Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants

Overcoming Challenges in Plant Biomechanics: Methodological Innovations and Technological Integration

Plant biomechanics, an emerging interdisciplinary field, plays an irreplaceable role in revealing the structure-function relationships in plant life processes. This field integrates classical mechanical theories with modern biological methods, providing novel perspectives for plant phenotype research and offering significant theoretical guidance for crop breeding, cultivation management, and ecological protection. This review comprehensively examines existing research from three dimensions: research perspectives, methodologies, and content. Using maize lodging as a case study, key scientific questions, research methods, and modeling strategies are analyzed across scales from molecular to population levels. Furthermore, this paper identifies the main challenges in plant biomechanics research, particularly in methodology development, theoretical framework refinement, model simulation, and 3D modeling. Finally, innovative directions and application prospects are explored for integrating plant biomechanics with artificial intelligence technology, multi-scale modeling, genetic improvement, and biomimetics. These research advances will pave new paths for theoretical innovation and practical applications in plant biomechanics.

Physical obstacles in the substrate cause maize root growth trajectories to switch from vertical to oblique

Hard pans, soil compaction, soil aggregation, and stones create physical barriers that can affect the development of a root system. Roots are known to exploit paths of least resistance to avoid such obstacles, but the mechanism through which this is achieved is not well understood. Here, we used a combination of 3D-printed substrates with a high-throughput live-imaging platform to study the responses of maize roots to a range of physical barriers. Using image analysis algorithms, we determined the properties of growth trajectories and identified how the presence of rigid circular obstacles affects the ability of a primary root to maintain its vertical trajectory. The results showed that the types of growth responses were limited, with both vertical and oblique trajectories being found to be stable and influenced by the size of the obstacles. When obstacles were of intermediate sizes, trajectories were unstable and changed in nature through time. We formalized the conditions required for root trajectory to change from vertical to oblique, linking the angle at which the root detaches from the obstacle to the root curvature due to gravitropism. Exploitation of paths of least resistance by a root might therefore be constrained by the ability of the root to curve and respond to gravitropic signals.

Extending cognition: a vegetal rejoinder to extensionless thought and to extended cognition

In this paper, we propose a crucial supplement to the framework of plant cognition, namely extending cognition. We argue that plants and other organisms with an open-ended body plan actively extend their cognition when growing tissues or organs. Their cognition expands with their body expansion. After considering the defining features of extending cognition, we present a model where growth, along with aspects of plant physiology (e.g. biochemical exudates), as well as the "negative extension" of growing away from obstacles or stressful environments, are the building blocks for a more refined understanding of plant cognition. We conclude by outlining the general implications of the theory of extending cognition and indicating directions for future research.

Quantitative analysis of the root posture of Arabidopsis thaliana mutants with wavy roots

Plant postures are affected by environmental stimuli. When the gravitational direction changes, the Arabidopsis thaliana mutants myosin xif xik (xif xik) and atp-binding cassette b19 (abcb19) exhibit aberrantly enhanced organ bending. Whether their phenotypes are due to the same mechanism is unknown. We characterized the primary root postures of these mutants. Their roots exhibited enhanced gravitropic bending with the same root-tip angles. The wavy roots of vertically grown plants were quantitatively evaluated using four indices. The straightness index (root base-to-tip length to total root-length ratio) was similar for xif xik and abcb19, and it slightly decreased for xif xik abcb19. The curvature index was similar for abcb19 and xif xik abcb19, but it decreased for xif xik, suggesting the ABCB19 deficiency caused the roots to curve more sharply. Combination of these indices for quantitative analyses of root postures may distinguish between similar wavy-root phenotypes and clarify genetic relationships.

