Spatiotemporal modelling of hormonal crosstalk explains the level and patterning of hormones and gene expression in Arabidopsis thaliana wild-type and mutant roots

A predictive model for ethylene-mediated auxin and cytokinin patterning in the Arabidopsis root

The interaction between auxin and cytokinin is important in many aspects of plant development. Experimental measurements of both auxin and cytokinin concentration and reporter gene expression clearly show the coexistence of auxin and cytokinin concentration patterning in Arabidopsis root development. However, in the context of crosstalk among auxin, cytokinin, and ethylene, little is known about how auxin and cytokinin concentration patterns simultaneously emerge and how they regulate each other in the Arabidopsis root. This work utilizes a wide range of experimental observations to propose a mechanism for simultaneous patterning of auxin and cytokinin concentrations. In addition to revealing the regulatory relationships between auxin and cytokinin, this mechanism shows that ethylene signaling is an important factor in achieving simultaneous auxin and cytokinin patterning, while also predicting other experimental observations. Combining the mechanism with a realistic in silico root model reproduces experimental observations of both auxin and cytokinin patterning. Predictions made by the mechanism can be compared with a variety of experimental observations, including those obtained by our group and other independent experiments reported by other groups. Examples of these predictions include patterning of auxin biosynthesis rate, changes in PIN1 and PIN2 patterns in pin3,4,7 mutants, changes in cytokinin patterning in the pls mutant, PLS patterning, and various trends in different mutants. This research reveals a plausible mechanism for simultaneous patterning of auxin and cytokinin concentrations in Arabidopsis root development and suggests a key role for ethylene pattern integration.

ZmPILS6 is an auxin efflux carrier required for maize root morphogenesis

Plant root systems play a pivotal role in plant physiology and exhibit diverse phenotypic traits. Understanding the genetic mechanisms governing root growth and development in model plants like maize is crucial for enhancing crop resilience to drought and nutrient limitations. This study focused on identifying and characterizing ZmPILS6, an annotated auxin efflux carrier, as a key regulator of various crown root traits in maize. ZmPILS6-modified roots displayed reduced network area and suppressed lateral root formation, which are desirable traits for the "steep, cheap, and deep" ideotype. The research revealed that ZmPILS6 localizes to the endoplasmic reticulum and plays a vital role in controlling the spatial distribution of indole-3-acetic acid (IAA or "auxin") in primary roots. The study also demonstrated that ZmPILS6 can actively efflux IAA when expressed in yeast. Furthermore, the loss of ZmPILS6 resulted in significant proteome remodeling in maize roots, particularly affecting hormone signaling pathways. To identify potential interacting partners of ZmPILS6, a weighted gene coexpression analysis was performed. Altogether, this research contributes to the growing knowledge of essential genetic determinants governing maize root morphogenesis, which is crucial for guiding agricultural improvement strategies.

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.

Systems approaches reveal that ABCB and PIN proteins mediate co-dependent auxin efflux

Members of the B family of membrane-bound ATP-binding cassette (ABC) transporters represent key components of the auxin efflux machinery in plants. Over the last two decades, experimental studies have shown that modifying ATP-binding cassette sub-family B (ABCB) expression affects auxin distribution and plant phenotypes. However, precisely how ABCB proteins transport auxin in conjunction with the more widely studied family of PIN-formed (PIN) auxin efflux transporters is unclear, and studies using heterologous systems have produced conflicting results. Here, we integrate ABCB localization data into a multicellular model of auxin transport in the Arabidopsis thaliana root tip to predict how ABCB-mediated auxin transport impacts organ-scale auxin distribution. We use our model to test five potential ABCB-PIN regulatory interactions, simulating the auxin dynamics for each interaction and quantitatively comparing the predictions with experimental images of the DII-VENUS auxin reporter in wild-type and abcb single and double loss-of-function mutants. Only specific ABCB-PIN regulatory interactions result in predictions that recreate the experimentally observed DII-VENUS distributions and long-distance auxin transport. Our results suggest that ABCBs enable auxin efflux independently of PINs; however, PIN-mediated auxin efflux is predominantly through a co-dependent efflux where co-localized with ABCBs.

