Sébastjen Schoenaers
email: sebastjen.schoenaers@uantwerpen.be

Daria Balcerowicz
email: daria.balcerowicz@uantwerpen.be

Gordon Breen
email: gordonjlbreen@gmail.com

Kristine Hill
email: kristine.hill@uni-tuebingen.de

Malgorzata Zdanio
email: malgorzata.zdanio@uantwerpen.be

Grégory Mouille
email: gregory.mouille@versailles.inra.fr

Tara J Holman

Jaesung Oh

Michael H Wilson
email: m.h.wilson@leeds.ac.uk

Natalia Nikonorova
email: natalia.nikonorova@ugent.be

Lam Dai Vu

Ive De Smet

Ranjan Swarup
email: ranjan.swarup@nottingham.ac.uk

Winnok H De Vos
email: winnok.devos@uantwerpen.be

Isabel Pintelon
email: isabel.pintelon@uantwerpen.be

Dirk Adriaensen
email: dirk.adriaensen@uantwerpen.be

Claire Grierson
email: claire.grierson@bristol.ac.uk

Malcolm J Bennett
email: malcolm.bennett@nottingham.ac.uk

Kris Vissenberg
email: kris.vissenberg@uantwerpen.be

The auxin-regulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth

Keywords: auxin, kinase, root hair, cell wall, pectin, tip growth, Arabidopsis, CrRLK1L, AUXIN RESPONSE FACTOR, FERONIA, AHA2

Root hairs facilitate a plant's ability to acquire soil anchorage and nutrients. Root hair growth is regulated by the plant hormone auxin and dependent on localized synthesis, secretion and modification of the root hair tip cell wall. However, the exact well wall regulators in root hairs controlled by auxin have yet to be determined. In this study, we describe the characterization of ERULUS (ERU), an auxin-induced Arabidopsis receptor-like kinase whose expression is directly regulated by ARF7 and ARF19 transcription factors. ERU belongs to the Catharanthus roseus RECEPTOR-LIKE KINASE 1-LIKE (CrRLK1L) subfamily of putative cell wall sensor proteins. Imaging of a fluorescent fusion protein revealed that ERU is localized to the apical root hair plasma membrane. ERU regulates cell wall composition in root hairs and modulates pectin dynamics through negative control of pectin methylesterase (PME) activity. Mutant eru (-/-) root hairs accumulate de-esterified homogalacturonan and exhibit aberrant pectin Ca 2+ binding site oscillations and increased PME activity. Up to 80% of the eru root hair phenotype is rescued by pharmacological supplementation with a PME inhibiting catechin extract. ERU transcription is altered in specific cell wall-related root hair mutants, suggesting it is a target for feedback regulation. Loss of ERU alters the phosphorylation status of FERONIA and H + -ATPases 1/2, regulators of apoplastic pH. Furthermore, H + -ATPases 1/2 and ERU are differentially phosphorylated in response to auxin. We conclude that ERULUS is a key auxincontrolled regulator of cell wall composition and pectin dynamics during root hair tip growth.

Introduction

Root hairs (RH) elongate via a tip-based growth mechanism [START_REF] Schoenaers | Molecular mechanisms regulating root hair tip growth: a comparison with pollen tubes[END_REF]. Several studies have shown that tip growth occurs in an oscillatory manner and is accompanied by oscillations of cytoplasmic Ca 2+ levels [START_REF] Monshausen | Imaging of the Yellow Cameleon 3.6 indicator reveals that elevations in cytosolic Ca 2+ follow oscillating increases in growth in root hairs of Arabidopsis[END_REF], extracellular reactive oxygen species (ROS) and pH [START_REF] Monshausen | Oscillations in extracellular pH and reactive oxygen species modulate tip growth of Arabidopsis root hairs[END_REF]. The plant hormone auxin is a key component of RH tip growth since several auxin response mutants exhibit RH phenotypes [START_REF] Balcerowicz | Cell Fate Determination and the Switch from Diffuse Growth to Planar Polarity in Arabidopsis Root Epidermal Cells[END_REF], whilst auxin supplementation promotes RH elongation [START_REF] Lee | Auxin, the organizer of the hormonal/environmental signals for root hair growth[END_REF] and the expression of the core RH transcription factor RSL4 changes in response to exogenous IAA application [START_REF] Yi | A basic helix-loop-helix transcription factor controls cell growth and size in root hairs[END_REF]. Auxin Response Factors (ARFs) control transcription of auxin-responsive genes [START_REF] Tiwari | The Roles of Auxin Response Factor Domains in Auxin-Responsive Transcription[END_REF]. However, despite the reported role of auxin in controlling RH elongation, besides RSL4 none of the tip growth related genes have been identified as direct targets of ARFs [START_REF] Mangano | Molecular link between auxin and ROS-mediated polar growth[END_REF]. Factors that control RH tip growth ultimately direct the delivery of CW and plasma membrane material to the expanding tip and control the modification (loosening/tightening) of the CW at the tip apex [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF]. Interestingly, the transcription of a number of CW related genes was altered in loss-of-function and overexpression lines of the auxin-regulated RH TF RSL4 [START_REF] Yi | A basic helix-loop-helix transcription factor controls cell growth and size in root hairs[END_REF]. However, no direct link between auxin signaling and RH CW composition or dynamics has been reported to date. RH growth is facilitated by the coordinated synthesis, secretion, recycling and remodelling of CW material. The formation of an organized and dynamic matrix of cellulose, hemicellulose and pectin polymers is required to control plasticity at the tip and provide structural support in the subapical stalk. Failure to do so often results in mutants with aberrant RH morphology [START_REF] Park | A role for CSLD3 during cellwall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF][START_REF] Pena | A Galacturonic Acid-Containing Xyloglucan Is Involved in Arabidopsis Root Hair Tip Growth[END_REF][START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF][START_REF] Diet | The Arabidopsis Root Hair Cell Wall Formation Mutant lrx1 Is Suppressed by Mutations in the RHM1 Gene Encoding a UDP-L -Rhamnose Synthase[END_REF]. Loss of FERONIA, a member of the Catharanthus roseus RLK1-like (CrRLK1L) subfamily of putative CW sensing proteins, was also shown to drastically impair RH morphogenesis [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF], whilst the RLK-VII member called MARIS regulates RH growth downstream of the CrRLK1L signaling pathway [START_REF] Boisson-Dernier | Receptor-like cytoplasmic kinase MARIS functions downstream of CrRLK1L-dependent signaling during tip growth[END_REF]. Despite these advances, the structural and regulatory complexity of the RH CW have proven difficult to dissect.

Here, we report on the characterization of ERULUS, a RH-specific member of the CrRLK1L subfamily. We show that ERU transcription is regulated by auxin, with its promoter being a direct target for ARF7 and ARF19 TFs. In addition, auxin treatment alters ERU phosphorylation status. We demonstrate that ERU localizes to the Arabidopsis apical RH plasma membrane and regulates RH growth through modulation of pectin methylation dynamics. Mutant plants lacking ERU exhibit short, bulged RHs, a higher pectin methylesterase (PME) activity and drastically altered pectin Ca 2+ binding site oscillations. Pharmacological inhibition of PME activity rescued up to 80% of the eru RH phenotype. Furthermore, loss of ERU function results in differential phosphorylation of FERONIA (FER) and H + -ATPases 1/2 (AHA1/2), regulators of apoplastic pH. In addition, AHA1/2 is differentially phosphorylated on auxin treatment. We conclude that auxin controls pectin related CW composition in growing RHs via the CrRLK1L family protein ERULUS, through a pathway that likely involves FER and AHA1/2 action.

Results

The receptor-like kinase ERU regulates tip growth in root hairs

To identify new root hair (RH) tip growth related genes, two Affymetrix ATH1 array datasets were cross-correlated. The first dataset was prepared using RNA from the root differentiation zones of wild type (WT; Col-0) plants and the rhd2 loss-of-function mutant that fails to extend RH bulges due to the absence of a functional ROS gradient [START_REF] Jones | Analysis of the root-hair morphogenesis transcriptome reveals the molecular identity of six genes with roles in root-hair development in Arabidopsis[END_REF]. The second dataset was prepared using FACS-sorted root epidermal cells from protoplasted lines in which either every epidermal cell was a RH (wer myb double mutant) or a non-hair cell (cpc try double mutant) [START_REF] Dinneny | Cell identity mediates the response of Arabidopsis roots to abiotic stress[END_REF]. Data integration led to the selection of 150 genes whose expression was positively correlated with RH tip growth.

Reverse genetic screens of the candidate genes identified a T-DNA insertion in a Catharanthus roseus receptor-like kinase 1-like (CrRLK1L) kinase named ERULUS (ERU), which, as previously reported, resulted in severely aberrant RH morphology (Figure 1A) [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF][START_REF] Bai | A Receptor-Like Kinase Mediates Ammonium Homeostasis and Is Important for the Polar Growth of Root Hairs in Arabidopsis[END_REF]. Genotypic analysis revealed that the T-DNA was inserted 1047 bp downstream of the start codon (Figure S1A) and resulted in a complete loss of ERU transcript (Figure S1B). The erulus (-/-) plants developed very short RHs (22.4% of the WT length, Figure 1A,B) that often bulged at the tip. RH positioning at the basal end of root epidermal cells was unaffected, and distinct trichoblast cell files were present in eru plants (Figure S1C). Contrary to previous findings, the short/bulged eru RH phenotype persisted when grown on minimal growth medium (Figure S1D,E) [START_REF] Bai | A Receptor-Like Kinase Mediates Ammonium Homeostasis and Is Important for the Polar Growth of Root Hairs in Arabidopsis[END_REF]. By insertion of the 2529 bp native promoter coupled to its coding sequence and GFP (ERUp::ERU-GFP) into the eru (-/-) mutant Arabidopsis background, we were able to fully complement the eru short RH phenotype (Figure 1A,B), demonstrating protein functionality. In addition, we no longer observed RH bulging in the complemented lines. 35S driven ERU overexpression (35S::ERU) in the eru or Col-0 background did not alter the final WT RH length or the RH profile (Figure 1B, Figure S1F-H).

To investigate at which stage of RH development ERU is involved, we constructed RH profiles and monitored single RH growth of 7-day-old WT and eru roots (Figure 1C,D). In WT roots, RHs elongated through tip growth at a constant growth rate until they reached maturity (600-700 µm) at a distance of ±3 mm from the root tip (Figure 1C). eru RHs grew much slower, but kept doing so for the same extent of time as WT RHs. Bulge formation occurred normally in eru plants, but mutant RHs were unable to make the subsequent switch to fast tip growth (Figure 1D). After bulge formation, WT RHs switched to tip growth with a constant growth rate of 0.93 ± 0.05 µm min -1 , whereas eru RHs grew at 0.30 ± 0.03 µm min -1 . Moreover, during the expected period of fast tip growth, eru RHs experienced occasional growth interruption after which slower than normal growth was regained. Based on our findings, we concluded that ERU is essential to controlling tip growth in RHs.