Gravitropic Gene Expression Divergence Associated With Adaptation to Contrasting Environments in an Australian Wildflower

Plants adapt to their local environment through complex interactions between genes, gene networks and hormones. Although the impact of gene expression on trait regulation and evolution has been recognised for many decades, its role in the evolution of adaptation is still a subject of intense exploration. We used a Multi-parent Advanced Generation Inter-Cross (MAGIC) population, which we derived from crossing multiple parents from two distinct coastal ecotypes of an Australia wildflower, Senecio lautus. We focused on studying the contrasting gravitropic behaviours of these ecotypes, which have evolved independently multiple times and show strong responses to natural selection in field experiments, emphasising the role of natural selection in their evolution. Here, we investigated how gene expression differences have contributed to the adaptive evolution of gravitropism. We studied gene expression in 60 pools at five time points (30, 60, 120, 240 and 480 min) after rotating half of the pools 90°. We found 428 genes with differential expression in response to the 90° rotation treatment. Of these, 81 genes (~19%) have predicted functions related to the plant hormones auxin and ethylene, which are crucial for the gravitropic response. By combining insights from Arabidopsis mutant studies and analysing our gene networks, we propose a preliminary model to explain the differences in gravitropism between ecotypes. This model suggests that the differences arise from changes in the transport and availability of the two hormones auxin and ethylene. Our findings indicate that the genetic basis of adaptation involves interconnected signalling pathways that work together to give rise to new ecotypes.

Curvature in plants

Curvatures are ubiquitous in the animal kingdom - the spiral shell of the nautilus and the corkscrew horns of the blackbuck being iconic examples. Dynamic changes in curvature (i.e., curving) are most striking in the locomotion of some animal species - swimming in fishes and mollusks, looping in leeches, undulatory locomotion in snakes and lampreys, and also sperm motility through flagellum beating. When it comes to plants, which are sessile organisms with a rigid body, the terms 'curvature' and 'curving' evoke very different images - leaves of grass swaying in the breeze, a trunk dangerously bent by a powerful gust of wind, a branch sagging under the weight of its own fruits, as well as the frail arabesques of twining plants like the morning glory and the ivy, which were so influential in the Art Nouveau movement and many other artistic traditions. These various vegetal curves not only prompt creative inspiration in the mind of the beholder, they also initiate signaling cascades leading to developmental responses of the plant. Conversely, curvature can result from a biologically active process in response to an internal or external stimulus. Active curving or decurving are indeed important aspects of the plastic interplay of the developmental program of plants and their environment. Although easily accessible to observation, curvature and curving have only recently become the focus of active research in plant development. Lying at the nexus of biology, physics and mathematics, they require an interdisciplinary approach. The aim of this primer is to give readers an intuitive but accurate understanding of what curvature and curving are, as observed in the plant kingdom, then a more formal definition. We will discuss their role in plant development, both as a signal and as a response, and finally the practical issues and solutions involved in measuring plant curvatures.

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.

Parametrization of biological assumptions to simulate growth of tree branching architectures

Modeling and simulating the growth of the branching of tree species remains a challenge. With existing approaches, we can reconstruct or rebuild the branching architectures of real tree species, but the simulation of the growth process remains unresolved. First, we present a tree growth model to generate branching architectures that resemble real tree species. Secondly, we use a quantitative morphometric approach to infer the shape similarity of the generated simulations and real tree species. Within a functional-structural plant model, we implement a set of biological parameters that affect the branching architecture of trees. By modifying the parameter values, we aim to generate basic shapes of spruce, pine, oak and poplar. Tree shapes are compared using geometric morphometrics of landmarks that capture crown and stem outline shapes. Five biological parameters, namely xylem flow, shedding rate, proprioception, gravitysense and lightsense, most influenced the generated tree branching patterns. Adjusting these five parameters resulted in the different tree shapes of spruce, pine, oak, and poplar. The largest effect was attributed to gravity, as phenotypic responses to this effect resulted in different growth directions of gymnosperm and angiosperm branching architectures. Since we were able to obtain branching architectures that resemble real tree species by adjusting only a few biological parameters, our model is extendable to other tree species. Furthermore, the model will also allow the simulation of structural tree-environment interactions. Our simplifying approach to shape comparison between tree species, landmark geometric morphometrics, showed that even the crown-trunk outlines capture species differences based on their contrasting branching architectures.

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.

