Multiscale systems analysis of root growth and development: modeling beyond the network and cellular scales

Tunable recurrent priming of lateral roots in Arabidopsis: More than just a clock?

Lateral root (LR) formation in Arabidopsis is a continuous, repetitive, post-embryonic process regulated by a series of coordinated events and tuned by the environment. It shapes the root system, enabling plants to efficiently explore soil resources and adapt to changing environmental conditions. Although the auxin-regulated modules responsible for LR morphogenesis and emergence are well documented, less is known about the initial priming. Priming is characterised by recurring peaks of auxin signalling, which, once memorised, earmark cells to form the new LR. We review the recent experimental and modelling approaches to understand the molecular processes underlying the recurring LR formation. We argue that the intermittent priming of LR results from interweaving the pattern of auxin flow and root growth together with an oscillatory auxin-modulated transcriptional mechanism and illustrate its long-range sugar-mediated tuning by light.

Root phenotypes for improved nitrogen capture

Background

Suboptimal nitrogen availability is a primary constraint for crop production in low-input agroecosystems, while nitrogen fertilization is a primary contributor to the energy, economic, and environmental costs of crop production in high-input agroecosystems. In this article we consider avenues to develop crops with improved nitrogen capture and reduced requirement for nitrogen fertilizer.

Scope

Intraspecific variation for an array of root phenotypes has been associated with improved nitrogen capture in cereal crops, including architectural phenotypes that colocalize root foraging with nitrogen availability in the soil; anatomical phenotypes that reduce the metabolic costs of soil exploration, improve penetration of hard soil, and exploit the rhizosphere; subcellular phenotypes that reduce the nitrogen requirement of plant tissue; molecular phenotypes exhibiting optimized nitrate uptake kinetics; and rhizosphere phenotypes that optimize associations with the rhizosphere microbiome. For each of these topics we provide examples of root phenotypes which merit attention as potential selection targets for crop improvement. Several cross-cutting issues are addressed including the importance of soil hydrology and impedance, phenotypic plasticity, integrated phenotypes, in silico modeling, and breeding strategies using high throughput phenotyping for co-optimization of multiple phenes.

Conclusions

Substantial phenotypic variation exists in crop germplasm for an array of root phenotypes that improve nitrogen capture. Although this topic merits greater research attention than it currently receives, we have adequate understanding and tools to develop crops with improved nitrogen capture. Root phenotypes are underutilized yet attractive breeding targets for the development of the nitrogen efficient crops urgently needed in global agriculture.

RootSlice-A novel functional-structural model for root anatomical phenotypes

Root anatomy is an important determinant of root metabolic costs, soil exploration, and soil resource capture. Root anatomy varies substantially within and among plant species. RootSlice is a multicellular functional-structural model of root anatomy developed to facilitate the analysis and understanding of root anatomical phenotypes. RootSlice can capture phenotypically accurate root anatomy in three dimensions of different root classes and developmental zones, of both monocotyledonous and dicotyledonous species. Several case studies are presented illustrating the capabilities of the model. For maize nodal roots, the model illustrated the role of vacuole expansion in cell elongation; and confirmed the individual and synergistic role of increasing root cortical aerenchyma and reducing the number of cortical cell files in reducing root metabolic costs. Integration of RootSlice for different root zones as the temporal properties of the nodal roots in the whole-plant and soil model OpenSimRoot/maize enabled the multiscale evaluation of root anatomical phenotypes, highlighting the role of aerenchyma formation in enhancing the utility of cortical cell files for improving plant performance over varying soil nitrogen supply. Such integrative in silico approaches present avenues for exploring the fitness landscape of root anatomical phenotypes.

Breeding crops for drought-affected environments and improved climate resilience

Breeding climate-resilient crops with improved levels of abiotic and biotic stress resistance as a response to climate change presents both opportunities and challenges. Applying the framework of the "breeder's equation," which is used to predict the response to selection for a breeding program cycle, we review methodologies and strategies that have been used to successfully breed crops with improved levels of drought resistance, where the target population of environments (TPEs) is a spatially and temporally heterogeneous mixture of drought-affected and favorable (water-sufficient) environments. Long-term improvement of temperate maize for the US corn belt is used as a case study and compared with progress for other crops and geographies. Integration of trait information across scales, from genomes to ecosystems, is needed to accurately predict yield outcomes for genotypes within the current and future TPEs. This will require transdisciplinary teams to explore, identify, and exploit novel opportunities to accelerate breeding program outcomes; both improved germplasm resources and improved products (cultivars, hybrids, clones, and populations) that outperform and replace the products in use by farmers, in combination with modified agronomic management strategies suited to their local environments.