ERU encodes a trichoblast plasma membrane localized receptor-like kinase enriched at the root hair tip

To determine the tissue-specific expression of ERU we constructed a transcriptional fusion of its promoter with the GFP reporter (ERUp::GFP). A public transcriptomics dataset indicated trichoblast specific expression [START_REF] Brady | A High-Resolution Root Spatiotemporal Map Reveals Dominant Expression Patterns[END_REF]. Visualization of >4 independent stably transformed T 3 WT plants carrying the ERUp::GFP transgene revealed that ERU transcription is restricted to trichoblast cell files (Figure 2A), confirming the public transcriptomics data [START_REF] Brady | A High-Resolution Root Spatiotemporal Map Reveals Dominant Expression Patterns[END_REF]. GFP was first detected in elongating epidermal cells, even before RH bulge formation. The ERU promoter was active throughout RH morphogenesis, then GFP signal intensity decreased gradually after RH maturation (Figure S2A). These findings were independently confirmed using GUS as an alternative reporter (Figure S2B-D).

Next, we investigated ERU subcellular localization. ERU contains a N-terminal signal peptide (M1-S27), a Malectin receptor-like domain (F28-A425) with 6 putative N-linked glycosylation sites (N81, N125, N252, N294, N359, N365), a hydrophobic transmembrane domain (I426-V446) and a C-terminal cytoplasmic domain (R447-P842) coding for a protein kinase. As such, ERU was likely to be trafficked via the secretory pathway to the plasma membrane. Bioinformatic analysis for non-redundant A. thaliana protein sequences with similarity to the ERU signal peptide combined with GO enrichment analysis revealed a strong overrepresentation of 'extracellular region' associated proteins (Figure S3A), amongst which included FERONIA, pectin lyase-like, pectin methylesterase inhibitor and proline rich extensin-like proteins. We identified a highly conserved hydrophobic motif (Figure S3B,C) with a presumable targeting function (N-terminal in 71 % of all cases) which was present in all identified proteins. In parallel, we transformed WT and eru Arabidopsis plants with a transgene containing the ERU coding sequence coupled to a C-terminal GFP reporter and driven by its native promoter (ERUp::ERU-GFP). In all independent lines, we observed that ERU-GFP specifically localized to the future site of RH formation, the RH bulge and the very tip of tip-growing RHs (Figure 2B). High resolution spinning disk confocal microscopy revealed that ERU-GFP localized to an endomembrane compartment which accumulated at the surface of the RH bulge (Figure 2C; movie S1) or the growing RH tip (Figure 2D-F; movie S2) and to the apical plasma membrane in RH bulges (Figure 2C; movie S1) and tip-growing RHs (Figure 2D-F; movie S2). ERU protein localization at the tip seemed highly dynamic yet displayed no oscillatory behaviour (movie S3; Figure S4). Hence, ERU represents a trichoblastspecific RLK that localizes to the apical plasma membrane of RHs.

ERU is regulated by auxin via ARF7 and ARF19 transcription factors which directly bind to its promoter

The plant hormone auxin is known to positively regulate root hair growth [START_REF] Lee | Auxin, the organizer of the hormonal/environmental signals for root hair growth[END_REF]. To assess the role of ERU in auxin-mediated RH development, we transferred 5-day-old WT and eru seedlings to medium containing different concentrations of IAA, NAA and 2,4D. Although auxin treated eru (-/-) RHs were markedly longer than untreated controls (up to 63% of the WT RH length) and no longer bulged, we were unable to fully complement their RH length defect (Figure S5A-D). Importantly, eru RH growth velocity remained 51% lower compared to WT RHs upon 20 nM IAA supplementation (Figure S5D). Hence, ERU represents an important component of the auxin signaling pathway required to promote RH growth.

In silico analysis of the ERU promoter sequence identified four canonical auxin response elements (AuxREs), positioned at 462, 1454, 1999 and 2596 bp upstream of the ATG start codon, and encoded by the TGTCTC/GAGACA conserved ARFAT sequence, or single nucleotide variants thereof (e.g. TGTCAC at -462, Figure 3A). In addition, multiple core TGTC/GACA auxin response elements were also present (Figure 3A). Auxin response factors (ARFs) bind to AuxREs to regulate auxin-mediated transcription [START_REF] Tiwari | The Roles of Auxin Response Factor Domains in Auxin-Responsive Transcription[END_REF]. Besides others, ARF7 and ARF19 are both actively transcribed in growing RHs [START_REF] Brady | A High-Resolution Root Spatiotemporal Map Reveals Dominant Expression Patterns[END_REF](Figure S5E). We quantified ERU transcription in response to auxin application in WT and arf7arf19 double mutant roots. In Col-0, ERU mRNA abundance peaked 30 min after auxin application after which it rapidly decreased to reach baseline levels after 120 min (Figure 3B). In contrast, in arf7arf19 roots ERU mRNA level remained very low. Hence, ERU transcript abundance is regulated in an ARF7/ARF19 dependent manner with expression dynamics consistent with being a primary auxin response gene.

To directly test whether ARF7 and/or ARF19 bind to the ERU promoter, we performed chromatin immuno-precipitation PCR (ChIP-PCR) studies. Chromatin was extracted from WT, arf7 (-/-) and arf19 (-/-) root cultures, after which ChIP-PCR studies were performed using ARF7 and ARF19 specific antibodies (Figure S5F). Real time PCR using primers specifically designed to amplify the regions associated with the -462 and -1454 localized ARFAT sites revealed that ARF7 (both AuxREs) and ARF19 (-462 AuxRE) directly bind to the ERU promoter (Figure 3C,D). Relative to arf7 and arf19 null mutants, ERU associated promoter DNA was significantly enriched in anti-ARF7 (Figure 3C) and anti-ARF19 (Figure 3D) immuno-precipitated fractions compared to the input DNA fractions (non-immunoprecipitated controls). Taken together, our results reveal ERU transcription is controlled by auxin and represents a direct target for at least ARF7 and ARF19 transcription factors.

ERU is phosphorylated at serine 497 in response to auxin Protein phosphorylation is an important post-translational modification controlling protein function. Auxin is known to induce proteome-wide phosphorylation changes [START_REF] Zhang | Quantitative Phosphoproteomics after Auxin-stimulated Lateral Root Induction Identifies an SNX1 Protein Phosphorylation Site Required for Growth[END_REF] and e.g. controls the phosphorylation status/activity of H + -ATPase during acid-growth directed hypocotyl elongation [START_REF] Takahashi | Auxin activates the plasma membrane H + -ATPase by phosphorylation during hypocotyl elongation in Arabidopsis[END_REF]. It was previously shown that ERU function depends on its phosphorylation status [START_REF] Zhou | Biological function analysis of the phosphorylation sites for Arabidopsis CAP1[END_REF]. To study the effect of auxin treatment on ERU phosphorylation, we checked ERU protein phosphorylation in a data set generated from Arabidopsis root tips in response to NAA (100 nM) treatment (unpublished results). We found that the abundance of the ERU peptide SNGFSSFFSNQGLGR, which corresponds to the serine 497 phosphosite (pS497), increased by a factor of 6.94 ± 2.87 (n=5) upon auxin treatment (Figure 4, Figure S6A). Since serine 497 lies within the cytoplasmic protein domain and has not been functionally annotated, it is unclear how its phosphorylation affects ERU action. Importantly however, our data illustrates a second (post-translational) means through which auxin may regulate ERU function.

ERU transcription is altered in pectin cell wall mutants ERU belongs to the CrRLK1L family of putative CW sensing proteins. To investigate whether ERU transcription is altered in response to changes in RH CW composition, we quantified ERU transcript in 7-day-old roots of several RH CW mutants (repressor of lrx1 1, rol1; leucine-rich repeat/extensin1, lrx1; leucine-rich repeat/extensin2, lrx2; enhancer of lrx1 7, enl7; procuste1, prc1; cellulose synthase-like d3, csld3; theseus1, the1). ROL1, or repressor of LRX1 1, encodes a UDP-L-Rhamnose synthase that is responsible for modification of the pectic polysaccharides rhamnogalacturonan I and II [START_REF] Diet | The Arabidopsis Root Hair Cell Wall Formation Mutant lrx1 Is Suppressed by Mutations in the RHM1 Gene Encoding a UDP-L -Rhamnose Synthase[END_REF]. The lrx1-1 mutant phenotype, which is the result of aberrant CW architecture, is suppressed by both allelic rol1 mutations [START_REF] Diet | The Arabidopsis Root Hair Cell Wall Formation Mutant lrx1 Is Suppressed by Mutations in the RHM1 Gene Encoding a UDP-L -Rhamnose Synthase[END_REF]. As such, it has been suggested that LRX1 could be involved in the establishment of a functional pectin matrix [START_REF] Diet | The Arabidopsis Root Hair Cell Wall Formation Mutant lrx1 Is Suppressed by Mutations in the RHM1 Gene Encoding a UDP-L -Rhamnose Synthase[END_REF]. LRX2 functions redundantly with LRX1, and Enhancer Of Lrx1 (ENL7) worsens the lrx1-1 phenotype, suggesting they are functionally related [START_REF] Diet | The enl mutants enhance the lrx1 root hair mutant phenotype of Arabidopsis thaliana[END_REF]. PROCUSTE1 (PRC1), CELLULOSE SYNTHASE-LIKE D3 (CSLD3) and THESEUS1 (THE1) encode a cellulose synthase (CESA6), a protein required for the synthesis of a non-cellulosic wall polysaccharide and normal cellulose and xyloglucan organization in RH CWs, and a CW/cellulose deficiency sensor protein of the CrRLK1L family, respectively [START_REF] Singh | Insight into the early steps of root hair formation revealed by the procusteI cellulose synthase mutant of Arabidopsis thaliana[END_REF][START_REF] Wang | AtCSLD3, a cellulose synthase-like gene important for root hair growth in Arabidopsis[END_REF][START_REF] Hématy | A receptor-like kinase mediates the response of Arabidopsis cells to the inhibition of cellulose synthesis[END_REF]. ERU transcription was 1.6-fold upregulated in the rol1-2 null mutant, and ̴ 2-fold downregulated in the lrx1-1, enl7 and lrx2-1 mutants, but remained unaffected in prc1-1, csld3 and the roots (Figure S7A). These findings suggest that some, but not all, CW perturbations alter ERU gene expression, indicative of feedback regulation from the CW. Notably, ERU transcript abundance was altered in the rol1 and lrx1-1 RH mutants which, in literature, have been related to pectin [START_REF] Diet | The Arabidopsis Root Hair Cell Wall Formation Mutant lrx1 Is Suppressed by Mutations in the RHM1 Gene Encoding a UDP-L -Rhamnose Synthase[END_REF].

