A unifying modeling of plant shoot gravitropism with an explicit account of the effects of growth

Analysis of root-environment interactions reveals mechanical advantages of growth-driven penetration of roots

Plant roots are considered highly efficient soil explorers. As opposed to the push-driven penetration strategy commonly used by many digging organisms, roots penetrate by growing, adding new cells at the tip, and elongating over a well-defined growth zone. However, a comprehensive understanding of the mechanical aspects associated with root penetration is currently lacking. We perform penetration experiments following Arabidopsis thaliana roots growing into an agar gel environment, and a needle of similar dimensions pushed into the same agar. We measure and compare the environmental deformations in both cases by following the displacement of fluorescent beads embedded within the gel, combining confocal microscopy and Digital Volume Correlation (DVC) analysis. We find that deformations are generally smaller for growing roots. To better understand the mechanical differences between the two penetration strategies, we develop a computational model informed by experiments. Simulations show that, compared to push-driven penetration, grow-driven penetration reduces frictional forces and mechanical work, with lower propagation of displacements in the surrounding medium. These findings shed light on the complex interaction of plant roots with their environment, providing a quantitative understanding based on a comparative approach.

Active shape control by plants in dynamic environments

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along the plant's axis, as in a rotating clinostat, leading to intricate shapes. We use a previously derived rod model to study the response of a growing plant and the joint effects of both stimuli at all rotation speeds. In the absence of rotation, we identify a universal planar shape towards which all shoots eventually converge. With rotation, we demonstrate the existence of a stable family of three-dimensional dynamic equilibria where the plant axis is fixed in space. Further, the effect of axial growth is to induce steady behaviors, such as solitary waves. Overall, this study offers insight into the complex out-of-equilibrium dynamics of a plant in three dimensions and further establishes that internal stimuli in active materials are key for robust shape control.

Temperature Effect on Rhizome Development in Perennial rice

Traditional agriculture is becoming increasingly not adapted to global climate change. Compared with annual rice, perennial rice has strong environmental adaptation and needs fewer natural resources and labor inputs. Rhizome, a kind of underground stem for rice to achieve perenniallity, can grow underground horizontally and then bend upward, developing into aerial stems. The temperature has a great influence on plant development. To date, the effect of temperature on rhizome development is still unknown. Fine temperature treatment of Oryza longistaminata (OL) proved that compared with higher temperatures (28-30 ℃), lower temperature (17-19 ℃) could promote the sprouting of axillary buds and enhance negative gravitropism of branches, resulting in shorter rhizomes. The upward growth of branches was earlier at low temperature than that at high temperature, leading to a high frequency of shorter rhizomes and smaller branch angles. Comparative transcriptome showed that plant hormones played an essential role in the response of OL to temperature. The expressions of ARF17, ARF25 and FucT were up-regulated at low temperature, resulting in prospectively asymmetric auxin distribution, which subsequently induced asymmetric expression of IAA20 and WOX11 between the upper and lower side of the rhizome, further leading to upward growth of the rhizome. Cytokinin and auxin are phytohormones that can promote and inhibit bud outgrowth, respectively. The auxin biosynthesis gene YUCCA1 and cytokinin oxidase/dehydrogenase gene CKX4 and CKX9 were up-regulated, while cytokinin biosynthesis gene IPT4 was down-regulated at high temperature. Moreover, the D3 and D14 in strigolactones pathways, negatively regulating bud outgrowth, were up-regulated at high temperature. These results indicated that cytokinin, auxins, and strigolactones jointly control bud outgrowth at different temperatures. Our research revealed that the outgrowth of axillary bud and the upward growth of OL rhizome were earlier at lower temperature, providing clues for understanding the rhizome growth habit under different temperatures, which would be helpful for cultivating perennial rice.

On the mechanical origins of waving, coiling and skewing in Arabidopsis thaliana roots

By masterfully balancing directed growth and passive mechanics, plant roots are remarkably capable of navigating complex heterogeneous environments to find resources. Here, we present a theoretical and numerical framework which allows us to interrogate and simulate the mechanical impact of solid interfaces on the growth pattern of plant organs. We focus on the well-known waving, coiling, and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined surfaces, serving as a minimal model of the intricate interplay with solid substrates. By modeling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations verify hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane responses. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling, and skewing patterns with substrate tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico plant organs behavior in relation to their environment.

