Abstract
Fungal hyphae extend at the apex, by the localized deposition of new plasma membrane and cell wall. We owe this insight to Max Otto Reinhardt (1854–1935), whose classic paper on the growth of fungal hyphae was published just over a century ago (Reinhardt 1892). Ever since then, a small but select company of microbiologists has grappled with the next question: How does apical growth come about? How does a hypha arrange its anatomy and functions so that new envelope is deposited exclusively at the apex? How does the characteristic hyphal morphology, a tube with tapered tip, maintain itself through space and time? How do branches, i.e., new apices, arise? Let us be clear from the outset that this is not primarily a problem in biochemistry, let alone molecular biology. Instead, the issue falls within the purview of physiology, the study of complex systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albritton NL, Meyer T, Stryer L (1992) Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 258:1812–1815
Armbruster BL, Weisenseel MH (1983) Ionic currents traverse growing hyphae and sporangia of the mycelial water mold Achlya debaryana. Protoplasma 115:65–69
Bartnicki-Garcia S (1990) Role of vesicles in apical growth and a new mathematical model of hyphal morphogenesis. In: Heath IB (ed) Tip growth in plant and fungal cells. Academic Press, San Diego, CA, pp 211–232
Bedlack RS Jr, Wei M-D, Loew LM (1992) Localized membrane depolarizations and localized calcium influx during electric field-guided neurite growth. Neuron 9:393–403
Berti A, Gradmann D, Slayman CL (1992) Calcium and voltage-dependent ion channels in Saccharomyces cerevisae. Philos Trans R Soc B 338:63–72
Blatt MR, Slayman CL (1987) Role of “active” potassium transport in the regulation of cytoplasmic pH by non-animal cells. Proc Natl Acad Sci USA 84:2737–2741
Blatt MR, Rodriguez-Navarro A, Slayman CL (1987) Potassium-proton symport in Neurospora: kinetic control by pH and membrane potential. J Membr Biol 98:169–187
Bowman BJ, Bowman EJ (1986) H+-ATPases from mitochondria, plasma membranes, and vacuoles of fungal cells. J Membr Biol 94:83–97
Bowman BJ, Blasco F, Slayman CW (1981) Purification and characterization of the plasma membrane ATPase of Neurospora crassa. J Biol Chem 256:12343–12349
Brawley SH, Robinson KR (1985) Cytochalasin treatment disrupts the endogenous currents associated with cell polarization in fucoid zygotes. J Cell Biol 100:1173–1184
Bray D, White JG (1988) Cortical flow in animal cells. Science 239:883–888
Brockerhoff SE, Davis TN (1992) Calmodulin concentrates at regions of cell growth in Saccharomyces cerevisiae. J Cell Biol 118:619–629
Bryant G, Wolfe J (1987) Electromechanical stresses produced in the plasma membranes of suspended cells applied electric fields. J Membr Biol 96:129–139
Caldwell JH, Van Brunt J, Harold FM (1986) Calcium-dependent anion channel in the water mold, Blastocladiella emersonii. J Membr Biol 89:85–97
Carafoli E (1987) Intracellular calcium homeostasis. Annu Rev Biochem 56:345–433
Cho CW, Harold FM, Schreurs WJA (1991) Electric and ionic dimensions of apical growth in Achlya hyphae. Exp Mycol 15:34–43
Conrad PA, Hepler PK (1988) The effect of 1,4-dihydropyridines on the initiation and development of gametophore buds in the moss Funaria. Plant Physiol 86:684–687
Cooper MS, Schliwa M (1986) Motility of cultured fish epidermal cells in the presence and absence of direct current electric fields. J Cell Biol 102:1384–1399
Cornelius G, Nakashima H (1987) Vacuoles play a decisive role in calcium homeostasis in Neurospora crassa. J Gen Microbiol 133:2341–2347
