Connecting the dots between root cross-section images and modelling tools to create a high resolution root system hydraulic maps in Zea mays

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. One-Sentence summary The use of cross-section images and modelling tools to generate a map the axial and radial hydraulic conductivity along different root types for the maize cultivar B73.


Introduction
Root hydraulics properties are one of the major functional plant properties influencing the root water uptake dynamics. Indeed, the radial hydraulic conductivity ( k r ) is a key component 56 of the water absorption and the axial hydraulic conductance ( k x ) defines the water transport along the root (Leitner et al., 2014) . Changes in the local root hydraulic properties, at the cell 58 and organ scale, are known to have global repercussions on the root hydraulic behavior (Tardieu et al., 2018;Meunier et al., 2020) and are considered as important breeding targets 60 to create drought resilient varieties (Maurel and Nacry, 2020) . The quantification of root hydraulic conductivity along the roots is therefore needed to have a quantitative 62 understanding of the root water uptake dynamics. /

Heymans et al. 2020 -Root hydraulic map -PREPRINT
The root radial conductivity is influenced by different factors. For instance, root anatomical 64 features define the baseline for radial water flow (Steudle, 2000;Heymans et al., 2019) . The modulation of aquaporin can modulate that baseline value by affecting the cell membrane 66 permeability on the short term (Parent et al., 2009) . On the long term, the development of hydrophobic barriers (Enstone et al., 2002) and the conductivity of plasmodesmata 68 (Couvreur et al., 2018) have also a crucial impact. On the other hand, the axial root conductance is a function of the xylem vessel area, maturation and number (Martre et al., 70 2001) .
The quantification of radial hydraulic properties is challenging due to the complexity of the 72 experimental procedures. It is even more complicated to assess it at different locations along the root axis and on different root types. The most direct way to estimate root radial 74 conductivity is with roots which grow in soil-less environments using a root pressure probe (Frensch and Steudle, 1989) . Other experimental techniques employed a pressure chamber 76 to measure water flow that were successively cut into smaller parts (Zwieniecki et al., 2002) , or employed the high pressure flow meter device (Tyree et al., 1994) . Recently, virtual 78 quantification of radial hydraulic properties was enabled with models such as the Model of Explicit Cross-section Hydraulic Anatomy (MECHA) (Couvreur et al., 2018) . An intermediate 80 technique uses inverse modeling method with the root architecture model of Doussan et al. (1998) and high resolution images of root water uptake (Zarebanadkouki et al., 2016) . The 82 estimation of axial hydraulic properties is easier than the radial ones since it can be calculated from Hagen-Poiseuille's equation with only a root cross-section image (Frensch 84 and Steudle, 1989) .
has been made to reproduce or to improve the spatial distribution of radial root hydraulic 88 conductivity and axial root hydraulic conductance in maize. . However many studies that used functional-structural root model to simulate water uptake use the hydraulic conductivity 90 that have been estimated by Doussan et al. (1998) , such as in R-SWMS (Javaux et al., 2008) , OpenSimRoot (Postma et al., 2017) or MARSHAL (Meunier et al., 2020) . Although 92 those estimations were groundbreaking for the community at the time, we now need to be able to quantify root hydraulic conductivities that directly match the data that we want to 94 assess. Therefore including the effect of root anatomical changes and taking into account cell hydraulic properties would improve the accuracy and prediction of root water uptake 96 models.
Here, we present a procedure to generate a high resolution hydraulic conductivity map from 98 experimental data using recent modeling tools. With free hand cross sections and fluorescent microscopy, we were able to extract easily anatomical features that can be used 100 to run the Generator of Root Anatomy in R (GRANAR) (Heymans et al., 2019) . Then, using the generated anatomical networks with MECHA (Couvreur et al., 2018) , we estimated the 102 k r and k x along the root axis of each maize root type. This model's coupling creates a way to generate a root hydraulic conductivity map that takes into account the impact of the anatomy 104 and the cell hydraulic properties. The method that we developed here does not rely on expensive equipment. It can be easily reproduced for other genotypes and different 106 environmental constraints.

