Kris Vissenberg

Herman Höfte

Cell Wall-Related Mechanisms underlying Plant Cell Expansion

Keywords: Acid growth, auxin, cell expansion, diffuse growth, feedback regulation, history, pectin, tip growth, wall models, wall relaxation

A central question in plant biology is how plant cells can expand while maintaining a strong cell wall. Two main mechanisms have been proposed for irreversible wall expansion, intussusception and chemorheological growth. We discuss here the molecular nature of the cross-links and how their removal can contribute to growth of both tip-growing or diffusely-growing cells. We also discuss recent observations suggesting that at least in some cases processive intussusception may contribute to cell wall expansion in plants.

Introduction

The cells of prokaryotes, fungi, oomycetes, many protists, algae and plants are all surrounded by strong cell walls. A central question is how the walls of such cells manage to expand while resisting the force of the cell's turgor pressure and preventing rupture. As nicely reviewed by Dumais [START_REF] Dumais | Modes of deformation of walled cells[END_REF], different solutions for this conundrum can be found in nature, two of which allow irreversible cell wall expansion (see Box 1): (i) growth by processive intussusception, which refers to cell wall area increase driven by the insertion of cell wall elements in a regularly arranged monolayer, as for instance observed in prokaryotes, and (ii) chemorheological growth, which is defined as the chemically-mediated flow of polymeric materials under stress. Here, the deformation of the wall depends on the rate of chemical reactions leading to the breakage of load-bearing cross-links within the network, as observed in plant cell walls.

The current consensus Is that plant cell expansion is driven by the turgor pressure and limited by the extensibility of the cell wall, which relaxes through a chemorheological mechanism (see Box 1). This view has evolved over time. Early landmark publications [START_REF] Nägeli | Über den inneren Bau der vegetabilischen Zellmembranen[END_REF][START_REF] Sachs | Lehrbuch der Botanik nach dem gegenwärtigen Stand der Wissenschaft[END_REF] proposed that primary cell walls grow by intussusception. An alternative view [START_REF] Strasburger | Another building block in the plant cell wall: Barley xyloglucan xyloglycosyl transferases link covalently xyloglucan and anionic oligosaccharides derived from pectin[END_REF] proposed that wall material is deposited through apposition onto the inner cell wall surface. Since such a mechanism on its own does not explain cell wall expansion, an additional process was needed to account for cell enlargement. During the same period there was the discovery of an 'influence', which moves from the site of light perception to the site of bending during phototropic bending of canary grass coleoptiles [START_REF] Darwin | The Power of Movement in Plants[END_REF]. This "influence" was later identified as auxin by [START_REF] Went | Wuchsstoff und Wachstum[END_REF], which, together with observations by [START_REF] Cholodny | Beiträge Zur Analyse Der Geotropischen Reaktion[END_REF], led to the Cholodny-Went theory that states that during tropic responses, asymmetric distribution of auxin throughout the organ stimulates differential growth responses, which results in organ bending [START_REF] Went | Phytohormones[END_REF]. This in turn led to the formulation of the acid growth theory [START_REF] Rayle | Enhancement of wall loosening and elongation by acid solutions[END_REF], in which auxin triggers an acidification of the apoplast, promoting relaxation of the cell wall, supposedly through pH-sensitive cell wall hydrolytic activities (see Box 2). This was clearly in line with a chemorheological growth model, also adopted by [START_REF] Lockhart | An analysis of irreversible plant cell elongation[END_REF], who formalized turgor-driven cell expansion, with the now famous formula E = 𝜑(P -Y), where E is the rate of extension, 𝜑 the plastic compliance, P the turgor pressure and Y the yield threshold and where Y drops and 𝜑 increases with decreasing pH. Finally, the identification of expansins, proteinaceous agents responsible for acid-promoted relaxation of stretched cell wall preparations [START_REF] Mcqueen-Mason | Two endogenous proteins that induce cell wall extension in plants[END_REF], provided a biochemical correlate for 𝜑 and acid growth.

