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.

Art-science collaborations: Generators of new ideas and serendipitous events.

An increasing number of collaborative projects between artists and scientists raises the question regarding their value, particularly when considering the redirection of resources. Here we provide a personal account of our collaborative efforts, as an artist and a scientist. We propose that one of the most significant outcomes is something that cannot be planned for in advance: serendipitous events. Such events lead to fresh perspectives and imaginative ideas, the fairy dust underlying many great works of art and science. The unexpected nature of these desired outcomes requires from us a leap of faith on the one hand, and a deep trust in our 'partner in crime' on the other.

Studying root-environment interactions in structured microdevices.

When interacting with the environment, plant roots integrate sensory information over space and time in order to respond appropriately under non-uniform conditions. The complexity and dynamic properties of soil across spatial and temporal scales pose a significant technical challenge for research into the mechanisms that drive metabolism, growth, and development in roots, as well as on inter-organismal networks in the rhizosphere. Synthetic environments, combining microscopic access and manipulation capabilities with soil-like heterogeneity, are needed to elucidate the intriguing antagonism that characterizes subsurface ecosystems. Microdevices have provided opportunities for innovative approaches to observe, analyse, and manipulate plant roots and advanced our understanding of their development, physiology, and interactions with the environment. Initially conceived as perfusion platforms for root cultivation under hydroponic conditions, microdevice design has, in recent years, increasingly shifted to better reflect the complex growth conditions in soil. Heterogeneous micro-environments have been created through co-cultivation with microbes, laminar flow-based local stimulation, and physical obstacles and constraints. As such, structured microdevices provide an experimental entry point into the complex network behaviour of soil communities.

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.

Fast estimation of plant growth dynamics using deep neural networks.

BACKGROUND: In recent years, there has been an increase of interest in plant behaviour as represented by growth-driven responses. These are generally classified into nastic (internally driven) and tropic (environmentally driven) movements. Nastic movements include circumnutations, a circular movement of plant organs commonly associated with search and exploration, while tropisms refer to the directed growth of plant organs toward or away from environmental stimuli, such as light and gravity. Tracking these movements is therefore fundamental for the study of plant behaviour. Convolutional neural networks, as used for human and animal pose estimation, offer an interesting avenue for plant tracking. Here we adopted the Social LEAP Estimates Animal Poses (SLEAP) framework for plant tracking. We evaluated it on time-lapse videos of cases spanning a variety of parameters, such as: (i) organ types and imaging angles (e.g., top-view crown leaves vs. side-view shoots and roots), (ii) lighting conditions (full spectrum vs. IR), (iii) plant morphologies and scales (100 µm-scale Arabidopsis seedlings vs. cm-scale sunflowers and beans), and (iv) movement types (circumnutations, tropisms and twining). RESULTS: Overall, we found SLEAP to be accurate in tracking side views of shoots and roots, requiring only a low number of user-labelled frames for training. Top views of plant crowns made up of multiple leaves were found to be more challenging, due to the changing 2D morphology of leaves, and the occlusions of overlapping leaves. This required a larger number of labelled frames, and the choice of labelling "skeleton" had great impact on prediction accuracy, i.e., a more complex skeleton with fewer individuals (tracking individual plants) provided better results than a simpler skeleton with more individuals (tracking individual leaves). CONCLUSIONS: In all, these results suggest SLEAP is a robust and versatile tool for high-throughput automated tracking of plants, presenting a new avenue for research focusing on plant dynamics.

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.

Correlations within polyprotein forced unfolding dwell-times introduce sequential dependency.

Polyproteins, comprised from proteins arrayed in tandem, respond to mechanical loads through partial unfolding and extension. This response to tension that enables their physiological function is related to the ability to dynamically regulate their elasticity. The unique arrangement of their individual mechanical components (proteins and polymeric linkers), and the interactions between them eventually determines their performance. The sequential unfolding-times within a polyprotein are inherently assumed to be independent and identically distributed (iid), thus expected to follow an exponential distribution. Nevertheless, a large body of literature using single molecule force spectroscopy (SMFS) provides evidence that forced unfolding-times of N proteins within a polyprotein do not follow the exponential distribution. Here we use SMFS with Atomic Force Microscopy to measure the unfolding kinetics of Poly-(I91)8 at 180 pN. The unfolding time-intervals were statistically analysed using three common approaches, all exhibiting an N-effect: hierarchical behavior with non-identical unfolding time distributions. Using continuous time random walk approach indicates that the unfolding times display subdiffusive features. Put together with free-energy reconstruction of the whole unfolding polyprotein, we provide physical explanation for this nontrivial behavior, according to which the elongating polypeptide chain with each unfolding event intervenes with the sequential unfolding probabilities and correlates them.

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.

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.

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.

Characterizing gibberellin flow in planta using photocaged gibberellins.