Multiple light signaling pathways control solar tracking in sunflowers

Sunflowers are famous for their ability to track the sun throughout the day and then reorient at night to face east the following morning. This occurs by differential growth patterns, with the east sides of stems growing more during the day and the west sides of stems growing more at night. This process, termed heliotropism, is generally believed to be a specialized form of phototropism; however, the underlying mechanism is unknown. To better understand heliotropism, we compared gene expression patterns in plants undergoing phototropism in a controlled environment and in plants initiating and maintaining heliotropic growth in the field. We found the expected transcriptome signatures of phototropin-mediated phototropism in sunflower stems bending towards monochromatic blue light. Surprisingly, the expression patterns of these phototropism-regulated genes are quite different in heliotropic plants. Most genes rapidly induced during phototropism display only minor differences in expression across solar tracking stems. However, some genes that are both rapidly induced during phototropism and are implicated in growth responses to foliar shade are rapidly induced on the west sides of stems at the onset of heliotropism, suggesting a possible role for red light photoreceptors in solar tracking. To test the involvement of different photoreceptor signaling pathways in heliotropism, we modulated the light environment of plants initiating solar tracking. We found that depletion of either red and far-red light or blue light did not hinder the initiation or maintenance of heliotropism in the field. Together, our results suggest that the transcriptional regulation of heliotropism is distinct from phototropin-mediated phototropism and likely involves inputs from multiple light signaling pathways.

A 2D model to study how secondary growth affects the self-supporting behaviour of climbing plants

Climbing plants exhibit specialized shoots, called "searchers", to cross spaces and alternate between spatially discontinuous supports in their natural habitats. To achieve this task, searcher shoots combine both primary and secondary growth processes of their stems in order to support, orientate and explore their extensional growth into the environment. Currently, there is an increasing interest in developing models to describe plant growth and posture. However, the interactions between the sensing activity (e.g. photo-, gravi-, proprioceptive sensing) and the elastic responses are not yet fully understood. Here, we aim to model the extension and rigidification of searcher shoots. Our model defines variations in the radius (and consequently in mass distribution) along the shoot based on experimental data collected in natural habitats of two climbing species: Trachelospermum jasminoides (Lindl.) Lem. and Condylocarpon guianense Desf.. Using this framework, we predicted the sensory aspect of a plant, that is, the plant's response to external stimuli, and the plant's proprioception, that is, the plant's "self-awareness". The results suggest that the inclusion of the secondary growth in a model is fundamental to predict the postural development and self-supporting growth phase of shoots in climbing plants.

Shoot gravitropism and organ straightening cooperate to arrive at a mechanically favorable shape in Arabidopsis

Gravitropism is the plant organ bending in response to gravity, while a straightening mechanism prevents bending beyond the gravitropic set-point angle. The promotion and prevention of bending occur simultaneously around the inflorescence stem tip. How these two opposing forces work together and what part of the stem they affect are unknown. To understand the mechanical forces involved, we rotated wild type and organ-straightening-deficient mutant (myosin xif xik) Arabidopsis plants to a horizontal position to initiate bending. The mutant stems started to bend before the wild-type stems, which led us to hypothesize that the force preventing bending was weaker in mutant. We modeled the wild-type and mutant stems as elastic rods, and evaluated two parameters: an organ-angle-dependent gravitropic-responsive parameter (β) and an organ-curvature-dependent proprioceptive-responsive parameter (γ). Our model showed that these two parameters were lower in mutant than in wild type, implying that, unexpectedly, both promotion and prevention of bending are weak in mutant. Subsequently, finite element method simulations revealed that the compressive stress in the middle of the stem was significantly lower in wild type than in mutant. The results of this study show that myosin-XIk-and-XIf-dependent organ straightening adjusts the stress distribution to achieve a mechanically favorable shape.

Multiple mechanisms behind plant bending

To survive, plants constantly adapt their body shape to their environment. This often involves remarkably rapid bending of their organs such as stems, leaves and roots. Since plant cells are enclosed by stiff cell walls, they use various strategies for bending their organs, which differ from bending mechanisms of soft animal tissues and involve larger physical forces. Here we attempt to summarize and link different viewpoints on bending mechanisms: genes and signalling, mathematical modelling and biomechanics. We argue that quantifying cell growth and physical forces could open a new level in our understanding of bending and resolve some of its paradoxes.