A quantitative model for spatio-temporal dynamics of root gravitropism

Plant organs adapt their morphology according to environmental signals through growth-driven processes called tropisms. While much effort has been directed towards the development of mathematical models describing the tropic dynamics of aerial organs, these cannot provide a good description of roots due to intrinsic physiological differences. Here we present a mathematical model informed by gravitropic experiments on Arabidopsis thaliana roots, assuming a subapical growth profile and apical sensing. The model quantitatively recovers the full spatio-temporal dynamics observed in experiments. An analytical solution of the model enables us to evaluate the gravitropic and proprioceptive sensitivities of roots, while also allowing us to corroborate the requirement for proprioception in describing root dynamics. Lastly, we find that the dynamics are analogous to a damped harmonic oscillator, providing intuition regarding the source of the observed oscillatory behavior and the importance of proprioception for efficient gravitropic control. In all, the model provides not only a quantitative description of root tropic dynamics, but also a mathematical framework for the future investigation of roots in complex media.

Plants sum and subtract stimuli over different timescales

Mounting evidence suggests that plants engage complex computational processes to quantify and integrate sensory information over time, enabling remarkable adaptive growth strategies. However, quantitative understanding of these computational processes is limited. We report experiments probing the dependence of gravitropic responses of wheat coleoptiles on previous stimuli. First, building on a mathematical model that identifies this dependence as a form of memory, or a filter, we use experimental observations to reveal the mathematical principles of how coleoptiles integrate multiple stimuli over time. Next, we perform two-stimulus experiments, informed by model predictions, to reveal fundamental computational processes. We quantitatively show that coleoptiles respond not only to sums but also to differences between stimuli over different timescales, constituting evidence that plants can compare stimuli-crucial for search and regulation processes. These timescales also coincide with oscillations observed in gravitropic responses of wheat coleoptiles, suggesting shoots may combine memory and movement in order to enhance posture control and sensing capabilities.

The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem

Shoot morphogenetic plasticity is crucial to the adaptation of plants to their fluctuating environments. Major insights into shoot morphogenesis have been compiled studying meristems, especially the shoot apical meristem (SAM), through a methodological effort in multiscale systems biology and biophysics. However, morphogenesis at the SAM is robust to environmental changes. Plasticity emerges later on during post-SAM development. The purpose of this review is to show that multiscale systems biology and biophysics is insightful for the shaping of the whole plant as well. More specifically, we review the shaping of axes and crowns through tropisms and elasticity, combining the recent advances in morphogenetic control using physical cues and by genes. We focus mostly on land angiosperms, but with growth habits ranging from small herbs to big trees. We show that generic (universal) morphogenetic processes have been identified, revealing feedforward and feedback effects of global shape on the local morphogenetic process. In parallel, major advances have been made in the analysis of the major genes involved in shaping axes and crowns, revealing conserved genic networks among angiosperms. Then, we show that these two approaches are now starting to converge, revealing exciting perspectives.

Evaluation of Gravitropism in Non-seed Plants

Tropisms are among the most important growth responses for plant adaptation to the surrounding environment. One of the most common tropisms is root gravitropism. Root gravitropism enables the plant to anchor securely to the soil enabling the absorption of water and nutrients. Most of the knowledge related to the plant gravitropism has been acquired from the flowering plants, due to limited research in non-seed plants. Limited research on non-seed plants is due in large part to the lack of standard research methods. Here, we describe the experimental methods to evaluate gravitropism in representative non-seed plant species, including the non-vascular plant moss Physcomitrium patens, the early diverging extant vascular plant lycophyte Selaginella moellendorffii and fern Ceratopteris richardii. In addition, we introduce the methods used for statistical analysis of the root gravitropism in non-seed plant species.