Material and methods
108 Five Zea mays (maize cultivar B73) plants were grown in pots for 14 days. The pot dimensions were 12 cm diameter, 25 cm deep and filled with sieved potting soil. The soil 110 was at field capacity when the germinated seeds were planted and never re-watered afterwards. The germination of the seed occurred in a petri dish maintained vertically in dark 112 condition between two wet filter papers. From the fifteen seeds that were put under germination, five were selected based on the length of the tap root (0.5 to 1 cm long) in order 114 to have an homogenous germination rate. Each seed was planted in a different pot. All plants grew in a greenhouse with the environmental settings of the greenhouse set to 60 % 116 for the relative humidity and a temperature of 25°C (+-3°C).
The root systems were excavated and washed at the end of the experiment (after 14 days). 118 The root systems were scanned and selected root samples were conserved in a Formaldehyde Alcohol Acetic Acid solution (Ruzin and Others, 1999) . The roots were 120 stained with berberine for one hour and post stained with aniline blue for 30 minutes before making free-hand cross-sections (Brundrett et al., 1988) . Three or more roots per type were 122 cut at every 5 cm or less to map anatomical features along the root segments. Cross section images were acquired with fluorescent microscope SM-LUX and the pictures were taken 124 using a Leica dfc320. The images were analysed with the ImageJ software. The anatomical features that we measured are listed in the table 1.
126 Table 1: List of the measured anatomical features acquired on the root cross section images that

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have been used to get the GRANAR parameters.

Measured anatomical features GRANAR parameters
To identify the type of hydrophobic barriers that were encountered on the cross-section 130 images, we used the berberine-aniline blue fluorescent staining procedure for suberin, lignin, and callose in plant tissue (Brundrett et al., 1988) . This procedure for visualizing exo -and 132 endodermal Casparian strips works also to identify the lignification of the xylem cell walls.
Xylem vessels with fully lignified cell walls were considered as mature xylem elements. 134 The root type selected for this analysis are the tap root, the basal root (embryonic root), the shoot born root on the first node and two types of lateral roots, the short ones (short ones) 136 and long ones (longer than 5 cm with second order lateral roots on it) (Passot et al., 2018) .
The choice of two classes of lateral root instead of three is due to experimental constraints. 138 We had to base the classification on root length instead of root growth rate. The threshold that we set is evaluating the difference between the long later root classified as type A in the  The root axial hydraulic conductance was estimated using the Hagen-Poiseuille equations.

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(eq. 1) ² 8πhμ Where A is the cell area of one xylem vessel, h is the cell length and µ is the viscosity of the xylem sap. Xylem sap being essentially water, the viscosity constant was assumed to be 174 equal to the one of the water.
As the root hydraulic conductivities obtained in this study are compared, among other 176 studies, with the ones estimated in Doussan et al. (1998), we added an assumption to the data provided from that study. This hypothesis is that the lateral roots have an average 178 growing rate of one centimeter per day (Passot et al., 2018) .
The details about the GRANAR-MECHA coupling is available in an online Jupyter NoteBook The whole script that was used to compute the root hydraulic maps from the root anatomical 188 measurement is presented as a Rmarkdown script stored in a GitHub repository ( https://github.com/granar/B73_HydraulicMap doi: 10.5281/zenodo.4320861). In the same 190 repository are stored all input and output data of this study. 194 To create hydraulic conductivity maps along the different maize root types taking into account the evolution of the anatomical features, we needed to capture anatomical 196 descriptors that are ready-to-use for downstream computational models. Anatomical features change along the root axis, as the root is narrower and less mature at the tip than at its basal 198 position. Across root types, anatomies may also differ. With the gathered root cross section images, we were able to extract the root anatomical features and place those features along 200 the root axes. Most of the root anatomical features that we computed follow a linear regression when they are plotted against the distance to the tip (Figure 1, Suppl. Fig 1).

