The Kinematics of Plant Nutation Reveals a Simple Relation between Curvature and the Orientation of Differential Growth

Bastien, Renaud; Meroz, Yasmine

doi:10.1371/journal.pcbi.1005238

Cited by 40 publications

(87 citation statements)

References 33 publications

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“…However this can be generalized to explicitly account for growth following previous work 2014. In addition, elasticity [58] and more complex integration of stimuli [51] can be integrated, as well as a generalization to 3D [50]. Moreover, this model assumes the signal is emitted from a point at the tip, however it is possible to consider the signals emitted from a more extended part of the organ, by assuming the signal is additive.…”

Section: Discussionmentioning

confidence: 99%

“…the model is general, making minimal assumptions about the building blocks of the system, it successfully accounts for the experimentally observed gravitropic kinematics of different organs from 11 angiosperms. The model also accounts for the kinematics of growing organs [49] in 3D [50], and has also been generalized to take into account time varying stimuli [51]. However, it is limited to the case of distant stimuli yielding a parallel vector field, such as gravity or sunlight, which approach any point along a plant from the same angle, and at the same intensity.…”

Section: A Minimal Model For Allotropism: the Growth-driven Reorimentioning

confidence: 99%

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A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

Bastien

Porat

Meroz

2019

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A variety of biological systems are not motile, but sessile in nature, relying on growth as the main driver of their movement. Groups of such growing organisms can form complex structures, such as the functional architecture of growing axons, or the adaptive structure of plant root systems. These processes are not yet understood, however the decentralized growth dynamics bear similarities to the collective behavior observed in groups of motile organisms, such as flocks of birds or schools of fish. Equivalent growth mechanisms make these systems amenable to a theoretical framework inspired by tropic responses of plants, where growth is considered implicitly as the driver of the observed bending towards a stimulus. We introduce two new concepts related to plant tropisms: point tropism, the response of a plant to a nearby point signal source, and allotropism, the growth-driven response of plant organs to neighboring plants. We first analytically and numerically investigate the 2D dynamics of single organs responding to point signals fixed in space. Building on this we study pairs of organs interacting via allotropism, i.e.each organ senses signals emitted at the tip of their neighbor and responds accordingly. In the case of local sensing we find a rich phase space. We describe the different phases, as well as the sharp transitions between them. We also find that the form of the phase space depends on initial conditions. This work sets the stage towards a theoretical framework for the investigation and understanding of systems of interacting growth-driven individuals.

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Section: Discussionmentioning

confidence: 99%

Section: A Minimal Model For Allotropism: the Growth-driven Reorimentioning

confidence: 99%

A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

Bastien

Porat

Meroz

2019

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“…indeed most of the growth oscillations reported in the literature so far occur during the nutation of the aerial organ, e.g. in sunflowers [26], or in very particular plant organs/cells such as pollen tubes and root hairs [21,27,28]. When oscillations of differential growth were observed during plant nutation, the oscillations were identified by comparing growth rates on opposing lateral sides of the plant organ [26].…”

Section: Discussionmentioning

confidence: 99%

“…One reason for the failure to include this term in the AC model may be that this regulatory mechanism can not be properly observed without clear and complete observations of plant movement, and all-inclusive plant kinematics are often not quantified or reported. Measurements of plant movement that focus on the first instants of the gravitropic reaction [17][18][19], or restrict analysis to the movement of the apical tip alone [18][19][20], give an incomplete picture of the kinematics of gravitropic movement and are insufficient for understanding its regulation [3,13,14,21].…”

Section: Introductionmentioning

confidence: 99%

Gravitropic Movement in Wheat Coleoptile is Regulated by Ultradian Growth Oscillations

Bastien¹,

Guayasamin

Douady

et al. 2017

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To stand straight and upright along their growth, plants needs to regulate actively their posture. Gravitropic movement, which occurs when plants modify their growth and curvature to orient their aerial organ against the force of gravity, is a major feature of this postural control. A recent model has shown that graviception and proprioception are sufficient to account for the gravitropic movement and subsequent organ posture demonstrated by a range of species. However, some plants, including wheat coleoptiles, exhibit a stronger regulation of posture than predicted by the model. Here, we performed an extensive kinematics study on wheat coleoptiles during a gravitropic perturbation experiment in order to better understand this unexpectedly strong regulation. Close temporal observation of the data revealed that both perturbed and unperturbed coleoptiles showed oscillatory pulses of elongation and curvature variation that propagated from the apex to the base of their aerial organs. In perturbed (tilted) coleoptiles, we discovered a non-trivial coupling between the oscillatory dynamics of curvature and elongation. This relationship appears to be critical to the postural control of the organ, and indicates the presence of a mechanism that is capable of affecting the relationship between elongation rate, differential growth, and curvature.

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“…Our theory is but the first step in understanding how growing systems respond to environmental stimuli. Natural questions that arise include testing the assumption of linear response experimentally, comparing the response functions for phototropic and gravitropic responses, which share many signal transduction processes, and incorporating additional effects such as internal cues [28], and the role of passive drooping of a growing shoot [29], all problems for the future.…”

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confidence: 99%

Spatiotemporal Integration in Plant Tropisms

Meroz

Bastien

Mahadevan

2018

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Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse light stimulus expresses the response function as function of experimentally tractable variables for the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging etc.Plant tropisms are the growth-driven responses of a plant organ which reorients itself in the direction of an environmental stimulus such as light, termed phototropism, or gravity, termed gravitropism. Tropisms driven by a directional stimulus lead to the asymmetric redistribution of a growth hormone such as auxin [1-5] which then directs growth. For example, in Fig. 1a we show snapshots of the negatively gravitropic response of a wheat seedling placed horizontally at time t = 0, where the seedling shoot detects the direction of gravity and grows to oppose it. This response is dynamical, and one might suspect that if the stimulus is changed intermittently, the spatiotemporal response itself will be complex. In the simple experiment described above, gravity acts continuously on the shoot with a constant magnitude. Thus it is not possible to distinguish between a response that integrates the stimulus over time and one that acts instantaneously. However experimental observations of gravitropism and phototropism dating back more than a century have shown that plants respond to time varying stimuli in a way that suggests that they do integrate the stimuli in time. For example, different combinations of stimuli that are intermittent in time [6][7][8][9][10] or which have reciprocal ratios of intensity and duration [11][12][13][14][15][16][17][18], so that the time-integrated stimulus is constant, lead to the same response, as shown in the insets in Figs. 2 and 3. Explanations of shoot phototropism assume that this follows from photobiology [19]. However, the fact that this phenomenon has also been observed in the context of gravitropism suggests that one must look for a common signal transduction pathway, naturally implicating the polar transport of the growth hormone auxin that is * Electronic address: jazz@tauex.tau.ac.il † Electronic address: lmahadev@g.harvard.edu critical in mediating tissue growth, which is indeed driven by either gravity or light. Furthermore, these observations of responses to ...

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The Kinematics of Plant Nutation Reveals a Simple Relation between Curvature and the Orientation of Differential Growth

Cited by 40 publications

References 33 publications

A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

Gravitropic Movement in Wheat Coleoptile is Regulated by Ultradian Growth Oscillations

Spatiotemporal Integration in Plant Tropisms

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