Methods for a Quantitative Comparison of Gravitropism and Posture Control Over a Wide Range of Herbaceous and Woody Species

Quantitative measurements of plant gravitropic response are challenging. Differences in growth rates between species and environmental conditions make it difficult to compare the intrinsic gravitropic responses of different plants. In addition, the bending movement associated with gravitropism is competing with the tendency of plants to grow straight, through a mechanism called proprioception (ability to sense its own shape). Disentangling these two tendencies is not trivial. Here, we use a combination of modeling, experiment and image analysis to estimate the intrinsic gravitropic and proprioceptive sensitivities of stems, using Arabidopsis as an example.

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.

Plant Wearable Sensors Based on FBG Technology for Growth and Microclimate Monitoring

Plants are primary resources for oxygen and foods whose production is fundamental for our life. However, diseases and pests may interfere with plant growth and cause a significant reduction of both the quality and quantity of agriculture products. Increasing agricultural productivity is crucial for poverty reduction and food security improvements. For this reason, the 2030 Agenda for Sustainable Development gives a central role to agriculture by promoting a strong technological innovation for advancing sustainable practices at the plant level. To accomplish this aim, recently, wearable sensors and flexible electronics have been extended from humans to plants for measuring elongation, microclimate, and stressing factors that may affect the plant’s healthy growth. Unexpectedly, fiber Bragg gratings (FBGs), which are very popular in health monitoring applications ranging from civil infrastructures to the human body, are still overlooked for the agriculture sector. In this work, for the first time, plant wearables based on FBG technology are proposed for the continuous and simultaneous monitoring of plant growth and environmental parameters (i.e., temperature and humidity) in real settings. The promising results demonstrated the feasibility of FBG-based sensors to work in real situations by holding the promise to advance continuous and accurate plant health growth monitoring techniques.

Nutations in growing plant shoots as a morphoelastic flutter instability

Growing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed 'circumnutations'. Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Conditions for the emergence of circumnutations in plant roots

The plant root system shows remarkably complex behaviors driven by environmental cues and internal dynamics, whose interplay remains largely unknown. A notable example is circumnutation growth movements, which are growth oscillations from side to side of the root apex. Here we describe a model capable of replicating root growth behaviors, which we used to analyze the role of circumnuntations, revealing their emergence I) under gravitropic stress, as a combination of signal propagation and sensitivity to the signal carriers; II) as a result of the interplay between gravitropic and thigmotropic responses; and III) as a behavioral strategy to detect and react to resource gradients. The latter function requires the presence of a hypothetical internal oscillator whose parameters are regulated by the perception of environmental resources.

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.

Nutations in Plant Shoots: Endogenous and Exogenous Factors in the Presence of Mechanical Deformations

We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms, and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

An Integrative Model of Plant Gravitropism Linking Statoliths Position and Auxin Transport

Gravity is a major cue for the proper growth and development of plants. The response of plants to gravity implies starch-filled plastids, the statoliths, which sediments at the bottom of the gravisensing cells, the statocytes. Statoliths are assumed to modify the transport of the growth hormone, auxin, by acting on specific auxin transporters, PIN proteins. However, the complete gravitropic signaling pathway from the intracellular signal associated to statoliths to the plant bending is still not well-understood. In this article, we build on recent experimental results showing that statoliths do not act as gravitational force sensor, but as position sensor, to develop a bottom-up theory of plant gravitropism. The main hypothesis of the model is that the presence of statoliths modifies PIN trafficking close to the cell membrane. This basic assumption, coupled with auxin transport and growth in an idealized tissue made of a one-dimensional array of cells, recovers several major features of the gravitropic response of plants. First, the model provides a new interpretation for the response of a plant to a steady stimulus, the so-called sine-law of plant gravitropism. Second, it predicts the existence of a gravity-independent memory process as observed recently in experiments studying the response to transient stimulus. The model suggests that the timescale of this process is associated to PIN turnover, calling for new experimental studies.

