Plant Biol (Stuttg) 2004; 6(5): 590-597
DOI: 10.1055/s-2004-821090
Original Paper

Georg Thieme Verlag Stuttgart KG · New York

A Logical (Discrete) Formulation for the Storage and Recall of Environmental Signals in Plants

M. Thellier1 , J. Demongeot2 , V. Norris1 , J. Guespin3 , C. Ripoll1 , R. Thomas4
  • 1Laboratoire AMMIS, FRE CNRS 2829, Faculté des Sciences, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France
  • 2TIMC-IMAG-CNRS UJF-INPG & IUF, Faculté de Médecine, 38706 La Tronche, France
  • 3Laboratoire de Microbiologie du Froid, Faculté des Sciences, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France
  • 4Centre for Non-linear Phenomena and Complex Systems, ULB, CP 231, Bd du Triomphe, 1050 Brussels, Belgium
Further Information

Publication History

Publication Date:
21 July 2004 (online)

Abstract

When subjected to an appropriate asymmetric stimulus, seedlings of Bidens pilosa L. “store” a symmetry-breaking instruction that will finally take effect (in the form of a differential growth of the cotyledonary buds) only if the plants are in a state in which they can “recall” this information. The ability of the plants to recall the stored symmetry-breaking instruction may be switched “on” or “off” by the application of a variety of stimuli. Although its detailed phenomenology is rather complicated, the overall behaviour of the plant storage/recall system can be modelled by use of an asynchronous, logical (discrete) description involving positive and negative feedback circuits, which are required for the existence of multi-stationarity and stability, respectively. The state tables, as used in this formalism, give a concise and easy-to-handle description of the evolution of the system and make it particularly easy to determine its stable states. This modelling approach may be extended to the formulation of many other experimental systems.

