for hyphal growth and branching. J Gen Microbiol 111: 153–164Google Scholar
  38. Quatrano RS, Griffing LR, Huber-Walchli V, Doubet RS (1985) Cytological and biochemical requirements for the establishment of a polar cell. J Cell Sci [Suppl S 2]: 129–141Google Scholar
  39. Reinhardt MO (1892) Das Wachstum der Pilzhyphen. Jahrb Wissenschaft Bot 23: 479–566Google Scholar
  40. Roberson RW, Fuller MS (1988) Ultrastructural aspects of the hyphal tip ofSclerotium rolfsii preserved by freeze substitution. Protoplasma 146: 143–149Google Scholar
  41. Robertson NF (1965) Presidential address: the fungal hypha. Trans Br Mycol Soc 48: 1–8Google Scholar
  42. Runeberg P, Raudaskoski M (1986) Cytoskeletal elements in the hyphae of the homobasidiomyceteSchizophyllum commune visualized with indirect immunofluorescence and NBD phallacidin. Eur J Cell Biol 41: 25–32Google Scholar
  43. Saunders PT, Trinci APJ (1979) Determination of tip shape in fungal hyphae. J Gen Microbiol 110: 469–473Google Scholar
  44. Schreurs WJA, Harold FM (1988) Transcellular proton current inAchlya bisexualis hyphae: relationship to polarized growth. Proc Natl Acad Sci USA 85: 1534–1538Google Scholar
  45. Steer WM, Steer JM (1989) Pollen tube tip growth. New Phytol 111: 323–358Google Scholar
  46. Trinci APJ, Saunders PT (1977) Tip growth of fungal hyphae. J Gen Microbiol 103: 243–248Google Scholar
  47. Tucker BE, Hoch HC, Staples RC (1986) The involvement of F actin inUromyces cell differentiation. The effects of cytochalasin E and phalloidin. Protoplasma 135: 88–101Google Scholar
  48. Wessels JGH (1986) Cell wall synthesis in apical hyphal growth. Intern Rev Cytology 104: 37–79Google Scholar
  49. —, Sietsma JH (1981) Cell wall synthesis and hyphal morphogenesis: a new model for apical growth. In: Robinson DG, Quader H (eds) Cell walls '81. Wissenschaftliche Verlagsgesellschaft, Stuttgart, pp 135–142Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • S. Bartnicki-Garcia
    • 1
  • F. Hergert
    • 2
  • G. Gierz
    • 2
  1. 1.Department of Plant PathologyUniversity of CaliforniaRiverside
  2. 2.Department of Mathematics and Computer ScienceUniversity of CaliforniaRiverside

Personalised recommendations