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.

Role of sugar and auxin crosstalk in plant growth and development

Under the natural environment, nutrient signals interact with phytohormones to coordinate and reprogram plant growth and survival. Sugars are important molecules that control almost all morphological and physiological processes in plants, ranging from seed germination to senescence. In addition to their functions as energy resources, osmoregulation, storage molecules, and structural components, sugars function as signaling molecules and interact with various plant signaling pathways, such as hormones, stress, and light to modulate growth and development according to fluctuating environmental conditions. Auxin, being an important phytohormone, is associated with almost all stages of the plant's life cycle and also plays a vital role in response to the dynamic environment for better growth and survival. In the previous years, substantial progress has been made that showed a range of common responses mediated by sugars and auxin signaling. This review discusses how sugar signaling affects auxin at various levels from its biosynthesis to perception and downstream gene activation. On the same note, the review also highlights the role of auxin signaling in fine-tuning sugar metabolism and carbon partitioning. Furthermore, we discussed the crosstalk between the two signaling machineries in the regulation of various biological processes, such as gene expression, cell cycle, development, root system architecture, and shoot growth. In conclusion, the review emphasized the role of sugar and auxin crosstalk in the regulation of several agriculturally important traits. Thus, engineering of sugar and auxin signaling pathways could potentially provide new avenues to manipulate for agricultural purposes.

Root growth responses to mechanical impedance are regulated by a network of ROS, ethylene and auxin signalling in Arabidopsis

The growth and development of root systems is influenced by mechanical properties of the substrate in which the plants grow. Mechanical impedance, such as by compacted soil, can reduce root elongation and limit crop productivity. To understand better the mechanisms involved in plant root responses to mechanical impedance stress, we investigated changes in the root transcriptome and hormone signalling responses of Arabidopsis to artificial root barrier systems in vitro. We demonstrate that upon encountering a barrier, reduced Arabidopsis root growth and a characteristic 'step-like' growth pattern is due to a reduction in cell elongation associated with changes in signalling gene expression. Data from RNA-sequencing combined with reporter line and mutant studies identified essential roles for reactive oxygen species, ethylene and auxin signalling during the barrier response. We propose a model in which early responses to mechanical impedance include reactive oxygen signalling integrated with ethylene and auxin responses to mediate root growth changes. Inhibition of ethylene responses allows improved growth in response to root impedance, an observation that may inform future crop breeding programmes.

Bootstrapping and Pinning down the Root Meristem; the Auxin-PLT-ARR Network Unites Robustness and Sensitivity in Meristem Growth Control

After germination, the meristem of the embryonic plant root becomes activated, expands in size and subsequently stabilizes to support post-embryonic root growth. The plant hormones auxin and cytokinin, together with master transcription factors of the PLETHORA (PLT) family have been shown to form a regulatory network that governs the patterning of this root meristem. Still, which functional constraints contributed to shaping the dynamics and architecture of this network, has largely remained unanswered. Using a combination of modeling approaches we reveal how the interplay between auxin and PLTs enables meristem activation in response to above-threshold stimulation, while its embedding in a PIN-mediated auxin reflux loop ensures localized PLT transcription and thereby, a finite meristem size. We furthermore demonstrate how this constrained PLT transcriptional domain enables independent control of meristem size and division rates, further supporting a division of labor between auxin and PLT. We subsequently reveal how the weaker auxin antagonism of the earlier active Arabidopsis response regulator 12 (ARR12) may arise from the absence of a DELLA protein interaction domain. Our model indicates that this reduced strength is essential to prevent collapse in the early stages of meristem expansion while at later stages the enhanced strength of Arabidopsis response regulator 1 (ARR1) is required for sufficient meristem size control. Summarizing, our work indicates that functional constraints significantly contribute to shaping the auxin-cytokinin-PLT regulatory network.