Crane FL, Sun IL, Clark MG, Grebing C, Lö H (1985) Transplasma-membrane redox systems in growth and development. Biochim Biophys Acta 811:233–264
Crombie T, Gow NAR, Gooday GW (1990) Influence of applied electric fields on yeast and hyphal tip growth of Candida albicans. J Gen Microbiol 136:311–317
Davenport RW, Kater SR (1992) Local increases in intracellular calcium elicit local filopodial responses in Helisoma neuronal growth cones. Neuron 9:405–416
Davies JM, Brownlee C, Jennings DH (1990) Measurement of intracellular pH in fungal hyphae using BCECF and digital imaging microscopy. J Cell Sci 96:731–736
Davies JM, Poole RJ, Rea PA, Sanders D (1992) Potassium transport into plant vacuoles energized directly by a proton-pumping inorganic pyrophosphatase. Proc Natl Acad Sci USA 89:11701–11705
DeSilva LR, Youatt J, Gooday GW, Gow NAR (1992) Inwardly directed ionic currents of Allomyces macrogynus and other water moulds indicate sites of proton-driven nutrient transport but are incidental to tip growth. Mycol Res 11:925–931
de Vries SD, Wessels GJH (1982) Polarized outgrowth of hyphae by constant electrical fields during reversion of Schizophyllum commune protoplasts. Exp Mycol 6: 95–98
Dicker W, Turian G (1990) Calcium deficiencies and apical hyperbranching in wild-type and “frost” and “spray” morphological mutants of Neurospora crassa. J Gen Microbiol 136:1413–1420
Eckert R (1972) Bioelectric control of ciliary activity. Science 176:473–481
Frankel J (1989) Pattern formation: ciliate studies and models. Oxford University Press, New York
Frankel J (1992) Positional information in cells and organisms. Trends Cell Biol 2:256–260
Fulton AB (1980) Calcium ions, electrical currents and the choreography of (some) eucaryotic cells. Cell 22: 5–6
Galpin FJ, Jennings DH (1975) Histochemical study of the hyphae and the distribution of adenosine triphosphatase in Dendryphiella salina. Trans Br Mycol Soc 65:477–483
Garrill A, Lew RR, Heath IB (1992) Stretch-activated Ca2+ and Ca2+-activiated K+ channels in the hyphal tip plasma membrane of the oomycete Saprolegnia ferax. J Cell Sci 101:721–730
Garrill A, Jackson SA, Lew RR, Heath IB (1993) Ion channel activity and tip growth: tip-localized stretch-activated channels generate an essential Ca2+ gradient in the oomycete Saprolegnia ferax. Eur J Cell Biol 60:358–365
Geiser JR, van Tuinen D, Brockerhoff SE, Neff MM, Davis TN (1991) Can calmodulin function without binding calcium? Cell 65:949–959
Gooday GW (1983) The hyphal tip. In: Smith JE (ed) Fungal differentiation. Marcel Dekker, New York, pp 315–356
Gow NAR (1984) Transhyphal electrical currents in fungi. J Gen Microbiol 130:3313–3318
Gow NAR (1989) Circulating ionic currents in microorganisms. Adv Microb Physiol 30:89–123
Gow NAR, Gooday GW (1987) Effects of antheridiol on growth, branching and electrical currents of hyphae of Achlya bisexualis. J Gen Microbiol 133:3531–3535
Gow NAR, Kropf DL, Harold FM (1984) Growing hyphae of Acylya bisexualis generate a longitudinal pH gradient in the surrounding medium. J Gen Microbiol 130: 2967–2974
Gradmann D, Hansen UP, Long WS, Slayman CL, Warncke J (1978) Current-voltage relationships for the plasma membrane and its principal electrogenic pump in Neurospora crassa. J Membr Biol 39:333–367
Gustin MC, Martinac B, Saimi Y, Culbertson MR, Kung C (1986) Ionic channels in yeast. Science 233:1195–1197
Gustin MC, Zhou X-L, Martinac B, Kung C (1988) A mechanosensitive ion channel in the yeast plasma membrane. Science 242:762–765
Harold FM (1977) Ion currents and physiological functions in microorganisms. Annu Rev Microbiol 31:181–203
Harold FM (1986) The Vital Force: A Study of Bioener-getics. Freeman, New York