Integrated root phenotypes for improved rice performance under low nitrogen availability

Greater nitrogen efficiency would substantially reduce the economic, energy and environmental costs of rice production. We hypothesized that synergistic balancing of the costs and benefits for soil exploration among root architectural phenes is beneficial under suboptimal nitrogen availability. An enhanced implementation of the functional-structural model OpenSimRoot for rice integrated with the ORYZA_v3 crop model was used to evaluate the utility of combinations of root architectural phenes, namely nodal root angle, the proportion of smaller diameter nodal roots, nodal root number; and L-type and S-type lateral branching densities, for plant growth under low nitrogen. Multiple integrated root phenotypes were identified with greater shoot biomass under low nitrogen than the reference cultivar IR64. The superiority of these phenotypes was due to synergism among root phenes rather than the expected additive effects of phene states. Representative optimal phenotypes were predicted to have up to 80% greater grain yield with low N supply in the rainfed dry direct-seeded agroecosystem over future weather conditions, compared to IR64. These phenotypes merit consideration as root ideotypes for breeding rice cultivars with improved yield under rainfed dry direct-seeded conditions with limited nitrogen availability. The importance of phene synergism for the performance of integrated phenotypes has implications for crop breeding.

Hormonal orchestration of root apical meristem formation and maintenance in Arabidopsis

Plant hormones are key regulators of a number of developmental and adaptive responses in plants, integrating the control of intrinsic developmental regulatory circuits with environmental inputs. Here we provide an overview of the molecular mechanisms underlying hormonal regulation of root development. We focus on key events during both embryonic and post-embryonic development, including specification of the hypophysis as a future organizer of the root apical meristem (RAM), hypophysis asymmetric division, specification of the quiescent centre (QC) and the stem cell niche (SCN), RAM maturation and maintenance of QC/SCN activity, and RAM size. We address both well-established and newly proposed concepts, highlight potential ambiguities in recent terminology and classification criteria of longitudinal root zonation, and point to contrasting results and alternative scenarios for recent models. In the concluding remarks, we summarize the common principles of hormonal control during root development and the mechanisms potentially explaining often antagonistic outputs of hormone action, and propose possible future research directions on hormones in the root.

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ-level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single-scale models are unable to capture the critical cross-scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.

Root architecture and hydraulics converge for acclimation to changing water availability

Because of intense transpiration and growth, the needs of plants for water can be immense. Yet water in the soil is most often heterogeneous if not scarce due to more and more frequent and intense drought episodes. The converse context, flooding, is often associated with marked oxygen deficiency and can also challenge the plant water status. Under our feet, roots achieve an incredible challenge to meet the water demand of the plant's aerial parts under such dramatically different environmental conditions. For this, they continuously explore the soil, building a highly complex, branched architecture. On shorter time scales, roots keep adjusting their water transport capacity (their so-called hydraulics) locally or globally. While the mechanisms that directly underlie root growth and development as well as tissue hydraulics are being uncovered, the signalling mechanisms that govern their local and systemic adjustments as a function of water availability remain largely unknown. A comprehensive understanding of root architecture and hydraulics as a whole (in other terms, root hydraulic architecture) is needed to apprehend the strategies used by plants to optimize water uptake and possibly improve crops regarding this crucial trait.

Auxin-mediated statolith production for root gravitropism

Root gravitropism is one of the most important processes allowing plant adaptation to the land environment. Auxin plays a central role in mediating root gravitropism, but how auxin contributes to gravitational perception and the subsequent response are still unclear. Here, we showed that the local auxin maximum/gradient within the root apex, which is generated by the PIN directional auxin transporters, regulates the expression of three key starch granule synthesis genes, SS4, PGM and ADG1, which in turn influence the accumulation of starch granules that serve as a statolith perceiving gravity. Moreover, using the cvxIAA-ccvTIR1 system, we also showed that TIR1-mediated auxin signaling is required for starch granule formation and gravitropic response within root tips. In addition, axr3 mutants showed reduced auxin-mediated starch granule accumulation and disruption of gravitropism within the root apex. Our results indicate that auxin-mediated statolith production relies on the TIR1/AFB-AXR3-mediated auxin signaling pathway. In summary, we propose a dual role for auxin in gravitropism: the regulation of both gravity perception and response.

Model selection and parameter estimation for root architecture models using likelihood-free inference

Plant root systems play vital roles in the biosphere, environment and agriculture, but the quantitative principles governing their growth and architecture remain poorly understood. The 'forward problem' of what root forms can arise from given models and parameters has been well studied through modelling and simulation, but comparatively little attention has been given to the 'inverse problem': what models and parameters are responsible for producing an experimentally observed root system? Here, we propose the use of approximate Bayesian computation (ABC) to infer mechanistic parameters governing root growth and architecture, allowing us to learn and quantify uncertainty in parameters and model structures using observed root architectures. We demonstrate the use of this platform on synthetic and experimental root data and show how it may be used to identify growth mechanisms and characterize growth parameters in different mutants. Our highly adaptable framework can be used to gain mechanistic insight into the generation of observed root system architectures.

Theoretical models for branch formation in plants

Various branch architectures are observed in living organisms including plants. Branch formation has traditionally been an area of interest in the field of developmental biology, and theoretical approaches are now commonly used to understand the complex mechanisms involved. In this review article, we provide an overview of theoretical approaches including mathematical models and computer simulations for studying plant branch formation. These approaches cover a wide range of topics. In particular, we focus on the importance of positional information in branch formation, which has been especially revealed by theoretical research in plants including computations of developmental processes.