___________________________________________________________________ Box 1: Processive intussusception vs chemorheology

Processive intussusception is illustrated by the growth of the sacculus of gram-negative bacteria [START_REF] Höltje | Growth of the stress-bearing and shape-maintaining murein sacculus of Escherichia coli[END_REF]. This structure is a peptidoglycan monolayer with an extremely regular structure consisting of long glycan chains, which support circumferential stress, interconnected by short peptide chains, which support axial stress. Surface deformation is controlled by a protein complex that concomitantly removes peptide bonds, depolymerizes one template glycan chain and synthesizes three new glycan chains (Figure 1A). The regularity of the cell wall structure is such that the "shape" of the new material determines the deformation anisotropy of the cell wall (Figure 1B). The much less regular plant cell walls are thought to undergo chemorheological growth (Figure 1C), which differs from intussusception in that the deformation is dictated by the anisotropic relaxation (the anisotropy results from the anisotropy of both wall structure (Figure 1D) and the stresses that are exerted upon the wall (Figure 1E) upon the removal of load-bearing bonds. The newly inserted wall material is thought to be amorphous or sufficiently flexible to passively fill in the voids created by the removal of load-bearing cross-links, and thus does not contribute to orienting the deformation [START_REF] Dumais | Modes of deformation of walled cells[END_REF].

___________________________________________________________________

___________________________________________________________________ Box 2. Auxin-controlled cell expansion: an interplay between pH and cell wall modifications.

Since the Cholodny-Went theory [START_REF] Went | Phytohormones[END_REF], we now know that during tropic and other growth responses [START_REF] Estelle | Plant tropisms: the ins and outs of auxin[END_REF][START_REF] Ma | Auxin-dependent cell elongation during the shade avoidance response[END_REF][START_REF] Fendrych | TIR1/AFB-Aux/IAA auxin perception mediates rapid cell wall acidification and growth of Arabidopsis hypocotyls[END_REF], auxin levels are positively correlated with cell elongation and auxin is redistributed through the action of different auxin transport proteins to the cells in the zone that will elongate [START_REF] Friml | AtPIN4 mediates sink-driven auxin gradients and root patterning in Arabidopsis[END_REF][START_REF] Noh | Multidrug resistance-like genes of Arabidopsis required for auxin transport and auxin-mediated development[END_REF]Rakusová et al. 2011).

Curiously however, auxin can also elicit opposite growth responses, depending on the organ or even the process within the same organ. For instance, in line with Cholodny-Went [START_REF] Du | Rapid auxin-mediated cell expansion[END_REF], lower auxin content or signaling in mutant Arabidopsis roots correlates with shorter epidermal cells and higher cell wall pH [START_REF] Barbez | Auxin steers root cell expansion via apoplastic pH regulation in Arabidopsis thaliana[END_REF]. In contrast, in the same roots during the gravitropic bending response, higher auxin levels correlate with the inhibition of cell elongation at the lower side of the root [START_REF] Band | Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism[END_REF]. Similarly, external auxin supply inhibits cell elongation [START_REF] Růžička | Ethylene regulates root growth through effects on auxin biosynthesis and transport-dependent auxin distribution[END_REF][START_REF] Swarup | Ethylene upregulates auxin biosynthesis in Arabidopsis seedlings to enhance inhibition of root cell elongation[END_REF]) and promotes surface alkalinization in the root's elongation zone [START_REF] Staal | Apoplastic alkalinization is instrumental for the inhibition of cell elongation in the Arabidopsis root by the ethylene precursor 1-aminocyclopropane-1-carboxylic acid[END_REF]. Such opposite responses also occur within etiolated Arabidopsis hypocotyls, where auxin application within 20 min activates plasma membrane-localized H + -ATPases leading to cell wall acidification and increased cell elongation [START_REF] Fendrych | TIR1/AFB-Aux/IAA auxin perception mediates rapid cell wall acidification and growth of Arabidopsis hypocotyls[END_REF], but where, during apical hook formation, auxin accumulation correlates with the inhibition of cell elongation at the future inner side of the hook [START_REF] Liao | Root hair-specific EXPANSIN A7 is required for root hair elongation in Arabidopsis[END_REF]. It should be noted, however, that no matter the growth response to auxin, cell elongation rate inversely correlates with the cell wall pH in accordance with the acid growth theory.