Spatio-temporal kinematic analysis of shoot gravitropism in Arabidopsis thaliana

Plant shoots can bend upward against gravity, a behavior known as shoot gravitropism. The conventional quantification of shoot bending has been restricted to measurements of shoot tip angle, which cannot fully describe the spatio-temporal bending process. Recently, however, advanced imaging analyses have been developed to quantify in detail the spatio-temporal changes in inclination angle and curvature of the shoot. We used one such method (KymoRod) to analyze the gravitropism of the Arabidopsis thaliana inflorescence stem, and successfully extracted characteristics that capture when and where bending occurs. Furthermore, we implemented an elastic spring theoretical model and successfully determined best fitted parameters that may explain typical bending behaviors of the inflorescence stem. Overall, we propose a data-model combined framework to quantitatively investigate shoot gravitropism in plants.

Multiscale integration of environmental stimuli in plant tropism produces complex behaviors

Plant tropism refers to the directed movement of an organ or organism in response to external stimuli. Typically, these stimuli induce hormone transport that triggers cell growth or deformation. In turn, these local cellular changes create mechanical forces on the plant tissue that are balanced by an overall deformation of the organ, hence changing its orientation with respect to the stimuli. This complex feedback mechanism takes place in a three-dimensional growing plant with varying stimuli depending on the environment. We model this multiscale process in filamentary organs for an arbitrary stimulus by explicitly linking hormone transport to local tissue deformation leading to the generation of mechanical forces and the deformation of the organ in three dimensions. We show, as examples, that the gravitropic, phototropic, nutational, and thigmotropic dynamic responses can be easily captured by this framework. Further, the integration of evolving stimuli and/or multiple contradictory stimuli can lead to complex behavior such as sun following, canopy escape, and plant twining.

The dynamics of plant nutation

In this article we advance a cutting-edge methodology for the study of the dynamics of plant movements of nutation. Our approach, unlike customary kinematic analyses of shape, period, or amplitude, is based on three typical signatures of adaptively controlled processes and motions, as reported in the biological and behavioral dynamics literature: harmonicity, predictability, and complexity. We illustrate the application of a dynamical methodology to the bending movements of shoots of common beans (Phaseolus vulgaris L.) in two conditions: with and without a support to climb onto. The results herewith reported support the hypothesis that patterns of nutation are influenced by the presence of a support to climb in their vicinity. The methodology is in principle applicable to a whole range of plant movements.

By hook or by crook: how and why do compound leaves stay curved during development?

This article comments on:

Rivière M, Corre Y, Peaucelle A, Derr J, Douady S. 2020. The hook shape of growing leaves results from an active regulatory process. Journal of Experimental Botany 71, 6408–6417.

Nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that nonmechanical stimuli can have on modifying the membrane state of stress in a thin shell.

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.

A mathematical model explores the contributions of bending and stretching forces to shoot gravitropism in Arabidopsis

Plant shoot gravitropism is a complex phenomenon resulting from gravity sensing, curvature sensing (proprioception), the ability to uphold self-weight and growth. Although recent data analysis and modelling have revealed the detailed morphology of shoot bending, the relative contribution of bending force (derived from the gravi-proprioceptive response) and stretching force (derived from shoot axial growth) behind gravitropism remains poorly understood. To address this gap, we combined morphological data with a theoretical model to analyze shoot bending in wild-type and lazy1-like 1 mutant Arabidopsis thaliana. Using data from actual bending events, we searched for model parameters that minimized discrepancies between the data and mathematical model. The resulting model suggests that both the bending force and the stretching force differ significantly between the wild type and mutant. We discuss the implications of the mechanical forces associated with differential cell growth and present a plausible mechanical explanation of shoot gravitropism.

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.

