Skip to main content

Bumps, the Elementary Excitatory Responses of Invertebrates

  • Conference paper
The Molecular Mechanism of Photoreception

Part of the book series: Dahlem Workshop Reports ((DAHLEM LIFE,volume 34))

Abstract

Due to the successful absorption of a photon, a rhodopsin molecule is light-activated and starts a sequence of causal steps which lead in the Limulus photoreceptor to the generation of a relatively large elementary excitatory response, the “bump.” A bump is a transient increase of the cation conductance of the visual cell membrane and follows photon absorption after a long, greatly variable delay (on the average, latency ca. 200 ms). The bump size also varies greatly (average amplitude Ā ca. 1 nA, or average current-time integral F̄ ca. 50 pAs), indicating the variation of the degree of amplification in the transduction process. A bump is based on the transient opening of a large number (up to 103–104) of ion-specific channels through the cell membrane.

The visual cell changes its sensitivity according to the ambient illumination. A major part of this adaptation is accomplished by a control process which mainly regulates the degree of amplification that determines the size of the bump (bump adaptation, according to the adapting bump model). There are at least two mechanisms responsible for light adaptation: a faster one, a feedback loop, which regulates the sensitivity of the photoreceptor cell by variation of the intracellular level of free calcium ions, and a slower one which is not — or is much less — calcium-dependent.

A plausible description of the mechanism of bump generation includes the enzymatic production of transmitter and transmitter diffusion to the light-controlled ion channels which are distributed over a large area of the photosensory membrane. A time-consuming process which activates an enzyme could determine the latency. Transmitter diffusion over the “bump-speck” could be responsible for the bump rise, and either the stochastic closure of ion channels or the time course of transmitter decay could determine the exponential bump decay.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adolph, A. 1964. Spontaneous slow potential fluctuations in the Limulus photoreceptor. J. Gen. Physiol. 48: 297–322.

    Article  PubMed  CAS  Google Scholar 

  2. Adolph, A. 1968. Thermal and spectral sensitivities of discrete slow potentials in Limulus eye. J. Gen. Physiol. 52: 584–599.

    Article  Google Scholar 

  3. Bacigalupo, J., and Lisman, J.E. 1983. Single-channel currents activated by light in Limulus ventral photoreceptors. Nature 304: 268–270.

    Article  PubMed  CAS  Google Scholar 

  4. Barlow, R.B., and Kaplan, E. 1977. Properties of visual cells in the lateral eye of Limulus in situ. J. Gen. Physiol. 69: 203–220.

    Article  PubMed  Google Scholar 

  5. Bayer, D.S., and Barlow, R.B. 1978. Physiological properties of photoreceptor cells in an organ culture medium. J. Gen. Physiol. 72: 539–563.

    Article  PubMed  CAS  Google Scholar 

  6. Baylor, D.A.; Lamb, T.D.; and Yau, K.-W. 1979. Responses of retinal rods to single photons. J. Physiol. 288: 613–634.

    PubMed  CAS  Google Scholar 

  7. Behbehani, M., and Srebro, R. 1974. Discrete waves and phototransduction in voltage-clamped ventral photoreceptors. J. Gen. Physiol. 64: 186–200.

    PubMed  CAS  Google Scholar 

  8. Blumenfeld, A.; Erusalimsky, J.; Heichal, O.; Selinger, Z.; and Minke, B. 1985. Light-activated guanosintriphpsphatase in Musca eye membranes mimics the prolonged depolarizing afterpotential in photoreceptor cells. Proc. Natl. Acad. Sci. USA 82: 7116–7120.

    Article  PubMed  CAS  Google Scholar 

  9. Bolsover, S.R., and Brown, J.E. 1982. Injection of guanosine and adenosine nucleotides into Limulus ventral photoreceptor cells. J. Physiol. 332: 325–342.

    PubMed  CAS  Google Scholar 

  10. Borsellino, A., and Fuortes, M.G.F. 1968. Response to single photons in visual cells of Limulus. J. Physiol. 196: 507–539.