Plant responses to hypergravity: a comprehensive review

Hypergravity is an effective novel stimulus to elucidate plant gravitational and mechanobiological behaviour. Here, we review the current understanding of phenotypic, physio-biochemical, and molecular plant responses to simulated hypergravity. Plants readily respond to altered gravity conditions, such as microgravity or hypergravity. Hypergravity-a gravitational force higher than that on the Earth's surface (> 1g)-can be simulated using centrifuges. Exposing seeds, seedlings, or plant cell cultures to hypergravity elicits characteristic morphological, physio-biochemical, and molecular changes. While several studies have provided insights into plant responses and underlying mechanisms, much is still elusive, including the interplay of hypergravity with gravitropism. Moreover, hypergravity is of great significance for mechano- and space/gravitational biologists to elucidate fundamental plant behaviour. In this review, we provide an overview of the phenotypic, physiological, biochemical, and molecular responses of plants to hypergravity. We then discuss the involvement of hypergravity in plant gravitropism-the directional growth along the gravity vector. Finally, we highlight future research directions to expand our understanding of hypergravity in plant biology.

Mechanosensing, from forces to structures

Sessile plants evolve diverse structures in response to complex environmental cues. These factors, in essence, involve mechanical stimuli, which must be sensed and coordinated properly by the plants to ensure effective growth and development. While we have accumulated substantial knowledge on plant mechanobiology, how plants translate mechanical information into three-dimensional structures is still an open question. In this review, we summarize our current understanding of plant mechanosensing at different levels, particularly using Arabidopsis as a model plant system. We also attempt to abstract the mechanosensing process and link the gaps from mechanical cues to the generation of complex plant structures. Here we review the recent advancements on mechanical response and transduction in plant morphogenesis, and we also raise several questions that interest us in different sections.

Gravity sensing and responses in the coordination of the shoot gravitropic setpoint angle

Gravity is one of the fundamental environmental cues that affect plant development. Indeed, the plant architecture in the shoots and roots is modulated by gravity. Stems grow vertically upward, whereas lateral organs, such as the lateral branches in shoots, tend to grow at a specific angle according to a gravity vector known as the gravitropic setpoint angle (GSA). During this process, gravity is sensed in specialised gravity-sensing cells named statocytes, which convert gravity information into biochemical signals, leading to asymmetric auxin distribution and driving asymmetric cell division/expansion in the organs to achieve gravitropism. As a hypothetical offset mechanism against gravitropism to determine the GSA, the anti-gravitropic offset (AGO) has been proposed. According to this concept, the GSA is a balance of two antagonistic growth components, that is gravitropism and the AGO. Although the nature of the AGO has not been clarified, studies have suggested that gravitropism and the AGO share a common gravity-sensing mechanism in statocytes. This review discusses the molecular mechanisms underlying gravitropism as well as the hypothetical AGO in the control of the GSA.

A perspective on plant robotics: from bioinspiration to hybrid systems

As miscellaneous as the Plant Kingdom is, correspondingly diverse are the opportunities for taking inspiration from plants for innovations in science and engineering. Especially in robotics, properties like growth, adaptation to environments, ingenious materials, sustainability, and energy-effectiveness of plants provide an extremely rich source of inspiration to develop new technologies-and many of them are still in the beginning of being discovered. In the last decade, researchers have begun to reproduce complex plant functions leading to functionality that goes far beyond conventional robotics and this includes sustainability, resource saving, and eco-friendliness. This perspective drawn by specialists in different related disciplines provides a snapshot from the last decade of research in the field and draws conclusions on the current challenges, unanswered questions on plant functions, plant-inspired robots, bioinspired materials, and plant-hybrid systems looking ahead to the future of these research fields.