Posture control in land plants: growth, position sensing, proprioception, balance, and elasticity

The colonization of the atmosphere by land plants was a major evolutionary step. The mechanisms that allow for vertical growth through air and the establishment and control of a stable erect habit are just starting to be understood. A key mechanism was found to be continuous posture control to counterbalance the mechanical and developmental challenges of maintaining a growing upright structure. An interdisciplinary systems biology approach was invaluable in understanding the underlying principles and in designing pertinent experiments. Since this discovery previously held views of gravitropic perception had to be reexamined and this has led to the description of proprioception in plants. In this review, we take a purposefully pedagogical approach to present the dynamics involved from the cellular to whole-plant level. We show how the textbook model of how plants sense gravitational force has been replaced by a model of position sensing, a clinometer mechanism that involves both passive avalanches and active motion of statoliths, granular starch-filled plastids, in statocytes. Moreover, there is a transmission of information between statocytes and other specialized cells that sense the degree of organ curvature and reset asymmetric growth to straighten and realign the structure. We give an overview of how plants have used the interplay of active posture control and elastic sagging to generate a whole range of spatial displays during their life cycles. Finally, a position-integrating mechanism has been discovered that prevents directional plant growth from being disrupted by wind-induced oscillations.

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.

Revealing the hierarchy of processes and time-scales that control the tropic response of shoots to gravi-stimulations

Gravity is a major abiotic cue for plant growth. However, little is known about the responses of plants to various patterns of gravi-stimulation, with apparent contradictions being observed between the dose-like responses recorded under transient stimuli in microgravity environments and the responses under steady-state inclinations recorded on earth. Of particular importance is how the gravitropic response of an organ is affected by the temporal dynamics of downstream processes in the signalling pathway, such as statolith motion in statocytes or the redistribution of auxin transporters. Here, we used a combination of experiments on the whole-plant scale and live-cell imaging techniques on wheat coleoptiles in centrifuge devices to investigate both the kinematics of shoot-bending induced by transient inclination, and the motion of the statoliths in response to cell inclination. Unlike previous observations in microgravity, the response of shoots to transient inclinations appears to be independent of the level of gravity, with a response time much longer than the duration of statolith sedimentation. This reveals the existence of a memory process in the gravitropic signalling pathway, independent of statolith dynamics. By combining this memory process with statolith motion, a mathematical model is built that unifies the different laws found in the literature and that predicts the early bending response of shoots to arbitrary gravi-stimulations.

A method for the quantification of phototropic and gravitropic sensitivities of plants combining an original experimental device with model-assisted phenotyping: Exploratory test of the method on three hardwood tree species

Perception of inclination in the gravity field and perception of light direction are two important environmental signals implicated in the control of plant shape and habit. However, their quantitative study in light-grown plants remains a challenge. We present a novel method here to determine the sensitivities to gravitropism and phototropism. The method combines: (i) an original experimental device of isotropic light to disentangle gravitropic and phototropic plant responses; and (ii) model-assisted phenotyping using recent models of tropism perception—the AC model for gravitropism alone and the ArC model for gravitropism combined with phototropism. We first assessed the validity of the AC and ArC models on poplar, the classical species model for woody plants. We then tested the method on three woody species contrasted by their habit and tolerance to shade: poplar (Populus tremula*alba), oak (Quercus petraea) and beech (Fagus sylvatica). The method was found to be effective to quantitatively discriminate the tested species by their ratio of tropistic sensitivities. The method thus appears as an interesting tool to quantitatively determine tropistic sensitivities, a prerequisite for assessing the role of tropisms in the control of the variability of the habit and/or tolerance to shade of woody species in the future.

Coupled ultradian growth and curvature oscillations during gravitropic movement in disturbed wheat coleoptiles

To grow straight and upright, plants need 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 (tilting) experiment in order to better understand this unexpectedly strong regulation. Close temporal observations 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 coleoptiles, we discovered a non-trivial coupling between the oscillatory dynamics of curvature and elongation. The relationship between those oscillations and the postural control of the organ remains unclear, but indicates the presence of a mechanism that is capable of affecting the relationship between elongation rate, differential growth, and curvature.

On the growth and form of shoots

Growing plant stems and shoots exhibit a variety of shapes that embody growth in response to various stimuli. Building on experimental observations, we provide a quantitative biophysical theory for these shapes by accounting for the inherent observed passive and active effects: (i) the active controllable growth response of the shoot in response to its orientation relative to gravity, (ii) proprioception, the shoot's growth response to its own observable current shape, and (iii) the passive elastic deflection of the shoot due to its own weight, which determines the current shape of the shoot. Our theory separates the sensed and actuated variables in a growing shoot and results in a morphospace diagram in terms of two dimensionless parameters representing a scaled local active gravitropic sensitivity, and a scaled passive elastic sag. Our computational results allow us to explain the variety of observed transient and steady morphologies with effective positive, negative and even oscillatory gravitropic behaviours, without the need for ad hoc complex spatio-temporal control strategies in terms of these parameters. More broadly, our theory is applicable to the growth of soft, floppy organs where sensing and actuation are dynamically coupled through growth processes via shape.