Harold FM (1990) To shape a cell: an inquiry into the causes of morphogenesis of microorganisms. Microbiol Rev 54:381–431
Harold FM (1991) Biochemical topology. From vectorial metabolism to morphogenesis. Biosci Rep 11:347–382
Harold FM, Caldwell JH (1990) Tips and currents: electro-biology of apical growth. In: Heath IB (ed) Tip growth in plant and fungal cells. Academic Press, San Diego, CA, pp 59–90
Harold RL, Harold FM (1986) Ionophores and cytochalasins modulate branching in Achlya bisexualis. J Gen Microbiol 132:213–219
Hausser I, Herth W, Reiss HD (1984) Calmodulin in tip-growing plant cells, visualized by fluorescing calmodulin-binding phenothiazines. Planta 162:33–39
Heath IB (1990) The roles of actin in tip growth of fungi. Int Rev Cytol 123:95–127
Herth W, Reiss H-D, Hartmann E (1990) Role of calcium ions in tip growth of pollen tubes and moss protonema cells. In: Heath IB (ed) Tip growth in plant and fungal cells. Academic Press, San Diego, CA, pp 91–118
Hille B (1992) Ionic channels of excitable membranes. 2nd edn. Sinauer, Sunderland, MA
Iida H, Yagawa Y, Anraku Y (1990) Essential role for induced Ca2+ influx followed by [Ca2+]i rise in maintaining viability of yeast cells late in the mating pheromone response pathway. J Biol Chem 265:13391–13399
Jackson SL, Heath IB (1989) Effects of exogenous calcium ions on tip growth, intracellular Ca2+ concentration and actin arrays in hyphae of the fungus Saprolegnia ferax. Exp Mycol 13:1–12
Jackson SL, Heath IB (1993) Roles of calcium ions in hyphal tip growth. Microbiol Rev 57:367–382
Jaffe LF (1968) Localization in the developing Fucus egg and the general role of localizing currents. Adv Morphog 7:295–328
Jaffe LF (1981) The role of ionic currents in establishing developmental pattern. Philos Trans R Soc Lond B 295:553–566
Jaffe LF, Nuccitelli R (1974) An ultrasensitive vibrating probe for measuring steady extracellular currents. J Cell Biol 63:614–628
Jaffe LF, Nuccitelli R (1977) Electrical controls of development. Annu Rev Biophys Bioeng 6:445–476
Jaffe LF, Robinson KR, Nuccitelli R (1974) Local cation entry and self-electrophoresis as an intracellular localization mechanism. Ann NY Acad Sci 238:372–389
Kauss H (1987) Some aspects of calcium-dependent regulation in plant metabolism. Annu Rev Plant Physiol 38:47–72
Klionsky DJ, Herman PK, Emr SD (1990) The fungal vacuole: composition, function and biogenesis. Microbiol Rev 54:266–292
Kovac L (1985) Calcium and Saccharomyces cerevisiae. Biochim Biophys Acta 840:317–323
Kropf DL (1986) Electrophysiological properties of Achlya hyphae: ionic currents studied by intracellular recording. J Cell Biol 102:1209–1216
Kropf DL, Harold FM (1982) Selective transport of nutrients via the rhizoids of the water mold Blastocladiella emersonii. J Bacteriol 151:429–437
Kropf DL, Lupa MDA, Caldwell JH, Harold FM (1983) Cell polarity: endogenous ion currents precede and predict branching in the water mold Achlya. Science 220:1385–1387
Kropf DL, Caldwell JH, Gow NAR, Harold FM (1984) Transcellular ion currents in the water mold Achlya: amino acid/proton symport as a mechanism of current entry. J Cell Biol 99:486–496
Kühtreiber WM, Jaffe LF (1990) Detection of extracellular calcium gradients with a calcium-specific vibrating electrode. J Cell Biol 110:1565–1573
Lew DJ, Simon SM (1991) Characterization of constitutive exocytosis in the yeast Saccharomyces cerevisiae. J Membr Biol 123:261–268
Lu KP, Osmani SA, Osmani AH, Means AR (1993) Essential roles for calcium and calmodulin in G2/M progression in Aspergillus nidulans. J Cell Biol 121: 621–630
Lund E (1947) Bioelectric fields and growth. University of Texas Press, Austin
