Motions of leaves and stems, from growth to potential use

A Reinforcement Learning approach to study climbing plant behaviour

A plant's structure is the result of constant adaptation and evolution to the surrounding environment. From this perspective, our goal is to investigate the mass and radius distribution of a particular plant organ, namely the searcher shoot, by providing a Reinforcement Learning (RL) environment, that we call Searcher-Shoot, which considers the mechanics due to the mass of the shoot and leaves. We uphold the hypothesis that plants maximize their length, avoiding a maximal stress threshold. To do this, we explore whether the mass distribution along the stem is efficient, formulating a Markov Decision Process. By exploiting this strategy, we are able to mimic and thus study the plant's behavior, finding that shoots decrease their diameters smoothly, resulting in an efficient distribution of the mass. The strong accordance between our results and the experimental data allows us to remark on the strength of our approach in the analysis of biological systems traits.

Morphology, anatomy and sleep movements of Ludwigia sedoides

The diurnal motion of higher plants, responding to the alternation of day and night, known as nyctinastic movements or "sleep movements", has been discussed frequently. We present the first description of the circadian rhythm of the water plant Ludwigia sedoides (Humb. & Bonpl.) H.Hara of the family Onagraceae, furthermore its morphology and anatomy. Our results indicate that the plant's movements are endogenous, although environmental factors certainly have an influence. The majority of plants with nyctinastic leaf movements have a pulvinus, as the crucial part of the plant enabling this movement. Although the basal section of the L. sedoides petiole is not swollen, the tissue functions similarly to a pulvinus. It consists of a central conducting tissue with thick-walled cells, which is surrounded by thin-walled motor cells that can undergo visible shrinking and swelling. Thus, the tissue functionally corresponds to a pulvinus. Examinations of cellular processes, like measurements of the turgor pressure in the petiole, need to be evaluated in future studies.

A digital sensor to measure real-time leaf movements and detect abiotic stress in plants

Plant and plant organ movements are the result of a complex integration of endogenous growth and developmental responses, partially controlled by the circadian clock, and external environmental cues. Monitoring of plant motion is typically done by image-based phenotyping techniques with the aid of computer vision algorithms. Here we present a method to measure leaf movements using a digital inertial measurement unit (IMU) sensor. The lightweight sensor is easily attachable to a leaf or plant organ and records angular traits in real-time for two dimensions (pitch and roll) with high resolution (measured sensor oscillations of 0.36 ± 0.53° for pitch and 0.50 ± 0.65° for roll). We were able to record simple movements such as petiole bending, as well as complex lamina motions, in several crops, ranging from tomato to banana. We also assessed growth responses in terms of lettuce rosette expansion and maize seedling stem movements. The IMU sensors are capable of detecting small changes of nutations (i.e. bending movements) in leaves of different ages and in different plant species. In addition, the sensor system can also monitor stress-induced leaf movements. We observed that unfavorable environmental conditions evoke certain leaf movements, such as drastic epinastic responses, as well as subtle fading of the amplitude of nutations. In summary, the presented digital sensor system enables continuous detection of a variety of leaf motions with high precision, and is a low-cost tool in the field of plant phenotyping, with potential applications in early stress detection.

The Adaptive Power of Ammophila arenaria: Biomimetic Study, Systematic Observation, Parametric Design and Experimental Tests with Bimetal

The aim of our study was to apply a biomimetic approach, inspired by the Ammophila arenaria. This organism possesses a reversible leaf opening and closing mechanism that responds to water and salt stress (hydronastic movement). We adopted a problem-based biomimetic methodology in three stages: (i) two observation studies; (ii) how to abstract and develop a parametric model to simulate the leaf movement; and (iii) experiments with bimetal, a smart material that curls up when heated. We added creases to the bimetal active layer in analogy to the position of bulliform cells. These cells determine the leaf-closing pattern. The experiments demonstrated that creases influence and can change the direction of the bimetal natural movement. Thus, it is possible to replicate the Ammophila arenaria leaf-rolling mechanism in response to temperature variation and solar radiation in the bimetal. In future works, we will be able to propose responsive facade solutions based on these results.