Space-time analysis of gravitropism in etiolated Arabidopsis hypocotyls using bioluminescence imaging of the IAA19 promoter fusion with a destabilized luciferase reporter

Imaging analysis was carried out during the gravitropic response of etiolated Arabidopsis hypocotyls, using an IAA19 promoter fusion of destabilized luciferase as a probe. From the bright-field images we obtained the local deflection angle to the vertical, A, local curvature, C, and the partial derivative of C with respect to time, [Formula: see text]. These were determined every 19.9 µm along the curvilinear length of the hypocotyl, at ~10 min intervals over a period of ~6 h after turning hypocotyls through 90° to the horizontal. Similarly from the luminescence images we measured the luminescence intensity of the convex and concave flanks of the hypocotyl as well as along the median of the hypocotyl, to determine differential expression of auxin-inducible IAA19. Comparison of these parameters as a function of time and curvilinear length shows that the gravitropic response is composed of three successive elements: the first and second curving responses and a decurving response (autostraightening). The maximum of the first curving response occurs when A is 76° along the entire length of the hypocotyl, suggesting that A is the sole determinant in this response; in contrast, the decurving response is a function of both A and C, as predicted by the newly-proposed graviproprioception model (Bastien et al., Proc Natl Acad Sci USA 110:755-760, 2013). Further, differential expression of IAA19, with higher expression in the convex flank, is observed at A = 44°, and follows the Sachs' sine law. This also suggests that IAA19 is not involved in the first curving response. In summary, the gravitropic response of Arabidopsis hypocotyls consists of multiple elements that are each determined by separate principles.

A new scenario for gravity detection in plants: the position sensor hypothesis

The detection of gravity plays a fundamental role during the growth and evolution of plants. Although progress has been made in our understanding of the molecular, cellular and physical mechanisms involved in the gravity detection, a coherent scenario consistent with all the observations is still lacking. In this special issue article, we discuss recent experiments showing that the response to inclination of shoots is independent of the gravity intensity, meaning that the gravity sensor detects an inclination and not a force. This result questions some of the commonly accepted hypotheses and leads to propose a new 'position sensor hypothesis'. The implications of this new scenario are discussed in light of the different observations available in the literature.

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

Nutation is an oscillatory movement that plants display during their development. Despite its ubiquity among plants movements, the relation between the observed movement and the underlying biological mechanisms remains unclear. Here we show that the kinematics of the full organ in 3D give a simple picture of plant nutation, where the orientation of the curvature along the main axis of the organ aligns with the direction of maximal differential growth. Within this framework we reexamine the validity of widely used experimental measurements of the apical tip as markers of growth dynamics. We show that though this relation is correct under certain conditions, it does not generally hold, and is not sufficient to uncover the specific role of each mechanism. As an example we re-interpret previously measured experimental observations using our model.

In his writings, Darwin considered nutation, the revolving movement of the apical tip of plants, as the most widespread plant movement. In spite of its ubiquity, plant nutation has not received as much attention as other plant movements, and its underlying mechanism remains unclear. A better understanding of this presumably growth-driven process is bound to shed light on basic growth processes in plants. In the work presented here we redefine the problem by describing the kinematics in three dimensions, as opposed to the typical description restricted to the horizontal plane. Within this framework we reveal a simple picture of the underlying dynamics, where the orientation of curvature follows the orientation of maximal differential growth. This parsimonious model recovers the major classes of nutation patterns, as shown both analytically and numerically. We then discuss the limitations of classical measurements where only the movement of the apical tip is tracked, suggesting more adequate measurements.