In Silico Roots: Room for Growth

Computational models are invaluable tools for understanding the hormonal and genetic control of root development. Thus far, models have focused on the crucial roles that auxin transport and metabolism play in determining the auxin signaling gradient that controls the root meristem. Other hormones such as cytokinins, gibberellins, and ethylene have predominantly been considered as modulators of auxin dynamics, but their underlying patterning mechanisms are currently unresolved. In addition, the effects of cell- and tissue-level growth dynamics, which induce dilution and displacement of signaling molecules, have remained unexplored. Elucidating these additional mechanisms will be essential to unravel how root growth is patterned in a robust and self-organized manner. Models incorporating growth will thus be crucial in unraveling the underlying logic of root developmental decision making.

An Integrative Systems Perspective on Plant Phosphate Research

The case for improving crop phosphorus-use-efficiency is widely recognized. Although much is known about the molecular and regulatory mechanisms, improvements have been hampered by the extreme complexity of phosphorus (P) dynamics, which involves soil chemistry; plant-soil interactions; uptake, transport, utilization and remobilization within plants; and agricultural practices. The urgency and direction of phosphate research is also dependent upon the finite sources of P, availability of stocks to farmers and reducing environmental hazards. This work introduces integrative systems approaches as a way to represent and understand this complexity, so that meaningful links can be established between genotype, environment, crop traits and yield. It aims to provide a large set of pointers to potential genes and research practice, with a view to encouraging members of the plant-phosphate research community to adopt such approaches so that, together, we can aid efforts in global food security.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Roots Withstanding their Environment: Exploiting Root System Architecture Responses to Abiotic Stress to Improve Crop Tolerance

To face future challenges in crop production dictated by global climate changes, breeders and plant researchers collaborate to develop productive crops that are able to withstand a wide range of biotic and abiotic stresses. However, crop selection is often focused on shoot performance alone, as observation of root properties is more complex and asks for artificial and extensive phenotyping platforms. In addition, most root research focuses on development, while a direct link to the functionality of plasticity in root development for tolerance is often lacking. In this paper we review the currently known root system architecture (RSA) responses in Arabidopsis and a number of crop species to a range of abiotic stresses, including nutrient limitation, drought, salinity, flooding, and extreme temperatures. For each of these stresses, the key molecular and cellular mechanisms underlying the RSA response are highlighted. To explore the relevance for crop selection, we especially review and discuss studies linking root architectural responses to stress tolerance. This will provide a first step toward understanding the relevance of adaptive root development for a plant's response to its environment. We suggest that functional evidence on the role of root plasticity will support breeders in their efforts to include root properties in their current selection pipeline for abiotic stress tolerance, aimed to improve the robustness of crops.

More than meets the eye: Emergent properties of transcription factors networks in Arabidopsis

Uncovering and mathematically modeling Transcription Factor Networks (TFNs) are the first steps in engineering plants with traits that are better equipped to respond to changing environments. Although several plant TFNs are well known, the framework for systematically modeling complex characteristics such as switch-like behavior, oscillations, and homeostasis that emerge from them remain elusive. This review highlights literature that provides, in part, experimental and computational techniques for characterizing TFNs. This review also outlines methodologies that have been used to mathematically model the dynamic characteristics of TFNs. We present several examples of TFNs in plants that are involved in developmental and stress response. In several cases, advanced algorithms capture or quantify emergent properties that serve as the basis for robustness and adaptability in plant responses. Increasing the use of mathematical approaches will shed new light on these regulatory properties that control plant growth and development, leading to mathematical models that predict plant behavior. This article is part of a Special Issue entitled: Plant Gene Regulatory Mechanisms and Networks, edited by Dr. Erich Grotewold and Dr. Nathan Springer.

X-Ray Computed Tomography Reveals the Response of Root System Architecture to Soil Texture

Root system architecture (RSA) impacts plant fitness and crop yield by facilitating efficient nutrient and water uptake from the soil. A better understanding of the effects of soil on RSA could improve crop productivity by matching roots to their soil environment. We used x-ray computed tomography to perform a detailed three-dimensional quantification of changes in rice (Oryza sativa) RSA in response to the physical properties of a granular substrate. We characterized the RSA of eight rice cultivars in five different growth substrates and determined that RSA is the result of interactions between genotype and growth environment. We identified cultivar-specific changes in RSA in response to changing growth substrate texture. The cultivar Azucena exhibited low RSA plasticity in all growth substrates, whereas cultivar Bala root depth was a function of soil hardness. Our imaging techniques provide a framework to study RSA in different growth environments, the results of which can be used to improve root traits with agronomic potential.