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The stele of the root axes (tap-, basal-, and shoot born-root) narrows close to the tip. As the stele area shrinks, the number of xylem vessels are also reduced. The correlation 204 between the stele and xylem areas is strong (0.899) but it is not suitable to do a linear regression. However when we look at the Napierian logarithm of those areas (Yang et al.,206 2019) , the linearity of this relationship is strong (R²: 0.9913, fig. 2). Thanks to the strong relationship between those anatomical features, we used it into the model parametrization 208 procedure instead of using directly the xylem size data of the anatomical features previously measured. For each of the GRANAR model parameters we have a simple function that depends on 216 the root type and the distance from its apex (Supplemental Table 1). With that information, we were able to build average root cross sections along each root type, at any longitudinal 218 position ( fig. 3).
In addition to the overview of the root cross section of the root system, we added the  (1998), and in a slightly higher range relative than the estimations by 280 Zarebanadkouki et al. (2016) and Meunier et al. (2018).
The use of the Hagen-Poiseuille equations to estimate the k x is straightforward when the 282 area of each xylem element is known. Our predicted range and trends both match direct measurements by Meunier et al. (2018) and estimations from Doussan et al. (1998).
284 Uncertainties related to the application of the Hagen-Poiseuille law have been discussed in the literature. Frensch and Steudle (1989) have shown that it may overestimate experimental 286 k x values by a factor of two to five. This could be due to the presence of perforation plates The uncertainty of identification of mature xylem vessels by the used staining procedure 290 could shift the transition zone shootward. We also assume that xylem sap has the same viscosity as water. This hypothesis could be discussed in relation to xylem sap temperature 292 or solute concentration (Bruno and Sparapano, 2007) .
The hydraulic conductivity map that we computed for this genotype in this precise 294 environmental condition ( Zea mays var. B73 in pots) is an example case. Our methodology allows the inclusion of the effect of root anatomical changes and takes into account the 296 selected cell hydraulic properties summarised in the material and methods section. The hydraulic conductivity map with five root types allows a better tuning for root water uptake 298 models. This root hydraulic conductivity map can be used with other modelling tools to estimate other variables such as the root system conductance, or the standard sink fraction, 300 as envisioned by Passot et al. (2019) . Future inverse modelling studies could reuse the anatomical networks that we build on their root system architecture. Then, change in the 302 modelling framework the cell hydraulic properties to match the macro hydraulic that would have been measured. 304 We developed a protocol that could be repeated in further studies (e.g. with different species, genotypes or environment). It is quicker than root pressure probing to estimate 306 radial water flow. GRANAR takes around one to twenty seconds to generate root cross sections that are presented in this study. MECHA takes around one to five min per root cross 308 sections to estimate the k r . On the opposite, one estimation for the k r from the root pressure probe takes at least three to five hours as steady root pressure has to be established after / Heymans et al. 2020 -Root hydraulic map -PREPRINT 310 the connection between the root and the device (Liu et al., 2009) . In both cases, making free-hand root cross-section takes around 10 to 20 minutes. 312 Meunier et al. (2020) showed that modifying hydraulic properties changes the root system hydraulic architecture and thus affects the whole root system conductance ( K rs ). Tuning root 314 hydraulic conductivity functions to match experimental data or test new hypotheses through simulation studies could therefore show the local impact of root anatomy or cell hydraulic 316 properties on the whole root conductance. A better understanding of the effect of local root traits on the global hydraulic behaviour of the root system could enhance the breeding efforts 318 towards more drought tolerant cultivars.

Conclusion
320 In this study, we showed how to use stained root cross section images and computational tools (organ scale models: GRANAR and MECHA) to create high resolution hydraulic maps 322 of a maize root system (var. B73 in our example). Our hydraulic map includes hydraulic information (radial and axial properties) and anatomical data along 5 root types (tap, basal, 324 shoot born, long laterals and short laterals).
Anatomical differences along the root axes and between root types seems to have an impact 326 on the radial and axial water flow through the roots. The values and trends shown in this study are in the same range as the estimations that can be found in the literature.
328 Side by side with measures from root pressure probing, our method has the advantages of being quick and output high resolution results. We expect our methodology to be of great 330 use for further root hydraulic studies. It will help match the hydraulic conductivities of root systems and experimental data, or test new hypotheses through simulation studies. These