    PubMed  CAS  Google Scholar 

  11. Brown, J.E., and Blinks, J.R. 1974. Changes in intracellular free calcium concentration during illumination of invertebrate photoreceptors. J. Gen. Physiol. 64: 643–665.

    Article  PubMed  CAS  Google Scholar 

  12. Brown, J.E.; Brown, P.K.; and Pinto, L.H. 1977. Detection of light induced changes of intracellular ionized calcium concentration in Limulus ventral nerve photoreceptors using Arsenazo III. J. Physiol. 267: 299–320.

    PubMed  CAS  Google Scholar 

  13. Brown, J.E., and Coles, J.A. 1979. Saturation of the response to light in Limulus ventral photoreceptors. J. Physiol. 296: 373–392.

    PubMed  CAS  Google Scholar 

  14. Brown, J.E.; Kaupp, U.B.; and Malbon, C.C. 1984. 3′, 5′-cyclic adenosine monophosphate and adenylate cyclase in phototransduction by Limulus ventral photoreceptors. J. Physiol. 353: 523–539.

    PubMed  CAS  Google Scholar 

  15. Brown, J.E., and Rubin, L.J. 1984. A direct demonstration that inositol-triphosphate induces an increase in intracellular calcium in Limulus photoreceptors. Biochem. Biophys. Res. Commun. 125: 1137–1142.

    Article  PubMed  CAS  Google Scholar 

  16. Brown, J.E.; Rubin, J.L.; Traver, A.P.; Ghalayini, A.J.; Irvine, R.F.; and Anderson, R.E. 1984. Myo-inositol polyphosphate may be a messenger for visual excitation in Limulus photoreceptors. Nature 311: 160–163.

    Article  PubMed  CAS  Google Scholar 

  17. Calhoon, R.; Tsuda, M.; and Ebrey, T.G. 1980. A light-activated GTPase from octopus photoreceptors. Biochem. Biophys. Res. Commun. 94: 1452–1457.

    Article  PubMed  CAS  Google Scholar 

  18. Coles, J.A., and Brown, J.E. 1976. Effects of increased intracellular pH-buffering capacity on the light response of Limulus ventral photoreceptor. Biochim. Biophys. Acta 436: 140–153.

    Article  PubMed  CAS  Google Scholar 

  19. Cone, R.A. 1973. The internal transmitter model of visual excitation, some quantitative implications. In Biochemistry and Physiology of Visual Pigments, ed. H. Langer, pp. 275–282. Berlin: Springer-Verlag.

    Google Scholar 

  20. Corson, D.W., and Fein, A. 1980. The pH dependence of discrete wave frequency in Limulus ventral photoreceptors. Brain Res. 193: 558–561.

    Article  PubMed  CAS  Google Scholar 

  21. Corson, D.W., and Fein, A. 1983. Chemical excitation of Limulus photoreceptors. J. Gen. Physiol. 82: 639–657.

    Article  PubMed  CAS  Google Scholar 

  22. Corson, D.W.; Fein, A.; and Walthall, W.W. 1983. Chemical excitation of Limulus photoreceptors II. J. Gen. Physiol. 82: 659–667.

    Article  PubMed  CAS  Google Scholar 

  23. Cosens, D.J., and Manning, A. 1969. Abnormal electrogram from a Drosophila mutant. Nature 224: 285–287.

    Article  PubMed  CAS  Google Scholar 

  24. Dirnberger, G.; Keiper, W.; Schnakenberg, J.; and Stieve, H. 1984. Comparison of time constants of single channel patches, quantum bumps, and noise analysis in Limulus ventral photoreceptors. J. Membr. Biol. 83: 39–43.

    Google Scholar 

  25. Dodge, F.A.; Knight, B.W.; and Toyoda, J.I. 1968. Voltage noise in Limulus visual cells. Science 160: 88–90.

    Article  PubMed  Google Scholar 

  26. Fein, A., and Charlton, J.S. 1977a. Enhancement and phototransduction in the ventral eye of Limulus. J. Gen. Physiol. 69: 553–569.

    Article  PubMed  CAS  Google Scholar 

  27. Fein, A., and Charlton, J.S. 1977b. A quantitative comparison of the effects of intracellular calcium injection and light adaptation on the photoresponse of Limulus ventral photoreceptors. J. Gen. Physiol. 70: 591–600.

