Root hydraulic conductivity is a limiting factor along the water pathways between the soil and the leaf, and root radial conductivity is itself defined by cell-scale hydraulic properties and anatomical features. However, quantifying the influence of anatomical features on the radial conductivity remains challenging due to complex time-consuming experimental procedures. We present an open-source computational tool, the Generator of Root Anatomy in R (GRANAR; http://granar.github.io), that can be used to rapidly generate digital versions of contrasted monocotyledon root anatomical networks. GRANAR uses a limited set of root anatomical parameters, easily acquired with existing image analysis tools. The generated anatomical network can then be used in combination with hydraulic models to estimate the corresponding hydraulic properties. We used GRANAR to reanalyze large maize (Zea mays) anatomical datasets from the literature. Our model was successful at creating virtual anatomies for each experimental observation. We also used GRANAR to generate anatomies not observed experimentally over wider ranges of anatomical parameters. The generated anatomies were then used to estimate the corresponding radial conductivities with the hydraulic model MECHA (model of explicit cross-section hydraulic architecture). Our simulations highlight the large importance of the width of the stele and the cortex. GRANAR is a computational tool that generates root anatomical networks from experimental data. It enables the quantification of the effect of individual anatomical features on the root radial conductivity.

Functional-structural root system models combine functional and structural root traits to represent the growth and development of root systems. In general, they are characterized by a large number of growth, architectural and functional root parameters, generating contrasted root systems evolving in a highly non-linear environment (soil, atmosphere), which makes the link between local traits and functioning unclear. On the other end of the root system modelling continuum, macroscopic root system models associate to each root system a set of plant-scale, easily interpretable parameters. However, as of today, it is unclear how these macroscopic parameters relate to root-scale traits and whether the upscaling of local root traits is compatible with macroscopic parameter measurements. The aim of this study was to bridge the gap between these two modelling approaches. We describe here the MAize Root System Hydraulic Architecture soLver (MARSHAL), a new efficient and user-friendly computational tool that couples a root architecture model (CRootBox) with fast and accurate algorithms of water flow through hydraulic architectures and plant-scale parameter calculations. To illustrate the tool’s potential, we generated contrasted maize hydraulic architectures that we compared with root system architectural and hydraulic observations. Observed variability of these traits was well captured by model ensemble runs. We also analysed the multivariate sensitivity of mature root system conductance, mean depth of uptake, root system volume and convex hull to the input parameters to highlight the key model parameters to vary for virtual breeding. It is available as an R package, an RMarkdown pipeline and a web application.

Root hydraulic properties play a central role in the global water cycle, in agricultural systems productivity, and in ecosystem survival as they impact the canopy water supply. However, the existing experimental methods to quantify root hydraulic conductivities, such as the root pressure probing, are particularly challenging, and their applicability to thin roots and small root segments is limited. Therefore, there is a gap in methods enabling easy estimations of root hydraulic conductivities in diverse root types. Here, we present a new pipeline to quickly estimate root hydraulic conductivities across different root types, at high resolution along root axes. Shortly, free-hand root cross-sections were used to extract a selected number of key anatomical traits.We used these traits to parametrize the Generator of Root Anatomy in R (GRANAR) model to simulate root anatomical networks. Finally, we used these generated anatomical networks within the Model of Explicit Cross-section Hydraulic Anatomy (MECHA) to compute an estimation of the root axial and radial hydraulic conductivities (k x and k r , respectively). Using this combination of anatomical data and computational models, we were able to create a root hydraulic conductivity atlas at the root system level, for 14-day-old pot-grown Zea mays (maize) plants of the var. B73. The altas highlights the significant functional variations along and between different root types. For instance, predicted variations of radial conductivity along the root axis were strongly dependent on the maturation stage of hydrophobic barriers. The same was also true for the maturation rates of the metaxylem vessels. Differences in anatomical traits along and across root types generated substantial variations in radial and axial conductivities estimated with our novel approach. Our methodological pipeline combines anatomical data and computational models to turn root crosssection images into a detailed hydraulic atlas. It is an inexpensive, fast, and easily applicable investigation tool for root hydraulics that complements existing complex experimental methods. It opens the way to high-throughput studies on the functional importance of root types in plant hydraulics, especially if combined with novel phenotyping techniques such as laser ablation tomography.