Magalhaes BP, Wayne R, Humber RA, Shields EJ, Roberts DW (1991) Calcium-regulated appressorium formation of the entomopathogenic fungus Zoophthora radicans. Protoplasma 160:77–88
McCaig CD (1989) Studies on the mechanism of embryonic frog nerve orientation in a small applied electric field. J Cell Sci 93:723–730
McCaig CD (1990) Nerve branching is induced and oriented by a small applied electric field. J Cell Sci 95:605–615
McGillivray AM, Gow NAR (1986) Applied electrical fields polarize the growth of mycelial fungi. J Gen Microbiol 131:751–756
McGillivray AM, Gow NAR (1987) The transhyphal electric current of Neurospora crassa is carried principally by protons. J Gen Microbiol 133:2875–2881
McKerracher LJ, Heath IB (1987) Cytoplasmic migration and intracellular organelle movements during tip growth of fungal hyphae. Exp Mycol 11:79–100
McLaughlin S, Poo M-M (1981) The role of electro-osmosis in the electric field-induced movement of charged macromolecules on the surfaces of cells. Biophys J 34:85–93
Miller AJ, Vogg G, Sanders D (1990) Cytosolic calcium homeostasis in fungi: Role of plasma membrane tran sport and intracellular sequestration of calcium. Proc Natl Acad Sci 87:9348–9352
Miller DD, Callaham DA, Gross DJ, Hepler PK (1992) Free Ca2+ gradient in growing pollen tubes of Lilium. J Cell Sci 101:7–12
Mitchell P (1961) Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism. Nature 191:144–148
Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Biol Rev Camb Philos Soc 41:445–502
Mitchell P (1979) Keilin’s respiratory chain concept and its chemiosmotic consequences. Science 206:1148–1159
Möller IM, Lin W (1986) Membrane-bound NADPH dehydrogenases in higher plant cells. Annu Rev Plant Physiol 37:309–334
Money NP, Harold FM (1993) Two water molds can grow without measurable turgor pressure. Planta 190:426–430
Nicholls DG, Ferguson SJ (1992) Bioenergetics 2. Academic Press, San Diego
Nuccitelli R (1983) Transcellular ion currents: signals and effectors of cell polarity. Mod Cell Biol 2:451–581
Nuccitelli R (1988) Ionic currents in morphogenesis. Experientia 44:657–666
Obermeyer G, Weisenseel MH (1991) Calcium channel blocker and calmodulin antagonists affect the gradient of free calcium ions in lily pollen tubes. Eur J Cell Biol 56:319–327
Obermeyer G, Lützelschwab M, Heumann H-G, Weisenseel MH (1992) Immunolocalization of H+- ATPase in the plasma membrane of pollen grams and pollen tubes of Lilium longiflorum. Protoplasma 171: 55–63
Okazaki Y, Tazawa M (1990) Calcium ion and turgor regulation in plant cells. J Membr Biol 114:189–194
Oliveira L (1990) The effect of organic calcium channel modulators on the germination of Vaucheria longicaulis aplanospores. Protoplasma 158:182–190
Oliveira L (1992) Regulation of aplanospore germination in Vaucheria: time-dependent responses to calcium modulators. Planta 188:279–288
Onuma EK, Hui S-K (1988) Electric field-directed shape changes, displacement, and cytoskeletal reorganizations are calcium dependent. J Cell Biol 106:2067–2075
Pall ML, Trevillyan JM, Hinman N (1981) Deficient cyclic adenosine 3′, 5′ monophosphate control in mutants of two genes of Neurospora crassa. Mol Cell Biol 1:1–8
Perlin DS, Kasamo K, Brooker RJ, Slayman CW (1984) Electrogenic H+ translocation by the plasma membrane ATPase of Neurospora. J Biol Chem 259:7884–7892
Picton JM, Steer MW (1982) A model for the mechanism of tip extension in pollen tubes. J Theor Biol 98:15–20
Pietrobon D, Di Virgilio F, Puzzan T (1990) Structural and functional aspects of calcium homeostasis in eukaryotic cells. Eur J Biochem 193:599–622
Potapova TV, Aslanidi KB, Belozerskaya TA, Levina NN (1988) Transcellular ionic currents studied by intracellular potential recordings in Neurospora crassa hyphae. FEBS Lett 241:173–176