    Article  PubMed  CAS  Google Scholar 

  28. Fein, A., and Corson, D.W. 1982. Internal injection of ATP can reduce discrete wave activity. Biol. Bull. 163: 395.

    Google Scholar 

  29. Fein, A., and Hanani, M. 1978. Light-induced increase in discrete waves in the dark in Limulus ventral photoreceptors. Brain Res. 156: 157–161.

    Article  PubMed  CAS  Google Scholar 

  30. Fein, A.; Payne, R.; Corson, D.; Berridge, M.J.; and Irvine, R.F. 1984. Photoreceptor excitation and adaptation by inositol 1, 4, 5-triphosphate. Nature 311: 157–160.

    Article  PubMed  CAS  Google Scholar 

  31. Goldring, M.A. 1982. Tests of models for the mechanism of the single photon response in Limulus ventral photoreceptors. Ph.D. Thesis, Brandeis University.

    Google Scholar 

  32. Grzywacz, N.M., and Hillman, P. 1985. Statistical test of linearity of photoreceptor transduction process: Limulus passes, others fail. Proc. Natl. Acad. Sci. US-Biol. Sci. 82: 232–235.

    Article  CAS  Google Scholar 

  33. Hamdorf, K., and Kirschfeld, K. 1980. “Prebumps”: Evidence for double-hits at functional subunits in a rhabdomeric photoreceptor. Z. Naturforsch. 35c: 173–174.

    Google Scholar 

  34. Hamdorf, K., and Kirschfeld, K. 1980. Reversible events in the transduction process of photoreceptors. Nature 283: 859–860.

    Article  PubMed  CAS  Google Scholar 

  35. Hanani, M., and Fein, A. 1981. Diamide, a sulfhydryl reagent, modifies the light response of Limulus ventral nerve photoreceptor. Neurosci. Lett. 21: 165–170.

    Article  PubMed  CAS  Google Scholar 

  36. Hanani, M., and Hillman, P. 1976. Adaptation and facilitation in the barnacle photoreceptor. J. Gen. Physiol. 67: 235–249.

    Article  PubMed  CAS  Google Scholar 

  37. Hillman, P. 1981. The biophysics of intermediate processes in photoreceptor transduction: “Silent” stages, nonlocalities, single-photon response and models. In Proceedings of the Symposium on the Biology of Photoreceptor Cells, pp. 443–475. Cambridge: Cambridge University Press.

    Google Scholar 

  38. Howard, J. 1983. Variations in the voltage response to single quanta of light in the photoreceptors of Locusta migratoria. Biophys. Struct. Mech. 9: 341–348.

    Article  Google Scholar 

  39. Ivens, I., and Stieve, H. 1984. Influence of the membrane potential on the intracellular light induced Ca2+ concentration change of the Limulus ventral photoreceptor monitored by Arsenazo III under voltage clamp conditions. Z. Naturforsch. 39c: 986–992.

    CAS  Google Scholar 

  40. Kaplan, E., and Barlow, R.B. 1980. Circadian clock in Limulus brain increases response and decreases noise of retinal photoreceptors. Nature 286: 393–395.

    Article  PubMed  CAS  Google Scholar 

  41. Kass, L., and Barlow, R.B. 1984. Efferent neurotransmission of circadian rhythms in Limulus lateral eye. J. Neurosci. 4: 908–917.

    PubMed  CAS  Google Scholar 

  42. Keiper, W. 1983. Zur Theorie der Photorezeption. Dissertation, RWTH Aachen, F.R. Germany.

    Google Scholar 

  43. Keiper, W.; Schnakenberg, J.; and Stieve, H. 1984. Statistical analysis of quantum bump parameters in Limulus ventral photoreceptor. Z. Naturforsch. 39c: 781–790.

    Google Scholar 

  44. Lillywhite, P.G. 1977. Single photon signals and transduction in an insect eye. J. Comp. Physiol. 122: 189–200.

    Article  Google Scholar 

  45. Lisman, J.E. 1985. The role of metarhodopsin in the generation of spontaneous quantum bumps in ultraviolet receptors of Limulus median eye. J. Gen. Physiol. 85: 171–187.