ERU is a regulator of cell wall metabolism in root hairs Next, we investigated whether differences existed in the CW composition of eru and WT RHs using micro Fourier Transform Infrared Spectroscopy (microFT-IR). We observed significant differences in IR absorbance at several distinct wavenumbers (Figure 5A), some of which had been annotated to specific CW components [START_REF] Kacuráková | FT-IR study of plant cell wall model compounds: Pectic polysaccharides and hemicelluloses[END_REF][START_REF] Séné | Fourier-Transform Raman and Fourier-Transform lnfrared Spectroscopy; An investigation of five higher plant cell walls and their components[END_REF][START_REF] Yang | Early salt stress effects on the changes in chemical composition in leaves of ice plant and Arabidopsis. A Fourier transform infrared spectroscopy study[END_REF]. These likely corresponded to the underrepresentation of the pectin (845-864) and xyloglucan (XYG) ring structures (922-949), and over representation of the glycosydic C-O-C linkage vibration of cellulose (1150 and 1161 doublet) in eru RHs (Figure 5B) [START_REF] Kacuráková | FT-IR study of plant cell wall model compounds: Pectic polysaccharides and hemicelluloses[END_REF][START_REF] Séné | Fourier-Transform Raman and Fourier-Transform lnfrared Spectroscopy; An investigation of five higher plant cell walls and their components[END_REF][START_REF] Yang | Early salt stress effects on the changes in chemical composition in leaves of ice plant and Arabidopsis. A Fourier transform infrared spectroscopy study[END_REF].

To probe the observed changes in CW composition, we analysed cellulose, xyloglucan and pectin distribution in the CW of WT and eru RHs using dyes, antibodies and confocal microscopy. Direct red 23 (also known as pontamine fast scarlett) was used to visualize cellulose [START_REF] Anderson | Real-time imaging of cellulose reorientation during cell wall expansion in Arabidopsis roots[END_REF]. In WT RHs, we detected high fluorescence intensity at the tip (consistent with the site of cellulose synthesis), and lower intensity in the RH stalk (Figure S7B). In agreement with our microFT-IR data, the fluorescence intensity in the stalk of eru RHs was much higher compared to WT RHs (Figure S7B). Cellulose overaccumulation could be due to a higher cellulose synthase (CesA) activity or normal CesA activity in combination with slower RH growth. To discriminate between both, we deduced the CW thickness from the acquired confocal images (Figure S7C) and cross-correlated it with the observed cellulose content (Figure S7D). The width of the CW correlated significantly with the cellulose content (Rho = 0.80). The CW of eru RHs was twice as thick as WT RHs. We calculated the CW volume for a hypothetical 200 µm RHs cylinder (Figure S7E,F) and found that it inversely related to RH growth speed (Figure S7G). The volume of the cytosol remained unaffected (Figure S7H). Hence, overaccumulation of cellulose in eru is likely a secondary effect of slow RH growth.

Next, we directly determined the overall XYG content in the RH primary CW using a monoclonal antibody with specificity towards several XYG oligosaccharides. In agreement with our microFT-IR spectra, we observed that eru RHs accumulate 1.7-fold less XYG compared to WT RHs (Figure S7I). We also investigated pectin composition using monoclonal antibodies towards methylesterified and deesterified HG epitopes (Figure 5). Interestingly, eru RHs had much lower methyl-esterified and far higher de-esterified HG levels in the RH stalk compared to WT, suggesting a higher degree of deesterification by pectin methylesterases (PMEs). The total HG content (the sum of methyl-esterified and de-esterified HG) remained unaffected (Figure 5C). Using a coupled enzymatic approach, we quantified PME activity in root tips (containing growing RHs) of WT and eru roots. Consistent with our previous observations, we detected a 1.6-fold increase in PME activity in the eru mutant. To verify that the observed RH growth effect was related to increased PME activity we supplemented WT and eru plants with different concentrations of Polyphenon 60 (PP60), a catechin extract shown to inhibit PMEactivity in a concentration-dependent manner by direct binding to PME or to its substrate pectin, thereby blocking PME access [START_REF] Lewis | Inhibition of pectin methyl esterase activity by green tea catechins[END_REF]. PP60 supplementation rescued eru RH length up to 80% that of WT RHs, showing that increased PME activity is a major factor contributing to the eru phenotype (Figure 6). Given the apparent role of ERU in regulating pectin dynamics and the low XYG content in the eru RH CW, we were interested to see if a XYG/pectin compensation mechanism could exist in RHs. The existence of such a mechanism in controlling CW biomechanics has been suggested before, but has never been illustrated in RHs [START_REF] Park | Changes in Cell Wall Biomechanical Properties in the Xyloglucan-Deficient xxt1/xxt2 Mutant of Arabidopsis[END_REF]. Unfortunately, pectin-deficient RH mutants have not been identified to date, making it impossible to test XYG accumulation therein. However, we found that XYG deficient xxt1/2/5 RHs contain 1.9-fold more pectin Ca 2+ binding sites and have a thicker CW (Figure S7L-N). The latter finding suggests that XYG and pectin can assume a compensatory role to maintain CW rigidity, which could explain the CW composition observed in eru RHs.

To further understand how pectin dynamics were affected in eru RHs, we visualized the availability of pectin Ca 2+ -binding sites (a direct consequence of de-esterification by PME-activity) via in vivo propidium iodide (PI) staining of growing RHs [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF]. Time lapse imaging revealed a higher PI intensity (consistent with higher PME activity), but much slower oscillations in eru RHs (Figure 5E,F; movie S4). In WT RHs pectin Ca 2+ binding sites oscillated at 0.018 ± 0.0009 Hz, and in 14 out of 20 RHs a secondary component at a frequency of 0.007 ± 0.002 Hz was present (Figure 5G,H), whereas in eru RHs, the main frequency of oscillation was drastically slower at 0.003 ± 0.0003 Hz and was characterized by an amplitude ̴ 13-fold greater than WT RHs (Figure 5G,H). Each eru oscillation was marked by a sudden and steep increase in PI fluorescence, followed by a gradual decrease to original levels, whereas in WT RHs, each oscillation was characterized by a discrete rise and equal decrease in PI signal intensity (movie S4). The average apical PI signal intensity in eru RHs remained 3-fold higher compared to WT RHs throughout acquisition (Figure S7J) and never reached WT levels, even after maturation (Figure S7K). Taken together, our data show that ERU plays a crucial role in CW composition and pectin metabolism through regulation of PME activity.

FERONIA and H + -ATPase 2 are differentially phosphorylated in ERU loss-off-function root tips

To identify downstream targets of the ERU kinase and gain insight in how ERU could regulate cell wall dynamics, we compared the phosphoproteome of WT and eru root tips (containing the root differentiation zone). We found that FERONIA (FER) and a peptide corresponding to H + -ATPase 1 and/or 2 (AHA1/2), all of which are involved in regulating apoplastic pH [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF][START_REF] Barbez | Auxin steers root cell expansion via apoplastic pH regulation in Arabidopsis thaliana[END_REF], were significantly differentially phosphorylated at serine 701 (pS701; SFGYLDPEYFR) and serine 904 (pS904; ELSEIAEQAKR), respectively (Figure 7, Figure S6B,C). FER pS701 phosphopeptide abundance had decreased 3.4-fold (Figure 7A) and AHA1/2 pS904 phosphopeptide abundance had increased by a factor of 2.9 (Figure 7C) in the eru mutant background, whereas overall peptide abundance remained unaffected (Figure 7B,D). FER pS701 is located in the cytoplasmic kinase domain and has not yet been functionally annotated. When expressed in yeast, phosphorylation of AHA1/2 S904, a cytoplasmic phosphosite located in the C-terminal autoinhibitory regulatory domain, leads to protein activation [START_REF] Fuglsang | Receptor kinasemediated control of primary active proton pumping at the plasma membrane[END_REF]. This domain also contains the presumable FER-targeted phosphosite AHA2 S899, which has been shown to regulate AHA2 proton pumping activity [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF]. As such, our data reveal that ERU might function through regulation of FER and AHA1/2 phosphorylation, which controls apoplastic pH and potentially indirectly also cell wall enzyme activity during cell elongation.

Interestingly, we found that auxin supplementation (100 nM NAA) caused a 1.6-and a 1.3-fold decrease in the abundance of the AHA1/2 GSYRELSEIAEQAK and AHA2 GLDIETPSHYTV phosphopeptides, corresponding to previously characterized AHA2 S899 and T947 phosphosites, known to activate AHA's pumping activity (Figure S6D-I). Importantly, these NAA-addition data should be interpreted with care as this data set does not reveal cell type-specific changes in the root so that the general changes could mask potential other effects present specifically in root hairs. Nevertheless, our results demonstrate an in planta regulation of AHA1/2 by both auxin and ERU, further supporting that both players are embedded in the same signalling network.

Discussion

RH tip growth represents one of nature's most rapid forms of cell elongation. A hormone-driven pathway controls CW rheology at the RH tip to withstand turgor pressure, yet to provide sufficient flexibility for growth. The hormone auxin controls RH expansion [START_REF] Lee | Auxin, the organizer of the hormonal/environmental signals for root hair growth[END_REF], yet knowledge about its direct targets for regulation of cell wall dynamics have been lacking, to date. We describe the characterisation of the cell wall receptor-like kinase ERULUS, a key regulator of RH expansion. Eru (-/-) plants exhibit a RH growth defect (Figure 1). We report that (1) ERU is specifically expressed in trichoblasts, (2) ERU is a key component of auxin-driven RH growth, (3) ERU is a direct target of at least ARF7 and ARF19, (4) ERU phosphorylation is altered in response to auxin, (5) ERU localizes to the apical RH plasma membrane (PM) and ( 6) ERU regulates CW composition/dynamics during RH elongation, possibly through affecting FER and AHA1/2 phosphostatus and subsequently their activity. Whilst our ERU subcellular localisation results contrast with the findings of [START_REF] Bai | A Receptor-Like Kinase Mediates Ammonium Homeostasis and Is Important for the Polar Growth of Root Hairs in Arabidopsis[END_REF], which can have various reasons, we demonstrate that our ERUp::ERU-GFP reporter rescued the eru (-/-) RH defect in Arabidopsis t., providing confidence that our ERU PM localisation results are valid [START_REF] Bai | A Receptor-Like Kinase Mediates Ammonium Homeostasis and Is Important for the Polar Growth of Root Hairs in Arabidopsis[END_REF].