Functional-structural root system models combine functional and structural root traits to represent the growth and development of root systems. In general, they are characterized by a large number of growth, architectural and functional root parameters, generating contrasted root systems evolving in a highly nonlinear environment (soil, atmosphere), which makes unclear what impact of each single root system on root system functioning actually is. On the other end of the root system modelling continuum, macroscopic root system models associate to each root system instance a set of plant-scale, easily interpretable parameters. However, as of today, it is unclear how these macroscopic parameters relate to root-scale traits and whether the upscaling of local root traits are compatible with macroscopic parameter measurements. The aim of this study was to bridge the gap between these two modelling approaches by providing a fast and reliable tool, which eventually can help performing plant virtual breeding.We describe here the MAize Root System Hydraulic Architecture soLver (MARSHAL), a new efficient and user-friendly computational tool that couples a root architecture model (CRootBox) with fast and accurate algorithms of water flow through hydraulic architectures and plant-scale parameter calculations, and a review of architectural and hydraulic parameters of maize.To illustrate the tool’s potential, we generated contrasted maize hydraulic architectures that we compared with architectural (root length density) and hydraulic (root system conductance) observations. Observed variability of these traits was well captured by model ensemble runs We also analyzed the multivariate sensitivity of mature root system conductance, mean depth of uptake, root system volume and convex hull to the input parameters to highlight the key parameters to vary for efficient virtual root system breeding. MARSHAL enables inverse optimisations, sensitivity analyses and virtual breeding of maize hydraulic root architecture. It is available as an R package, an RMarkdown pipeline, and a web application.One-sentence summaryWe developed a dynamic hydraulic-architectural model of the root system, parameterized for maize, to generate contrasted hydraulic architectures, compatible with field and lab observations and that can be further analyzed in soil-root system models for virtual breeding.Authors contributionsF.M., X.D., M.J. and G.L. designed the study and defined its scope; F.M. and G.L. developed the model while associated tools were created by A.H. and G.L.; F.M. ran the model simulations and analyzed the results together with M.J and G.L.; F.M. and M.J. wrote the first version of this manuscript; all co-authors critically revised it.

Root hydraulic conductivity is an important determinant of plant water uptake capacity. In particular, the root radial conductivity is often thought to be a limiting factor along the water pathways between the soil and the leaf. The root radial conductivity is itself defined by cell scale hydraulic properties and anatomical features. However, quantifying the influence of anatomical features on the radial conductivity remains challenging due to complex, and time-consuming, experimental procedures. We present a new computation tool, the Generator of Root ANAtomy in R (GRANAR) that can be used to rapidly generate digital versions of root anatomical networks. GRANAR uses a limited set of root anatomical parameters, easily acquired with existing image analysis tools. The generated anatomical network can then be used in combination with hydraulic models to estimate the corresponding hydraulic properties. Heymans et al. 2019 -GRANAR -A Generator of Root ANAtomy in R -Preprint We used GRANAR to re-analyse large maize (Zea mays) anatomical datasets from the literature. Our model was successful at creating virtual anatomies for each experimental observation. We also used GRANAR to generate anatomies not observed experimentally, over wider ranges of anatomical parameters. The generated anatomies were then used to estimate the corresponding radial conductivities with the hydraulic model MECHA. This enabled us to quantify the effect of individual anatomical features on the root radial conductivity. In particular, our simulations highlight the large importance of the width of the stele and the cortex. GRANAR is an open-source project available here: http://granar.github.io Keywords Root anatomy, radial conductivity, anatomical model, Zea mays , aerenchyma, reanalysis One-Sentence summary: Generator of Root ANAtomy in R (GRANAR) is a new open-source computational tool that can be used to rapidly generate digital versions of root anatomical networks.

Root hydraulic properties play a central role in the global water cycle, agricultural systems productivity, and ecosystem survival as they impact the global canopy water supply. However, the available experimental methods to quantify root hydraulic conductivities, such as the root pressure probing, are particularly challenging and their applicability on thin roots and small root segments is limited. There is a gap in methods enabling easy estimations of root hydraulic conductivities across a diversity of root types and at high resolution along root axes. In this case study, we analysed Zea mays (maize) plants of the var. B73 that were grown in pots for 14 days. Root cross-section data were used to extract anatomical measurements. We used the Generator of Root Anatomy in R (GRANAR) model to generate root anatomical networks from anatomical features. Then we used the Model of Explicit Cross-section Hydraulic Anatomy (MECHA) to compute an estimation of the root axial and radial hydraulic conductivities (kx and kr, respectively), based on the generated anatomical networks and cell hydraulic properties from the literature. The root hydraulic conductivity maps obtained from the root cross-sections suggest significant functional variations along and between different root types. Predicted variations of kr along the root axis were strongly dependent on the maturation stage of hydrophobic barriers. The same was also true for the maturation rates of the metaxylem. The different anatomical features, as well as their evolution along the root type add significant variation to the kr estimation in between root type and along the root axe. Under the prism of root types, anatomy, and hydrophobic barriers, our results highlight the diversity of root radial and axial hydraulic conductivities, which may be veiled under low-resolution measurements of the root system hydraulic conductivity. While predictions of our root hydraulic maps match the range and trend of measurements reported in the literature, future studies could focus on the quantitative validation of hydraulic maps. From now on, a novel method, which turns root cross-section images into hydraulic maps will offer an inexpensive and easily applicable investigation tool for root hydraulics, in parallel to root pressure probing experiments.