Gibberellins (GAs) are ubiquitous plant hormones that coordinate central developmental and adaptive growth processes in plants. Accurate movement of GAs throughout the plant from their sources to their destination sites is emerging to be a highly regulated and directed process. We report on the development of novel photocaged gibberellins that, in combination with a genetically encoded GA-response marker, provide a unique platform to study GA movement at high-resolution, in real time and in living, intact plants. By applying this platform to the Arabidopsis thaliana endogenous bioactive gibberellin GA4, we measure kinetic parameters of its flow, such as decay length and velocity, in vivo.

Photosynthetic artificial organelles sustain and control ATP-dependent reactions in a protocellular system.

Inside cells, complex metabolic reactions are distributed across the modular compartments of organelles. Reactions in organelles have been recapitulated in vitro by reconstituting functional protein machineries into membrane systems. However, maintaining and controlling these reactions is challenging. Here we designed, built, and tested a switchable, light-harvesting organelle that provides both a sustainable energy source and a means of directing intravesicular reactions. An ATP (ATP) synthase and two photoconverters (plant-derived photosystem II and bacteria-derived proteorhodopsin) enable ATP synthesis. Independent optical activation of the two photoconverters allows dynamic control of ATP synthesis: red light facilitates and green light impedes ATP synthesis. We encapsulated the photosynthetic organelles in a giant vesicle to form a protocellular system and demonstrated optical control of two ATP-dependent reactions, carbon fixation and actin polymerization, with the latter altering outer vesicle morphology. Switchable photosynthetic organelles may enable the development of biomimetic vesicle systems with regulatory networks that exhibit homeostasis and complex cellular behaviors.

Coexisting origins of subdiffusion in internal dynamics of proteins.

Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.

Intermittent Granular Dynamics at a Seismogenic Plate Boundary.

Earthquakes at seismogenic plate boundaries are a response to the differential motions of tectonic blocks embedded within a geometrically complex network of branching and coalescing faults. Elastic strain is accumulated at a slow strain rate on the order of 10^{-15} s^{-1}, and released intermittently at intervals >100 yr, in the form of rapid (seconds to minutes) coseismic ruptures. The development of macroscopic models of quasistatic planar tectonic dynamics at these plate boundaries has remained challenging due to uncertainty with regard to the spatial and kinematic complexity of fault system behaviors. The characteristic length scale of kinematically distinct tectonic structures is particularly poorly constrained. Here, we analyze fluctuations in Global Positioning System observations of interseismic motion from the southern California plate boundary, identifying heavy-tailed scaling behavior. Namely, we show that, consistent with findings for slowly sheared granular media, the distribution of velocity fluctuations deviates from a Gaussian, exhibiting broad tails, and the correlation function decays as a stretched exponential. This suggests that the plate boundary can be understood as a densely packed granular medium, predicting a characteristic tectonic length scale of 91±20 km, here representing the characteristic size of tectonic blocks in the southern California fault network, and relating the characteristic duration and recurrence interval of earthquakes, with the observed sheared strain rate, and the nanosecond value for the crack tip evolution time scale. Within a granular description, fault and blocks systems may rapidly rearrange the distribution of forces within them, driving a mixture of transient and intermittent fault slip behaviors over tectonic time scales.

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.

Directional memory arises from long-lived cytoskeletal asymmetries in polarized chemotactic cells.

Chemotaxis, the directional migration of cells in a chemical gradient, is robust to fluctuations associated with low chemical concentrations and dynamically changing gradients as well as high saturating chemical concentrations. Although a number of reports have identified cellular behavior consistent with a directional memory that could account for behavior in these complex environments, the quantitative and molecular details of such a memory process remain unknown. Using microfluidics to confine cellular motion to a 1D channel and control chemoattractant exposure, we observed directional memory in chemotactic neutrophil-like cells. We modeled this directional memory as a long-lived intracellular asymmetry that decays slower than observed membrane phospholipid signaling. Measurements of intracellular dynamics revealed that moesin at the cell rear is a long-lived element that when inhibited, results in a reduction of memory. Inhibition of ROCK (Rho-associated protein kinase), downstream of RhoA (Ras homolog gene family, member A), stabilized moesin and directional memory while depolymerization of microtubules (MTs) disoriented moesin deposition and also reduced directional memory. Our study reveals that long-lived polarized cytoskeletal structures, specifically moesin, actomyosin, and MTs, provide a directional memory in neutrophil-like cells even as they respond on short time scales to external chemical cues.

Collisional statistics and dynamics of two-dimensional hard-disk systems: From fluid to solid.

We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the collisional statistical properties. We analyze the distribution functions of velocity, free flight time, and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single-particle dynamical properties behave analogously in collisional and continuous-time representations, exhibiting apparent crossovers between the fluid and the solid phases. We find that, both in collisional and continuous-time representation, the mean-squared displacement, velocity autocorrelation functions, intermediate scattering functions, and self-part of the van Hove function (propagator) closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids, and supercooled liquids close to the glass or jamming transition.