ERU is a member of the CrRLK1L family of putative CW sensing kinases and contains a malectin-like domain, which has been hypothesized to bind specific CW polysaccharides or glycoproteins [START_REF] Nissen | Understanding CrRLK1L Function: Cell Walls and Growth Control[END_REF]. Several CrRLK1L proteins associate with CW modification or sensing during expansion [START_REF] Nissen | Understanding CrRLK1L Function: Cell Walls and Growth Control[END_REF]. We illustrate that ERU has a role in controlling the CW machinery in RHs. CW turnover and modification is concentrated at the tip. We found that ERU localizes to the tip PM in growing RHs, throughout all RH developmental stages (Figure 2B-F, movie S1-3). The ERU signal peptide is likely to encode an extracellular localization signal (Figure S3), targeting the malectin-like domain to the CW where it could potentially interact with carbohydrate-containing ligands or small signaling peptides (such as RALFs interacting with FER [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF][START_REF] Stegmann | The receptor kinase FER is a RALF-regulated scaffold controlling plant immune signaling[END_REF]).

At the growing RH apex, the load bearing capacity of the CW is thought to be determined by the interconnectivity of the cellulose/XYG "grid" and the fluidity of the pectin matrix, yet empirical data to support this theory is scarce. In pollen tubes, highly methyl-esterified HG (major pectin component) is exocytotically secreted at the RH tip [START_REF] Bosch | Pectin Methylesterases and Pectin Dynamics in Pollen Tubes[END_REF]. Subsequent de-esterification by PMEs would then generate de-esterified HG that can be degraded by pectin lyases (resulting in higher CW flexibility) or interact through egg-boxes with Ca 2+ ions to generate a stiff crosslinked matrix [START_REF] Cabrera | Egg box conformation of oligogalacturonides: The time-dependent stabilization of the elicitor-active conformation increases its biological activity[END_REF]. The availability of pectin Ca 2+ -binding sites was shown to oscillate at the same frequency as the RH growth velocity, implicating that PME activity may oscillate too [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF]. eru RHs exhibit aberrant CW composition. The mutant has a thicker, cellulose-enriched CW (Figure S7B-D), and much lower amounts of XYG (Figure S7I). In addition, ERU functions as a negative regulator of PME activity (Figure 5C,D) since eru RHs were devoid of methyl-esterified and enriched in de-esterified HG, whilst PME-activity was higher in mutant root extracts. This finding is supported by the fact that pharmacological treatment with a PME-inhibiting catechin extract resulted in a highly substantial rescue of the eru phenotype (Figure 6). Moreover, HG Ca 2+ -binding site oscillations were drastically altered in mutant RHs (Figure 5E-H, Figure S7J,K, movie S4), illustrating a continuously higher potential of the CW to bind Ca 2+ and thus provide a highly crosslinked HG matrix. In line with previous findings, we found that a pectin/XYG compensation mechanism to control CW biomechanics might also exist in RHs, thereby explaining lower XYG abundance in the highly rigid pectin-altered eru CW (Figure S7L-N) [START_REF] Park | Changes in Cell Wall Biomechanical Properties in the Xyloglucan-Deficient xxt1/xxt2 Mutant of Arabidopsis[END_REF]. Further characterization of XYG/pectin functional dependency would increase our understanding of how CW plasticity is regulated. Consistent with its role as a putative CW sensor, ERU transcription was altered in specific RH CW mutants, suggesting ERU/CW feedback regulation (Figure S7A).

The mechanism linking ERU-mediated regulation of cell wall composition and PME activity is currently unknown. In primary root cell expansion, RAPID ALKALINIZATION FACTOR (RALF)-induced apoplastic alkalinisation is mediated by the physical interaction between RALF and the CrRLK1L FER, and subsequent FER kinase-controlled phosphorylation of AHA2, regulating AHA2 pumping activity [START_REF] Haruta | A peptide hormone and its receptor protein kinase regulate plant cell expansion[END_REF]. In addition, the constitutively expressed AHA1 was also found to regulate root apoplastic pH. The FER/AHA2 mechanism has been illustrated in primary root cell elongation, but not shown to regulate RH development. Importantly, we now found that the eru mutation results in differential phosphorylation of FER and AHA1/2, suggesting that a similar mechanism might operate in RH tips (Figure 7). PME-activity, which is strongly affected in eru RHs, is highly pH-dependent, and likely contributes to apical pH oscillations during RH growth since PME-mediated HG demethylesterification releases protons as a byproduct [START_REF] Sénéchal | Homogalacturonan-modifying enzymes: Structure, expression, and roles in plants[END_REF]. In addition, RALF4 was found to be highly co-regulated with pectin modifying enzymes [START_REF] Wolf | Growth Control: A Saga of Cell Walls, ROS, and Peptide Receptors[END_REF]. Moreover, the enzymes that regulate CW XYG remodelling function at a specific pH-optimum [START_REF] Maris | Differences in enzymic properties of five recombinant xyloglucan endotransglucosylase/hydrolase (XTH) proteins of Arabidopsis thaliana[END_REF]. Hence, altered extracellular pH dynamics, both by altered PME activity and AHA1/2 pumping activity could explain the diverse defects observed in the eru CW. It is tempting to hypothesize that ERU is part of a FER-ERU-AHA1/2 apoplastic pH-regulating mechanism that alters CW metabolism in the RH tip and that, in turn, is sensitive for CW changes (by both FER and ERU). Whether the altered phosphorylation of AHA1/2 is a direct consequence of the activity of ERU or FER or another kinase remains to be shown.

Recently, it was shown that FER-mediated control of CW pH is auxin-dependent [START_REF] Barbez | Auxin steers root cell expansion via apoplastic pH regulation in Arabidopsis thaliana[END_REF]. We report that in roots AHA1/2 is differentially phosphorylated at S899 and T947 in response to auxin treatment (Figure S6F-I). More so, ERU is regulated by auxin at the transcriptional (through direct binding of ARF7 and ARF19 to its promoter) and post-translational level (through auxin-induced phosphorylation). Collectively, these data reveal that auxin is strongly embedded within the pathway(s) controlling CW composition and dynamics in RHs.

Main-text figure legends

STAR Methods

KEY RESOURCES TABLE CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents shoul be directed to and will be fulfilled by the Lead Contact, Kris Vissenberg (kris.vissenberg@uantwerpen.be).

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Growth conditions

Seeds were surface sterilized prior sowing. For phenotyping and microscopy, seeds were plated on RH growth medium (3 mM KNO 3 , 2 mM Ca(NO 3 ) 2 .4H 2 O, 0.5 mM MgSO 4 .7H 2 O, 1mM NH 4 H 2 PO 4 , 1 mg ml -1 thiamine, 0.5 mg ml -1 pyridoxine-HCl, 0.5 mg ml - O and 25 µM Fe-Na EDTA) containing 0.8% phytagel and 1% sucrose at pH 5.7 or minimal medium (0.1 mM KCl, 0.1 mM CaCl 2 , 1 mM NaCl, 1% w/v sucrose, 2% w/v agarose, pH 6). If applicable, the medium was supplemented with the indicated hormone or polyphenon 60 concentrations. For selection of transformants, seeds were sown on 1/2 Murashige and Skoog (MS) medium with vitamins (Duchefa, Netherlands), supplemented with 50 µg l -1 kanamycin, 25 µg l -1 hygromycin, 25 µg l -1 rifampicin and 50 µg l -1 gentamycin. Seeds were stratified for 2-3 days at 4°C in the dark before incubation in a growth chamber with 16 h light/8 h dark conditions, at 22°C. For ChIP-qPCR, plants were grown in 100 ml liquid media (3.2 g l -1 Gamborg's B5 basal salt, 1 g l -1 MES hydrate, 20 g l -1 sucrose, 1 ml l -1 Gamborg's B5 vitamin mix 1000X concentrated, pH 5.8) with gentle shaking in the dark for several weeks. For realtime-PCR analysis of ERU transcription in WT and arf7arf19 roots, seeds were grown for 7 days in continuous light on 1/2 MS medium (1% sucrose) before being transferred to medium containing 1 µM NAA or an equivalent volume of DMSO (control). Roots were harvested 0.5, 1, 2, 4 or 6h after transferring. For phosphoproteome analysis of auxin-treated seedlings, Arabidopsis thaliana (ecotype Col-0) seedlings were grown vertically on ½ MS medium (0.8% agar, 1 % sucrose) containing 100 nM 1-naphthaleneacetic acid (NAA) or DMSO as a control at 22 °C and under continuous light conditions. At 11 days after germination, 1 cm root tips were harvested in 5 biological replicates.

Plant material

Arabidopsis thaliana ecotype Columbia-0 (Col-0; N1092) and mutant eru (SALK_083442C), rol1-2 (CS16373), lrx1-1 (CS16370), lrx2-1 (CS16371), the1-4 (SAIL_683_H03; kindly donated by Prof. Lenhard), prc1-1 (CS297), enl7 (CS25258), arf7 (N24607), arf19 (N24617), arf7arf19 (N24629) and xxt1/2/5 (N67828) seeds were obtained from the Nottingham Arabidopsis Stock Centre (ABRC) or kindly donated. Plants homozygous for the eru T-DNA insert were selected by PCR using T-DNA and gene-specific primers (Table S1).

METHOD DETAILS

Phenotyping

Images were collected using a Nikon AZ100 multizoom macroscope for determination of the RH length, and construction of a RH profile. RH length was measured using FIJI. For constructing a RH profile, the length of individual RHs and their distance to the root tip were measured. RH lengths were classified in 0.25 mm (normal medium) or 0.05 mm (auxin supplementation) intervals depending of their distance to the root tip, and averaged within each interval. Five independent roots were analysed. RH growth time-lapse movies were acquired using a Zeiss Axioplan microscope with a Zeiss Achroplan 100x (na 1.25) oil immersion Ph3 objective. Eru and Col-0 seedlings were grown on solid RH medium and gently overlaid by a cover glass. Images were collected for approx. 1 hour with a framerate of 20 s. The RH length gain was measured for each frame in FIJI for > 5 RHs.

semi-quantitative RT-PCR and real-time PCR

Total RNA was isolated from 6-day-old WT, eru, rol1-2, lrx1-1, lrx2-1, the1-4, prc1-1 and enl7 roots (PureLink®Plant RNA kit, Life Technologies), 7-day-old WT and arf7arf19 roots, or 7-day-old roots of 6 independent WT x 35S::ERU lines (TRIzol reagent) and DNase treated (RQ1 RNase-Free DNase, Promega). cDNA was reverse transcribed from 500 ng (CW mutants and 35S::ERU lines) or 100 ng (arf7arf19 mutant) of RNA using oligo(dT)20 primers. For genotyping by semi-quantitative RT-PCR ERU, ACT2 and EF1α cDNA was amplified for 35 cycles (primers: table S1). For real-time PCR, taqman assays (CW mutants and 35S::ERU lines) specific to ERULUS (At02270065_s1) and ACT2 (At02329915_s1) or ACT8 (At02270958) were used, or ERU and TUB3 primers (for arf7arf19) were designed for SYBR green based qPCR (table S1). Three technical and three biological repeats were performed for each duplex PCR. Data was analysed using the ΔΔCt method.