KymoRod: a method for automated kinematic analysis of rod-shaped plant organs

A major challenge in plant systems biology is the development of robust, predictive multiscale models for organ growth. In this context it is important to bridge the gap between the, rather well-documented molecular scale and the organ scale by providing quantitative methods to study within-organ growth patterns. Here, we describe a simple method for the analysis of the evolution of growth patterns within rod-shaped organs that does not require adding markers at the organ surface. The method allows for the simultaneous analysis of root and hypocotyl growth, provides spatio-temporal information on curvature, growth anisotropy and relative elemental growth rate and can cope with complex organ movements. We demonstrate the performance of the method by documenting previously unsuspected complex growth patterns within the growing hypocotyl of the model species Arabidopsis thaliana during normal growth, after treatment with a growth-inhibiting drug or in a mechano-sensing mutant. The method is freely available as an intuitive and user-friendly Matlab application called KymoRod.

Inclination not force is sensed by plants during shoot gravitropism

Gravity perception plays a key role in how plants develop and adapt to environmental changes. However, more than a century after the pioneering work of Darwin, little is known on the sensing mechanism. Using a centrifugal device combined with growth kinematics imaging, we show that shoot gravitropic responses to steady levels of gravity in four representative angiosperm species is independent of gravity intensity. All gravitropic responses tested are dependent only on the angle of inclination from the direction of gravity. We thus demonstrate that shoot gravitropism is stimulated by sensing inclination not gravitational force or acceleration as previously believed. This contrasts with the otolith system in the internal ear of vertebrates and explains the robustness of the control of growth direction by plants despite perturbations like wind shaking. Our results will help retarget the search for the molecular mechanism linking shifting statoliths to signal transduction.

How do plants read their own shapes?

Contents 333 I. 333 II. 334 III. 334 IV. 336 336 References 337 SUMMARY: Although the sensing of shape and deformation was historically involved in the control of animal locomotion, it is now increasingly being incorporated in developmental biology. Proprioception, the perception of the self, is particularly key to the question of the reproducibility of shapes: the many regulators of growth may lead to a large array of geometries, but shape sensing restricts these diverse outputs to a limited number of forms. Mechanistically, and in addition to geometrical feedback onto the diffusion and transport of molecular factors, we highlight the role of shape-derived mechanical stress and strain in this process. Through examples at the cell, tissue and organism scales, it appears that such mechanical feedback adds robustness to morphogenesis. Interestingly, synergies exist between shape sensing and response to external cues, such as wind and gravity. Understanding the molecular basis of proprioception is now within reach and opens up many avenues for an integrative view of development.

Morphometric analyses of petioles of seedlings grown in a spaceflight experiment

Gravity is a constant unidirectional stimulus on Earth, and gravitropism in plants involves three phases: perception, transduction, and response. In shoots, perception takes place within the endodermis. To investigate the cellular machinery of perception in microgravity, we conducted a spaceflight study with Arabidopsis thaliana seedlings, which were grown in microgravity in darkness using the Biological Research in Canisters (BRIC) hardware during space shuttle mission STS-131. In the 14-day-old etiolated plants, we studied seedling development and the morphological parameters of the endodermal cells in the petiole. Seedlings from the spaceflight experiment (FL) were compared to a ground control (GC), which both were in the BRIC flight hardware. In addition, to assay any potential effects from growth in spaceflight hardware, we performed another control by growing seedlings in Petri dishes in standard laboratory conditions (termed the hardware control, HC). Seed germination was significantly lower in samples grown in flight hardware (FL, GC) compared to the HC. In terms of cellular parameters of endodermal cells, the greatest differences also were between seedlings grown in spaceflight hardware (FL, GC) compared to those grown outside of this hardware (HC). Specifically, the endodermal cells were significantly smaller in seedlings grown in the BRIC system compared to those in the HC. However, a change in the shape of the cell, suggesting alterations in the cell wall, was one parameter that appears to be a true microgravity effect. Taken together, our results suggest that caution must be taken when interpreting results from the increasingly utilized BRIC spaceflight hardware system and that it is important to perform additional ground controls to aid in the analysis of spaceflight experiments.