It thus seems that auxin, depending on the context, can trigger either acidification or alkalinization of the cell wall. [START_REF] Lin | TMK-based cell-surface auxin signaling activates cell-wall acidification[END_REF] recently explained this dual action by showing that two antagonistically acting auxin signalling pathways converge on the apoplastic pH: the cell surface-located TRANSMEMBRANE KINASE1 (TMK1), which interacts with and mediates the phosphorylation of plasma membrane H + -ATPases for apoplast acidification and the stronger intracellular canonical auxin signalling that promotes net cellular H + influx and apoplast alkalinization. The picture is more complex, however, since TMK1 can also mediate slower transcriptional responses. Indeed, [START_REF] Cao | TMK1-mediated auxin signalling regulates differential growth of the apical hook[END_REF] showed that the differential growth response during apical hook formation also depends on TMK1, where local auxin accumulation in cells at the inner side of the hook, leads to cleavage of the C-terminus of TMK1, which then stabilizes IAA32 and IAA34 proteins that are specific regulators of auxin signaling (by repressing auxin response transcription factor (ARF) activity).

The study of apical hook formation provided additional insights into the link between auxin levels, cell wall pH and cell expansion. Indeed, [START_REF] Jonsson | Mechanochemical feedback mediates tissue bending required for seedling emergence[END_REF] observed that higher auxin levels at the inner side of the hook correlate with higher methylesterification levels of the pectin homogalacturonan (HG). Using mutants and transgenics, the authors show that auxin prevents HG de-methylesterification, but interestingly, that changes in HG methylesterification alter the auxin response domain through a so far unidentified feedback loop. We will discuss below the potential relevance of pectin de-methylesterification for the control of cell elongation. The same group also provided evidence that xyloglucan (XG) is required to limit cell growth rates at the inner side of the hook, and that XG is required for the auxin maxima in the inner side cells by transcriptional regulation of auxin transporters through ARF2 [START_REF] Aryal | Interplay between cell wall and auxin mediates the control of differential cell elongation during apical hook development[END_REF]. Auxin therefore controls apical hook formation through changes in cell wall chemistry, and in turn, the cell wall provides mechanochemical feedback towards auxin.

___________________________________________________________________

Chemorheological cell wall expansion

As also discussed in chapters ULVSKOV and DOBLIN in this book, much of the literature is focused on the nature of the cross-links and on how they are broken to allow relaxation of the network. In the most advanced model, in terms of experimental validation and modeling, the load-bearing network of the primary cell wall consists of cellulose microfibrils, which make lateral contacts at a small number of locations (Zhang et al. 2021). Recent studies, using AFM (atomic force microscopy), cryo-focused ion beam milling and cryo-electron tomography [START_REF] Nicolas | Cryo-electron tomography of the onion cell wall shows bimodally oriented cellulose fibers and reticulated homogalacturonan networks[END_REF], provided new insights into the cell wall architecture. These studies used the outer epidermal cell walls of onion bulbs as a model, which are up to 7 µm thick and consist of multiple lamellae, each ~40 nm thick. Each lamella consists of fields of aligned microfibrils, the overall orientation of which alternates in the successive lamellae between -45° and + 45° relative to the cell's long axis. The fibrils are surrounded by a reticulated matrix, referred to by the authors as « meshing », which consists primarily of homogalacturonan pectins. This meshing forms patches with no preferential orientation as well as segments in between the aligned fibers. Meshing was most abundant at the inner surface of the cell wall, and levels abruptly dropped off around 1 µm into the wall. AFM combined with coarse grain modeling on walls before and after stretching, showed that tensile mechanics of the cell wall are dominated by complex movements of cellulose microfibrils (bundling, sliding), with no significant contribution from the matrix (Zhang et al. 2021). At least a subset of the lateral contact sides between microfibrils are thought to be sandwiched together by tightly-bound XG chains (at least in non-Commelinoid species) (see chapter DOBLIN for a description of the cell wall polysaccharides). The latter cross-links were referred to as "biomechanical hotspots" [START_REF] Cosgrove | Diffuse growth of plant cell wall[END_REF]. The existence of a XG fraction closely associated with cellulose was shown by [START_REF] Pauly | Molecular domains of the cellulose/xyloglucan network in the cell walls of higher plants[END_REF] and later by Vissenberg et al. (2005), who used an in vivo XG-endotransglycosylase (XET) assay, in which fluorescently labelled XG-oligosaccharides are covalently incorporated into existing XG by XET action. Upon removal of these incorporated XGoligosaccharides by a XG-specific β-endoglucanase (XEG), a substantial portion of the XG remained in the cell wall, suggesting that they were in close contact with cellulose and hence protected against XEG enzyme action. The existence of such hybrid XGcellulose structures, recalcitrant to XEG-treatment, was later confirmed by the discovery of a class of specialized fungal β-endoglucanases (members of the glycosyl hydrolase family 12, which is absent in plants) that specifically removes these structures while leaving the bulk of the "unprotected" XG intact [START_REF] Park | A revised architecture of primary cell walls based on biomechanical changes induced by substrate-specific endoglucanases[END_REF]. If pathogenic fungi have evolved such highly specialized enzymes, one can expect that the structures that they target have some critical role in the cell wall's architecture. Interestingly, Cosgrove and colleagues indeed showed that this class of β-endoglucanases caused a sustained deformation (creep) of isolated cell walls in an extensometer, which was not the case for XEGs [START_REF] Park | A revised architecture of primary cell walls based on biomechanical changes induced by substrate-specific endoglucanases[END_REF], such as those used by Vissenberg et al. (2005). In an elegant series of experiments using AFM, they could also show at the nanoscale that these fungal enzymes promoted the relaxation of stressed walls by removing connections between individual microfibrils (Zhang et al. 2017). The same group also identified expansins as endogenous creep-promoting proteins, suggesting that they also disrupt these biomechanical hotspots, but through a poorly understood, non-enzymatic mechanism [START_REF] Mcqueen-Mason | Two endogenous proteins that induce cell wall extension in plants[END_REF]Wang et al. 2013).