A mechano-sensing mechanism for waving in plant roots

Arabidopsis roots grown on inclined agar surfaces exhibit unusual sinusoidal patterns known as root-waving. The origin of these patterns has been ascribed to both genetic and environmental factors. Here we propose a mechano-sensing model for root-waving, based on a combination of friction induced by gravitropism, the elasticity of the root and the anchoring of the root to the agar by thin hairs, and demonstrate its relevance to previously obtained experimental results. We further test the applicability of this model by performing experiments in which we measure the effect of gradually changing the inclination angles of the agar surfaces on the wavelength and other properties of the growing roots. We find that the observed dynamics is different than the dynamics reported in previous works, but that it can still be explained using the same mechano-sensing considerations. This is supported by the fact that a scaling relation derived from the model describes the observed dependence of the wavelength on the tilt angle for a large range of angles. We also compare the prevalence of waving in different plant species and show that it depends on root thickness as predicted by the model. The results indicate that waving can be explained using mechanics and gravitropism alone and that mechanics may play a greater role in root growth and form than was previously considered.

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.

Environmental-biomechanical reciprocity and the evolution of plant material properties

Abiotic-biotic interactions have shaped organic evolution since life first began. Abiotic factors influence growth, survival, and reproductive success, whereas biotic responses to abiotic factors have changed the physical environment (and indeed created new environments). This reciprocity is well illustrated by land plants who begin and end their existence in the same location while growing in size over the course of years or even millennia, during which environment factors change over many orders of magnitude. A biomechanical, ecological, and evolutionary perspective reveals that plants are (i) composed of materials (cells and tissues) that function as cellular solids (i.e. materials composed of one or more solid and fluid phases); (ii) that have evolved greater rigidity (as a consequence of chemical and structural changes in their solid phases); (iii) allowing for increases in body size and (iv) permitting acclimation to more physiologically and ecologically diverse and challenging habitats; which (v) have profoundly altered biotic as well as abiotic environmental factors (e.g. the creation of soils, carbon sequestration, and water cycles). A critical component of this evolutionary innovation is the extent to which mechanical perturbations have shaped plant form and function and how form and function have shaped ecological dynamics over the course of evolution.

Plant Gravitropism: From Mechanistic Insights into Plant Function on Earth to Plants Colonizing Other Worlds

Gravitropism, the growth of roots and shoots toward or away from the direction of gravity, has been studied for centuries. Such studies have not only led to a better understanding of the gravitropic process itself, but also paved new paths leading to deeper mechanistic insights into a wide range of research areas. These include hormone biology, cell signal transduction, regulation of gene expression, plant evolution, and plant interactions with a variety of environmental stimuli. In addition to contributions to basic knowledge about how plants function, there is accumulating evidence that gravitropism confers adaptive advantages to crops, particularly under marginal agricultural soils. Therefore, gravitropism is emerging as a breeding target for enhancing agricultural productivity. Moreover, research on gravitropism has spawned several studies on plant growth in microgravity that have enabled researchers to uncouple the effects of gravity from other tropisms. Although rapid progress on understanding gravitropism witnessed during the past decade continues to be driven by traditional molecular, physiological, and cell biological tools, these tools have been enriched by technological innovations in next-generation omics platforms and microgravity analog facilities. In this chapter, we review the field of gravitropism by highlighting recent landmark studies that have provided unique insights into this classic research topic while also discussing potential contributions to agriculture on Earth and beyond.

Embodiment in distributed information processing: "Solid" plants versus "liquid" ant colonies

Information processing is an essential part of biology, enabling coordination of intra-organismal processes such as development, environmental adaptation and inter-organismal communication. Whilst in animals with specialised brain tissue a substantial amount of information processing occurs in a centralised manner, most biological computing is distributed across multiple entities, such as cells in a tissue, roots in a root system or ants in a colony. Physical context, called embodiment, also affects the nature of biological computing. While plants and ant colonies both perform distributed computing, in plants the units occupy fixed positions while individual ants move around. This distinction, solid versus liquid brain computing, shapes the nature of computations. Here we compare information processing in plants and ant colonies, highlighting how similarities and differences originate in, as well as make use of, the differences in embodiment. We end with a discussion on how this embodiment perspective may inform the debate on plant cognition.

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.