Localized auxin peaks in concentration-based transport models of the shoot apical meristem

We study the formation of auxin peaks in a generic class of concentration-based auxin transport models, posed on static plant tissues. Using standard asymptotic analysis, we prove that, on bounded domains, auxin peaks are not formed via a Turing instability in the active transport parameter, but via simple corrections to the homogeneous steady state. When the active transport is small, the geometry of the tissue encodes the peaks' amplitude and location: peaks arise where cells have fewer neighbours, that is, at the boundary of the domain. We test our theory and perform numerical bifurcation analysis on two models that are known to generate auxin patterns for biologically plausible parameter values. In the same parameter regimes, we find that realistic tissues are capable of generating a multitude of stationary patterns, with a variable number of auxin peaks, that can be selected by different initial conditions or by quasi-static changes in the active transport parameter. The competition between active transport and production rate determines whether peaks remain localized or cover the entire domain. In particular, changes in the auxin production that are fast with respect to the cellular life cycle affect the auxin peak distribution, switching from localized spots to fully patterned states. We relate the occurrence of localized patterns to a snaking bifurcation structure, which is known to arise in a wide variety of nonlinear media, but has not yet been reported in plant models.

Micron-scale phenotyping quantification and three-dimensional microstructure reconstruction of vascular bundles within maize stalks based on micro-CT scanning

Vascular bundles within maize (Zea mays L.) stalks play a key role in the mechanical support of plant architecture as well as in water and nutrient transportation. Convenient and accurate phenotyping of vascular bundles may help phenotypic identification of germplasm resources for breeding. Based on practical sample preparation procedures for maize stalks, we acquired serials of cross-sectional images using a micro-computed tomography (CT) imaging device. An image processing pipeline dedicated to the phenotyping of vascular bundles was also developed to automatically segment and validate vascular bundles from the cross-sectional images of maize stalks, from which phenotypic traits of vascular bundles, i.e. number, area, and spatial distribution, were calculated. More profound quantification of spatial distribution was given as area ratio of vascular bundles, which described the distribution of vascular bundles associated with the centroid of maize stalks. In addition, three-dimensional visualisation was performed to reveal the spatial configuration and distribution of vascular bundles. The proposed method significantly improves computation accuracy for the phenotypic traits of vascular bundles compared with previous methods, and is expected to be useful for illustrating relationships between phenotypic traits of vascular bundles and their function.

Root System Architecture and Abiotic Stress Tolerance: Current Knowledge in Root and Tuber Crops

The challenge to produce more food for a rising global population on diminishing agricultural land is complicated by the effects of climate change on agricultural productivity. Although great progress has been made in crop improvement, so far most efforts have targeted above-ground traits. Roots are essential for plant adaptation and productivity, but are less studied due to the difficulty of observing them during the plant life cycle. Root system architecture (RSA), made up of structural features like root length, spread, number, and length of lateral roots, among others, exhibits great plasticity in response to environmental changes, and could be critical to developing crops with more efficient roots. Much of the research on root traits has thus far focused on the most common cereal crops and model plants. As cereal yields have reached their yield potential in some regions, understanding their root system may help overcome these plateaus. However, root and tuber crops (RTCs) such as potato, sweetpotato, cassava, and yam may hold more potential for providing food security in the future, and knowledge of their root system additionally focuses directly on the edible portion. Root-trait modeling for multiple stress scenarios, together with high-throughput phenotyping and genotyping techniques, robust databases, and data analytical pipelines, may provide a valuable base for a truly inclusive 'green revolution.' In the current review, we discuss RSA with special reference to RTCs, and how knowledge on genetics of RSA can be manipulated to improve their tolerance to abiotic stresses.

Tree Topology Estimation

Tree-like structures are fundamental in nature, and it is often useful to reconstruct the topology of a tree - what connects to what - from a two-dimensional image of it. However, the projected branches often cross in the image: the tree projects to a planar graph, and the inverse problem of reconstructing the topology of the tree from that of the graph is ill-posed. We regularize this problem with a generative, parametric tree-growth model. Under this model, reconstruction is possible in linear time if one knows the direction of each edge in the graph - which edge endpoint is closer to the root of the tree - but becomes NP-hard if the directions are not known. For the latter case, we present a heuristic search algorithm to estimate the most likely topology of a rooted, three-dimensional tree from a single two-dimensional image. Experimental results on retinal vessel, plant root, and synthetic tree data sets show that our methodology is both accurate and efficient.

Measurement of plant growth in view of an integrative analysis of regulatory networks

As the regulatory networks of growth at the cellular level are elucidated at a fast pace, their complexity is not reduced; on the contrary, the tissue, organ and even whole-plant level affect cell proliferation and expansion by means of development-induced and environment-induced signaling events in growth regulatory processes. Measurement of growth across different levels aids in gaining a mechanistic understanding of growth, and in defining the spatial and temporal resolution of sampling strategies for molecular analyses in the model Arabidopsis thaliana and increasingly also in crop species. The latter claim their place at the forefront of plant research, since global issues and future needs drive the translation from laboratory model-acquired knowledge of growth processes to improvements in crop productivity in field conditions.