Interestingly, expansin activity requires low pH (≤ 5), consistent with the acid growth theory. Expansins also promote cell expansion of intact cells (see references in [START_REF] Marowa | Expansins: roles in plant growth and potential applications in crop development[END_REF])), as shown by ectopic administration on tomato apical meristems [START_REF] Pien | local expression of expansin induces the entire process of leaf development and modifies cell shape[END_REF] or by overexpression in Arabidopsis stems and rosettes [START_REF] Cho | Altered expression of expansin modulates leaf growth and pedicel abscission in Arabidopsis thaliana[END_REF][START_REF] Goh | Variable expansin expression in Arabidopsis leads to different growth responses[END_REF]). An essential in vivo role for expansins in cell elongation was pinpointed by the demonstration that root hair growth was reduced in loss-of-function mutants for the root hair-specific expansin OsEXPA17 in rice (ZhiMing et al. 2011) or in RNAi lines for AtEXPA7 in Arabidopsis [START_REF] Liao | Root hair-specific EXPANSIN A7 is required for root hair elongation in Arabidopsis[END_REF], that leaves and petioles were smaller and often twisted in antisense lines for AtEXPA10 [START_REF] Cho | Altered expression of expansin modulates leaf growth and pedicel abscission in Arabidopsis thaliana[END_REF], that pollen tube growth was reduced in double atexpa4/atexpb5 mutants and that the root meristem size was reduced in a mutant for AtEXPA4 [START_REF] Liu | Two expansin genes, AtEXPA4 and AtEXPB5, are redundantly required for pollen tube growth and AtEXPA4 is involved in primary root elongation in Arabidopsis thaliana[END_REF].

It should be noted that creep measurements in general are carried out on isolated and often heat-inactivated fragments from cucumber or Arabidopsis hypocotyls, mungbean epicotyls, oat coleoptiles or the above mentioned onion peels [START_REF] Suslov | Cell wall expansion as viewed by the creep method[END_REF]. The cells in these tissues are unique in that cell expansion occurs uncoupled from cell wall deposition, perhaps as an adaptation allowing rapid growth. Indeed, the outer epidermal cell walls of young cells are multilayered and very thick (> 1µm, up to 7 µm for onion cell walls) (Zhang et al. 2021;[START_REF] Suslov | Onion epidermis as a new model to study the control of growth anisotropy in higher plants[END_REF], in comparison to much thinner walls (35 to 50 nm) described for instance for anticlinal cell walls of pavement cells [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]. A study using Arabidopsis hypocotyls showed that such thick walls are deposited during a slow growth phase, after which they undergo significant thinning during a rapid growth phase [START_REF] Refrégier | Interaction between wall deposition and cell elongation in dark-grown hypocotyl cells in Arabidopsis[END_REF]). The use of such tissues has allowed the assessment of the remodeling capacity of multilayered walls without having to worry about the replenishment of new cell wall material. The observation of the uncoupling of wall synthesis and cell elongation led Bonner to conclude in 1934 [START_REF] Bonner | Studies on the growth hormone of plants. V. The relation of cell elongation to cell wall formation[END_REF]) "Increase of wall area due primarily to active intussusception of new material is therefore excluded, at least in the case of the Avena coleoptile.". Subsequent studies using similar materials were often less careful in avoiding extrapolation to plant cell expansion in general.