References

  • 1 Boon F., de Palma A.. Boolean formalism and urban development.  Lecture Notes in Biomath.. (1979);  29 402-439
  • 2 Bourgeade P., Boyer N., De Jaegher G., Gaspar T.. Carry-over of thigmomorphogenetic characteristics in calli derived from Bryonia dioica internodes.  Plant Cell Tissue Organ Cult.. (1989);  19 199-211
  • 3 Corbineau F.. Le contrôle de la germination des semences par l'environnement gazeux (The control of seed germination by the gas environment).  La Vie des Sciences. (1995);  12 223-237
  • 4 Dee D., Ghil M.. Boolean difference equations. I. Formulation and dynamic behaviour.  Siam J. Appl. Math.. (1984);  44 11-126
  • 5 Demongeot J., Kaufman M., Thomas R.. Positive feedback circuits and memory.  C. R. Acad. Sci. Paris, Sciences de la Vie/Life Sciences. (2000a);  323 69-79
  • 6 Demongeot J., Thomas R., Thellier M.. A mathematical model for storage and recall functions in plants.  C. R. Acad. Sci. Paris, Sciences de la Vie/Life Sciences. (2000b);  323 93-97
  • 7 Desbiez M. O., Kergosien Y., Champagnat P., Thellier M.. Memorization and delayed expression of regulatory messages in plants.  Planta. (1984);  160 392-399
  • 8 Desbiez M. O., Gaspar T., Crouzillat D., Frachisse J. M., Thellier M.. Effect of cotyledonary prickings on growth, ethylene metabolism and peroxidase activity in Bidens pilosa. .  Plant Physiol. Biochem.. (1987);  25 137-143
  • 9 Desbiez M. O., Mikulecky D., Thellier M.. Growth messages in plants: principle of a possible modelling, and further experimental characteristics.  J. Biol. Syst.. (1994);  2 127-130
  • 10 Desbiez M. O., Tort M., Monnier C., Thellier M.. Asymmetrical triggering of the cell cycle in opposite buds of a young plant, after a slight cotyledonary wound.  C. R. Acad. Sci. Paris, Sciences de la Vie/Life Sciences. (1998);  321 403-407
  • 11 Desbiez M. O., Tort M., Thellier M.. Control of a symmetry-breaking process in the course of the morphogenesis of plantlets of Bidens pilosa L.  Planta. (1991);  184 397-402
  • 12 Falkner G., Falkner R.. Objectivistic views in biology: an obstacle to our understanding of self-organisation processes in aquatic ecosystems.  Freshwater Biology. (2000);  44 553-559
  • 13 Falkner R., Falkner G.. Distinct adaptivity of the phosphate uptake system of the cyanobacterium Anabaena variabilis reflects information processing about preceding phosphate supply.  J. Trace Microprobe Techn.. (2003);  21 363-375
  • 14 Gammer K., Gritsch M., Peeva A., Kögler R., Hutter H.. SIMS investigation of gettering centers in ion-implanted and annealed silicon.  J. Trace Microprobe Techn.. (2002);  20 47-55
  • 15 Henry-Vian C., Vian A., Davies E., Dietrich A., Ledoigt G., Desbiez M. O.. Changes in the polysomal mRNA population upon wound signal expression or storage in Bidens pilosa. .  Plant Physiol.. (1995a);  33 337-344
  • 16 Henry-Vian C., Vian A., Davies E., Ledoigt G., Desbiez M. O.. Wounding regulates polysomal incorporation of hsp70 and tch1 transcripts during signal storage and retrieval.  Physiol. Plant. (1995b);  95 387-392
  • 17 Jablonska E., Lamb M. J.. Epigenetic Inheritance and Evolution. Oxford, New York, Tokyo; Oxford University Press (1995)
  • 18 Kaufman M.. Role of multistationarity in an immune response model: a combined discrete and continuous approach. Perelson, A. S., ed. Theoretical Immunology. Redwood City, CA; Addison Wesley (1988): 199-222
  • 19 Kaufman M., Urbain J., Thomas R.. Towards a logical analysis of the immune response.  J. Theor. Biol.. (1985);  114 527-561
  • 20 Kergosien Y., Thellier M., Desbiez M. O.. Préséances entre bourgeons axillaires chez Bidens pilosa L.: modélisation au niveau macroscopique en termes de catastrophes, ou au niveau microscopique en termes de “pompes et fuites” cellulaires (Precedence between axillary buds in Bidens pilosa L.: modelling at a macroscopic level in terms of catastrophes, or at a microscopic level in terms of cell “pumps and leaks”). In Elaboration et Justification des Modèles: Applications en Biologie, Part I.  Elaboration et Justification des Modèles: Applications en Biologie, Part I. Paris; Maloine (1979): 323-343
  • 21 Knight H., Brandt S., Knight M. R.. A history of stress alters drought calcium signalling pathways in Arabidopsis. .  Plant J.. (1998);  16 681-687