Cytokinin-Controlled Gradient Distribution of Auxin in Arabidopsis Root Tip

The plant root is a dynamic system, which is able to respond promptly to external environmental stimuli by constantly adjusting its growth and development. A key component regulating this growth and development is the finely tuned cross-talk between the auxin and cytokinin phytohormones. The gradient distribution of auxin is not only important for the growth and development of roots, but also for root growth in various response. Recent studies have shed light on the molecular mechanisms of cytokinin-mediated regulation of local auxin biosynthesis/metabolism and redistribution in establishing active auxin gradients, resulting in cell division and differentiation in primary root tips. In this review, we focus our attention on the molecular mechanisms underlying the cytokinin-controlled auxin gradient in root tips.

Gibberellin signaling mediates lateral root inhibition in response to K+-deprivation

The potassium ion (K+) is vital for plant growth and development, and K+-deprivation leads to reduced crop yields. Here we describe phenotypic, transcriptomic, and mutant analyses to investigate the signaling mechanisms mediating root architectural changes in Arabidopsis (Arabidopsis thaliana) Columbia. We showed effects on root architecture are mediated through a reduction in cell division in the lateral root (LR) meristems, the rate of LR initiation is reduced but LR density is unaffected, and primary root growth is reduced only slightly. This was primarily regulated through gibberellic acid (GA) signaling, which leads to the accumulation of growth-inhibitory DELLA proteins. The short LR phenotype was rescued by exogenous application of GA but not of auxin or by the inhibition of ethylene signaling. RNA-seq analysis showed upregulation by K+-deprivation of the transcription factors JUNGBRUNNEN1 (JUB1) and the C-repeat-binding factor (CBF)/dehydration-responsive element-binding factor 1 regulon, which are known to regulate GA signaling and levels that regulate DELLAs. Transgenic overexpression of JUB1 and CBF1 enhanced responses to K+ stress. Attenuation of the reduced LR growth response occurred in mutants of the CBF1 target gene SFR6, implicating a role for JUB1, CBF1, and SFR6 in the regulation of LR growth in response to K+-deprivation via DELLAs. We propose this represents a mechanism to limit horizontal root growth in conditions where K+ is available deeper in the soil.

Differential Subcellular Distribution of Cytokinins: How Does Membrane Transport Fit into the Big Picture?

Cytokinins are a class of phytohormones, signalling molecules specific to plants. They act as regulators of diverse physiological processes in complex signalling pathways. It is necessary for plants to continuously regulate cytokinin distribution among different organs, tissues, cells, and compartments. Such regulatory mechanisms include cytokinin biosynthesis, metabolic conversions and degradation, as well as cytokinin membrane transport. In our review, we aim to provide a thorough picture of the latter. We begin by summarizing cytokinin structures and physicochemical properties. Then, we revise the elementary thermodynamic and kinetic aspects of cytokinin membrane transport. Next, we review which membrane-bound carrier proteins and protein families recognize cytokinins as their substrates. Namely, we discuss the families of "equilibrative nucleoside transporters" and "purine permeases", which translocate diverse purine-related compounds, and proteins AtPUP14, AtABCG14, AtAZG1, and AtAZG2, which are specific to cytokinins. We also address long-distance cytokinin transport. Putting all these pieces together, we finally discuss cytokinin distribution as a net result of these processes, diverse in their physicochemical nature but acting together to promote plant fitness.