    Article  PubMed  CAS  Google Scholar 

  46. Lisman, J.E., and Brown, J.E. 1972. The effects of intracellular ionophoretic injection of calcium and sodium ions on the light response of Limulus ventral photoreceptors. J. Gen. Physiol. 59: 701–719.

    Article  PubMed  CAS  Google Scholar 

  47. Lisman, J.E., and Brown, J.E. 1975a. Light-induced changes of sensitivity in Limulus ventral photoreceptors. J. Gen. Physiol. 66: 473–488.

    Article  PubMed  CAS  Google Scholar 

  48. Lisman, J.E., and Brown, J.E. 1975b. Effects of intracellular injection of calcium buffers on light adaptation in Limulus ventral photoreceptors. J. Gen. Physiol. 66: 489–506.

    Article  PubMed  CAS  Google Scholar 

  49. Maaz, G.; Nagy, K.; Stieve, H.; and Klomfaß, J. 1981. The electrical light response of the Limulus ventral nerve photoreceptor, a superposition of distinct components — observable by variation of the state of light adaptation. J. Comp. Physiol. 141: 303–310.

    Article  Google Scholar 

  50. Maaz, G., and Stieve, H. 1980. The correlation of the receptor potential with the light induced transient increase in intracellular calcium-concentration measured by absorption change of Arsenazo III injected into Limulus ventral nerve photoreceptor cell. Biophys. Struct. Mech. 6: 191–208.

    Article  PubMed  CAS  Google Scholar 

  51. Martinez, J.M., and Srebro, R. 1976. Calcium and the control of discrete wave latency in the ventral photoreceptor of Limulus. J. Physiol. 261: 535–562.

    PubMed  CAS  Google Scholar 

  52. Minke, B. 1979. Transduction in photoreceptors with bistable pigments: Intermediate processes. Biophys. Struct. Mech. 5: 163–174.

    Article  Google Scholar 

  53. Minke, B. 1982. Light-induced reduction in excitation efficiency in the trp-mutant of Drosophila. J. Gen. Physiol. 79: 361–385.

    Article  PubMed  CAS  Google Scholar 

  54. Minke, B. 1983. The trp is a Drosophila mutant sensitive to developmental temperature. J. Comp. Physiol. 151: 483–486.

    Article  Google Scholar 

  55. Minke, B., and Stephenson, R.S. 1985. The characteristics of chemically induced noise in musca photoreceptors. J. Comp. Physiol. 156: 339–356.

    Article  CAS  Google Scholar 

  56. Minke, B.; Wu, C.F.; and Pak, W.L. 1975. Induction of photoreceptor voltage noise in the dark in Drosophila mutant. Nature 258: 84–87.

    Article  PubMed  CAS  Google Scholar 

  57. Nagy, K., and Stieve, H. 1983. Changes in intracellular calcium ion concentration, in the course of dark adaptation measured by Arsenazo III in the Limulus photoreceptor. Biophys. Struct. Mech. 9: 207–223.

    Article  Google Scholar 

  58. Pak, W.L.; Conrad, S.K.; Kremer, N.E.: Larrivee, D.C.; Schinz, R.H.; and Wong, F. 1980. Photoreceptor function. In Development and Neurobiology of Drosophila, eds. O. Siddiqu, P. Babu, L.M. Hall, and J.C. Hall, pp. 331–346. New York: Plenum Publishing Corp.

    Google Scholar 

  59. Pak, W.L.; Ostroy, S.E.; Deland, M.C.; and Wu, C.F. 1976. Photoreceptor mutant of Drosophila: Is a protein involved in intermediate steps of phototransduction? Science 194: 956–959.

    Article  CAS  Google Scholar 

  60. Payne, R. 1980. Voltage noise accompanying chemically-induced depolarization of insect photoreceptors. Biophys. Struct. Mech. 6: 235–251.