The Inducible Accumulation of Cell Wall-Bound p-Hydroxybenzoates Is Involved in the Regulation of Gravitropic Response of Poplar

Lignin in Populus species is acylated with p-hydroxybenzoate. Monolignol p-hydroxybenzoyltransferase 1 (PHBMT1) mediates p-hydroxybenzoylation of sinapyl alcohol, eventually leading to the modification of syringyl lignin subunits. Angiosperm trees upon gravistimulation undergo the re-orientation of their growth along with the production of specialized secondary xylem, i.e., tension wood (TW), that generates tensile force to pull the inclined stem or leaning branch upward. Sporadic evidence suggests that angiosperm TW contains relatively a high percentage of syringyl lignin and lignin-bound p-hydroxybenzoate. However, whether such lignin modification plays a role in gravitropic response remains unclear. By imposing mechanical bending and/or gravitropic stimuli to the hybrid aspens in the wild type (WT), lignin p-hydroxybenzoate deficient, and p-hydroxybenzoate overproduction plants, we examined the responses of plants to gravitropic/mechanical stress and their cell wall composition changes. We revealed that mechanical bending or gravitropic stimulation not only induced the overproduction of crystalline cellulose fibers and increased the relative abundance of syringyl lignin, but also significantly induced the expression of PHBMT1 and the increased accumulation of p-hydroxybenzoates in TW. Furthermore, we found that although disturbing lignin-bound p-hydroxybenzoate accumulation in the PHBMT1 knockout and overexpression (OE) poplars did not affect the major chemical composition shifts of the cell walls in their TW as occurred in the WT plants, depletion of p-hydroxybenzoates intensified the gravitropic curving of the plantlets in response to gravistimulation, evident with the enhanced stem secant bending angle. By contrast, hyperaccumulation of p-hydroxybenzoates mitigated gravitropic response. These data suggest that PHBMT1-mediated lignin modification is involved in the regulation of poplar gravitropic response and, likely by compromising gravitropism and/or enhancing autotropism, negatively coordinates the action of TW cellulose fibers to control the poplar wood deformation and plant growth.

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.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

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.

Mechanostimulation: a promising alternative for sustainable agriculture practices

Plants memorize events associated with environmental fluctuations. The integration of environmental signals into molecular memory allows plants to cope with future stressors more efficiently-a phenomenon that is known as 'priming'. Primed plants are more resilient to environmental stresses than non-primed plants, as they are capable of triggering more robust and faster defence responses. Interestingly, exposure to various forms of mechanical stimuli (e.g. touch, wind, or sound vibration) enhances plants' basal defence responses and stress tolerance. Thus, mechanostimulation appears to be a potential priming method and a promising alternative to chemical-based priming for sustainable agriculture. According to the currently available method, mechanical treatment needs to be repeated over a month to alter plant growth and defence responses. Such a long treatment protocol restricts its applicability to fast-growing crops. To optimize the protocol for a broad range of crops, we need to understand the molecular mechanisms behind plant mechanoresponses, which are complex and depend on the frequency, intervals, and duration of the mechanical treatment. In this review, we synthesize the molecular underpinnings of plant mechanoperception and signal transduction to gain a mechanistic understanding of the process of mechanostimulated priming.

Plant tropisms as a window on plant computational processes

Plants are living information-processing organisms with highly adaptive behavior, allowing them to prosper in a harsh and fluctuating environment in spite of being sessile. Lacking a central nervous system, plants are distributed systems orchestrating complex computational processes performed at the tissue level. Here I consider plant tropisms as a useful input-output system boasting a robust mathematical description, naturally permitting a dialogue between mathematical modeling and biological observations. I propose tropisms as an ideal framework for the study of plant computational processes, allowing us to infer the relationship between observed tropic responses and known stimuli. I concentrate on macroscopic models, and elucidate this approach by presenting recent examples focusing on computational processes involved at different hierarchical levels of interactions: a plant's interaction with itself and its internal state, with the abiotic environment, and with neighboring plants.