New insights into root gravitropic signalling

An important feature of plants is the ability to adapt their growth towards or away from external stimuli such as light, water, temperature, and gravity. These responsive plant growth movements are called tropisms and they contribute to the plant's survival and reproduction. Roots modulate their growth towards gravity to exploit the soil for water and nutrient uptake, and to provide anchorage. The physiological process of root gravitropism comprises gravity perception, signal transmission, growth response, and the re-establishment of normal growth. Gravity perception is best explained by the starch-statolith hypothesis that states that dense starch-filled amyloplasts or statoliths within columella cells sediment in the direction of gravity, resulting in the generation of a signal that causes asymmetric growth. Though little is known about the gravity receptor(s), the role of auxin linking gravity sensing to the response is well established. Auxin influx and efflux carriers facilitate creation of a differential auxin gradient between the upper and lower side of gravistimulated roots. This asymmetric auxin gradient causes differential growth responses in the graviresponding tissue of the elongation zone, leading to root curvature. Cell biological and mathematical modelling approaches suggest that the root gravitropic response begins within minutes of a gravity stimulus, triggering genomic and non-genomic responses. This review discusses recent advances in our understanding of root gravitropism in Arabidopsis thaliana and identifies current challenges and future perspectives.

Molecular systems governing leaf growth: from genes to networks

Arabidopsis leaf growth consists of a complex sequence of interconnected events involving cell division and cell expansion, and requiring multiple levels of genetic regulation. With classical genetics, numerous leaf growth regulators have been identified, but the picture is far from complete. With the recent advances made in quantitative phenotyping, the study of the quantitative, dynamic, and multifactorial features of leaf growth is now facilitated. The use of high-throughput phenotyping technologies to study large numbers of natural accessions or mutants, or to screen for the effects of large sets of chemicals will allow for further identification of the additional players that constitute the leaf growth regulatory networks. Only a tight co-ordination between these numerous molecular players can support the formation of a functional organ. The connections between the components of the network and their dynamics can be further disentangled through gene-stacking approaches and ultimately through mathematical modelling. In this review, we describe these different approaches that should help to obtain a holistic image of the molecular regulation of organ growth which is of high interest in view of the increasing needs for plant-derived products.

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.

Jasmonates: Emerging Players in Controlling Temperature Stress Tolerance

The sedentary life of plants has forced them to live in an environment that is characterized by the presence of numerous challenges in terms of biotic and abiotic stresses. Phytohormones play essential roles in mediating plant physiology and alleviating various environmental perturbations. Jasmonates are a group of oxylipin compounds occurring ubiquitously in the plant kingdom that play pivotal roles in response to developmental and environmental cues. Jasmonates (JAs) have been shown to participate in unison with key factors of other signal transduction pathway, including those involved in response to abiotic stress. Recent findings have furnished large body of information suggesting the role of jasmonates in cold and heat stress. JAs have been shown to regulate C-repeat binding factor (CBF) pathway during cold stress. The interaction between the integrants of JA signaling and components of CBF pathway demonstrates a complex relationship between the two. JAs have also been shown to counteract chilling stress by inducing ROS avoidance enzymes. In addition, several lines of evidence suggest the positive regulation of thermotolerance by JA. The present review provides insights into biosynthesis, signal transduction pathway of jasmonic acid and their role in response to temperature stress.

Root structural and functional dynamics in terrestrial biosphere models--evaluation and recommendations

There is wide breadth of root function within ecosystems that should be considered when modeling the terrestrial biosphere. Root structure and function are closely associated with control of plant water and nutrient uptake from the soil, plant carbon (C) assimilation, partitioning and release to the soils, and control of biogeochemical cycles through interactions within the rhizosphere. Root function is extremely dynamic and dependent on internal plant signals, root traits and morphology, and the physical, chemical and biotic soil environment. While plant roots have significant structural and functional plasticity to changing environmental conditions, their dynamics are noticeably absent from the land component of process-based Earth system models used to simulate global biogeochemical cycling. Their dynamic representation in large-scale models should improve model veracity. Here, we describe current root inclusion in models across scales, ranging from mechanistic processes of single roots to parameterized root processes operating at the landscape scale. With this foundation we discuss how existing and future root functional knowledge, new data compilation efforts, and novel modeling platforms can be leveraged to enhance root functionality in large-scale terrestrial biosphere models by improving parameterization within models, and introducing new components such as dynamic root distribution and root functional traits linked to resource extraction.

Branching out in roots: uncovering form, function, and regulation

Root branching is critical for plants to secure anchorage and ensure the supply of water, minerals, and nutrients. To date, research on root branching has focused on lateral root development in young seedlings. However, many other programs of postembryonic root organogenesis exist in angiosperms. In cereal crops, the majority of the mature root system is composed of several classes of adventitious roots that include crown roots and brace roots. In this Update, we initially describe the diversity of postembryonic root forms. Next, we review recent advances in our understanding of the genes, signals, and mechanisms regulating lateral root and adventitious root branching in the plant models Arabidopsis (Arabidopsis thaliana), maize (Zea mays), and rice (Oryza sativa). While many common signals, regulatory components, and mechanisms have been identified that control the initiation, morphogenesis, and emergence of new lateral and adventitious root organs, much more remains to be done. We conclude by discussing the challenges and opportunities facing root branching research.

Image-based high-throughput field phenotyping of crop roots

Current plant phenotyping technologies to characterize agriculturally relevant traits have been primarily developed for use in laboratory and/or greenhouse conditions. In the case of root architectural traits, this limits phenotyping efforts, largely, to young plants grown in specialized containers and growth media. Hence, novel approaches are required to characterize mature root systems of older plants grown under actual soil conditions in the field. Imaging methods able to address the challenges associated with characterizing mature root systems are rare due, in part, to the greater complexity of mature root systems, including the larger size, overlap, and diversity of root components. Our imaging solution combines a field-imaging protocol and algorithmic approach to analyze mature root systems grown in the field. Via two case studies, we demonstrate how image analysis can be utilized to estimate localized root traits that reliably capture heritable architectural diversity as well as environmentally induced architectural variation of both monocot and dicot plants. In the first study, we show that our algorithms and traits (including 13 novel traits inaccessible to manual estimation) can differentiate nine maize (Zea mays) genotypes 8 weeks after planting. The second study focuses on a diversity panel of 188 cowpea (Vigna unguiculata) genotypes to identify which traits are sufficient to differentiate genotypes even when comparing plants whose harvesting date differs up to 14 d. Overall, we find that automatically derived traits can increase both the speed and reproducibility of the trait estimation pipeline under field conditions.

Image-based high-throughput field phenotyping of crop roots

Current plant phenotyping technologies to characterize agriculturally relevant traits have been primarily developed for use in laboratory and/or greenhouse conditions. In the case of root architectural traits, this limits phenotyping efforts, largely, to young plants grown in specialized containers and growth media. Hence, novel approaches are required to characterize mature root systems of older plants grown under actual soil conditions in the field. Imaging methods able to address the challenges associated with characterizing mature root systems are rare due, in part, to the greater complexity of mature root systems, including the larger size, overlap, and diversity of root components. Our imaging solution combines a field-imaging protocol and algorithmic approach to analyze mature root systems grown in the field. Via two case studies, we demonstrate how image analysis can be utilized to estimate localized root traits that reliably capture heritable architectural diversity as well as environmentally induced architectural variation of both monocot and dicot plants. In the first study, we show that our algorithms and traits (including 13 novel traits inaccessible to manual estimation) can differentiate nine maize (Zea mays) genotypes 8 weeks after planting. The second study focuses on a diversity panel of 188 cowpea (Vigna unguiculata) genotypes to identify which traits are sufficient to differentiate genotypes even when comparing plants whose harvesting date differs up to 14 d. Overall, we find that automatically derived traits can increase both the speed and reproducibility of the trait estimation pipeline under field conditions.

An approach to multiscale modelling with graph grammars

BACKGROUND AND AIMS

Functional-structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

METHODS

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

KEY RESULTS

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

CONCLUSIONS

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.

Mechanical modelling quantifies the functional importance of outer tissue layers during root elongation and bending

Root elongation and bending require the coordinated expansion of multiple cells of different types. These processes are regulated by the action of hormones that can target distinct cell layers. We use a mathematical model to characterise the influence of the biomechanical properties of individual cell walls on the properties of the whole tissue. Taking a simple constitutive model at the cell scale which characterises cell walls via yield and extensibility parameters, we derive the analogous tissue-level model to describe elongation and bending. To accurately parameterise the model, we take detailed measurements of cell turgor, cell geometries and wall thicknesses. The model demonstrates how cell properties and shapes contribute to tissue-level extensibility and yield. Exploiting the highly organised structure of the elongation zone (EZ) of the Arabidopsis root, we quantify the contributions of different cell layers, using the measured parameters. We show how distributions of material and geometric properties across the root cross-section contribute to the generation of curvature, and relate the angle of a gravitropic bend to the magnitude and duration of asymmetric wall softening. We quantify the geometric factors which lead to the predominant contribution of the outer cell files in driving root elongation and bending.

Systems biology approaches to understand the role of auxin in root growth and development

The past decade has seen major advances in our understanding of auxin regulated root growth and developmental processes. Key genes have been identified that regulate and/or mediate auxin homeostasis, transport, perception and response. The molecular and biochemical reactions that underpin auxin signalling are non-linear, with feed-forward and feedback loops contributing to the robustness of the system. As our knowledge of auxin biology becomes increasingly complex and their outputs less intuitive, modelling is set to become much more important. For the last several decades modelling efforts have focused on auxin transport and, latterly, on auxin response. Recently researchers have employed multi-scale modelling approaches to predict emergent properties at the tissue and organ scales. Such innovative modelling approaches are proving very promising, revealing new mechanistic insights about how auxin functions within a multicellular context to control plant growth and development. In this review we initially describe examples of models capturing auxin transport and response pathways, and then discuss increasingly complex models that integrate multiple hormone response pathways, tissues and/or scales.

Modelling hormonal response and development

As our knowledge of the complexity of hormone homeostasis, transport, perception, and response increases, and their outputs become less intuitive, modelling is set to become more important. Initial modelling efforts have focused on hormone transport and response pathways. However, we now need to move beyond the network scales and use multicellular and multiscale modelling approaches to predict emergent properties at different scales. Here we review some examples where such approaches have been successful, for example, auxin-cytokinin crosstalk regulating root vascular development or a study of lateral root emergence where an iterative cycle of modelling and experiments lead to the identification of an overlooked role for PIN3. Finally, we discuss some of the remaining biological and technical challenges.

Modeling the effects of light and sucrose on in vitro propagated plants: a multiscale system analysis using artificial intelligence technology

BACKGROUND

Plant acclimation is a highly complex process, which cannot be fully understood by analysis at any one specific level (i.e. subcellular, cellular or whole plant scale). Various soft-computing techniques, such as neural networks or fuzzy logic, were designed to analyze complex multivariate data sets and might be used to model large such multiscale data sets in plant biology.

METHODOLOGY AND PRINCIPAL FINDINGS

In this study we assessed the effectiveness of applying neuro-fuzzy logic to modeling the effects of light intensities and sucrose content/concentration in the in vitro culture of kiwifruit on plant acclimation, by modeling multivariate data from 14 parameters at different biological scales of organization. The model provides insights through application of 14 sets of straightforward rules and indicates that plants with lower stomatal aperture areas and higher photoinhibition and photoprotective status score best for acclimation. The model suggests the best condition for obtaining higher quality acclimatized plantlets is the combination of 2.3% sucrose and photonflux of 122-130 µmol m(-2) s(-1).

CONCLUSIONS

Our results demonstrate that artificial intelligence models are not only successful in identifying complex non-linear interactions among variables, by integrating large-scale data sets from different levels of biological organization in a holistic plant systems-biology approach, but can also be used successfully for inferring new results without further experimental work.

Mathematical models light up plant signaling

Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis thaliana, have revealed many of the mechanisms by which these responses are actuated. In recent years, mathematical modeling has become a complementary tool to the experimental approach that has furthered our understanding of biological mechanisms. In this review, we present modeling examples encompassing a range of different biological processes, in particular those regulated by light. Current issues and future directions in the modeling of plant systems are discussed.

Root systems biology: integrative modeling across scales, from gene regulatory networks to the rhizosphere

Genetic and genomic approaches in model organisms have advanced our understanding of root biology over the last decade. Recently, however, systems biology and modeling have emerged as important approaches, as our understanding of root regulatory pathways has become more complex and interpreting pathway outputs has become less intuitive. To relate root genotype to phenotype, we must move beyond the examination of interactions at the genetic network scale and employ multiscale modeling approaches to predict emergent properties at the tissue, organ, organism, and rhizosphere scales. Understanding the underlying biological mechanisms and the complex interplay between systems at these different scales requires an integrative approach. Here, we describe examples of such approaches and discuss the merits of developing models to span multiple scales, from network to population levels, and to address dynamic interactions between plants and their environment.

Predictive modelling of complex agronomic and biological systems

Biological systems are tremendously complex in their functioning and regulation. Studying the multifaceted behaviour and describing the performance of such complexity has challenged the scientific community for years. The reduction of real-world intricacy into simple descriptive models has therefore convinced many researchers of the usefulness of introducing mathematics into biological sciences. Predictive modelling takes such an approach another step further in that it takes advantage of existing knowledge to project the performance of a system in alternating scenarios. The ever growing amounts of available data generated by assessing biological systems at increasingly higher detail provide unique opportunities for future modelling and experiment design. Here we aim to provide an overview of the progress made in modelling over time and the currently prevalent approaches for iterative modelling cycles in modern biology. We will further argue for the importance of versatility in modelling approaches, including parameter estimation, model reduction and network reconstruction. Finally, we will discuss the difficulties in overcoming the mathematical interpretation of in vivo complexity and address some of the future challenges lying ahead.

Lateral root development in Arabidopsis: fifty shades of auxin

The developmental plasticity of the root system represents a key adaptive trait enabling plants to cope with abiotic stresses such as drought and is therefore important in the current context of global changes. Root branching through lateral root formation is an important component of the adaptability of the root system to its environment. Our understanding of the mechanisms controlling lateral root development has progressed tremendously in recent years through research in the model plant Arabidopsis thaliana (Arabidopsis). These studies have revealed that the phytohormone auxin acts as a common integrator to many endogenous and environmental signals regulating lateral root formation. Here, we review what has been learnt about the myriad roles of auxin during lateral root formation in Arabidopsis.

Vertex-element models for anisotropic growth of elongated plant organs

New tools are required to address the challenge of relating plant hormone levels, hormone responses, wall biochemistry and wall mechanical properties to organ-scale growth. Current vertex-based models (applied in other contexts) can be unsuitable for simulating the growth of elongated organs such as roots because of the large aspect ratio of the cells, and these models fail to capture the mechanical properties of cell walls in sufficient detail. We describe a vertex-element model which resolves individual cells and includes anisotropic non-linear viscoelastic mechanical properties of cell walls and cell division whilst still being computationally efficient. We show that detailed consideration of the cell walls in the plane of a 2D simulation is necessary when cells have large aspect ratio, such as those in the root elongation zone of Arabidopsis thaliana, in order to avoid anomalous transverse swelling. We explore how differences in the mechanical properties of cells across an organ can result in bending and how cellulose microfibril orientation affects macroscale growth. We also demonstrate that the model can be used to simulate growth on realistic geometries, for example that of the primary root apex, using moderate computational resources. The model shows how macroscopic root shape can be sensitive to fine-scale cellular geometries.

Jasmonates: biosynthesis, perception, signal transduction and action in plant stress response, growth and development. An update to the 2007 review in Annals of Botany

BACKGROUND

Jasmonates are important regulators in plant responses to biotic and abiotic stresses as well as in development. Synthesized from lipid-constituents, the initially formed jasmonic acid is converted to different metabolites including the conjugate with isoleucine. Important new components of jasmonate signalling including its receptor were identified, providing deeper insight into the role of jasmonate signalling pathways in stress responses and development.

SCOPE

The present review is an update of the review on jasmonates published in this journal in 2007. New data of the last five years are described with emphasis on metabolites of jasmonates, on jasmonate perception and signalling, on cross-talk to other plant hormones and on jasmonate signalling in response to herbivores and pathogens, in symbiotic interactions, in flower development, in root growth and in light perception.

CONCLUSIONS

The last few years have seen breakthroughs in the identification of JASMONATE ZIM DOMAIN (JAZ) proteins and their interactors such as transcription factors and co-repressors, and the crystallization of the jasmonate receptor as well as of the enzyme conjugating jasmonate to amino acids. Now, the complex nature of networks of jasmonate signalling in stress responses and development including hormone cross-talk can be addressed.

Jasmonates: biosynthesis, perception, signal transduction and action in plant stress response, growth and development. An update to the 2007 review in Annals of Botany

BACKGROUND

Jasmonates are important regulators in plant responses to biotic and abiotic stresses as well as in development. Synthesized from lipid-constituents, the initially formed jasmonic acid is converted to different metabolites including the conjugate with isoleucine. Important new components of jasmonate signalling including its receptor were identified, providing deeper insight into the role of jasmonate signalling pathways in stress responses and development.

SCOPE

The present review is an update of the review on jasmonates published in this journal in 2007. New data of the last five years are described with emphasis on metabolites of jasmonates, on jasmonate perception and signalling, on cross-talk to other plant hormones and on jasmonate signalling in response to herbivores and pathogens, in symbiotic interactions, in flower development, in root growth and in light perception.

CONCLUSIONS

The last few years have seen breakthroughs in the identification of JASMONATE ZIM DOMAIN (JAZ) proteins and their interactors such as transcription factors and co-repressors, and the crystallization of the jasmonate receptor as well as of the enzyme conjugating jasmonate to amino acids. Now, the complex nature of networks of jasmonate signalling in stress responses and development including hormone cross-talk can be addressed.

Soil conditions and cereal root system architecture: review and considerations for linking Darwin and Weaver

Charles Darwin founded root system architecture research in 1880 when he described a root bending with gravity. Curving, elongating, and branching are the three cellular processes in roots that underlie root architecture. Together they determine the distribution of roots through soil and time, and hence the plants' access to water and nutrients, and anchorage. Most knowledge of these cellular processes comes from seedlings of the model dicotyledon, Arabidopsis, grown in soil-less conditions with single treatments. Root systems in the field, however, face multiple stimuli that interact with the plant genetics to result in the root system architecture. Here we review how soil conditions influence root system architecture; focusing on cereals. Cereals provide half of human calories, and their root systems differ from those of dicotyledons. We find that few controlled-environment studies combine more than one soil stimulus and, those that do, highlight the complexity of responses. Most studies are conducted on seedling roots; those on adult roots generally show low correlations to seedling studies. Few field studies report root and soil conditions. Until technologies are available to track root architecture in the field, soil analyses combined with knowledge of the effects of factors on elongation and gravitropism could be ranked to better predict the interaction between genetics and environment (G×E) for a given crop. Understanding how soil conditions regulate root architecture can be effectively used to design soil management and plant genetics that best exploit synergies from G×E of roots.

Bridging the genotype-phenotype gap: what does it take?

The genotype-phenotype map (GP map) concept applies to any time point in the ontogeny of a living system. It is the outcome of very complex dynamics that include environmental effects, and bridging the genotype-phenotype gap is synonymous with understanding these dynamics. The context for this understanding is physiology, and the disciplinary goals of physiology do indeed demand the physiological community to seek this understanding. We claim that this task is beyond reach without use of mathematical models that bind together genetic and phenotypic data in a causally cohesive way. We provide illustrations of such causally cohesive genotype-phenotype models where the phenotypes span from gene expression profiles to development of whole organs. Bridging the genotype-phenotype gap also demands that large-scale biological ('omics') data and associated bioinformatics resources be more effectively integrated with computational physiology than is currently the case. A third major element is the need for developing a phenomics technology way beyond current state of the art, and we advocate the establishment of a Human Phenome Programme solidly grounded on biophysically based mathematical descriptions of human physiology.