Crosstalk among hydrogen sulfide (H2S), nitric oxide (NO) and carbon monoxide (CO) in root-system development and its rhizosphere interactions: A gaseous interactome

Root development in higher plants is achieved by a precise intercellular communication which determines cell fate in the primary embryonic meristem where the gasotransmitters H₂S, NO and CO participate dynamically. Furthermore, the rhizosphere interaction of these molecules with microbial and soil metabolism also affects root development. NO regulates root growth and architecture in association with several other biomolecules like auxin indole-3-acetic acid (IAA), ethylene, jasmonic acid (JA), strigolactones, alkamides and melatonin. The CO-mediated signal transduction pathway in roots is closely linked to the NO-mediated signal cascades. Interestingly, H₂S acts also as an upstream component in IAA and NO-mediated crosstalk during root development. Heme oxygenase (HO) 1 generates CO and functions as a downstream component in H₂S-mediated adventitious rooting and H₂S-CO crosstalk. Likewise, reactive oxygen species (ROS), H₂S and NO crosstalk are important components in the regulation of root architecture. Deciphering these interactions will be a potential biotechnological tool which could provide benefits in crop management in soils, especially under adverse environmental conditions. This review aims to provide a comprehensive update of the complex networks of these gasotransmitters during the development of roots.

Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10-7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

All Roads Lead to Auxin: Post-translational Regulation of Auxin Transport by Multiple Hormonal Pathways

Auxin is a key hormonal regulator, that governs plant growth and development in concert with other hormonal pathways. The unique feature of auxin is its polar, cell-to-cell transport that leads to the formation of local auxin maxima and gradients, which coordinate initiation and patterning of plant organs. The molecular machinery mediating polar auxin transport is one of the important points of interaction with other hormones. Multiple hormonal pathways converge at the regulation of auxin transport and form a regulatory network that integrates various developmental and environmental inputs to steer plant development. In this review, we discuss recent advances in understanding the mechanisms that underlie regulation of polar auxin transport by multiple hormonal pathways. Specifically, we focus on the post-translational mechanisms that contribute to fine-tuning of the abundance and polarity of auxin transporters at the plasma membrane and thereby enable rapid modification of the auxin flow to coordinate plant growth and development.

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.

Auxin fluxes through plasmodesmata modify root-tip auxin distribution

Auxin is a key signal regulating plant growth and development. It is well established that auxin dynamics depend on the spatial distribution of efflux and influx carriers on the cell membranes. In this study, we employ a systems approach to characterise an alternative symplastic pathway for auxin mobilisation via plasmodesmata, which function as intercellular pores linking the cytoplasm of adjacent cells. To investigate the role of plasmodesmata in auxin patterning, we developed a multicellular model of the Arabidopsis root tip. We tested the model predictions using the DII-VENUS auxin response reporter, comparing the predicted and observed DII-VENUS distributions using genetic and chemical perturbations designed to affect both carrier-mediated and plasmodesmatal auxin fluxes. The model revealed that carrier-mediated transport alone cannot explain the experimentally determined auxin distribution in the root tip. In contrast, a composite model that incorporates both carrier-mediated and plasmodesmatal auxin fluxes re-capitulates the root-tip auxin distribution. We found that auxin fluxes through plasmodesmata enable auxin reflux and increase total root-tip auxin. We conclude that auxin fluxes through plasmodesmata modify the auxin distribution created by efflux and influx carriers.

How grass keeps growing: an integrated analysis of hormonal crosstalk in the maize leaf growth zone

We studied the maize leaf to understand how long-distance signals, auxin and cytokinin, control leaf growth dynamics. We constructed a mathematical model describing the transport of these hormones along the leaf growth zone and their interaction with the local gibberellin (GA) metabolism in the control of cell division. Assuming gradually declining auxin and cytokinin supply at the leaf base, the model generated spatiotemporal hormone distribution and growth patterns that matched experimental data. At the cellular level, the model predicted a basal leaf growth as a result of cell division driven by auxin and cytokinin. Superimposed on this, GA synthesis regulated growth through the control of the size of the region of active cell division. The predicted hormone and cell length distributions closely matched experimental data. To correctly predict the leaf growth profiles and final organ size of lines with reduced or elevated GA production, the model required a signal proportional to the size of the emerged part of the leaf that inhibited the basal leaf growth driven by auxin and cytokinin. Excision and shading of the emerged part of the growing leaf allowed us to demonstrate that this signal exists and depends on the perception of light intensity.