How Mechanical Forces Shape Plant Organs

Plants produce organs of various shapes and sizes. While much has been learned about genetic regulation of organogenesis, the integration of mechanics in the process is also gaining attention. Here, we consider the role of forces as instructive signals in organ morphogenesis. Turgor pressure is the primary cause of mechanical signals in developing organs. Because plant cells are glued to each other, mechanical signals act, in essence, at multiple scales, through cell wall contiguity and water flux. In turn, cells use such signals to resist mechanical stress, for instance, by reinforcing their cell walls. We show that the three elemental shapes behind plant organs - spheres, cylinders and lamina - can be actively maintained by such a mechanical feedback. Combinations of this 3-letter alphabet can generate more complex shapes. Furthermore, mechanical conflicts emerge at the boundary between domains exhibiting different growth rates or directions. These secondary mechanical signals contribute to three other organ shape features - folds, shape reproducibility and growth arrest. The further integration of mechanical signals with the molecular network offers many fruitful prospects for the scientific community, including the role of proprioception in organ shape robustness or the definition of cell and organ identities as a result of an interplay between biochemical and mechanical signals.

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 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.

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.

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.

Spatio-temporal integration in plant tropisms

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 stimulus expresses the response function as a function of experimentally tractable variables, which we calculate for the case of 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.

Characterising the morphological characters and carbohydrate metabolism of oat culms and their association with lodging resistance

Lodging resistance can be improved by enhancing the mechanical strength of culms, and culm carbohydrates could improve this mechanical strength. Culm carbohydrates can regulate development of the culm and affect its toughness. The present study determines the relationship between lodging and carbohydrate content in oat culms. Field experiments were conducted in alpine regions in 2017 and 2018 using three oat varieties with different lodging resistance. Lodging-related morphological characteristics were directly determined and culm carbohydrate content and enzyme activity related to cellulose synthesis and sucrose metabolism were evaluated with ultraviolet spectrophotometry. Results showed that the lower the gravity height or the lower ratio of gravity height to plant height, the stronger the lodging resistance of the varieties. Higher culm nonstructural (NSC) and structural (SC) carbohydrate content contributed to the ability of culms to resist lodging, especially the content of cellulose and sucrose. PCA showed that sucrose metabolism and SC content were closely related to lodging resistance. Correlation analysis showed that the lodging index (LI) was significantly negatively correlated with NSC. Sucrose content was highly and significantly positively correlated with NSC. Additionally, the activities of sucrose phosphate synthase (SPS) and sucrose synthase (SS) were highly and significantly positively correlated with sucrose and cellulose content. The relationship between field characters and oat lodging, as well as the regulatory mechanism of carbohydrate content on lodging resistance of the culm are discussed.

Switching the Direction of Stem Gravitropism by Altering Two Amino Acids in AtLAZY1

From germination to flowering, gravity influences plant growth and development. A rice (Oryza sativa) mutant with a distinctly prostrate growth habit led to the discovery of a gene category that participates in the shaping of plant form by gravity. Each so-called LAZY gene includes five short regions of conserved sequence. The importance of each of these regions in the LAZY1 gene of Arabidopsis (Arabidopsis thaliana; AtLAZY1) was tested by mutating each region and measuring how well transgenic expression of the resulting protein variant rescued the large inflorescence branch angle of an atlazy1 mutant. The effect of each alteration on subcellular localization was also determined. Region I was required for AtLAZY1 to reside at the plasma membrane, which is necessary for its function. Mutating region V severely disrupted function without affecting subcellular localization. Regions III and IV could be mutated without large impact on function or localization. Altering region II with two conservative amino acid substitutions (L92A/I94A) had the profound effect of switching shoot gravity responses from negative (upward bending) to positive (downward bending), resulting in a "weeping" inflorescence phenotype. Mechanical weakness of the stem was ruled out as an explanation for the downward bending. Instead, experiments demonstrated that the L92A/I94A change to AtLAZY1 reversed the auxin gradient normally established across stems by the gravity-sensing mechanism. This discovery opens up new avenues for studying how auxin gradients form across organs and new approaches for engineering plant architecture for agronomic and other practical purposes.