    Article  Google Scholar 

  61. Payne, R. 1981. Suppression of noise in a photoreceptor by oxidative metabolism. J. Comp. Physiol. 142: 181–188.

    Article  CAS  Google Scholar 

  62. Payne, R. 1982. Fluoride blocks in inactivation step of transduction in a locust photoreceptor. J. Physiol. 325: 261–269.

    PubMed  CAS  Google Scholar 

  63. Payne, R., and Howard, J. 1981. Response of an insect photoreceptor: a simple log-normal model. Nature 290: 415–416.

    Article  Google Scholar 

  64. Saibil, H.R., and Michel-Villaz, M. 1984. Squid rhodopsin and GTP-binding protein crossreact with vertebrate photoreceptor enzymes. Proc. Natl. Acad. Sci. USA 81: 5111–5115.

    Article  PubMed  CAS  Google Scholar 

  65. Scholes, J. 1965. Discontinuity of the excitation process in locust visual cells. Cold S.H. Symp. Quant. Biol. 30: 517–527.

    CAS  Google Scholar 

  66. Srebro, R., and Behbehani, M. 1972. Light adaptation of discrete waves in the Limulus photoreceptor. J. Gen. Physiol. 60: 86–101.

    Article  PubMed  CAS  Google Scholar 

  67. Srebro, R., and Behbehani, M. 1972. The thermal origin of spontaneous activity in the Limulus photoreceptor. J. Physiol. 224: 349–361.

    PubMed  CAS  Google Scholar 

  68. Srebro, R., and Behbehani, M. 1974. Light adaptation in the ventral photoreceptor of Limulus. J. Gen. Physiol. 64: 166–185.

    PubMed  CAS  Google Scholar 

  69. Stern, J.; Chinn, K.; Robinson, P.; and Lisman, J.E. 1985. The effect of nucleotides on the rate of spontaneous quantum bumps in Limulus ventral photoreceptors. J. Gen. Physiol., in press.

    Google Scholar 

  70. Stern, J.H., and Lisman, J.E. 1982. Internal dialysis of Limulus ventral photoreceptor. Proc. Natl. Acad. Sci. USA 79: 7580–7584.

    Article  PubMed  CAS  Google Scholar 

  71. Stieve, H. 1983. Transduction of light energy to electrical signals in photoreceptor cells. In The Biology of Photoreception, Society for Experimental Biology Symposium XXXVI, eds. D.J. Cosens and D. Vince-Prince, pp. 249–274. Great Britain: Society for Experimental Biology.

    Google Scholar 

  72. Stieve, H., and Bruns, M. 1978. Extracellular calcium, magnesium, and sodium ion competition in the conductance control of the photosensory membrane of Limulus ventral nerve photoreceptor. Z. Naturforsch. 33c: 574–579.

    CAS  Google Scholar 

  73. Stieve, H., and Bruns, M. 1980. Dependence of bump rate and bump size in Limulus ventral nerve photoreceptor on light adaptation and calcium concentration. Biophys. Struct. Mech. 6: 271–285.

    Article  CAS  Google Scholar 

  74. Stieve, H., and Bruns, M. 1983. Bump latency distribution and bump adaptation of Limulus ventral nerve photoreceptor in varied extracellular calcium concentration. Biophys. Struct. Mech. 9: 329–339.

    Article  Google Scholar 

  75. Stieve, H.; Bruns, M.; and Gaube, H. 1983. The intensity dependence of the receptor potential of the Limulus ventral nerve photoreceptor in two defined states of light-and dark adaptation. Z. Naturforsch. 38c: 1043–1054.

    Google Scholar 

  76. Stieve, H.; Bruns, M.; and Gaube, H. 1984. The sensitivity shift due to light adaptation depending on the extracellular calcium ion concentration in Limulus ventral nerve photoreceptor. Z. Naturforsch. 39c: 662–679.

    CAS  Google Scholar 

  77. Stieve, H.; and Klomfaß, J. 1981. Calcium dependence of light evoked membrane current signal and membrane voltage signal and their changes due to light adaptation in Limulus photoreceptor. Biophys. Struct. Mech. 7: 345.