Fluctuations shape plants through proprioception

Plants constantly experience fluctuating internal and external mechanical cues, ranging from nanoscale deformation of wall components, cell growth variability, nutating stems, and fluttering leaves to stem flexion under tree weight and wind drag. Developing plants use such fluctuations to monitor and channel their own shape and growth through a form of proprioception. Fluctuations in mechanical cues may also be actively enhanced, producing oscillating behaviors in tissues. For example, proprioception through leaf nastic movements may promote organ flattening. We propose that fluctuation-enhanced proprioception allows plant organs to sense their own shapes and behave like active materials with adaptable outputs to face variable environments, whether internal or external. Because certain shapes are more amenable to fluctuations, proprioception may also help plant shapes to reach self-organized criticality to support such adaptability.

The hook shape of growing leaves results from an active regulatory process

The rachis of most growing compound leaves observed in nature exhibits a stereotypical 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 reveals non-zero intrinsic curvature profiles for the rachis during its growth, indicating that the hook shape is actively regulated. We show a robust spatial organization of growth, curvature, rigidity, and lignification, and their interplay. Regulatory 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 curvature but not to its loss. Altogether, our results suggest a role for proprioception in the regulation of the leaf hook shape, likely mediated via mechanical strain.

A General 3D Model for Growth Dynamics of Sensory-Growth Systems: From Plants to Robotics

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

Plant Bioinspired Ecological Robotics

Plants are movers, but the nature of their movement differs dramatically from that of creatures that move their whole body from point A to point B. Plants grow to where they are going. Bio-inspired robotics sometimes emulates plants' growth-based movement; but growing is part of a broader system of movement guidance and control. We argue that ecological psychology's conception of "information" and "control" can simultaneously make sense of what it means for a plant to navigate its environment and provide a control scheme for the design of ecological plant-inspired robotics. In this effort, we will outline several control laws and give special consideration to the class of control laws identified by tau theory, such as time to contact.

Mechanical basis for thermonastic movements of cold-hardy Rhododendron leaves

The profusion of rhododendrons in cold climates is as remarkable as the beauty of their blooms. The cold-hardiness of some of the montane species is in part due to reversible leaf movements triggered under frigid conditions wherein the leaves droop at the leaf stalks (petioles) and their margins roll up around the midrib. We probe the mechanics of these movements using leaf dissection studies that reveal that the through-thickness differential expansion necessary for leaf rolling is anisotropically distributed transverse to and along the midrib. Numerical simulations and theoretical analyses of bilayer laminae show that the longitudinal expansion amplifies the transverse rolling extent. The curvature diversion scales with the in-plane Poisson's ratio, suitably aided by the stiff midrib that serves as a symmetry breaking constraint that controls the competition between the longitudinal and transverse rolling. Comparison of leaf rolling with and without the petiole indicates that the petiole flexibility and leaf rolling are in part mechanically coupled responses, implicating the hydraulic pathways that maintain the critical level of midrib stiffness necessary to support the longitudinal expansion. The study highlights the importance of curvature diversion for efficient nastic and tropic leaf movements that enhance cold-hardiness and drought resistance, and for morphing more general hinged laminae.

Tree crowns grow into self-similar shapes controlled by gravity and light sensing

Plants have developed different tropisms: in particular, they reorient the growth of their branches towards the light (phototropism) or upwards (gravitropism). How these tropisms affect the shape of a tree crown remains unanswered. We address this question by developing a propagating front model of tree growth. Being length-free, this model leads to self-similar solutions after a long period of time, which are independent of the initial conditions. Varying the intensities of each tropism, different self-similar shapes emerge, including singular ones. Interestingly, these shapes bear similarities to existing tree species. It is concluded that the core of specific crown shapes in trees relies on the balance between tropisms.