ELIMÄKI Locus Is Required for Vertical Proprioceptive Response in Birch Trees

Tree architecture has evolved to support a top-heavy above-ground biomass, but this integral feature poses a weight-induced challenge to trunk stability. Maintaining an upright stem is expected to require vertical proprioception through feedback between sensing stem weight and responding with radial growth. Despite its apparent importance, the principle by which plant stems respond to vertical loading forces remains largely unknown. Here, by manipulating the stem weight of downy birch (Betula pubescens) trees, we show that cambial development is modulated systemically along the stem. We carried out a genetic study on the underlying regulation by combining an accelerated birch flowering program with a recessive mutation at the ELIMÄKI locus (EKI), which causes a mechanically defective response to weight stimulus resulting in stem collapse after just 3 months. We observed delayed wood morphogenesis in eki compared with WT, along with a more mechanically elastic cambial zone and radial compression of xylem cell size, indicating that rapid tissue differentiation is critical for cambial growth under mechanical stress. Furthermore, the touch-induced mechanosensory pathway was transcriptionally misregulated in eki, indicating that the ELIMÄKI locus is required to integrate the weight-growth feedback regulation. By studying this birch mutant, we were able to dissect vertical proprioception from the gravitropic response associated with reaction wood formation. Our study provides evidence for both local and systemic responses to mechanical stimuli during secondary plant development.

The Cytoskeleton and Its Role in Determining Cellulose Microfibril Angle in Secondary Cell Walls of Woody Tree Species

Recent advances in our understanding of the molecular control of secondary cell wall (SCW) formation have shed light on molecular mechanisms that underpin domestication traits related to wood formation. One such trait is the cellulose microfibril angle (MFA), an important wood quality determinant that varies along tree developmental phases and in response to gravitational stimulus. The cytoskeleton, mainly composed of microtubules and actin filaments, collectively contribute to plant growth and development by participating in several cellular processes, including cellulose deposition. Studies in Arabidopsis have significantly aided our understanding of the roles of microtubules in xylem cell development during which correct SCW deposition and patterning are essential to provide structural support and allow for water transport. In contrast, studies relating to SCW formation in xylary elements performed in woody trees remain elusive. In combination, the data reviewed here suggest that the cytoskeleton plays important roles in determining the exact sites of cellulose deposition, overall SCW patterning and more specifically, the alignment and orientation of cellulose microfibrils. By relating the reviewed evidence to the process of wood formation, we present a model of microtubule participation in determining MFA in woody trees forming reaction wood (RW).

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.

Brassinosteroids Inhibit Autotropic Root Straightening by Modifying Filamentous-Actin Organization and Dynamics

When positioned horizontally, roots grow down toward the direction of gravity. This phenomenon, called gravitropism, is influenced by most of the major plant hormones including brassinosteroids. Epi-brassinolide (eBL) was previously shown to enhance root gravitropism, a phenomenon similar to the response of roots exposed to the actin inhibitor, latrunculin B (LatB). This led us to hypothesize that eBL might enhance root gravitropism through its effects on filamentous-actin (F-actin). This hypothesis was tested by comparing gravitropic responses of maize (Zea mays) roots treated with eBL or LatB. LatB- and eBL-treated roots displayed similar enhanced downward growth compared with controls when vertical roots were oriented horizontally. Moreover, the effects of the two compounds on root growth directionality were more striking on a slowly-rotating two-dimensional clinostat. Both compounds inhibited autotropism, a process in which the root straightened after the initial gravistimulus was withdrawn by clinorotation. Although eBL reduced F-actin density in chemically-fixed Z. mays roots, the impact was not as strong as that of LatB. Modification of F-actin organization after treatment with both compounds was also observed in living roots of barrel medic (Medicago truncatula) seedlings expressing genetically encoded F-actin reporters. Like in fixed Z. mays roots, eBL effects on F-actin in living M. truncatula roots were modest compared with those of LatB. Furthermore, live cell imaging revealed a decrease in global F-actin dynamics in hypocotyls of etiolated M. truncatula seedlings treated with eBL compared to controls. Collectively, our data indicate that eBL-and LatB-induced enhancement of root gravitropism can be explained by inhibited autotropic root straightening, and that eBL affects this process, in part, by modifying F-actin organization and dynamics.