Rathore KS, Cork RJ, Robinson KR (1991) A cytoplasmic gradient of Ca2+ is correlated with the growth of lily pollen tubes. Dev Biol 148:612–619
Reinhardt MO (1892) Das Wachstum der Pilzhyphen: Ein Beitrag zur Kenntnis des Flächenwachstums vegetalischer Zellmembranen. Jahrb Wiss Bot 23:479–566
Reiss H-D, Herth W (1985) Nifedipine-sensitive calcium channels are involved in polar growth of lily pollen tubes. J Cell Sci 76:247–254
Reiss H-D, Herth W, Nobiling R (1985) Development of membrane- and calcium-gradients during pollen germination of Lilium longiflorum. Planta 163:84–90
Reissig JL, Kinney SG (1983) Calcium as a branching signal in Neurospora crassa. J Bacteriol 154:1397–1402
Robinson KR (1985) The responses of cells to electrical fields: a review. J Cell Biol 101:2023–2027
Robson GD, Wiebe MG, Trinci APJ (1991) Involvement of Ca2+ in the regulation of hyphal extension and branching in Fusarium graminearum A3/5. Exp Mycol 15:263–272
Rodriguez-Navarro A, Blatt MR, Slayman CL (1986) A potassium-proton symport in Neurospora crassa. J Gen Physiol 87:649–674
Roncal T, Ugalde UO, Irastorza A (1993) Calcium-induced conidiation in Penicillium cyclopium: calcium triggers cytosolic alkalinization at the hyphal tip. J Bacteriol 175:879–886
Sabie FT, Gadd GM (1989) Involvement of a Ca2+-calmodulin interaction in the yeast-mycelial (Y-M) transition of Candida albicans. Mycopathologia 108: 47–54
Sanders DL, Slayman CL (1982) Control of intracellular pH: Predominant role of oxidative metabolism, not proton transport, in the eukaryotic microorganism Neurospora. J Gen Physiol 80:377–402
Sanders D, Hansen U-P, Slayman CL (1981) Role of the plasma membrane proton pump in pH regulation in non-animal cells. Proc Natl Acad Sci USA 78:5903–5907
Sanders D, Slaymann CL, Pall ML (1983) Stoichiometry of H+/amino acid cotransport in Neurospora crassa revealed by current-voltage analysis. Biochim Biophys Acta 735:67–76
Schiefelbein JW, Shipley A, Rowse P (1992) Calcium influx at the tip of growing root-hair cells of Arabidopsis thaliana. Planta 187:455–459
Schmid J, Harold FM (1988) Dual roles for calcium ions in apical growth of Neurospora crassa. J Gen Microbiol 134:2623–2631
Schnepf E (1986) Cellular polarity. Annu Rev Plant Physiol 37:23–47
Schreurs WJA, Harold FM (1988) Transcellular proton current in Achlya bisexualis hyphae: relationship to polarized growth. Proc Natl Acad Sci USA 85:1534–1538
Schreurs WJA, Harold RL, Harold FM (1989) Chemotropism and branching as alternative responses of Achlya bisexualis to amino acids. J Gen Microbiol 135:2519–2528
Serrano R (1989) Structure and function of plasma membrane ATPase. Annu Rev Plant Physiol Plant Mol Biol 40:61–94
Skulachev VP (1988) Membrane bioenergetics. Springer, Berlin Heidelberg New York
Slayman CL (1965a) Electrical properties of Neurospora crassa: effects of external cations on the intracellular potential. J Gen Physiol 49:69–92
Slayman CL (1965b) Electrical properties of Neurospora crassa: respiration and the intracellular potential. J Gen Physiol 49:93–116
Slayman CL (1970) Movement of ions and electrogenesis in microorganisms. Am Zool 10:377–392
Slayman CL (1980) Transport control phenomena in Neurospora. In: Spanswick RM, Lucas WJ, Dainty J (eds) Plant membrane transport: current conceptual issues. Elsevier-North Holland, Amsterdam, pp 179–190
Slayman CL (1987) The plasma membrane ATPase of Neurospora: a proton-pumping electroenzyme. J Bioenerg Biomembr 19:1–20
Slayman CL, Sanders D (1985) Steady-state kinetic analysis of an electroenzyme. Biochem Soc Symp 50:11–29