Towards a framework for collective behavior in growth-driven systems, based on plant-inspired allotropic pairwise interactions

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 state-space. We describe the different states, as well as the sharp transitions between them. We also find that the form of the state-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.

How water flow, geometry, and material properties drive plant movements

Plants are dynamic. They adjust their shape for feeding, defence, and reproduction. Such plant movements are critical for their survival. We present selected examples covering a range of movements from single cell to tissue level and over a range of time scales. We focus on reversible turgor-driven shape changes. Recent insights into the mechanisms of stomata, bladderwort, the waterwheel, and the Venus flytrap are presented. The underlying physical principles (turgor, osmosis, membrane permeability, wall stress, snap buckling, and elastic instability) are highlighted, and advances in our understanding of these processes are summarized.

Fluttering of growing leaves as a way to reach flatness: experimental evidence on Persea americana

Simple leaves show unexpected growth motions: the midrib of the leaves swings periodically in association with buckling events of the leaf blade, giving the impression that the leaves are fluttering. The quantitative kinematic analysis of this motion provides information about the respective growth between the main vein and the lamina. Our three-dimensional reconstruction of an avocado tree leaf shows that the conductor of the motion is the midrib, presenting continuous oscillations and inducing buckling events on the blade. The variations in the folding angle of the leaf show that the lamina is not passive: it responds to the deformation induced by the connection to the midrib to reach a globally flat state. We model this movement as an asymmetric growth of the midrib, which directs an inhomogeneous growth of the lamina, and we suggest how the transition from the folded state to the flat state is mechanically organized.

The functions of foliar nyctinasty: a review and hypothesis

Foliar nyctinasty is a plant behaviour characterised by a pronounced daily oscillation in leaf orientation. During the day, the blades of nyctinastic plant leaves (or leaflets) assume a more or less horizontal position that optimises their ability to capture sunlight for photosynthesis. At night, the positions that the leaf blades assume, regardless of whether they arise by rising, falling or twisting, are essentially vertical. Among the ideas put forth to explain the raison d'être of foliar nyctinasty are that it: (i) improves the temperature relations of plants; (ii) helps remove surface water from foliage; (iii) prevents the disruption of photoperiodism by moonlight; and (iv) directly discourages insect herbivory. After discussing these previous hypotheses, a novel tritrophic hypothesis is introduced that proposes that foliar nyctinasty constitutes an indirect plant defence against nocturnal herbivores. It is suggested that the reduction in physical clutter that follows from nocturnal leaf closure may increase the foraging success of many types of animals that prey upon or parasitise herbivores. Predators and parasitoids generally use some combination of visual, auditory or olfactory cues to detect prey. In terrestrial environments, it is hypothesised that the vertical orientation of the blades of nyctinastic plants at night would be especially beneficial to flying nocturnal predators (e.g. bats and owls) and parasitoids whose modus operandi is death from above. The movements of prey beneath a plant with vertically oriented foliage would be visually more obvious to gleaning or swooping predators under nocturnal or crepuscular conditions. Such predators could also detect sounds made by prey better without baffling layers of foliage overhead to damp and disperse the signal. Moreover, any volatiles released by the prey would diffuse more directly to the awaiting olfactory apparatus of the predators or parasitoids. In addition to facilitating the demise of herbivores by carnivores and parasitoids, foliar nyctinasty, much like the enhanced illumination of the full moon, may mitigate feeding by nocturnal herbivores by altering their foraging behaviour. Foliar nyctinasty could also provide a competitive advantage by encouraging herbivores, seeking more cover, to forage on or around non-nyctinastic species. As an added advantage, foliar nyctinasty, by decreasing the temperature between plants through its effects on re-radiation, may slow certain types of ectothermic herbivores making them more vulnerable to predation. Foliar nyctinasty also may not solely be a behavioural adaptation against folivores; by discouraging foraging by granivores, the inclusive fitness of nyctinastic plants may be increased.