Photon Transport in Phototropic Organisms

  • A. R. Steinhardt


Phototropism can be defined as a change of the direction of growth of certain plants as caused by unilateral stimuli of light. Most organisms exhibiting phototropism are of a cylindrical form. The change in the direction of growth is coupled to differential growth within the plant organ caused by an asymmetric distribution of photon fluxes within the cylindrical organism.


Absorption Profile Action Spectrum Geometrical Optic Lens Effect Irregular Domain 
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.


Xw(φ), yw(φ)

parameter representation for the wavefronts

Xc(φ), yc(φ)

parameter representation for the caustic


azimuth of intersection incident ray/cylinder

field of refracted rays given in an implicit form

γi, γo

angle of incidence and refraction, respectively


angle enclosed by refracted rays and x-axis


parameter determining a specific wavefront


azimuth of intersection refracted ray/cylinder in the image plane


without argument: phaseshift




expansion coefficient for a bundle of rays


curvature of the wavefronts


radius of curvature of the caustic


Airy function


focusing factor


angle enclosed of \(\vec E\)-vector of light and plane of incidence

Ic, Id

coherent and diffuse intensity, respectively

Uċ, Ud

average coherent and average diffuse intensity, respectively


diffuse flux vector


Greens’ function

Im, Km

modified Bessel functions of integer order


energy absorbed by a photoreceptor


Response of a biological system


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bergman K, Burke PV, Cerda-Olmedo E et al. (1969) Phycomyces. Bact Rev 33:99–157PubMedGoogle Scholar
  2. Born M, Wolf E (1980) Principles of optics. Pergamon, Oxford, p 170Google Scholar
  3. Brinkworth BJ (1972) Interpretation of the kubelka-munk coefficients in reflection theory. Appl Opt 11:1434PubMedCrossRefGoogle Scholar
  4. Burkhard DG, Shealy DL (1981) Simplified formula for the illuminance in an optical system. Appl Opt 20:897PubMedCrossRefGoogle Scholar
  5. Castle FS (1966) A kinetic model for adaptation and the light growth response of phycomyces. J. Gen Phys 49:925–935CrossRefGoogle Scholar
  6. Cerda-Olmedo E, Lipson E (eds) (1987) Phycomyces. Cold Spring Harbor Lab, Cold Spring HarborGoogle Scholar
  7. Curry GM, Gruen HE (1957) Negative phototrophism of Phycomyces in the ultra-violet. Natura (Lond) 179:1028–1029CrossRefGoogle Scholar
  8. Dohrmann U (1983) In-vitro riboflavin binding and endogenous flavins in Phycomyces blakesleeanus. Planta 159:357–365CrossRefGoogle Scholar
  9. Fukshansky L, Steinhardt AR (1987) Spatial factors in Phycomyces photbtropism: Analysis of balanced responses. J. Theor Biol, 129:301–323CrossRefGoogle Scholar
  10. Galland P, Lipson E (1985) Action spectra for phototropic balance in Phycomyces blakesleeanus: Dependence on reference wavelength and intensity range. Photochem Photobiol 41:323–329PubMedCrossRefGoogle Scholar
  11. Humphry VR (1956) The effects of paraffin oil on phototropic and geotropic responses in avena coleoptiles. Ann Bot 30:39–45Google Scholar
  12. Ishimaru A (1978) Wave propagation and scattering in random media, Vol 1. Academic Press, Lond New YorkGoogle Scholar
  13. Kline M, Kay IW (1965) Electromagnetic theory and geometrical optics, Chap. 5. Intersci, New YorkGoogle Scholar
  14. Landau LD, Lifshitz EM (1977) Lehrbuch der theoretischen Physik, Vol II, Chap 59. Academie Verlag, BerlinGoogle Scholar
  15. Lipschutz MM (1969) Differential geometry, Chap 9. McGraw-Hill, New YorkGoogle Scholar
  16. Massey V, Müller F, Feldberg R (1969) The reactivity of flavoproteins with sulfite. J Biol Chem 244:3999–4006PubMedGoogle Scholar
  17. Poe RC et al. (1986) System analysis of Phycomyces light growth response: double mutants. Biol Cybern 55:105PubMedGoogle Scholar
  18. Schäfer E, Fukshansky L, Shropshire W Jr (1984) Action spectroscopy of photoreversible pigment systems. In: Shropshire W Jr., Mohr H (eds) Photomorphogenesis. Encycl Plant Physiol, New Ser 16A:358–400, Springer, Berlin Heidelberg New York TokyoGoogle Scholar
  19. Seyfried M (1984) Spektroskopische Eigenschaften von Phytochrom in vivo. PhD thesis, Univ FreiburgGoogle Scholar
  20. Shropshire W Jr (1974) Phototropism. In: Schenk GO (ed) Progress in photobiology. Proc 6th Int Congr Photobiol Dtsch Ges Lichtforsch eV, pp 1–6, Springer, Berlin Heidelberg New YorkGoogle Scholar
  21. Steinhardt AR (1987) Theoretische Untersuchungen zur räumlichen Signalperzeption in phototropisch aktiven Organen. PhD thesis, Univ FreiburgGoogle Scholar
  22. Steinhardt AR, Fukshansky L (1985) Diffusion approximation for scattering in a cylinder: Optics of phototropism. J Opt Soc Am A, 2:1725–1734CrossRefGoogle Scholar
  23. Steinhardt AR, Fukshansky L (1987) Geometrical optics approach to the intensity distribution in finite cylindrical media. Appl Opt 26:3778–3789PubMedCrossRefGoogle Scholar
  24. Steinhardt AR, Shropshire W Jr, Fukshansky L (1987) Invariant properties of absorption profiles in sporangiophores of phycomyces under balancing bilateral illumination. Photochem Photobiol 45:515–523CrossRefGoogle Scholar
  25. Steinhardt AR, Popescu T, Fukshansky L (1989) Is the dichroic photoreceptor for Phycomyces phototropism located at the plasma membrane or at the tonoplast? Photochem Photobiol 49:79–87CrossRefGoogle Scholar
  26. Strubecker K (1964) Differentialgeometrie. Gruyter, Berlin, 1:69Google Scholar
  27. Zankel KL, Burke PV, Delbrück M (1967) Absorption and screening in Phycomyces. J Gen Physiol 50:1893–1906PubMedCrossRefGoogle Scholar
  28. Ziegler H (1950) Inversion phototropischer reaktionen. Planta 38:474–498CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • A. R. Steinhardt

There are no affiliations available

Personalised recommendations