Cloning of ERULUS and Arabidopsis transformation

Constructs were generated using gateway cloning. To construct the ERUp::GFP transgene, a 619bp sequence upstream of the translational start codon of ERULUS was amplified from col-0 genomic DNA using Platinum high fidelity DNA polymerase (Life Technologies). To create the 35S::ERU overexpression construct and the 35S::ERU-GFP overexpressed reporter construct, the entire ERULUS cds without stop codon was obtained by PCR. Primers: table S1. All DNA fragments were cloned to the pDONR207 entry vector, transformed in E. coli and the plasmids obtained from single colonies were verified by Sanger sequencing. Recombination was performed with isolated plasmid by LR reaction into the pGWB2 (35S promoter, no tag) or pGWB5 (35S promoter, C-terminal GFP) destination vectors. To obtain the translational protein-reporter transgene a genomic DNA segment containing the promoter and the coding region of ERULUS (3148 bp) was synthesized in the pENTR221 donor vector using The GeneArt® Gene Synthesis service (Life Technologies). This construct was recombined into the pGWB4 (no promoter, C-terminal GFP) binary vector. Agrobacterium tumefaciens C58 or LBA4404 strain transformed with the constructs was used to transform Col-0 and eru Arabidopsis plants using the floral dipping method [START_REF] Clough | Floral dip: a simplified method for Agrobacteriummediated transformation of Arabidopsis thaliana[END_REF]. Agrobacterium carrying the construct of interest was cultered in 5 mL liquid LB medium (10 g L -1 tryptone, 5 g L -1 NaCl, 5 g L -1 yeast extract) containing 50 µg l -1 kanamycin, 25 µg l -1 hygromycin, 25 µg l -1 rifampicin and 50 µg l -1 gentamycin for 48h at 28°C while shaking. Subsequently, using 1 mL of this pre-culture, a main culture was set up (24h, 28°C, shaking). This culture was centrifuged (8000g, 10min, 4°C) and the bacteria were resuspended in 500 mL transformation buffer (50 g L -1 sucrose, 0.74 g L -1 MgCl 2 , 100 µL silwet-L77). The inflorescence of >50 Arabidopsis plants were dipped in this solution for 2.5min. Well-watered flower-dipped plants were covered with a plastic sheet for 24h to garuantee high humidity, after which they were left to fully mature and set seeds. Transformed seeds were selected by antibiotics resistance. Homozygous T 3 progeny was used for analysis.

ARF7/ARF19 ChIP-qPCR

Root cultures were pre-treated with 1 μM NAA to remove Aux/IAA proteins. DNA and protein complexes were cross-linked by submersing the tissue in 40 ml of Fixation Buffer (0,1 M sucrose, 50 mM NaCl, 10 mM KH 2 PO 4 , pH 7, 1 % formaldehyde, 10 μM MG132) and vacuum for 20 min. The reaction was stopped by adding cold glycine (0.125 M). Nuclei were isolated as described by [START_REF] Bowler | Chromatin techniques for plant cells[END_REF] and re-suspended in 1 ml Sonication Buffer (10 mM potassium phosphate, pH 7, 0.1 M NaCl, 0.3% sarkosyl, 10 mM EDTA, 0.1 mM PMSF, 1X Sigma plant protease inhibitor cocktail) [START_REF] Bowler | Chromatin techniques for plant cells[END_REF]. The chromatin was sonicated to yield fragments of 200-500 bp. 200 μl of sonicated chromatin was subsequently added to 1 ml Immuno-precipitation Buffer (50 mM Hepes, pH 7.5, 150 mM KCl, 5 mM MgCl 2 , 0.1% Triton X-100) and incubated with 3 μg of affinity purified anti-ARF19 or anti-ARF7 IgGs at 4°C on a slow-moving rotator for 4h. Anti-ARF7 antibody was produced in rabbits using an E. coliexpressed His-tagged antigenic region from aa 795-1039 [START_REF] Lavenus | Inference of the Arabidopsis lateral root gene regulatory network suggests a bifurcation mechanism that defines primordia flanking and central zones[END_REF]. The latter was used to affinity-purify the resulting antiserum. His-tagged ARF19 peptide (aa 541-720) was expressed in E. coli and used for antibody production in sheep [START_REF] Cho | A secreted peptide acts on BIN2-mediated phosphorylation of ARFs to potentiate auxin response during lateral root development[END_REF]. The anti-ARF19 crude antisera were affinity-purified using Pierce Sulfo link resin as per their instructions. Protein G Dynabeads® (Invitrogen) were added and incubated overnight. Elution and reverse crosslinking of the immunoprecipitated and non-immunoprecipitated chromatin samples were performed by heating to 95°C in 0.5 M NaCl solution for 20 min. Upon cooling, 4 μl of 20 mg ml -1 Proteinase K was added and the samples were incubated at 55 °C overnight, then at 65 °C for 6h. The magnetic beads were removed and DNA extracted from the remaining solution using phenol (buffered to pH 8):chloroform:isoamyl alcohol, 25:24:1. Precipitated DNA from the immunoprecipitated samples was re-suspended in 30 μl and the input DNA in 300 μl of water. Input and immunoprecipitated samples were diluted 10-fold and 5 μl thereof was used in a 12 μl volume reaction of SYBR green master mix and 1 μM each of forward and reverse oligonucleotides (SI table 1). The primers were designed based on the location of putative ARF binding sites. The putative 1500bp promoter region of ERULUS was examined for cis-elements using Place (http://www.dna.affrc.go.jp/PLACE/). All qPCR reactions were performed as triplicate technical replicates using a Roche LightCycler 480 qPCR machine. ChIP experiments are representative of three biological replicates.

Micro-Fourier transform IR spectroscopy (mFT-IR)

Six day old Col-0 and eru roots were dehydrated in ethanol and rehydrated overnight in distilled water. The dense RH collet at the hypocotyl-root junction was excised and dried at RT on a gold coated microscopy slide. FT-IR spectra were collected in an area of 30 x 30 µm where the stalks of multiple RHs overlapped using a Thermo Scientific Nicolet iN10 MX infrared imaging microscope equipped with a liquid nitrogen-cooled camera sensor coupled to the Thermo Scientific OMNIC Picta software. Spectra were collected in cooled reflection mode (dual transmission) ranging from 830 cm -1 to 1800 cm -1 with 3.857 cm -1 intervals. 64 spectra were co-added for each sample to increase the signal-tonoise ratio. The WT (n=72) and eru (n=46) spectra were baseline-corrected. Statistics were performed for each wavenumber using a student t-test (parametric) or kruskal wallis test (non-parametric) in R statistics or Multi-Experiment Viewer (MeV) respectively.

Immunolocalization and staining

Five day old Col-0 and eru seedlings grown on solid RH medium were covered with isotonic fixation buffer (50 mM PIPES, 5 mM MgSO 4 , 5 mM EGTA, 4% paraformaldehyde, 0.1% glutaraldehyde, 1 % sucrose, pH 6.9) for 30 min, transferred to the same fixation buffer for 90 min and subsequently washed three times with 50 mM PIPES buffer (pH 6.9). Aspecific binding sites were blocked with PIPES buffer containing 3% BSA. After washing (PIPES 3x) seedlings were incubated overnight at 4°C with a 1:5 dilution of the Rat IgM primary antibody against methylesterified (LM20), de-esterified homogalacturonan (LM19) or xyloglucan (LM25)(Plant Probes, UK). After washing, the samples were incubated with 1:100 Alexa Fluor 488 Goat anti-Rat IgM secondary antibodies for 1 hour at RT. Washed samples were then mounted on a slide with PIPES buffer and visualized using a Nikon Eclipse E600 coupled to a D-Eclipse C1 confocal unit (Nikon, Brussels, Belgium), equipped with 488nm Argon laser and Plan Apo 60x (na 1.2) water immersion objective. The gain was adjusted so that no fluorescence signal was detectable for the negative control (no primary antibody), and subsequently images were collected for eru and WT roots using identical settings. For LM20 and LM19, fluorescence intensity plots were acquired from the RH stalk along 7 cross sectioning lines for each RH. Maximal intensity values were extracted from baselined (background subtracted) spectra. Cellulose and pectin Ca 2+ binding sites were stained using Direct Red 23 and propidium iodide respectively. Five day old seedlings were fixed for 2h (see above), washed for 30 min, stained for 30 min using 0.01% w/v direct red 23 or 30 µM PI in PIPES, washed for 30 min and mounted in PIPES buffer for visualization using a D-Eclipse C1 confocal unit. The thickness of the CW was measured on the obtained confocal images according to the following procedure. For each RH, intensity values along RH intersecting lines were obtained. The resulting plots show a background fluorescence level, and a subsequent peak in intensity corresponding to the signal coming from the CW. Each intensity plot was baselined (background subtracted) to make them comparable amongst the RH population, and a general intensity cutoff was set. The width of the intensity peak above the cutoff was calculated and considered to be an approximation for the cell wall width.

Pectin methylesterase activity assay

The PME activity was measured in accordance with [START_REF] Grsic-Rausch | A coupled spectrophotometric enzyme assay for the determination of pectin methylesterase activity and its inhibition by proteinaceous inhibitors[END_REF], but with minor adjustments. Root tips were cut at the top of the differentiation zone and flash frozen. The soluble protein fraction was extracted from 10 mg of tissue by homogenization in 100 µL of 50 mM sodium phosphate buffer (containing 500 mM NaCl, protease inhibitor cocktail, pH 7.5) and subsequent centrifugation at 11,500 g (20 min, 4°C). PME activity was determined in triplicate immediately following extraction. The reaction was performed in an final volume of 110 µL, consisting of reaction mix (89,4 µL 50 mM phosphate buffer, 4 mM NAD + , 0.35U formaldehyde dehydrogenase from Pseudomonas F1879 Sigma, 1U alcohol oxidase from Pichia pastoris A2404 Sigma, pH 7.5), 8 µL 0.5% pectin from citrus peel (P9135 Sigma) and 10 µL protein extract (samples), 4 µL recombinant pectinesterase from orange peel (positive control; P5400 Sigma), or 10 µL phosphate buffer (negative control). NADH absorbance was measured at 340 nm each 40 sec during 45 min (Biotek, Synergy MX), its concentration calculated using the extinction coefficient (6.220 M -1 cm -1 ) and the result normalized to the total protein concentration [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding[END_REF]. PME assay results are representative of three biological replicates.