  • 22 Korobeinikova I. A., Pronchev G. B., Yermakov A. N.. An application of FAB mass spectrometry in analysis of a composition of atmospheric water.  J. Trace Microprobe Techn.. (2002);  20 105-117
  • 23 Leclercq J., Dumont J.. Boolean analysis of cell regulation networks.  J. Theor. Biol.. (1983);  104 507-534
  • 24 Mendoza L., Thieffry D., Alvarez-Buylla E. R.. Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analysis.  Bioinformatics. (1999);  15 593-606
  • 25 Nicolis C. A.. Boolean approach to climate dynamics.  Quart. J. R. Met. Soc.. (1982);  108 707-715
  • 26 Novick A., Weiner M.. Enzyme induction is an all-or-non phenomenon.  Proc. Natl. Acad. Sci. USA. (1957);  43 553-566
  • 27 Pastoret P. P., Thiry E., Thomas R.. Logical description of Bovine Herpes virus type I latent infection.  J. Gen. Virol.. (1986);  67 885-897
  • 28 Sánchez L., Thieffry D.. A logical analysis of the Drosophila gap-gene system.  J. Theor. Biol.. (2001);  211 115-141
  • 29 Sánchez L., Vanhelden J., Thieffry D.. Establishment of the dorso-ventral pattern during embryonic development of Drosophila melanogaster: a logical analysis.  J. Theor. Biol.. (1997);  189 377-389
  • 30 Slack J. M. W.. Serial thresholds and homeotic variation.  Lecture Notes in Biomath.. (1979);  29 473-480
  • 31 Snoussi E. H.. Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach.  Dynamics and Stability of Systems. (1989);  4 189-207
  • 32 Tafforeau M.. Etude de la phase précoce de transduction des signaux environnementaux chez le lin: une approche protéomique (Investigation on the initial phase in the transduction of environmental stimuli in flax: a proteomic approach). University of Rouen (France), Doctorate thesis. (2002): 227
  • 33 Tafforeau M., Verdus M. C., Norris V., White G., Demarty M., Thellier M., Ripoll C.. SIMS study of the calcium-deprivation step related to epidermal meristem production induced in flax by cold shock or radiation from a GSM telephone.  J. Trace Microprobe Techn.. (2002a);  20 611-623
  • 34 Tafforeau M., Verdus M. C., Charlionet R., Cabin-Flaman A., Ripoll C.. 2-D electrophoresis investigation of short-term response of flax seedlings to a cold shock.  Electrophoresis. (2002b);  23 2534-2540
  • 35 Takahashi K., Isobe M., Knight M. R., Trewavas A. J., Muto S.. Hypoosmotic shock induces increases in cytosolic Ca2+ in tobacco suspension-culture cells.  Plant Physiol.. (1997);  113 587-594
  • 36 Thellier M., Le Sceller L., Norris V., Verdus M. C., Ripoll C.. Long-distance transport, storage and recall of morphogenetic information in plants. The existence of a sort of primitive plant “memory”.  C. R. Acad. Sci. Paris, Sciences de la Vie/Life Sciences. (2000);  323 81-91
  • 37 Thieffry D., Colet M., Thomas R.. Formalization of regulatory networks: a logical method and its automatization.  Math. Modelling Sci. Computing. (1993);  2 144-151
  • 38 Thomas R.. Some biological examples.  Lecture Notes in Biomath.. (1979);  29 354-401
  • 39 Thomas R.. Regulatory networks seen as asynchronous automata: a logical description.  J. Theor. Biol.. (1991);  153 1-23
  • 40 Thomas R., D'Ari R.. Biological Feedback. Boca Raton; CRC Press (1990)
  • 41 Thomas R., Gathoye A. M., Lambert L.. A complex control circuit, regulation of immunity in temperate bacteriophages.  Eur. J. Biochem.. (1976);  71 211-227
  • 42 Thomas R., Kaufman M.. Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits.  Chaos. (2001);  11 180-195
  • 43 Thomas R., Van Ham P.. Analyse formelle de circuits de régulation génétique: contrôle de l'immunité chez les bactériophages lambdoïdes (Formal analysis of circuits of genetic regulation: immunity control of lamdoid bacteriophages).  Biochimie. (1974);  56 1529-1547
  • 44 Van Ham P.. How to deal with variables with more than two levels.  Lecture Notes in Biomath.. (1979);  29 326-343
  • 45 Verdus M. C., Thellier M., Ripoll C.. Storage of environmental signals in flax: their morphogenetic effect as enabled by a transient depletion of calcium.  Plant J.. (1997);  12 1399-1410
  • 46 Wagner F., Falkner R., Falkner G.. Information about previous phosphate fluctuations is stored via an adaptative response of the high-affinity uptake system of the cyanobacterium Anacystis nidulans. .  Planta. (1995);  197 147-155

M. Thellier

Laboratoire AMMIS
Faculté des Sciences
Université de Rouen

FRE CNRS 2829

76821 Mont-Saint-Aignan Cedex

France

Email: michel.thellier@univ-rouen.fr

Section Editor: M. C. Ball