Slayman CL, Slayman CW (1962) Measurement of membrane potential in Neurospora. Science 136:876–877
Slayman CL, Slayman CW (1974) Depolarization of the plasma membrane of Neurospora crassa during active transport of glucose. Proc Natl Acad Sci USA 71: 1935–1939
Slayman CL, Long WS, Lu C Y-H (1973) The relationship between ATP and an electrogenic pump in the plasma membrane of Neurospora crassa. J Membr Biol 14: 305–338
Steer MW, Steer JM (1989) Pollen tube tip growth. New Phytol 111:325–358
Stollberg J, Fraser SE (1988) Acetylcholine receptors and Concanavaline A-binding sites on cultured Xenopus muscle cells: electrophoresis, diffusion and aggregation. J Cell Biol 107:1397–1408
Stossel TP (1993) On the crawling of animal cells. Science 260:1086–1094
Stump RF, Robinson KR, Harold RL, Harold FM (1980) Endogenous electric currents in the water mold Blasto-cladiella emersonii during growth and sporulation. Proc Natl Acad Sci USA 77:6673–6677
Sun GH, Ohya Y, Anraku Y (1992) Yeast calmodulin localizes to sites of cell growth. Protoplasma 166:110–112
Suryanarayana K, des S Thomas D (1986) Asexual spore release from the saprolegniaceous water molds: involvement of calmodulin. J Gen Microbiol 132:593–598
Takeuchi Y, Schmid J, Caldwell JH, Harold FM (1988) Transcellular ion currents and extension of Neurospora crassa hyphae. J Membr Biol 101:33–41
Terry BR, Findlay GP, Tyerman SD (1992) Direct effects of Ca2+-channel blockers on plasma membrane cation channels of Amaranthus tricolor protoplasts. J Exp Bot 43:1457–1473
Thiel RL, Schreurs WJA, Harold FM (1988) Transcellular ion currents during sporangium development in the water mould Achlya bisexualis. J Gen Microbiol 134: 1089–1097
Tsien RW, Tsien RY (1990) Calcium channels stores and oscillations. Annu Rev Cell Biol 6:715–760
Turian G, Ton-That TC, Ortega-Perez R (1985) Acid tip linear growth in the fungi: requirements for H+/Ca2+ inverse gradients and cytoskeleton integrity. Bot Helv 95:311–322
Van Brunt J, Caldwell JH, Harold FM (1982) Circulation of potassium across the plasma membrane of Blastocladiella emersonii: K+ channel. J Bacteriol 150:1449–1461
Wang C, Rathore KS, Robinson KR (1989) The responses of pollen to applied electric fields. Dev Biol 136:405–410
Warncke J, Slayman CL (1980) Metabolic modulation of stoichiometry in a proton pump. Biochim Biophys Acta 591:224–233
Wessels JGH (1986) Cell wall synthesis in apical hyphal growth. Int Rev Cytol 104:37–79
Wessels JGH (1990) Role of cell wall architecture in fungal tip growth generation. In: Heath IB (ed) Tip growth in plant and fungal cells. Academic Press, New York, pp 1–29
White RG, Hyde GJ, Overall RL (1990) Microtubule arrays in regenerating Mougeotia protoplasts may be oriented by applied electric fields. Protoplasma 158: 73–85
Youatt J (1993) Calcium in microorganisms. CRC Crit Rev Microbiol 19:83–97
Youatt J, McKinnon I (1993) Manganese (Mn2+) reverses the inhibition of fungal growth by EGTA. Microbios 74:77–92
Youatt J, Gow NAR, Gooday GW (1988) Bioelectric and biosynthetic aspects of cell polarity in Allomyces macrogynus. Protoplasma 146:118–126
Zhou X-L, Stumpf MA, Hoch HC, Kung C (1991) A mechanosensitive channel in whole cells and in membrane patches of the fungus Uromyces. Science 253: 1415–1417
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Harold, F.M. (1994). Ionic and Electrical Dimensions of Hyphal Growth. In: Wessels, J.G.H., Meinhardt, F. (eds) Growth, Differentiation and Sexuality. The Mycota, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11908-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-11908-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11910-5
Online ISBN: 978-3-662-11908-2
eBook Packages: Springer Book Archive