<p>Schnepf et al., (2020) defined benchmark scenarios for root growth models, soil water flow models, root water flow models, and for water flow in the coupled soil-root system. All benchmarks and corresponding reference solutions were published in the form of Jupyter Notebooks on the GitHub repository <em>https://github.com/RSAbenchmarks/collaborative-comparison</em>. Several groups of functional-structural model developers have joined this benchmarking activity and provided the results of their individual implementations of the different scenarios.</p> <p>The focus of this contribution is on water uptake from a drying soil by a static root architecture. The numerical solutions of the different participating simulators as compared to the provided reference solution.</p> <p>The participating simulators are CPlantBox, DuMu<sup>x</sup>, R-SWMS, OpenSimRoot and SRI. They have in common that they simulate water flow in the 3D soil domain, water flow inside the root system that is represented as a mathematical tree graph, and the coupling between the two domains in form of a volumetric sink term that describes the transfer of water between the two domains. The simulators differ in the numerical schemes used for solving the water flow equations in roots and soil domains, as well as in the way the sink term is formulated, in particular in the way the possibly increased rhizosphere resistance to water flow is accounted for. </p> <p>The results to the water flow in soil benchmarks show how the different simulators perform against the analytical solution to a problem of infiltration into an initially dry soil, as well as a problem of evaporation from initially moist soil. All of the simulators could accurately predict the infiltration front in different soil types as well as the actual evaporation curves.</p> <p>The coupled problem of root water uptake by a static root architecture from an initially already dry soil posed a bigger challenge to the different simulators and revealed some diversity between the different solutions. The Benchmark with an initially rather dry soil defined a potential transpiration that immediately induced water stress of the plant. The simulators had to simulate the consequent rhizosphere drying and associated increase in rhizosphere resistance. All of the soil simulators smoothed the gradients in the rhizosphere at the soil grid size such that root water uptake was significantly overestimated unless the rhizosphere resistance was explicitly accounted for in the root water uptake model. As a result, all simulators came close to the reference solution (that itself is a numerical solution, see Schnepf et al. 2020 for details). </p> <p>In this study, we showed that all simulators are generally able to solve the benchmark problems but minor differences occur amongst the simulators when simulating different soil types. Benchmarking led to model improvements and helped interpret model results in a more informed way. The availability of “reference solutions“ made modellers aware of the range of validity of their numerical solution and encouraged them to improve either their numerical solution or to introduce new processes Future efforts may aim to extend the benchmarks from water flow to further processes, such as solute transport or rhizodeposition.</p> <p> </p> <p>Schnepf et al., 2020, <em>Front. Plant Sci.</em> 11</p>

With global warming, climate zones are projected to shift poleward, and the frequency and intensity of droughts to increase, driving threats to crop production and ecosystems. Plant hydraulic traits play major roles in coping with such droughts, and process-based plant hydraulics (water flowing along decreasing pressure or total water potential gradients) has newly been implemented in land surface models. An enigma reported for the past 35 years is the observation of water flowing along increasing water potential gradients across roots. By combining the most advanced modelling tool from the emerging field of plant micro-hydrology with pioneering cell solute mapping data, we found that the current paradigm of water flow across roots of all vascular plants is incomplete: it lacks the impact of solute concentration (and thus negative osmotic potential) gradients across living cells. This gradient acts as a water pump as it reduces water tension without loading solutes in plant vasculature (xylem). Importantly, water tension adjustments in roots may have large impacts in leaves due to the tension-cavitation feedback along stems. Here, we mathematically demonstrate the water pumping mechanism by solving water flow equations analytically on a triple-cell system. Then we show that the simplistic upscaled equations hold in 2- and 3-D maize, grapevine and Arabidopsis complex hydraulic anatomies, and that water may flow uphill of water potential gradients toward xylem as observed experimentally. Besides its contribution to the fundamental understanding of plant water relations, this study lays new foundations for future multidisciplinary research encompassing plant physiology and ecohydrology, and has the ambition to mathematically capture a keystone process for the accurate forecasting of plant water status in crop models and LSMs.