Indeed, the problem is more complex for the majority of expanding cell walls, in which wall deposition and cell expansion are tightly coupled. This is illustrated by the anticlinal (perpendicular to the organ surface) walls of Arabidopsis epidermal pavement cells, which showed, on cryo-Scanning Electron Microscopy (SEM) sections, a thickness of 35 to 50 nm on each side of the middle lamella [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]. Such walls can thus accommodate not more than a single cellulose layer (estimated to have a thickness of around 40 nm as determined by Field Emission Scanning Electron Microscopy (FESEM) and AFM in dried onion cell walls [START_REF] Wang | A comparative genome analysis of PME and PMEI families reveals the evolution of pectin metabolism in plant cell walls[END_REF] or a few cellulose layers, if we assume that these walls have a denser architecture than onion outer cell walls. As discussed below, expansion of such walls cannot occur without a continuous insertion of new wall material.

Very few studies have addressed in plants how new cell wall material is inserted into the structure and how critical cross-links are formed. [START_REF] Ray | Radioautographic study of cell wall deposition in growing plant cells[END_REF] fed oat coleoptile segments with Glucose-H 3 in the presence or absence of auxin and used electron microscope radio-autography to observe in which parts of the cell wall cellulose and matrix polysaccharides were incorporated. Consistent with the more recent observation of the activity of cellulose synthase complexes in the plasma membrane [START_REF] Mcfarlane | The cell biology of cellulose synthesis[END_REF], they observed that cellulose was deposited close to the plasma membrane, whereas hemicellulose also penetrated into deeper cell layers. [START_REF] Anderson | Metabolic click-labeling with a fucose analog reveals pectin delivery, architecture, and dynamics in Arabidopsis cell walls[END_REF] used click chemistry upon feeding Arabidopsis seedlings with alkynylated fucose to show the incorporation of newly synthesized polymers, presumably fucose-containing rhamnogalacturonan I (RG-I), into the outer cell wall of root epidermis cells. They observed deposits of the polymer aligned with cellulose microfibrils and reorientation of these polymers associated with cell elongation consistent with the multinet growth theory by [START_REF] Roelofsen | Architecture and growth of the primary cell wall in some plant hairs and in the phycomyces sporangiophore[END_REF], the above mentioned AFM observations by Zhang et al (2017) and the results from coarse grain modeling (Zhang et al. 2021). More detailed observations were reported for the Charophyte Chara corallina [START_REF] Boyer | Enzyme-less growth in Chara and terrestrial plants[END_REF].

Charophytes are freshwater green algae, which descended from a common ancestor with land plants [START_REF] Derksen | Wall architecture with high porosity is established at the tip and maintained in growing pollen tubes of Nicotiana tabacum[END_REF]). This proximity is reflected in a very similar composition of the cell walls [START_REF] Popper | Evolution and diversity of plant cell walls: from algae to flowering plants[END_REF]. In Chara, calcium-pectate cross-links rather than XG-cellulose bonds appear to be the load-bearing structures of the cell wall [START_REF] Boyer | Enzyme-less growth in Chara and terrestrial plants[END_REF]. A large body of evidence shows that these cell walls expand as a result of the insertion of pectate, which chelates calcium from load-bearing bonds, thus causing the relaxation of the cell wall and the formation of new load-bearing bonds. It should be noted that in this system, the insertion of new wall material is sufficient to promote wall expansion, which is reminiscent of intussusception (Figure 1B). The difference, however, is that in Dumais' view, the flexible pectin only adopts its structure by occupying the void created upon the turgor-driven relaxation of the cell wall network after removal of load-bearing cross-links [START_REF] Dumais | Modes of deformation of walled cells[END_REF]) and hence does not orient the deformation like the insertion of new material in bacterial cell walls for instance.

In what follows we will first discuss the role of pectin metabolism in cell expansion and then compare models for cell wall expansion in tip-growing and diffusely growing cells.

Pectin structure-function relationships, the tip of the iceberg ?

