On the growth and form of shoots

Chelakkot, Raghunath; Mahadevan, L.

doi:10.1098/rsif.2017.0001

Cited by 46 publications

(71 citation statements)

References 27 publications

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“…Here a finite persistence length along the chain is assumed but the chain is typically short in the sense that it does not reach its limit of coiling. Some of the previous studies [56,57] consider only a single active bead along the polymer, others focus on the dynamics of an active semi-flexible chain using either simulation or field theory [58][59][60]. Lastly, very recently, a one-dimensional chain of active beads (i.e.…”

Section: Introductionmentioning

confidence: 99%

How does a flexible chain of active particles swell?

Kaiser

Babel

Hagen

et al. 2015

The Journal of Chemical Physics

115

146

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We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

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Section: Introductionmentioning

confidence: 99%

How does a flexible chain of active particles swell?

Kaiser

Babel

Hagen

et al. 2015

The Journal of Chemical Physics

115

146

View full text Add to dashboard Cite

show abstract

“…5B), in particular during the first stages of development. The plant can play on its spontaneous curvature via tropisms and differential elongation (8)(9)(10). However the change of shape of the Averrhoa carambola leaf could not be explained by a switch from negative to positive gravitropism only.…”

Section: Discussionmentioning

confidence: 97%

Hook shape of growing leaves results from an active regulation

Rivière

Peaucelle

et al. 2020

Preprint

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The rachis of most growing compound leaves observed in nature exhibit a stereotyped hook shape. In this study, we focus on the canonical case of Averrhoa carambola. Combining kinematics and mechanical investigation, we characterize this hook shape and shed light on its establishment and maintenance. We show quantitatively that the hook shape is a conserved bent zone propagating at constant velocity and constant distance from the apex throughout development. A simple mechanical test first reveals non-zero spontaneous curvature profiles for the growing leaves, indicating that the hook shape is actively regulated. It then evidences the robust spatial organization of growth, curvature, rigidity and lignification and their interplay. Regulation processes appear to be specifically localized: in particular, differential growth occurs where the elongation rate drops. Finally, impairing the graviception of the leaf on a clinostat led to reduced hook curvatures but not to its loss. Altogether our results suggest a role for proprioception in the regulation of the apical hook, likely mediated via mechanical strain. Posture regulation | Gravitropism | Kinematics | Biomechanics | Leaf development | Plant morphogenesis | Plant movementCorrespondence: julien.derr@univ-paris-diderot.fr Material and methodsCulture conditions for Averrhoa carambola plants. Carambola seeds obtained from commercially available star Rivière et al. | bioRχiv | February 26, 2020 | 1-8

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“…Lastly we note that this framework does not currently include mechanics or elasticity, disregarding any elastic responses of the organ to physical forces. However this can be naturally implemented in the Frenet-Serret frame of reference (Goriely, 2017; Chelakkot and Mahadevan, 2017; Agostinelli et al, 2020), which we plan in future work.…”

Section: Discussionmentioning

confidence: 99%

A general 3D model for growth dynamics of sensory-growth systems: from plants to robotics

Porat

Tedone

Palladino

et al. 2020

Preprint

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2In recent years there has been a rise in interest in the development of self-growing robotics 3 inspired by the moving-by-growing paradigm of plants. In particular, climbing plants capitalize on 4 their slender structures to successfully negotiate unstructured environments, while employing 5 a combination of two classes of growth-driven movements: tropic responses, which direct 6 growth in the direction of an external stimulus, and inherent nastic movements, such as periodic 7 circumnutations, which promote exploration. In order to emulate these complex growth dynamics 8 in a 3D environment, a general and rigorous mathematical framework is required. Here we 9 develop a general 3D model for rod-like organs adopting the Frenet-Serret frame, providing a 10 useful framework from the standpoint of robotics control. Differential growth drives the dynamics 11 of the organ, governed by both internal and external cues. We describe the numerical method 12 required to implement this model, and perform numerical simulations of a number of key scenarios, 13 showcasing the applicability of our model. In the case of responses to external stimuli, we consider 14 a distant stimulus (such as sunlight and gravity), a point stimulus (a point light source), and a 15 line stimulus which emulates twining of a climbing plant around a support. We also simulate 16 circumnutations, the response to an internal oscillatory cue, associated with search processes. 17 Lastly we also demonstrate the superposition of both the response to an external stimulus 18 together with circumnutations. Lastly we consider a simple example illustrating the possible use of 19 an optimal control approach in order to recover tropic dynamics, in a way which may be relevant 20 for robotics use. In all, the model presented here is general and robust, paving the way for a 21 deeper understanding of plant response dynamics, as well as novel control systems for newly 22 developed self-growing robots. 23

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On the growth and form of shoots

Cited by 46 publications

References 27 publications

How does a flexible chain of active particles swell?

How does a flexible chain of active particles swell?

Hook shape of growing leaves results from an active regulation

A general 3D model for growth dynamics of sensory-growth systems: from plants to robotics

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