Microscopy

WT x ERU prom ::GFP plants were grown for 6 d on RH medium and placed on a slide with ddH 2 O. Images were acquired using a Nikon Eclipse E600 coupled to a D-Eclipse C1 confocal unit (Nikon, Brussels, Belgium). Propidium iodide (0.1 mg ml -1 ) was used as a counterstain. WT x ERUprom::GFP fluorescence profiles were extracted from images collected using a Nikon AZ100 multizoom macroscope coupled to 488nm fluorescence unit. ERU-GFP subcellular localization was visualized using the above mentioned confocal microscope and a 60x water immersion objective (for overview images), and a Zeiss Axiovert 200 (Carl Zeiss, Jena, Germany) equipped with a microlens-enhanced dual spinning disk confocal system, a three-line argonkrypton laser and a 63x oil immersion lens for higher resolution images (Ultraview ERS; PerkinElmer, Seer Green, UK). For the latter, 4-6 d old seedlings were mounted in liquid RH growth medium and Zstacks were collected from actively growing RHs using a step size of 0.4-1 µm. FIJI was used to generate 3D renderings and maximal projections of the acquired Z-stacks (Volume viewer and 3D project plugins). For timelapse acquisition, 5-d old seedlings were grown on slides overlayed with a thin layer of solid RH growth medium. The roots were overlaid with a coverslip and left to recover for 1h prior imaging at 4 sec intervals. Pectin Ca 2+ binding site oscillations were visualized using propidium iodide staining, as described by [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF], with small adjustments [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF]. WT and eru (-/-) seedlings were grown in square petri dishes for 4-5 days on standard RH growth medium overlaying microscopy slides. The slides were excised from the medium, the seedlings were covered with a 10 µM PI solution in liquid RH growth medium, overlayed with a large coverslip, and left to recover for 30 min in a climate controlled environment (22°C). A fully automated Nikon Ti wide-field microscope (Nikon Instruments, Paris, France), with a 60x (na 1.2) oil immersion objective was used to collect PI fluorescence and transmitted light images every 3 seconds for 10-20 min at a resolution of 0.12 µm pixel -1 . Samples were illuminated with a Lumencor Spectra-X solid state light source (550/15nm; laser power 5%) and detected through a multiple dichroic and 620/40 bandpass filter on a CS-Ri2 scientific CMOS camera. Image acquisition was performed using Nikon NIS Elements with exposure times set to 100 ms (transmission) and 500 ms (fluorescence), closing the shutters in between consecutive acquisitions. RHs showing normal cytoplasmic streaming and the presence of a dynamic clear zone at the tip were selected for imaging. The acquired PI fluorescence time series for individual RHs were imported in FIJI as a stack and all frames were aligned with the stackreg plugin using Rigid registration. As such, a time series was acquired in which the tip was stationary from frame to frame, allowing the use of a single region of interest (ROI) for data extraction. For each frame, the average fluorescence intensity of the background and a 1.4 µm² ROI at the RH tip were measured. For each timepoint, the background signal intensity was subtracted from the apical PI fluorescence intensity. To correct for bleaching, the obtained PI fluorescence time series were de-trended in Autosignal v1.7 (Systat Software, Inc.). A Fast Fourier Transform Radix 2 algorithm was employed in Autosignal v1.7 to perform frequency analysis of the acquired oscillograms. Hence, the PI fluorescence time series for individual RHs were transformed in order to show the PI oscillatory behaviour as a spectrum of frequencies and their corresponding amplitude. For each oscillogram, the well-defined highest amplitude frequencies were isolated to describe the main PI oscillatory behaviour. Kymographs were constructed using the multi kymograph plugin in FIJI.

Phosphoproteome analysis

Briefly, 100 mg of finely ground plant material was suspended in homogenization buffer containing 50 mM Tris-HCl buffer (pH 8), 30% sucrose, 5 mM EDTA, and 1 mM DTT in Milli-Q water and appropriate amounts of the cOmplete TM protease inhibitor mixture (Roche) and the PhosSTOP TM phosphatase inhibitor mixture (Roche). After sonication and removal of cell debris by centrifugation, a methanol/chloroform precipitation was carried out with the supernatant as described previously [START_REF] Vu | Up-to-Date Workflow for Plant (Phospho)proteomics Identifies Differential Drought-Responsive Phosphorylation Events in Maize Leaves[END_REF]. Pellets were washed with 80% acetone and re-suspended in 8 M urea. Alkylation of cysteines was carried out in the presence of 15 mM tris(carboxyethyl)phosphine (TCEP, Pierce) and 30 mM iodoacetamide (Sigma-Aldrich). Three mg of protein material was digested with 10 µg of MS grade endoproteinase-Lys-C (Wako Chemicals GmbH), followed by an overnight digestion with 30 µg of trypsin (Promega) at 37°C. The digest was acidified to pH ≤ 3 with trifluoroacetic acid (TFA) and desalted using SampliQ C18 SPE cartridges (Agilent) according to the manufacturer's guidelines. The desalted peptides were fully dried in a vacuum centrifuge and then re-suspended in 500 μl of loading solvent [80% (v/v) acetonitrile, 6% (v/v) TFA], from which 100 μl were kept for proteome analysis while 400 μl were proceeded further with phospho-enrichment using MagReSyn® Ti-IMAC (ReSyn Biosciences) as described previously [START_REF] Vu | Up-to-Date Workflow for Plant (Phospho)proteomics Identifies Differential Drought-Responsive Phosphorylation Events in Maize Leaves[END_REF]. Samples were vacuum dried and dissolve in 30 μl 2% (v/v) acetonitrile and 0.1% (v/v) TFA prior to LC-MS/MS analysis. Each sample was analyzed via LC-MS/MS on an Ultimate 3000 RSLC nano LC (Thermo Fisher Scientific, Bremen, Germany) in-line connected to a Q Exactive mass spectrometer (Thermo Fisher Scientific). The peptides were first loaded on a trapping column (made in-house, 100 μm internal diameter (I.D.) × 20 mm, 5 μm beads C18 Reprosil-HD, Dr. Maisch, Ammerbuch-Entringen, Germany). After flushing the trapping column, peptides were loaded in solvent A (0.1% formic acid in water) on a reverse-phase column (made in-house, 75 µm I.D. x 250 mm, 1.9 µm Reprosil-Pur-basic-C18-HD beads, Dr. Maisch, packed in the needle) and eluted by an increase in solvent B (0.1% formic acid in acetonitrile) in a linear gradient from 2% solvent B to 55% solvent B in 120 minutes, followed by a 5-min washing step with 99% solvent B, all at a constant flow rate of 300 nL min -1 . The mass spectrometer was operated in datadependent, positive ionization mode, automatically switching between MS and MS/MS acquisition for the 5 most abundant peaks in a given MS spectrum. The source voltage was set at 4.1 kV and the capillary temperature at 275°C. One MS1 scan (m/z 400-2,000, AGC target 3 × 106 ions, maximum ion injection time 80 ms), acquired at a resolution of 70,000 (at 200 m/z), was followed by up to 5 tandem MS scans (resolution 17,500 at 200 m/z) of the most intense ions fulfilling predefined selection criteria (AGC target 5 × 104 ions, maximum ion injection time 80 ms, isolation window 2 Da, fixed first mass 140 m/z, spectrum data type: centroid, under-fill ratio 2%, intensity threshold 1.3xE4, exclusion of unassigned, 1, 5-8, >8 positively charged precursors, peptide match preferred, exclude isotopes on, dynamic exclusion time 12 s). The HCD collision energy was set to 25% Normalized Collision Energy and the polydimethylcyclosiloxane background ion at 445.120025 Da was used for internal calibration (lock mass). Database search and data analysis was performed using MaxQuant v.1.5.4.1 and Perseus 1.5.5.3, respectively as described previously [START_REF] Vu | Up-to-Date Workflow for Plant (Phospho)proteomics Identifies Differential Drought-Responsive Phosphorylation Events in Maize Leaves[END_REF]. For phosphoproteome data (eru data set), only phosphosites with localization probabilities larger than 0.75 were retained for analysis. Two-sample T-tests were performed with a cut-off p-value of 0.05. For NAA phosphoproteomics, a two-sample t-test was carried out with permutation-based false discovery rate (FDR) < 0.05 and 250 randomizations to correct for multiple-hypothesis testing.

Bioinformatic analysis

A search for non-redundant A. thaliana proteins with sequence homology to the 27 AA signal peptide sequence was performed using the pBLAST algorithm for short input sequences. The corresponding FASTA sequences were retrieved for all 100 peptide hits using the NCBI batch entrez tool and blasted against the annotated A. thaliana protein library using the Tair WU-BLAST2 tool (www.arabidopsis.org/wublast/index2.jsp) to identify the unique proteins corresponding to the aligned peptides. The AGI codes of the 51 unique proteins originating from the top 100 BLAST hits were subsequently used for Gene Ontology enrichment analysis (cellular component annotation database; Bonferroni correction). The whole protein FASTA sequences corresponding to the 51 identified proteins were retrieved using the Tair bulk data retrieval tool, and subsequently used for motif analysis. MEME version 4.11.2 was used for motif discovery, and set to compute the 3 most prominent motifs with a width of 6-20 AA. Data on root cell specific transcription of ARF7 and ARF19 was collected from the eFP browser [START_REF] Winter | An "electronic fluorescent pictograph" browser for exploring and analyzing large-scale biological data sets[END_REF].

QUANTIFICATION AND STATISTICAL ANALYSIS

Image analysis was performed in Fiji. Detailed procedures for image processing are described in the method details. Statistics were performed in Perseus version 1.5.5.3 (phosphoproteomics) or R [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]. All data er represented as mean ± SEM, and n indicates the sample size as the number of independent samples. The sample size for individual experiments is stated in the figure captions and method details. Significance (α = 0.05) was assessed by two-way analysis of variance (ANOVA; parametric) using linear mixed-effects models followed by a TukeyHSD (for pairwise statistical analysis), or Kruskal-Wallis tests (non-parametric). MicroFT-IR data were analyzed in MultiExperiment Viewer (www.tm4.org/mev, version 4.8.1) using Kruskal-Wallis (for non-parametric distributed wavenumbers) or student t-tests (for normally distributed wavenumbers). Normality was assessed by Shapiro Wilkinson tests (nonnormal distribution < W=0.95 < normal distribution). Correlation analysis was performed using the non-parametric Spearman's rank correlation test. . Yellow and red represents low and high transcription respectively. (F) Anti-ARF7 and anti-ARF19 antibodies are antigen-specific. Western blots using polyclonal anti-ARF7 (rabbit) and anti-ARF19 (sheep) with root culture nuclei preparations of WT and arf7 or arf19 Arabidopsis plants. In Col-0 samples, specific staining is observed at expected molecular weights (~130 kDa). ARF7 and ARF19 staining is absent in arf7 and arf19 knock-out mutants respectively.

  provided FT-IR access; T.J.H., J.O., M.H.W., R.S. performed the auxin micro-array analysis; K.H. performed ChIP-experiments; N.N. and L.D.V. performed (phospho)proteomics; S.S., D.B. and K.H. performed qPCR; S.S. performed bio-informatics and statistics; S.S., D.B., G.M., M.H.W., I.D.S., K.H., R.S., R.B., M.J.B., C.G. and K.V. analysed and interpreted data; S.S., D.B., M.J.B. and K.V. wrote the paper.

Figure 1 .

 1 Figure 1. eru RH phenotype and growth characteristics. (A) Representative roots of 7d old WT, eru, WT x 35S::ERU and eru x ERUp::ERU-GFP seedlings, and close-ups of RHs showing the typical short/bulged phenotype. (Scale bars: overview root, 500 µm; close-ups, 200 µm). (B) Graph showing the average final RH length of WT and ERU knockout, overexpression and complementation lines, relative (%) to the WT (n>10). (C) RH profile constructed from 7d old WT and eru seedlings (n=5). The average RH length was determined for very young RHs (1.15 mm from the root tip) until fully mature RHs (5.9 mm from the root tip). (D) growth dynamics of individual WT and eru RHs, showing consecutive frames of growing RHs that were followed for 1h (scale bar, 20 µm), the average growth curve and growth speed (left), and a stunted growth curve for a single representative eru RH (right). Arrows indicate growth pauses. RH growth dynamics were followed starting from the bulge phase and throughout the tip growth phase. Error bars represent SE. Significance codes p-value: 0.05 '*' 0.01 '**' 0.001 '***' 0. See also Figure S1.

Figure 2 .

 2 Figure 2. ERULUS tissue-specific transcription and ERULUS subcellular localization. (A) Confocal images of 7d old WT x ERUp::GFP showing that the ERU promoter activity is restricted to RH cell files only, throughout RH morphogenesis (scale bar: left, 500 µm; top right and middle, 100 µm; bottom, 25 µm). Grey-scale spinning-disc images of WT x ERUp::ERU-GFP showing ERU-GFP localization to (B) the future site of bulge formation, the bulge apex and the very tip of tip-growing RHs (scale bar, 20 µm), (C) vesicles and the apex during bulge formation (scale, 5 µm), (D) vesicles and the apical plasma membrane during RH tip growth (scale bar, 10 µm). (E) sequential subapical (left) to apical (right) mediolateral sections of the RH depicted in (D). (F) Frontal maximal projection of the tip from the RH depicted in (D). See also Figure S2-4 and movie S1-3.

Figure 3 .

 3 Figure 3. ERU is a target of auxin signaling. (A) The 3 kb promoter region upstream of the ERU start codon, showing four ARFAT (TGTCTC) sequences, for which two were assayed by qPCR after anti-ARF7 and anti-ARF19 ChIP (green markings). (B) ERU transcription time series after application of 1 µM NAA, in WT and the arf7 arf19 double mutant (n=3). (C) ChIP-qPCR data showing that ARF7 binds directly to both ARFAT sequences in the ERU promoter (n=3). (D) ChIP-qPCR data showing ARF19 binds directly to the -475 to -353 ARFAT sequence of the ERU promoter (n=3). Error bars represent SE. Significance codes p-value: 0.05 '*' 0.01 '**' <0.001 '***'. See also Figure S5.

Figure 4 .

 4 Figure 4. ERU is differentially phosphorylated at serine 497 in response to auxin. Abundance of the ERU phosphopeptide corresponding to serine 497 in mock (black dots) and auxin supplemented (grey dots) root samples. Inset: average serine 497 ERU phosphopeptide abundance (n = 5). Error bars represent SE. Significance codes p-value: 0.05 '*'. See also Figure S6.

Figure 5 .

 5 Figure 5. ERU regulates pectin cell wall dynamics. (A) microFT-IR statistical output showing for which wavenumbers the t-value crosses the threshold of significance (orange lines; α = 0.05, df= 106). Negative values represent lower IR absorbance in eru vs. WT RHs. Positive values represent higher IR absorbance in eru vs. WT RH. (B)Table showing wavenumbers at which the IR absorbance differs

Figure 6 .

 6 Figure 6. The eru phenotype is partially rescued by pharmacological inhibition of PME-activity. (A) final RH length of WT and eru RHs in the presence of different polyphenon 60 (pp60) concentrations. (B) representative images of WT and eru roots 2 days after pp60 supplementation (scale, 500 µm). Error bars represent SE. Significance codes p-value: 0.05 '*' 0.01 '**' <0.001 '***'.

Figure 7 .

 7 Figure 7. The eru (-/-) mutation affects FERONIA and H + -ATPase 1/2 phosphorylation status. (A) FER pS701 abundance normalized to the FER protein abundance. (B) FER peptide abundance resulting from proteome analysis. (C) AHA1/2 pS904 abundance normalized to the AHA protein abundance. (D) AHA2 and AHA1 peptide abundance resulting from proteome analysis. Dots represent abundance values in individual WT (black) and eru (orange) root tip samples. Bar plots represent the mean of those values. Error bars represent SE. Significance codes p-value: 0.05 '*' 0.01 '**' <0.001 '***'.

Figure 3 Figure 4 Figure5Figure 6

 346 Figure 3

Figure 7

 7 Figure 7

Figure S5 .

 S5 Figure S5. Effect of auxin on the eru phenotype, ARF7/19 root transcription, anti-ARF7/19 western blots, Related to Figure 3. (A-D) Supplementation with auxin cannot rescue the eru phenotype. WT and eru seedlings were transferred to plates containing different concentrations of IAA, NAA and 2,4D. (A) Bar plots showing the effect of auxin addition on the average length of newly emerged RHs. At least 10 RHs were measured for 30 roots per treatment and line. (B) representative images of auxin treated WT and eru roots. Scale bar, 0.5 mm. (C) eru and WT RH profiles after 20 nM IAA supplementation (n=24). (D) Linear interpolation of the RH growth zone. Each line represents the region of linear RH elongation for a single root (n=24). Average RH growth velocity, derived from the slope of individual root RH growth zone interpolations (n=24). Error bars represent SE. (E) ARF7 and ARF19 are transcribed in trichoblasts. Root cell-specific transcription of ARF7 (right) and ARF19 (left) as extracted from public transcriptomics data [S1]. Yellow and red represents low and high transcription respectively. (F) Anti-ARF7 and anti-ARF19 antibodies are antigen-specific. Western blots using polyclonal anti-ARF7 (rabbit) and anti-ARF19 (sheep) with root culture nuclei preparations of WT and arf7 or arf19 Arabidopsis plants. In Col-0 samples, specific staining is observed at expected molecular weights (~130 kDa). ARF7 and ARF19 staining is absent in arf7 and arf19 knock-out mutants respectively.

Figure S6 .

 S6 Figure S6. Annotated LC-MS/MS spectra for the identified phosphopeptides and AHA1/2 phosphorylation is response to auxin, Related to Figure 4.LC-MS/MS spectra for the (A) ERU S497, (B) FER S701, (C) AHA2 S904, (D) AHA2 S899 and (E) AHA2 T947 peptide. AHA1/2 and AHA2 are dephosphorylated at serine 899 and threonine 947 respectively in response to auxin. (F) abundance of the AHA1/2 S899 associated phosphopeptide in individual replicates of mock treated (black dots) and auxin treated (grey dots) root samples. (G) average S899 phosphopeptide abundance (n=5). (H) abundance of the AHA2 T947 associated phosphopeptide in individual replicates of mock treated (black dots) and auxin treated (grey dots) root samples. (I) average T947 phosphopeptide abundance (n=5). Graph and statistics based on centered log2 transformed values for the complete data set (unpublished results). Error bars represent SE. Significance codes p-value: 0.05 '*' 0.01 '**' <0.001 '***'.

Figure S7 .

 S7 Figure S7. ERU transcription in CW mutants, eru CW defects and the effect of xyloglucan (XYG) deficiency on pectin composition, Related to Figure 5. (A) ERU transcription is affected in specific RH mutants. qPCR data showing the transcription of ERU in the roots of WT (Col-0) and several CW RH mutants (n=3). Images of mature RHs of the lines used. Scale bar = 400 µm. (B-K) Eru RH CWs are affected in cellulose, XYG and pectin. WT and eru RHs were stained with direct red 23. (B) cellulose content and images of WT and eru RHs. The arrow shows higher cellulose deposition at the tip. Scale bar, 20 µm. (C) CW width as extracted from S4B cross-sectional intensity plots. (D) Correlation of the CW width and cellulose content revealing a positive correlation (Rho=0.80; p<0.001). (E) Virtual 200 µm section of the RH stalk. CW and cytoplasm volume calculated from the S4B staining. ! = growth speed vector. (F) The CW volume is inversely related with (G) the RH growth speed. (H) The cytosol volume is unaffected (n=8). (I) The XYG content is reduced in eru RH CWs. Lm25 signal intensity (n=10 roots with > 5 RH per root). Confocal images of lm25-stained RHs. Scale bar, 20 µm. (J-K) PI staining of pectin Ca 2+ egg-boxes. (J) average PI fluorescence intensity at the tip of growing WT and eru RHs. (K) average PI fluorescence intensity in the stalk of WT and eru RHs (n=6). representative confocal images of WT and eru RHs stained with PI. Scale bar, 20 µm. (L) PI stained WT and xxt1/2/5 RHs. Scale bar, 10 µm. (M) pectin Ca 2+ binding site abundance. (N) CW width from PI stained RHs. Error bars represent SE. Multiple RHs were measured for at least 6 roots per genotype. Significance codes p-value: 0.05 '*' 0.01 '**' <0.001 '***'.

  1 nicotinic acid, 0.56 mM myo-inositol, 2.3 mM MES, 25 µM KCl, 17.5 µM H 3 BO 3 , 1 µM MnSO 4 .H 2 O, 1 µM ZnSO 4 .7H 2 O, 0.25 µM CuSO 4 .5H 2 O, 0.25 µM (NH 4 ) 6 MoO 24 .4H 2

Table S1 : Overview of the primers that were used for genotyping, RT-PCR, cloning, ChIP-qPCR and realtime PCR, Related to STAR Methods.

 S1

Acknowledgments

The authors would like to thank the Research Foundation-Flanders (FWO), the Interuniversity Attraction Poles Programme -Belgian State -Belgian Science Policy [IUAP VI/33], the Biotechnology and Biological Sciences Research Council (BBSRC) and the University of Antwerp (TTBOF/29267) for funding. M.H.W., T.J.H., J.O., K.H., R.S. and M.J.B. acknowledge the support of the Biotechnology and Biological Sciences Research Council (BBSRC) and Engineering and Physical Sciences Research Council (EPSRC) funding to the Centre for Plant Integrative Biology (CPIB) BB/D019613/1; K.H. acknowledges BBSRC Professonial Research Fellowship funding to M.J.B., grant BB/G023972/1; and M.J.B. acknowledges the Royal Society-Wolfson Merit Award. G.B. was supported by the BBSRC Strategic Studentship BS/S/H/2005/12044, awarded to C.G.. Contributions of C.G. were funded by BBSRC Grant G19475 and the Royal Society of London Research Grant 'Arabidopsis Root Hair Functional Genomics. J.O. acknowledges the R & D programme of "Plasma Advanced Technology for Agriculture and Food (Plasma Farming)" through the National Fusion Research Institute of Korea (NFRI) funded by the Government funds. We thank Brigitte van de Cotte for assisting with (phospho)proteomics sample preparation. L.D.V. is the recipient of a VIB International Ph.D. program fellowship. The UltraVIEW VoX spinning disk confocal microscope was purchased with support of the Hercules Foundation (Hercules Type 1: AUHA 09/001).

Author contributions K.V. conceived the project; S.S., D.B., G.B., C.G. identified and phenotyped the mutant; S.S., D.B., W.D.V. performed microscopy. I.P. and D.A. provided microscopy access. S.S.; D.B. and M.Z. performed cloning and gene expression studies; S.S. performed cell wall analysis and immuno-localizations; G.M.

Declaration of Interests

The authors declare no competing interests.

Supplemental movie legends movie S1. Representative 3D rendering of ERU-GFP subcellular protein localization in growing


Sandor Bilicz

Marc Lambert

Szabolcs Gyimothy. Combination of Maximin Emmanuel Vazquez

Szabolcs Gyimothy

Combination of Maximin and Kriging Prediction Methods for Eddy-Current Testing Database Generation

Combination of Maximin and Kriging Prediction Methods for Eddy-Current Testing Database Generation

Sándor BILICZ [START_REF] Pávó | Design method for optimal database used for inverse problems in ECT[END_REF][START_REF] Pávó | Adaptive inversion database for electromagnetic nondestructive evaluation[END_REF] , Marc LAMBERT 1 , Emmanuel VAZQUEZ [START_REF] Bettinger | Design of experiments for response diversity[END_REF] and Szabolcs GYIMÓTHY 2 1 Département de Recherche en Électromagnétisme, Laboratoire des Signaux et Systèmes UMR8506 (CNRS-SUPELEC-Univ Paris-Sud), Gif-sur-Yvette, France 2 Budapest University of Technology and Economics, Hungary [START_REF] Bettinger | Design of experiments for response diversity[END_REF] École Supérieure d'Électricité (SUPELEC), Gif-sur-Yvette, France

Abstract

The numerical simulation of eddy-current non-destructive testing methods involves high complexity and expensive computational load. However, one needs to reach reliable solutions for these problems in order to be able, in particular, to solve the related inverse problem. A way to overcome such a difficulty is to propose a "surrogate modelization" of ECT experiments through the generation of a problem-specific database (for a given ECT application), containing the calculated probe responses ("data") for well-chosen defect configurations (at certain values of "defect parameters"). Surrogate models attempt to imitate the behaviour of the rigorous model but remain much simpler (thus faster to run). In other words, the expensive "simulator" is replaced by a cheap "emulator" in the inversion process. The emulator is always based on some "true" data (computed by the simulator). The choice of these samples strongly influences the performance of the emulation and then requires some sophisticated design-of-experiment (DOE) methods. In our context, DOE attempts to achieve an "optimal sampling" of the given ECT experiment.

However, the construction of such databases is not a simple task. The database should be "optimal" in some sense. Optimality is a rather general property. In our context, it means that the database achieves a prescribed precision when one applies a given interpolation method (based on the stored data points), while the size of the database remains as small as possible. Nowadays, the generation of optimal databases is quite challenging and an intensively studied field in non-destructive evaluation. To the best of our knowledge, the most preferred approach of database generation so far is the application of mesh generation methods (mostly originated from finite-element meshing techniques), see for instance [1, 2].

The present contribution provides a new methodology of optimal database generation. Let us introduce the following notation: the n th entry of the database consists of a Ddimensional parameter vector p n (the defect is characterized by D parameters), and an Mdimensional data vector z n (z n can be complex, e.g., the impedance variation of a probe coil). The parameter vectors, which relate to all possible defects that one expects to find in the given experiment, span the parameter space P. The data vectors, which are related to the parameter vectors in the parameter space, span the data space Z. The basic idea of our method is to construct a database, whose data points z n (n=1, 2, …, N) are as spread as possible over Z. In other words, the data space Z is uniformly sampled by the database.

The proposed methodology is a combination of a maximin method (a well-known tool in decision theory, game theory, statistics) and a kriging prediction (a stochastic method for interpolating functions, based on some observed function values, using a Gaussian process to model the functions). A close idea appears in a quite different context in [3] but the methodology presented therein does not work in the case of high-dimensional data spaces, like in our ECT application (note that M might be several hundred).

The sought uniform output sample distribution is attempted to achieve by using the maximin method. In our context, maximin means maximizing the minimal distance between any pair of output samples. In other words, a sample distribution is aimed where the distance of all output samples from their nearest neighbour is as large as possible. We propose an incremental algorithm to generate databases of this maximin property. Once the distance function (usually depending on the direct solver) has been choosen the method consists in mainly two stages. At the beginning, some initial samples are chosen by hand. Then, samples are inserted one-by-one according to a maximin criterion applied onto the choosen distance function. The latter has to be computed for a large number of input space's samples which is numerically expensive, then a kriging approach is used to predict the distance functions at unobserved locations.

To illustrate the method numerical simulations will be discussed and comparison of the performances of the databases generated by such a method and a "classical" method will be carried out. Preliminary results show that the proposed algorithm spreads the data vectors on the data space better than some conventional sampling methods.

Acknowledgments

This research is partially supported by the French ANR through the "INDIAC"project and by the DIGITEO cluster's project N° 2008-15D. Laboratoire des Signaux et Systèmes et SUPELEC are founding members of the DIGITEO cluster.


Philippe Beaune
email: beaune@emse.fr

Michel Beigbeder

Mihaela Juganaru-Mathieu

ENSM-SE at INEX 2012: Basic Experiments

Introduction

Our objective in the INEX 2012 campaign was to integrate the semantic tags and the linked data in our proximity retrieval model. This model was sucessfully used in previous INEX campaigns and obtained good results, particularly in 2007 with the second place in the Ad Hoc Track Focused Task [START_REF] Fuhr | Overview of the inex 2007 ad hoc track[END_REF], and in 2010 with the first place in the Ad Hoc Track Relevant in Context Task [START_REF] Arvola | Overview of the inex 2010 ad hoc track[END_REF] Though we had several discomfitures with the collection because i) there were several versions of the collection, the last one available at the end of June, one week before the initial run submission deadline, ii) the different versions were difficult to follow because they were not clearly identified, iii) not every documents were well formed according to the XML format, iv) the provided DTD gives little information on the actual structure and its semantics, v) the documents contains many semantic annotations but the underlying ideas used to generate them are not documented making them difficult to apprehend. We present in section 2 how we processed the documents to alleviate the problems with the DTD.

Thus we only have been able to do some basic experiments presented in section 3. In section 4 we present our work in progress.

Collection preparation

The collection comes with 3 164 040 documents, of which 4 749 are not well formed according to the XML format. We deleted these documents in our experiments as they only represent 0,15% of the collection.

Structure was extremely difficult to apprehend with the provided DTD (wikipedia-lod-xml.dtd) because almost every elements can contain any other one.

Here is a small extract of this DTD:

10 <!ELEMENT wikipedia ( heading | list | paragraph | table | hr | list | preblock )* > 11 12 <!ELEMENT heading ANY > 13 <!ATTLIST heading level CDATA #IMPLIED > 14 15 <!ELEMENT list ( listitem+ ) > 16 <!ATTLIST list type NMTOKEN #REQUIRED > 17 18 <!ELEMENT listitem ANY > 19 20 <!ELEMENT paragraph ANY >
Some XML elements (such as wikipedia and list) are well defined because they could only contain a small number of meaningful elements. But 46 of the 70 XML tags defined in this DTD can contain any content, such as heading, listitem and paragraph.

With this DTD the following extract can be a part of a valid document:

[...] <heading> <listitem> <paragraph> <heading> [...]
where the structure has no sense using the usual meaning of the words heading, paragraph and so on.

So we decided to build a new collection where each document validates the very simple following DTD: <!ELEMENT article ( title, CDATA ) > <!ELEMENT title CDATA> Some elements were deleted, for example yagoproperties and dbpediaproperties. For the other elements we only kept their textual content. We also ignored all the attributes except the attribute @name, whose value was kept as text. This operation was done with xsltproc and processing the whole collection lasted more than 17 hours.

We also tried to use TreeTagger [START_REF] Schmid | Probabilistic Part-of-Speech Tagging Using Decision Trees[END_REF] but it was too slow to process the whole collection because each document needed around one second to be processed.

Finally, the collection and its very simple structure was indexed with zettair1 with the light stemmer on, lasting 40 minutes.

Runs

Three runs were allowed for participants in INEX 2012. Two of our runs were produced with zettair, the first one, Emse-085, used a language model with a Dirichlet smoothing. The second one, Emse-086, used the well known BM25 model with k 1 = 1.2, k 3 = +∞ and b = 0.75. Both these runs were produced within 30 seconds for the 140 queries.

The third run, Emse-087 used our proximity model developed for the previous INEX campaigns [START_REF] Beigbeder | ENSM-SE at INEX 2009 : Scoring with proximity and semantic tag information[END_REF][START_REF] Beigbeder | Focused retrieval with proximity scoring[END_REF], and its execution needed 2 minutes and 45 seconds.

For the present we do not have the assessments so no evaluation was performed.

Proximity model

Our proximity model works with the following type of structured documents:

document ← (part) + part ← text part ← (part) + part ← title ⊕ (part) +
For plain text our model computes a score based on a fuzzy neighbouring parameterized function. For a document composed of a concatenation of parts, the score is the sum of the part scores. For a document/part with a title, title words are considered as close to any word of the part content.

First choice

The provided DTD doesn't permit us to easily construct a collection fulfilling the above description.The title of the documents was easy to extract, but as the part titles and the parts themselves are not nested, extracting these titles to insert them in their corresponding part is not possible in XSLT [START_REF] Møller | Static validation of xsl transformations[END_REF]. So we considered the XML documents as: document ← title ⊕ text and we applied our model in this simplified case.

Future works

We detected that the tag heading could be the title of parts, but the parts themselves are not explicit and clearly delimited. We will construct a new collection fulfilling our document model using a high level programming language using the library libxml and build the nesting based on the assumption that the attribute @level of the tag heading indicates the actual nesting.

We will also consider the tags yagoproperties and dbpediaproperties as parts of the newer documents. This work is in progress.

http://www.seg.rmit.edu.au/zettair/