As discussed in detail in chapter MOHNEN in this book, pectins are characterized by the presence of galacturonic acid (GalA) and constitute the most diverse family of cell wall polysaccharides in plants. Among those, HG, a linear polymer of α-1,4-linked GalA is, in many cell types of non-Commelinoid species, the most abundant cell wall polymer.

For instance, it represents 20% of the cell wall dry mass in Arabidopsis leaf tissue [START_REF] Zablackis | Characterization of the cell-wall polysaccharides of Arabidopsis thaliana leaves[END_REF] and even over 50% in the outer walls of the onion epidermis [START_REF] Wilson | Saccharide analysis of onion outer epidermal walls[END_REF]. HGs are found as part of different block-copolymers (HG-RG-I, HG-xylogalacturonan, HG-RG-II the proteoglycan ARABINOXYLAN PECTIN ARABINOGALACTAN PROTEIN1 (APAP1; [START_REF] Tan | An Arabidopsis cell wall proteoglycan consists of pectin and arabinoxylan covalently linked to an arabinogalactan Protein[END_REF])) and perhaps also as homogeneous independent HG polymers. The function of this structural modularity is not understood in most cases.

HGs are unique in the plant cell wall in that their charge patterns are precisely regulated. Indeed, they are thought to be secreted in a methylesterified form to become selectively de-esterified by cell wall-associated pectin methylesterases (PMEs) (see MOHNEN for a detailed discussion on HG methylesterification). This generates negatively charged residues in the polymer at pH values above the pKa of the polymer (which can range from 3.5 to 5 depending on its charge density [START_REF] Ralet | Enzymatcally and chemically de-esterified lime pectins: physico-chemical characterisation, polyelectrolyte behaviour and calcium binding properties[END_REF].

Why does polymer charge matter that much? Firstly, anionic polymers, such as pectins but also glucuronated AGPs [START_REF] Lopez-Hernandez | Calcium binding by arabinogalactan polysaccharides is important for normal plant development[END_REF], trap counterions and thus may affect the apoplastic pH, the proton motive force and ion currents across the plasma membrane [START_REF] Grignon | pH and ionic conditions in the apoplast[END_REF][START_REF] Sentenac | A model for predicting ionic equilibrium concentrations in cell walls[END_REF], which control turgor and morphogenesis [START_REF] Weisenseel | Ionic currents as control mechanism in cytomorphogenesis. In Cytomorphogenesis in Plants[END_REF][START_REF] Hoffmann | Plasmamembrane H + -ATPases sustain pollen tube growth and fertilization[END_REF]). In addition, pectins, like many other polymers, form cross-linked networks that contain water in their interstices. The water retention capacity increases dramatically with increasing polymer charge, going from water-polymer ratios of 5:1 for uncharged polymers, up to 3000:1 for charged polymers [START_REF] Osada | Stimuli-responsive polymer gels and their application to chemomechanical systems[END_REF]. To understand this, one should keep in mind that the volume of an ionized polymer gel is determined by its osmotic pressure, which is the sum of three forces: (i) the rubber elasticity, (ii) the polymer-polymer affinity and (iii) the counterion pressure (Tanaka 1981). The rubber elasticity derives from the elasticity of the individual polymer strands. The magnitude of this pressure depends on the temperature, whereas the sign depends only on the volume of the gel (positive for a condensed gel, with polymer ends held close together or negative for a swollen gel, with polymer ends stretched far apart). The polymerpolymer affinity depends on the solubility of the polymers. Poor solubility will tend to draw polymers together creating a negative pressure. This pressure is temperature insensitive and decreases with increasing gel volume. The counterion pressure is the osmotic pressure resulting from counterions sequestered by the polymer's charges (Donnan effect). This pressure increases with temperature and is positive, since it tends to draw water into the polymer's interior and push its exterior parts away from one another. Changes in the "environment" (temperature, pH, ionic strength, calcium concentration, mechanical stresses, etc) of the gel will affect the three parameters in independent and often discontinuous ways. For instance, increasing the temperature will increase the osmotic pressure of the gel due to the increased rubber elasticity and counterion pressure. The resulting volume increase will lead to a decrease in polymerpolymer affinity, which, beyond a certain threshold, will again be counteracted by the negative pressure due to the stretching of the polymers. This leads to complex emergent behaviors, including discontinuous changes in volume (phase transitions) in response to even minute changes in the "environment" or the composition of the gel (Tanaka 1981) (Figure 2A,B). So it is easy to understand how even subtle chemical changes (e.g. de-methylesterification, de-acetylation, polymer cleavage) that affect one or more of these three parameters, can strongly affect the hydration capacity of the gel and hence that of the cell wall.