Salicylic Acid Affects Root Meristem Patterning via Auxin Distribution in a Concentration-Dependent Manner

The phytohormone salicylic acid (SA) is well known for its induction of pathogenesis-related proteins and systemic acquired resistance; SA also has specific effects on plant growth and development. Here we analyzed the effect of SA on Arabidopsis (Arabidopsis thaliana) root development. We show that exogenous SA treatment at low (below 50 µM) and high (greater than 50 µM) concentrations affect root meristem development in two different PR1-independent ways. Low-concentration SA promoted adventitious roots and altered architecture of the root apical meristem, whereas high-concentration SA inhibited all growth processes in the root. All exposures to exogenous SA led to changes in auxin synthesis and transport. A wide range of SA treatment concentrations activated auxin synthesis, but the effect of SA on auxin transport was dose dependent. Mathematical modeling of auxin synthesis and transport predicted auxin accumulation or depletion in the root tip following low- or high-concentration SA treatments, respectively. SA-induced auxin accumulation led to the formation of more layers of columella initials, an additional cortical cell layer (middle cortex), and extra files of epidermis, cortex, and endodermis cells. Suppression of SHORT ROOT and activation of CYCLIN D6;1 mediated the changes in radial architecture of the root. We propose that low-concentration SA plays an important role in shaping root meristem structure and root system architecture.

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.

Deciphering Auxin-Ethylene Crosstalk at a Systems Level

The auxin and ethylene pathways cooperatively regulate a variety of developmental processes in plants. Growth responses to ethylene are largely dependent on auxin, the key regulator of plant morphogenesis. Auxin, in turn, is capable of inducing ethylene biosynthesis and signaling, making the interaction of these hormones reciprocal. Recent studies discovered a number of molecular events underlying auxin-ethylene crosstalk. In this review, we summarize the results of fine-scale and large-scale experiments on the interactions between the auxin and ethylene pathways in Arabidopsis. We integrate knowledge on molecular crosstalk events, their tissue specificity, and associated phenotypic responses to decipher the crosstalk mechanisms at a systems level. We also discuss the prospects of applying systems biology approaches to study the mechanisms of crosstalk between plant hormones.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions

Background

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology.

Methods

Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty.

Results

The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model’s structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described.

Conclusions

Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0484-3) contains supplementary material, which is available to authorized users.

Crosstalk Complexities between Auxin, Cytokinin, and Ethylene in Arabidopsis Root Development: From Experiments to Systems Modeling, and Back Again

Understanding how hormones and genes interact to coordinate plant growth in a changing environment is a major challenge in plant developmental biology. Auxin, cytokinin, and ethylene are three important hormones that regulate many aspects of plant development. This review critically evaluates the crosstalk between the three hormones in Arabidopsis root development. We integrate a variety of experimental data into a crosstalk network, which reveals multiple layers of complexity in auxin, cytokinin, and ethylene crosstalk. In particular, data integration reveals an additional, largely overlooked link between the ethylene and cytokinin pathways, which acts through a phosphorelay mechanism. This proposed link addresses outstanding questions on whether ethylene application promotes or inhibits receptor kinase activity of the ethylene receptors. Elucidating the complexity in auxin, cytokinin, and ethylene crosstalk requires a combined experimental and systems modeling approach. We evaluate important modeling efforts for establishing how crosstalk between auxin, cytokinin, and ethylene regulates patterning in root development. We discuss how a novel methodology that iteratively combines experiments with systems modeling analysis is essential for elucidating the complexity in crosstalk of auxin, cytokinin, and ethylene in root development. Finally, we discuss the future challenges from a combined experimental and modeling perspective.