    Article  Google Scholar 

  78. Stieve, H., and Klomfaß, J. 1983. Distribution and bump latency and bump shape parameters in dependence on adaptation and external Ca2+ concentration in Limulus photoreceptor. Abstract. Jahrestagung, Deutsche Gesellschaft für Biophysik, Neuherberg.

    Google Scholar 

  79. Stieve, H., and Pflaum, M. 1978. The response height versus stimulus intensity curve of the ventral nerve photoreceptor of Limulus depending on adaptation and external calcium concentration. Vision Res. 18: 747–749.

    Article  PubMed  CAS  Google Scholar 

  80. Stieve, H.; Pflaum, M.; Klomfaß, J.; and Gaube, H. 1985. Calcium/sodium binding competition in the gating of light-activated membrane conductance studied by voltage clamp technique in Limulus ventral nerve photoreceptor. Z. Naturforsch., in press.

    Google Scholar 

  81. Vandenberg, C.A., and Montai, M. 1984a. Light-regulated biochemical events in invertebrate photoreceptors I. Biochemistry 23: 2339–2347.

    Article  PubMed  CAS  Google Scholar 

  82. Vandenberg, C.A., and Montai, M. 1984b. Light-regulated biochemical events in invertebrate photoreceptors II. Biochemistry 23: 2347–2353.

    Article  PubMed  CAS  Google Scholar 

  83. Williams, D.S. 1983. Changes of photoreceptor performance associated with the daily turnover of photoreceptor membrane in locusts. J. Comp. Physiol. 150: 509–519.

    Article  Google Scholar 

  84. Wong, F. 1978. Nature of light-induced conductance changes in ventral photoreceptors of Limulus. Nature 276: 76–79.

    Article  PubMed  CAS  Google Scholar 

  85. Wong, F. 1985. Molecular analysis of visual mutation in Drosophila. Proc. Symp. Cont. Sens. Neurobiol., in press.

    Google Scholar 

  86. Wong, F.; Hokanson, K.M.; and Chang, T.L. 1985. Molecular basis of an inherited retinal defect in Drosophila. Inv. Ophthalmol. Vis., in press.

    Google Scholar 

  87. Wong, F.; Knight, B.W.; and Dodge, F.A. 1980. Dispersion of latencies in photoreceptors of Limulus and the adapting bump model. J. Gen. Physiol. 76: 517–537.

    Article  PubMed  CAS  Google Scholar 

  88. Wong, F.; Knight, B.W.; and Dodge, F.A. 1982. Adapting bump model for ventral photoreceptors of Limulus. J. Gen. Physiol. 79: 1089–1113.

    Article  PubMed  CAS  Google Scholar 

  89. Yeandle, S. 1958. Electrophysiology of the visual system — discussion. Am. J. Ophthalmol. 46: 82.

    Google Scholar 

  90. Yeandle, S., and Fuortes, M.G.F. 1964. Probability of occurrence of discrete potential waves in the eye of Limulus. J. Gen. Physiol. 47: 443–463.

    Article  PubMed  Google Scholar 

  91. Yeandle, S., and Spiegler, J.B. 1973. Light-evoked and spontaneous discrete waves in the ventral nerve photoreceptor of Limulus. J. Gen. Physiol. 61: 552–572.

    Article  PubMed  CAS  Google Scholar 

  92. Yeandle, S., and Spiegler, J.B. 1974. Independence of location of light absorption and discrete wave. J. Gen. Physiol. 64: 494–502.

    Article  PubMed  Google Scholar 

  93. Yoshika, T.; Inoue, H.; Inomata, K.; Hayashi, F.; Takagi, M.; and Takenaka, T. 1981. The parallel study of protein phosphorylation and phosphatidyl-inositol metabolism in the photoreceptor of squid retina. Proc. Jpn. Acad. 57: 309.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

H. Stieve

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Dr. S. Bernhard, Dahlem Konferenzen, Berlin

About this paper

Cite this paper

Stieve, H. (1986). Bumps, the Elementary Excitatory Responses of Invertebrates. In: Stieve, H. (eds) The Molecular Mechanism of Photoreception. Dahlem Workshop Reports, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70444-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70444-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70446-8

  • Online ISBN: 978-3-642-70444-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics