In Silico Roots: Room for Growth

Computational modeling of plant root development: the art and the science

Plant root development, like any developmental process, arises from the interplay between processes like gene expression, cell-cell signaling, cell growth and division, and tissue mechanics, which unfold over a wide range of temporal and spatial scales. Computational models are uniquely suited to integrate these different processes and spatio-temporal scales to investigate how their interplay determines developmental outcomes and have become part of mainstream plant developmental research. Still, for non-modeling experts, it often remains unclear how models are built, why a particular modeling approach was chosen, and how to interpret and value model outcomes. This review attempts to explain the science behind the art of model building, illustrating the simplifications that are often made to keep models simple to understand and when these are and are not justified. Similarly, it discusses when it is safe to ignore certain processes like growth or tissue mechanics and when it is not. Additionally, this review discusses a range of major breakthrough modeling articles. Their approaches are linked to classical concepts and models in developmental biology like the French flag positional information gradient of Lewis Wolpert and the repetitive patterning mechanism proposed by Turing, in addition to highlighting the lessons they taught us on plant root development.

Necessity for modeling hormonal crosstalk in arabidopsis root development?

Hormones play vital roles in plant root development. Mathematical models have been employed to study hormone functions. However, models developed by different research groups focus on different aspects of hormones and therefore cannot be used to study root growth as an integrative system that involves the functions of all hormones. To use modeling to study root development, the crosstalk nature of hormones requires the further development of mathematical models to understand their interplay in the context of diverse experimental data. This opinion article discusses what new insights can be developed by modeling hormonal crosstalk beyond experimental data. We propose that one integrative model should be developed to integrate all experimental data for elucidating root growth.

Modeling Arabidopsis root growth and development

Modeling has been used to explore various aspects of primary root development and growth in Arabidopsis thaliana, thanks to enormous advances in the genetic and biochemical bases of cell division, cell growth and differentiation, and, more recently, progress in measuring these processes. Modeling has facilitated the characterization of the regulations involved in these processes and the system properties that they confer. Recently, the mechanical-physical properties of root growth have started to be determined with the help of modeling. Here we review recent progress in modeling approaches used to examine root development and growth, from the transcriptional and signaling regulation of cell decisions to the mechanical basis of morphogenesis, and we highlight common features and future challenges.

Computer models of cell polarity establishment in plants

Plant development is a complex task, and many processes involve changes in the asymmetric subcellular distribution of cell components that strongly depend on cell polarity. Cell polarity regulates anisotropic growth and polar localization of membrane proteins and helps to identify the cell's position relative to its neighbors within an organ. Cell polarity is critical in a variety of plant developmental processes, including embryogenesis, cell division, and response to external stimuli. The most conspicuous downstream effect of cell polarity is the polar transport of the phytohormone auxin, which is the only known hormone transported in a polar fashion in and out of cells by specialized exporters and importers. The biological processes behind the establishment of cell polarity are still unknown, and researchers have proposed several models that have been tested using computer simulations. The evolution of computer models has progressed in tandem with scientific discoveries, which have highlighted the importance of genetic, chemical, and mechanical input in determining cell polarity and regulating polarity-dependent processes such as anisotropic growth, protein subcellular localization, and the development of organ shapes. The purpose of this review is to provide a comprehensive overview of the current understanding of computer models of cell polarity establishment in plants, focusing on the molecular and cellular mechanisms, the proteins involved, and the current state of the field.

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.

Computational modeling and quantitative physiology reveal central parameters for brassinosteroid-regulated early cell physiological processes linked to elongation growth of the Arabidopsis root

Brassinosteroids (BR) are key hormonal regulators of plant development. However, whereas the individual components of BR perception and signaling are well characterized experimentally, the question of how they can act and whether they are sufficient to carry out the critical function of cellular elongation remains open. Here, we combined computational modeling with quantitative cell physiology to understand the dynamics of the plasma membrane (PM)-localized BR response pathway during the initiation of cellular responses in the epidermis of the Arabidopsis root tip that are be linked to cell elongation. The model, consisting of ordinary differential equations, comprises the BR-induced hyperpolarization of the PM, the acidification of the apoplast and subsequent cell wall swelling. We demonstrate that the competence of the root epidermal cells for the BR response predominantly depends on the amount and activity of H+-ATPases in the PM. The model further predicts that an influx of cations is required to compensate for the shift of positive charges caused by the apoplastic acidification. A potassium channel was subsequently identified and experimentally characterized, fulfilling this function. Thus, we established the landscape of components and parameters for physiological processes potentially linked to cell elongation, a central process in plant development.

Cytokinin promotes growth cessation in the Arabidopsis root

The Arabidopsis root offers good opportunities to investigate how regulated cellular growth shapes different tissues and organs, a key question in developmental biology. Along the root's longitudinal axis, cells sequentially occupy different developmental states. Proliferative meristematic cells give rise to differentiating cells, which rapidly elongate in the elongation zone, then mature and stop growing in the differentiation zone. The phytohormone cytokinin contributes to this zonation by positioning the boundary between the meristem and the elongation zone, called the transition zone. However, the cellular growth profile underlying root zonation is not well understood, and the cellular mechanisms that mediate growth cessation remain unclear. By using time-lapse imaging, genetics, and computational analysis, we analyze the effect of cytokinin on root zonation and cellular growth. We found that cytokinin promotes growth cessation in the distal (shootward) elongation zone in conjunction with accelerating the transition from elongation to differentiation. We estimated cell-wall stiffness by using osmotic treatment experiments and found that cytokinin-mediated growth cessation is associated with cell-wall stiffening and requires the action of an auxin influx carrier, AUX1. Our measurement of growth and cell-wall mechanical properties at a cellular resolution reveal mechanisms via which cytokinin influences cell behavior to shape tissue patterns.

Modeling Auxin Signaling in Roots: Auxin Computations

Auxin signaling and patterning is an inherently complex process, involving polarized auxin transport, metabolism, and signaling, its effect on developmental zones, as well as growth rates, and the feedback between all these different aspects. This complexity has led to an important role for computational modeling in unraveling the multifactorial roles of auxin in plant developmental and adaptive processes. Here we discuss the basic ingredients of auxin signaling and patterning models for root development as well as a series of key modeling studies in this area. These modeling studies have helped elucidate how plants use auxin signaling to compute the size of their root meristem, the direction in which to grow, and when and where to form lateral roots. Importantly, these models highlight how auxin, through patterning of and collaborating with other factors, can fulfill all these roles simultaneously.

A coupled mechano-biochemical model for cell polarity guided anisotropic root growth

Plants develop new organs to adjust their bodies to dynamic changes in the environment. How independent organs achieve anisotropic shapes and polarities is poorly understood. To address this question, we constructed a mechano-biochemical model for Arabidopsis root meristem growth that integrates biologically plausible principles. Computer model simulations demonstrate how differential growth of neighboring tissues results in the initial symmetry-breaking leading to anisotropic root growth. Furthermore, the root growth feeds back on a polar transport network of the growth regulator auxin. Model, predictions are in close agreement with in vivo patterns of anisotropic growth, auxin distribution, and cell polarity, as well as several root phenotypes caused by chemical, mechanical, or genetic perturbations. Our study demonstrates that the combination of tissue mechanics and polar auxin transport organizes anisotropic root growth and cell polarities during organ outgrowth. Therefore, a mobile auxin signal transported through immobile cells drives polarity and growth mechanics to coordinate complex organ development.

A perspective on cell proliferation kinetics in the root apical meristem

Organogenesis in plants is primarily postembryonic and relies on a strict balance between cell division and cell expansion. The root is a particularly well-suited model to study cell proliferation in detail since the two processes are spatially and temporally separated for all the different tissues. In addition, the root is amenable to detailed microscopic analysis to identify cells progressing through the cell cycle. While it is clear that cell proliferation activity is restricted to the root apical meristem (RAM), understanding cell proliferation kinetics and identifying its parameters have required much effort over many years. Here, we review the main concepts, experimental settings, and findings aimed at obtaining a detailed knowledge of how cells proliferate within the RAM. The combination of novel tools, experimental strategies, and mathematical models has contributed to our current view of cell proliferation in the RAM. We also discuss several lines of research that need to be explored in the future.

Bundling up the Role of the Actin Cytoskeleton in Primary Root Growth

Primary root growth is required by the plant to anchor in the soil and reach out for nutrients and water, while dealing with obstacles. Efficient root elongation and bending depends upon the coordinated action of environmental sensing, signal transduction, and growth responses. The actin cytoskeleton is a highly plastic network that constitutes a point of integration for environmental stimuli and hormonal pathways. In this review, we present a detailed compilation highlighting the importance of the actin cytoskeleton during primary root growth and we describe how actin-binding proteins, plant hormones, and actin-disrupting drugs affect root growth and root actin. We also discuss the feedback loop between actin and root responses to light and gravity. Actin affects cell division and elongation through the control of its own organization. We remark upon the importance of longitudinally oriented actin bundles as a hallmark of cell elongation as well as the role of the actin cytoskeleton in protein trafficking and vacuolar reshaping during this process. The actin network is shaped by a plethora of actin-binding proteins; however, there is still a large gap in connecting the molecular function of these proteins with their developmental effects. Here, we summarize their function and known effects on primary root growth with a focus on their high level of specialization. Light and gravity are key factors that help us understand root growth directionality. The response of the root to gravity relies on hormonal, particularly auxin, homeostasis, and the actin cytoskeleton. Actin is necessary for the perception of the gravity stimulus via the repositioning of sedimenting statoliths, but it is also involved in mediating the growth response via the trafficking of auxin transporters and cell elongation. Furthermore, auxin and auxin analogs can affect the composition of the actin network, indicating a potential feedback loop. Light, in its turn, affects actin organization and hence, root growth, although its precise role remains largely unknown. Recently, fundamental studies with the latest techniques have given us more in-depth knowledge of the role and organization of actin in the coordination of root growth; however, there remains a lot to discover, especially in how actin organization helps cell shaping, and therefore root growth.

A Self-Organized PLT/Auxin/ARR-B Network Controls the Dynamics of Root Zonation Development in Arabidopsis thaliana

During organogenesis, coherent organ growth arises from spatiotemporally coordinated decisions of individual cells. In the root of Arabidopsis thaliana, this coordination results in the establishment of a division and a differentiation zone. Cells continuously move through these zones; thus, a major question is how the boundary between these domains, the transition zone, is formed and maintained. By combining molecular genetics with computational modeling, we reveal how an auxin/PLETHORA/ARR-B network controls these dynamic patterning processes. We show that after germination, cell division causes a drop in distal PLT2 levels that enables transition zone formation and ARR12 activation. The resulting PLT2-ARR12 antagonism controls expansion of the division zone (the meristem). The successive ARR1 activation antagonizes PLT2 through inducing the cell-cycle repressor KRP2, thus setting final meristem size. Our work indicates a key role for the interplay between cell division dynamics and regulatory networks in root zonation and transition zone patterning.

Root Plasticity in the Pursuit of Water

One of the greatest challenges of terrestrial vegetation is to acquire water through soil-grown roots. Owing to the scarcity of high-quality water in the soil and the environment's spatial heterogeneity and temporal variability, ranging from extreme flooding to drought, roots have evolutionarily acquired tremendous plasticity regarding their geometric arrangement of individual roots and their three-dimensional organization within the soil. Water deficiency has also become an increasing threat to agriculture and dryland ecosystems due to climate change. As a result, roots have become important targets for genetic selection and modification in an effort to improve crop resilience under water-limiting conditions. This review addresses root plasticity from different angles: Their structures and geometry in response to the environment, potential genetic control of root traits suitable for water-limiting conditions, and contemporary and future studies of the principles underlying root plasticity post-Darwin's 'root-brain' hypothesis. Our increasing knowledge of different disciplines of plant sciences and agriculture should contribute to a sustainable management of natural and agricultural ecosystems for the future of mankind.