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

Thellier, Michel; Demongeot, Jacques; Norris, Victor; Guespin, Janine; Ripoll, Camille; Thomas, René

doi:10.1055/s-2004-821090

Cited by 18 publications

(13 citation statements)

References 40 publications

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“…Interestingly, removing both cotyledons 5 min after the symmetry‐breaking signal was introduced to one cotyledon did not abolish asymmetric growth, suggesting that a rapidly elicited long‐distance signal mediates storage and retrieval of information about previous wound experience. Several mathematical models were created using the B. pilosus system for storage and recall of environmental signals in plants (Demongeot, Thomas & Thellier 2000; Thellier et al. 2000, 2004; Demongeot, Thellier & Thomas 2006).…”

Section: ‘Memory’ Formation In Plant–herbivore Interactionsmentioning

confidence: 99%

Molecular mechanisms underlying plant memory in JA‐mediated defence responses

Gàlis

Gaquerel

Pandey

et al. 2009

Plant Cell & Environment

119

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Plants must respond to biotic and abiotic challenges to optimize their Darwinian fitness in nature. Many of these challenges occur repeatedly during a plant's lifetime, and their sequence and timing can profoundly influence the fitness outcome of a plant's response. The ability to perceive, store and recall previous stressful events is likely useful for efficient, rapid and cost-effective responses, but we know very little about the mechanisms involved. Using jasmonate-elicited anti-herbivore defence responses as an example, we consider how 'memories' of previous attacks could be created in (1) the biosynthetic processes involved in the generation of the oxylipin bursts elicited by herbivore attacks; (2) the perception of oxylipins and their transduction into cellular events by transcription factors and transcriptional activators; and (3) the role of small RNAs in the formation of long-term stress imprints in plants.

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Section: ‘Memory’ Formation In Plant–herbivore Interactionsmentioning

confidence: 99%

Molecular mechanisms underlying plant memory in JA‐mediated defence responses

Gàlis

Gaquerel

Pandey

et al. 2009

Plant Cell & Environment

119

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“…Starting from the conceptual model of plant memory, it is interesting to try to elaborate a more mathematical model to become able to make quantitative predictions that can be tested experimentally. Several approaches have already been followed (Kergosien et al 1979;Desbiez et al 1994;Demongeot et al 2000Demongeot et al , 2006Thellier et al 2004). However, two challenges are the existence of multiple timescales and the requirement to go beyond a single type of biological processes (e.g.…”

Section: Case Study III Of Systems-theory-modelling-towards a Conceptmentioning

confidence: 99%

Rhythms in Plants

Mancuso¹,

Shabala²

2015

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“…Such a system has been proposed in [1] to model genetic and metabolic regulations and is encountered in plant growth [7,6,17,19], embryogenesis [11,9] and neural networks [23,18], in which hormones (like auxine), proteins (like transduction peptide) or neuro-transmitters (like Gaba) secreted by a part of the system (e.g. apex in plants) inhibit the growth or activity of the other parts (e.g.…”

Section: A Pure Potential System the N-switch Modelmentioning

confidence: 99%

Liénard systems and potential-Hamiltonian decomposition I – methodology

Demongeot

Glade

Forest

2007

Comptes Rendus. Mathématique

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Following the Hodge decomposition of regular vector fields we can decompose the second member of any Liénard system into 2 (non-unique) polynomials, the first corresponding to potential and the second to Hamiltonian dynamics. This polynomial Hodge decomposition is called potential-Hamiltonian, denoted PH-decomposition, and we give it for any polynomial differential system of dimension 2. We will give in a future Note an algorithm expliciting the PH-decomposition in the neighborhood of particular orbits, like a limit-cycle for Liénard systems, the method being applicable for any polynomial differential system of dimension 2. To cite this article: J. Demongeot et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007). RésuméSystèmes de Liénard et décomposition potentielle-hamiltonienne I -méthodologie. Un système de Liénard est un système différentiel du second ordre, du type : dx/dt = y, dy/dt = −g(x) + yf (x), où g et f sont des polynômes. Un tel système est susceptible d'être décomposé, de manière non unique, en 2 parties polynomiales, l'une potentielle et l'autre hamiltonienne, c'est-à-dire qu'il existe 2 polynômes P et H vérifiant : dx/dt = −∂P /∂x + ∂H/∂y, dy/dt = −∂P /∂y − ∂H/∂x. On montre, en utilisant la décomposition de Hodge des champs de vecteurs réguliers, que le second membre d'un tel système est décomposable en 2 polynômes, l'un correspondant à une dynamique de gradient et l'autre à une dynamique hamiltonienne. Cette décomposition de Hodge polynomiale est appelée potentielle-hamiltonienne, notée PH-décomposition, et nous en donnons la formule pour tout système différentiel polynomial du plan. Nous donnerons, dans une Note ultérieure, un algorithme permettant d'obtenir une formule explicite de la PH-décomposition au voisinage d'orbites particulières, telles qu'un cycle-limite dans le cas des systèmes de Liénard, la méthode étant applicable à tout système différentiel polynomial du plan. Pour citer cet article : J. Demongeot et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).Les systèmes de Liénard sont des Equations Différentielles Ordinaires de Dimension 2 (2D-EDO) du type : dx/dt = y, dy/dt = −g(x) + yf (x), où f et g sont des polynômes.Le système de van der Pol (cf. Fig. 1) en est un bon exemple [2][3][4], utilisé pour modéliser de nombreux systèmes biologiques régulés, dont le système cardiaque. Les polynômes g et f d'un système de van der Pol sont définis par :L'unique cycle-limite d'un système de van der Pol, lorsqu'il existe, est une courbe non algébrique difficile à approximer et il peut être très utile, dans les applications, d'en avoir une estimation polynomiale. Nous proposons donc, de manière générale, une décomposition des EDO régulières, dite potentielle-hamiltonienne, dont l'existence est fondée théoriquement sur la décomposition de Hodge [5][6][7][8].Une ODE est dite potentiel-hamiltonienne décomposable, s'il existe un couple de polynômes (P , H ), tel que : dx/dt = −∂P /∂x + ∂H/∂y, dy/dt = −∂P /∂y − ∂H/∂x.La partie du flot de vecteurs vitesse définie par P correspond à une dynamique de descent...

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

Cited by 18 publications

References 40 publications

Molecular mechanisms underlying plant memory in JA‐mediated defence responses

Molecular mechanisms underlying plant memory in JA‐mediated defence responses

Rhythms in Plants

Liénard systems and potential-Hamiltonian decomposition I – methodology

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