A unified model of shoot tropism in plants: photo-, gravi- and Propio-ception

Land plants rely mainly on gravitropism and phototropism to control their posture and spatial orientation. In natural conditions, these two major tropisms act concurrently to create a photogravitropic equilibrium in the responsive organ. Recently, a parsimonious model was developed that accurately predicted the complete gravitropic and proprioceptive control over the movement of different organs in different species in response to gravitational stimuli. Here we show that the framework of this unifying graviproprioceptive model can be readily extended to include phototropism. The interaction between gravitropism and phototropism results in an alignment of the apical part of the organ toward a photogravitropic set-point angle. This angle is determined by a combination of the two directional stimuli, gravity and light, weighted by the ratio between the gravi- and photo-sensitivities of the plant organ. In the model, two dimensionless numbers, the graviproprioceptive number B and the photograviceptive number M, control the dynamics and the shapes of the movement. The extended model agrees well with two sets of detailed quantitative data on photogravitropic equilibrium in oat coleoptiles. It is demonstrated that the influence of light intensity I can be included in the model in a power-law-dependent relationship M(I). The numbers B and M and the related photograviceptive number D are all quantitative genetic traits that can be measured in a straightforward manner, opening the way to the phenotyping of molecular and mechanical aspects of shoot tropism.

Mechanosensitive control of plant growth: bearing the load, sensing, transducing, and responding

As land plants grow and develop, they encounter complex mechanical challenges, especially from winds and turgor pressure. Mechanosensitive control over growth and morphogenesis is an adaptive trait, reducing the risks of breakage or explosion. This control has been mostly studied through experiments with artificial mechanical loads, often focusing on cellular or molecular mechanotransduction pathway. However, some important aspects of mechanosensing are often neglected. (i) What are the mechanical characteristics of different loads and how are loads distributed within different organs? (ii) What is the relevant mechanical stimulus in the cell? Is it stress, strain, or energy? (iii) How do mechanosensing cells signal to meristematic cells? Without answers to these questions we cannot make progress analyzing the mechanobiological effects of plant size, plant shape, tissue distribution and stiffness, or the magnitude of stimuli. This situation is rapidly changing however, as systems mechanobiology is being developed, using specific biomechanical and/or mechanobiological models. These models are instrumental in comparing loads and responses between experiments and make it possible to quantitatively test biological hypotheses describing the mechanotransduction networks. This review is designed for a general plant science audience and aims to help biologists master the models they need for mechanobiological studies. Analysis and modeling is broken down into four steps looking at how the structure bears the load, how the distributed load is sensed, how the mechanical signal is transduced, and then how the plant responds through growth. Throughout, two examples of adaptive responses are used to illustrate this approach: the thigmorphogenetic syndrome of plant shoots bending and the mechanosensitive control of shoot apical meristem (SAM) morphogenesis. Overall this should provide a generic understanding of systems mechanobiology at work.

Spaceflight exploration in plant gravitational biology

Before there was access to space, all experiments on plant tropisms were conducted upon the background of gravity. The gravity vector could be disrupted, such as with clinorotation and random positioning machines, and by manipulating incident angles of root growth with respect to gravity, such as with Darwin's plants on slanted plates, but gravity could not be removed from the experimental equation. Access to microgravity through spaceflight has opened new doors to plant research. Here we provide an overview of some of the methodologies of conducting plant research in the unique spaceflight environment.

Gravity sensing, a largely misunderstood trigger of plant orientated growth

Gravity is a crucial environmental factor regulating plant growth and development. Plants have the ability to sense a change in the direction of gravity, which leads to the re-orientation of their growth direction, so-called gravitropism. In general, plant stems grow upward (negative gravitropism), whereas roots grow downward (positive gravitropism). Models describing the gravitropic response following the tilting of plants are presented and highlight that gravitropic curvature involves both gravisensing and mechanosensing, thus allowing to revisit experimental data. We also discuss the challenge to set up experimental designs for discriminating between gravisensing and mechanosensing. We then present the cellular events and the molecular actors known to be specifically involved in gravity sensing.