Oscillatory model of crassulacean acid metabolism with a dynamic hysteresis switch

Proceedings of the Royal Society B: Biological Sciences

Volumn 266, Issue 1414, 1999, Pages 93-101

  Blasius, B ^a   Neff, R ^a   Beck, F ^a   Luttge U ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Biological clock; Crassulacean acid metabolism; Endogenous rhythm; Hysteresis switch; Limit cycle oscillation; Lipid membrane order parameter

Indexed keywords

CARBON DIOXIDE; MALIC ACID; WATER;

ARTICLE; CELL VACUOLE; CIRCADIAN RHYTHM; DYNAMICS; LIPID MEMBRANE; MEMBRANE MODEL; METABOLISM; OSCILLATION; PHOTOSYNTHESIS; PLANT; PRIORITY JOURNAL; TEMPERATURE; TIME; TONOPLAST;

EID: 0033531175     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.1999.0608     Document Type: Article

References (33)

1. Anderson, C. M. & Wilkins, M. B. 1989a Control of the circadian rhythm of carbon dioxide assimilation in Bryophyllum leaves by exposure to darkness and high carbon dioxide concentrations. Planta 177, 401-408.
2. Anderson, C. M. & Wilkins, M. B. 1989b Period and phase control by temperature in the circadian rhythm of carbon dioxide fixation in illuminated leaves of Bryophyllum fedtschenkoi. Planta 177, 456-469.
3. Anderson, C. M. & Wilkins, M. B. 1989. Phase resetting of the circadian rhythm of carbon dioxide assimilation in Bryophyllum leaves in relation to their malate content following brief exposure to high and low temperatures, darkness and carbon dioxide. Planta 180, 61-73.
4. Blasius, B. 1997 Zeitreihenanalyse und Modellierung regulärer und irregulärer Photosyntheseoszillationen bei Crassulaceen-Säurestoffwechsel-Pflanzen. PhD thesis, TU-Darmstadt.
5. Blasius, B., Beck, F. & Lüttge, U. 1997 A model for photosynthetic oscillations in crassulacean acid metabolism (CAM). J. Theor. Biol. 184, 345-351.
6. Blasius, B., Beck, F. & Lüttge, U. 1998 Oscillatory model of crassulaccan acid metabolism: structural analysis and stability boundaries with a discrete hysteresis switch. Pl. Cell Env. 21, 775-784.
7. Buchanan-Bollig, I. C. & Smith, A. C. 1984 Circadian rhythms in crassulacean acid metabolism: phase relationship between gas exchange, leaf water relations and malate metabolism in Kalanchoë daigremontiana. Planta 161, 314-319.
8. Cockburn, W., Ting, I. P. & Sternberg, L. O. 1979 Relationships between stomatal behaviour and internal carbon dioxide concentration in crassulacean acid metabolism plants. Plant Physiol. 63, 1029-1032.
9. Dunlap, J. C. 1993 Genetic analysis of circadian clocks. A. Rev. Physiol. 55, 683-728.
10. Fitz Hugh, R. 1961 Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466.
11. Goldbeter, A. 1995 A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. Lond. B 261, 319-324.
12. Grams, T. E. E., Beck, F. & Lüttge, U. 1996 Generation of rhythmic and arrhythmic behaviour of crassulacean acid metabolism in Kalanchoë daigremontiana under continuous light by varying the irradiance or temperature: Measurements in vivo and model simulations. Planta 198, 110-117.
13. Grams, T. E. E., Borland, A. M., Roberts, A., Griffiths, H., Beck, F. & Lüttge, U. 1997 On the mechanism of reinitiation of endogenous CAM-rhythm by temperature changes. Plant Physiol. 113, 1309-1317.
14. Hartwell, J., Smith, L. H., Wilkins, M. B., Jenkins, G. I. & Nimmo, H. G. 1996 Higher plant phosphoenolpyruvate carboxylase kinase is regulated at the level of translatable mRNA in response to light or a circadian rhythm. Plant J. 10, 1071-1078.
15. Jähnig, F. 1979 Molecular theory of lipid membrane order. J. Chem. Phys. 70, 3279-3290.
16. Kliemchen, A., Schomburg, M., Galla, H.-J., Lüttge, U. & Kluge, M. 1993 Phenotypic changes in the fluidity of the tonoplast membrane of Crassulacean-acid-metabolism plants in response to temperature and salinity stress. Planta 189, 403-409.
17. Kluge, A. & Ting, I. P. 1978 Crassulacean acid metabolism: analysis of an ecological adaption. Berlin, Heidelberg, Newrk: Springer.
18. Lüttge, U. 1987 Carbon dioxide and water demand: Crassulacean acid metabolism (CAM), a versatile ecological adaptation exemplifying the need for integration in ecophysiological work. New Phytol. 106, 593-629.
19. Lüttge, U. 1998 Order and deterministic chaos in the endogenous rhythm of crassulacean acid metabolism. Cell. Molec. Biol. Lett. 2 (Suppl. 1), 179-190.
20. Lüttge, U. & Beck, F. 1992 Endogenous rhythms and chaos in crassulacean acid metabolism. Planta 188, 28-38.
21. Murray, J. D. 1993 Mathematical biology. Berlin, Heidelberg, New York: Springer.
22. Nagumo, J. S., Arimoto, S. & Yoshizawa, S. 1962 An active pulse transmission line simulating nerve axon. Proc. IRE. 50, 2061-2071.
23. Neff, R., Blasius, B., Beck, F. & Lüttge, U. 1998 Thermodynamics and energetics of the tonoplast membrane operating as a hysteresis switch in an oscillatory model of crassulacean acid metabolism. J. Memb. Biol. 165, 37-43.
24. Njus, D., Sulzmann, F. M. & Hastings, J. W. 1974 Membrane model for the circadian clock. Nature 248, 116-120.
25. 2-Stoffwechsel bei Pflanzen mit diurnalem Säurestoffwechsel. Planta 56, 28-70.
26. Nungesser, D., Kluge, M., Tolle, H. & Oppelt, W. 1984 A dynamic computer model of the metabolic and regulatory process in crassulacean acid metabolism. Planta 162, 204-214.
27. Osmond, C. B. 1978 Crassulacean acid metabolism: a curiosity in context. A. Rev. Plant Plysiol. 29, 379-414.
28. Steudle, E., Smith, J. A. C. & Lüttge, U. 1980 Water relation parameters of individual mesophyllcells of the Crassulacean acid metabolism plant Kalanchoë daigremontiana Hamet et Perrier. Plant Physiol. 66, 155-1163.
29. Stone, L. & Ezrati, S. 1996 Chaos, cycles and spatiotemporal dynamics in plant ecology. J. Ecol. 84, 279-291.
30. Theißen, G. & Saedler, H. 1998 Molecular architects of plant body plans. Prog. Bot. 59, 227-256.
31. Wilkins, M. B. 1959 An endogenous rhythm in the rate of dark fixation of carbon dioxide in leaves of Bryophyllum. I. Some preliminary experiments. J. Exp. Bot. 10, 377-390.
32. Wilkins, M. B. 1992 Circadian rhythms: their origin and control. New Phytol. 121, 347-375.
33. Winter, K. & Smith J. A. C. (eds) 1996 Crassulacean acid metabolism. Biochemistry, ecophysiology and evolution. In Ecological studies, vol. 114. Berlin, Heidelberg, New York: Springer.