A recovery principle provides insight into auxin pattern control in the Arabidopsis root

Regulated auxin patterning provides a key mechanism for controlling root growth and development. We have developed a data-driven mechanistic model using realistic root geometry and formulated a principle to theoretically investigate quantitative auxin pattern recovery following auxin transport perturbation. This principle reveals that auxin patterning is potentially controlled by multiple combinations of interlinked levels and localisation of influx and efflux carriers. We demonstrate that (1) when efflux carriers maintain polarity but change levels, maintaining the same auxin pattern requires non-uniform and polar distribution of influx carriers; (2) the emergence of the same auxin pattern, from different levels of influx carriers with the same nonpolar localisation, requires simultaneous modulation of efflux carrier level and polarity; and (3) multiple patterns of influx and efflux carriers for maintaining an auxin pattern do not have spatially proportional correlation. This reveals that auxin pattern formation requires coordination between influx and efflux carriers. We further show that the model makes various predictions that can be experimentally validated.

Computational Modeling of Auxin: A Foundation for Plant Engineering

Since the development of agriculture, humans have relied on the cultivation of plants to satisfy our increasing demand for food, natural products, and other raw materials. As we understand more about plant development, we can better manipulate plants to fulfill our particular needs. Auxins are a class of simple metabolites that coordinate many developmental activities like growth and the appearance of functional structures in plants. Computational modeling of auxin has proven to be an excellent tool in elucidating many mechanisms that underlie these developmental events. Due to the complexity of these mechanisms, current modeling efforts are concerned only with single phenomena focused on narrow spatial and developmental contexts; but a general model of plant development could be assembled by integrating the insights from all of them. In this perspective, we summarize the current collection of auxin-driven computational models, focusing on how they could come together into a single model for plant development. A model of this nature would allow researchers to test hypotheses in silico and yield accurate predictions about the behavior of a plant under a given set of physical and biochemical constraints. It would also provide a solid foundation toward the establishment of plant engineering, a proposed discipline intended to enable the design and production of plants that exhibit an arbitrarily defined set of features.

Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin

Understanding the mechanisms regulating root development under drought conditions is an important question for plant biology and world agriculture. We examine the effect of osmotic stress on abscisic acid (ABA), cytokinin and ethylene responses and how they mediate auxin transport, distribution and root growth through effects on PIN proteins. We integrate experimental data to construct hormonal crosstalk networks to formulate a systems view of root growth regulation by multiple hormones. Experimental analysis shows: that ABA-dependent and ABA-independent stress responses increase under osmotic stress, but cytokinin responses are only slightly reduced; inhibition of root growth under osmotic stress does not require ethylene signalling, but auxin can rescue root growth and meristem size; osmotic stress modulates auxin transporter levels and localization, reducing root auxin concentrations; PIN1 levels are reduced under stress in an ABA-dependent manner, overriding ethylene effects; and the interplay among ABA, ethylene, cytokinin and auxin is tissue-specific, as evidenced by differential responses of PIN1 and PIN2 to osmotic stress. Combining experimental analysis with network construction reveals that ABA regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin.

Some fundamental aspects of modeling auxin patterning in the context of auxin-ethylene-cytokinin crosstalk

The activities of hormones in the Arabidopsis root depend on cellular context and exhibit either synergistic or antagonistic interactions. Patterning in Arabidopsis root development is coordinated via a localized auxin concentration maximum in the root tip, mediating transcription of key regulatory genes. Auxin concentration and response are each regulated by diverse interacting hormones and gene expression and therefore cannot change independently of those hormones and genes. For example, experimental data accumulated over many years have shown that both ethylene and cytokinin regulate auxin concentration and response. Using the crosstalk of auxin-ethylene-cytokinin as a paradigm, we discuss the links between experimental data, reaction kinetics and spatiotemporal modeling to dissect hormonal crosstalk. In particular, we discuss how kinetic equations for modeling auxin concentration are formulated based on experimental data and also the underlying assumptions for deriving those kinetic equations. Furthermore, we show that, by integrating kinetic equations with spatial root structure, modeling of spatiotemporal hormonal crosstalk is a powerful tool for analyzing and predicting the roles of multiple hormone interactions in auxin patterning. Finally, we summarize important considerations in developing a spatiotemporal hormonal crosstalk model for plant root development.