Abstract
A mathematical model has been developed to evaluate the contribution of phototactic responses in light-induced accumulations. A set of differential equations describes the organism density inside and outside of the light trap as well as on its border.
The model predicts that organisms first occupy the rim of the light trap and then gradually fill the interior. This has been substantiated experimentally. Computer simulations of light-induced accumulations in a light trap agree with the measured values. The distance from the trap within which organisms respond phototactically depends on the organism density, which determines the amount of stray light, and on the zero threshold for both phototaxis and photophobic response.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adler, J., Dahl, M. M.: A method for measuring the motility of bacteria and for comparing random and non-random motility. J. Gen. Microbiol. 46, 161–173 (1967)
Carrier, G. F., Pearson, C. E.: Partial differential equations. New York, San Francisco, London: Academic Press 1976
Checcucci, A., Favati, L., Grassi, S., Piaggesi, T.: The measurement of phototactic activity in Euglena gracilis. Klebs. Monitore Zool. Ital. 9, 83–98 (1975)
Clayton, R. K.: Patterns of accumulation resulting from taxes and changes in motility of microorganisms. Arch. Mikrobiol. 27, 311–319 (1957)
Clayton, R. K.: Phototaxis in microorganisms. In: Photophysiology (A. C. Giese, ed.), Vol. 2, pp. 51–77. New York, London: Academic Press 1964
Diehn, B.: Mechanism and computer simulation of the phototactic accumulation of Euglena in a beam of light. Photochem. Photobiol. 11, 407–418 (1970)
Diehn, B., Feinleib, M., Haupt, W., Hildebrand, E., Lenci, F., Nultsch, W.: Terminology of behavioural responses of motile microorganisms. Photochem. Photobiol. 26, 559–560 (1977)
Doetsch, G.: Anleitung zum praktischen Gebrauch der Laplace-Transformation. München: Oldenbourg 1956
Feinleib, M. E.: Photomovement of microorganisms. Photochem. Photobiol. 27, 849–854 (1978)
Häder, D.-P.: Untersuchungen zur Photophobotaxis bei Phormidium uncinatum. Diss. Mbg. 1973
Häder, D.-P.: Evidence of electrical potential changes in photophobically reacting blue-green algae. Arch. Microbiol. 118, 115–119 (1978)
Häder, D.-P.: Photomovement. In: Encyclopedia of plant physiology (W. Haupt, M. E. Feinleib, eds.), Vol. 7, pp. 268–309. Heidelberg, Berlin, New York: Springer 1979
Häder, D.-P., Burkart, U.: Mathematical model for photophobic accumulations of blue-green algae in light traps. J. Math. Biology 5, 293–304 (1978)
Häder, D.-P., Wenderoth, K.: Role of three basic light reactions in photomovement of desmids. Planta 137, 207–214 (1977)
Keller, E. F., Segel, L. A.: Model for chemotaxis. J. Theor. Biol. 30, 225–234 (1971a)
Keller, E. F., Segel, L. A.: Traveling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol. 30, 235–248 (1971b)
Nossal, R., Weiss, G. H.: Analysis of a densitometry assay for bacterial chemotaxis. J. Theor. Biol. 41, 143–147 (1973)
Nultsch, W.: Der Einfluß des Lichtes auf die Bewegung der Cyanophyceen. I. Mitt. Phototopotaxis bei Phormidium autumnale. Planta 56, 632–647 (1961)
Nultsch, W.: Der Einfluß des Lichtes auf die Bewegung der Cyanophyceen. III. Mitt. Photophobotaxis von Phormidium uncinatum. Planta 58, 647–663 (1962)
Nultsch, W.: Phototaxis and photokinesis in bacteria and blue-green algae. In: Behaviour of microorganisms (A. Pérez-Miravete, ed.), pp. 70–82. New York, London: Plenum Press 1973
Nultsch, W.: Phototaxis and photokinesis. In: Primitive sensory and communication systems (M. J. Carlile, ed.), pp. 29–90. London, New York, San Francisco: Academic Press 1975
Odell, G. M., Keller, E. F.: Travelling bands of chemotactic bacteria revisited. J. Theor. Biol. 56, 243–247 (1976)
Rosen, G.: Analytical solution to the initial-value problem for travelling bands of chemotactic bacteria. J. Theor. Biol. 49, 311–321 (1975)
Schuchart, H.: Phototaxis methodology. In: Proc. Int. School Badia Fiesolana, Pisa, Lito Felici (G. Colombetti, ed.), pp. 85–108, 1975
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Burkart, U., Häder, D.P. Phototactic attraction in light trap experiments: A mathematical model. J. Math. Biology 10, 257–269 (1980). https://doi.org/10.1007/BF00276985
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00276985