Abstract
Twining plants exhibit a striking oscillation of their stems in their quest for a support. The oscillations, called circumnutation, have periods generally of 1–5 hr, and virtually all species have a preferred direction of twining. I seek to explain these chiral asymmetries in plant behavior by hypothesizing a chiral asymmetry in plant anatomy. Such asymmetries already exist, for example, in phyllotaxis. I explore wave phenomena on asymmetric but isotropic rings, and seek systems which will only support (stable) waves in one direction around the ring, and not in the other. Simulations indicate that (1) oscillatory reaction-diffusion systems do not support unidirectional waves on rings; (2) excitable reaction-diffusion systems do support unidirectional waves on rings; and (3) unidirectional phase-locking (discrete unidirectional waves) occurs in rings of coupled oscillators. Thus, chiral asymmetries of circumnutating plants cannot be explained by continuum oscillator phenomena, but can be explained by general discrete oscillators, or excitable phenomena on the continuum.
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Literature
Andersen, H. 1976. A mathematical model for circumnutations. Technical Report 2/1976, Lund Institute of Technology, Lund, Sweden.
Badot, P.-M. 1987. Approche cellulaire du mécanisme du mouvement révolutif des tiges volubiles. Étude de quelques paramètres physico-chimiques.Annales Scientifiques de l'Université de Besançon, Géologie, 4ème ser.,8(50), 53–110.
Badot, P.-M., B. Bonnet and B. Millet. 1990a. Implication possible de canaux potassiques dans le mécanisme du mouvement révolutif des tiges volubiles.C. r. Acad. Sci. Paris 311, sér. III, 445–451.
Badot, P.-M., D. Melin and J.-P. Garrec. 1990b. Circumnutation inPhaseolus vulgaris. II. Potassium content in the free-moving part of the shoot.Plant Physiol. Biochem. 28, 123–128.
Brown, A. 1991. Gravity perception and circumnutation in plants. InAdvances in Space Biology and Medicine, S. L. Bontinget al. (Eds), Vol. 1, pp. 129–153. Greenwich, CT: JAI Press.
Brown, A. H. and D. K. Chapman. 1977. Effects of increased gravity force on nutation of sunflower hypocotyls.Plant Physiol. 59, 636–640.
Brown, A. and D. Chapman. 1984. Circumnutation observed without a significant gravitational force in spaceflight.Science 225, 230–232.
Brown, A., D. Chapman, R. Lewis and A. Venditti. 1990. Circumnutation of sunflower hypocotyls in satellite orbit.Plant Physiol. 94, 233–238.
Darwin, C. 1865. On the movements and habits of climbing plants.J. Linn. Soc. Bot. 9, 1–118.
Darwin C. 1876.The Movements and Habits of Climbing Plants. New York: D. Appleton.
Darwin, C. and F. Darwin. 1880.The Power of Movement in Plants. London: John Murray.
Doedel, E. 1986.AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations.
Ermentrout, G. 1992a. Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators.SIAM J. appl. Math. 52(6), 1665–1687.
Ermentrout, G. B. 1992b.xtc software package.
Ermentrout, G. and N. Kopell. 1991. Multiple pulse interactions and averaging in systems of coupled neural oscillators.J. math. Biol. 29, 195–217.
Goldsworthy, A. 1983. The evolution of plant action potentials.J. theor. Biol. 103, 645–648.
Hyver, C., D. Melin and B. Millet. 1982. Mouvements révolutifs: une interpretation physicochimique? InLes Mécanismes de l'Irritabilité et du Fonctionnement des Rythmes chez les Végétaux, H. Greppin and E. Wagner (Eds), pp. 20–34. Colloque de Cartigny.
Johnsson, A. and D. Heathcote. 1973. Experimental evidence and models on circumnutations.Z. Pflanzenphysiol. Bd. 70, 371–405.
Kopell, N. and L. N. Howard. 1973. Plane wave solutions to reaction-diffusion equations.Stud. appl. Math. LII(4), 291–328.
Lubkin, S. 1992. Circumnutation modeled by reaction-diffusion equations. Ph.D. thesis, Cornell University.
Lubkin, S. and R. Rand. 1994. Oscillatory reaction-diffusion equations on rings.J. math. Biol. (in press).
Millet, B., D. Melin, B. Bonnet, C. A. Ibrahim and J. Mercier. 1984. Rhythmic circumnutation movement of the shoots inPhaseolus vulgaris 1.Chronobiol. Int. 1, 11–19.
Millet, B., D. Melin and P.-M. Badot. 1988. Circumnutation inPhaseolus vulgaris. I. Growth, osmotic potential and cell ultrastructure in the free-moving part of the shoot.Physiol. Plant. 72, 133–138.
Mohl, H. 1827.Uber den Bau und das Winden der Ranken und Schlingpflanzen. Tübingen.
Niklas, K. 1992.Plant Biomechanics: An Engineering Approach to Plant Form and Function. Chicago: University of Chicago Press.
Palm, L. H. 1827.Uber das Winden der Pflanzen. Stuttgart.
Pauwelussen, J. P. 1981. Nerve impulse propagation in a branching nerve system: a simple model.Physica D 4, 67–88.
Pauwelussen, J. P. 1982. One way traffic of pulses in a neuron.J. math. Biol. 15, 151–171.
Rinzel, J. 1981. Models in neurobiology. InNonlinear Phenomena in Physics and Biology, R. H. Ennset al. (Eds), pp. 345–367. NATO Advanced Studies Institute on Nonlinear Phenomena in Physics and Biology.
Silk, W. K. 1989. Growth rate patterns which maintain a helical tube.J. theor. Biol. 138, 311–327.
Simons, P. 1992.The Action Plant: Movement and Nervous Behaviour in Plants. Oxford: Blackwell.
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Lubkin, S. Unidirectional waves on rings: Models for chiral preference of circumnutating plants. Bltn Mathcal Biology 56, 795–810 (1994). https://doi.org/10.1007/BF02458268
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DOI: https://doi.org/10.1007/BF02458268