This idea is nicely illustrated by studies of the mucilage that is released from the Arabidopsis seed coat upon seed imbibition. The released portion of the mucilage is a hydrogel consisting mainly of RG-I (Šola et al. 2019). Genetic studies showed that the removal of one or more galactose residues from a RG-I side chain by the βgalactosidase MUM2 is essential for mucilage release [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a beta-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF]). The authors provided evidence that galactoses in RG-I side chains, when oxidized by a putative galactose oxidase, encoded by the RUBY gene, are able to form hemi-acetal cross-links with neighboring sugars during dehydration (Šola et al. 2019). Mucilage swelling therefore appears to depend on preventing cross-linking through the enzymatic removal of galactose residues from RG-I side chains.

To understand the in vivo function of pectins, it should be kept in mind that their concentration in the cell wall is an order of magnitude higher than in the gels used in most in vitro physicochemical studies. Such concentrated gels can have tensile moduli close to those of plant cell walls (Zsivanovits et al. 2004), suggesting that, besides cellulose, pectins can significantly contribute to the mechanical properties of the cell wall. In addition, uni-axially oriented HG chains can form crystalline fibrils. This was shown in vitro using X-ray diffraction on oriented HG preparations of high Degree of Methylesterification (DM), gelified at low pH in the presence of sucrose, or calcium cross-linked low DM HG, where the two types of fibrils showed different crystal units [START_REF] Palmer | An X-ray diffraction investigation of pectinic and pectic acids[END_REF][START_REF] Sterling | Structure of oriented gels of calcium polyuronates[END_REF]Walkinshaw andArnott 1981a, 1981b). Pectin fibrils were also shown to exist in vivo (Figure 3). For instance, electron microscopy and X-ray diffraction revealed predominantly axially oriented pectin fibrils in fresh collenchyma cell walls of Petasites vulgaris petioles (Roelofsen and Kreger 1951) (Figure 3A). "Noncellulosic fibrillar galacturonic acid" was also observed in vivo, pointing out from the cell wall into the extracellular medium of liquid plant cell cultures [START_REF] Leppard | Lignofibrils on the external cell wall surface of cultured plant cells[END_REF] (Figure 3B), in the inner (cytoplasmic-facing) cell wall surface of these cells, or in root epidermal cell walls (Figure 3C). These structures with a diameter in the order of 20 nm, were initially christened "lignofibrils", due to their weak UV absorption properties and Phloroglucinol-HCl staining. The UV absorption, however, could, besides lignin, also come from tyrosine-rich proteins such as polycationic extensin-related proteins, which can form polyelectrolyte complexes with pectate [START_REF] Cannon | Self-assembly of the plant cell wall requires an extensin scaffold[END_REF]Valentin et al. 2010). This may go some way to explain why these fibres were reported to be largely resistant to pectinases [START_REF] Leppard | Lignofibrils on the external cell wall surface of cultured plant cells[END_REF]). Pectin fibrils were also observed in the lumen of poplar xylem fiber cells [START_REF] Arend | Unique occurrence of pectin-like fibrillar cell wall deposits in xylem fibres of poplar[END_REF]) (Figure 3D). More recently, superresolution microscopy revealed uni-axially oriented HG in the anticlinal cell walls of pavement cells in the Arabidopsis epidermis [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]) Figure 3E). The significance of this for cell expansion will be discussed below.

A last, so far poorly explored, aspect relevant for the regulation of cell expansion is how substitution and charge patterns of HGs may govern interactions with other polysaccharides or proteins. Well-studied examples for other polysaccharides are the periodic (glucuronic acid (GlcA), me-GlcA or acetyl) substitution patterns on xylan backbones that condition cellulose binding [START_REF] Grantham | An even pattern of xylan substitution is critical for interaction with cellulose in plant cell walls[END_REF] or, in the animal extracellular matrix, the sulfate substitution patterns of the glucoronoaminoglucan heparin that govern, often highly specific, interactions with proteins [START_REF] Capila | Heparin-protein interactions[END_REF]. HGs can also be acetylated or xylosylated (at position 2 or 3) and can have random or blockwise charge patterns. In addition, specific repeated substitution patterns (such as GalA4MeAc) could be inferred from the profiling of oligogalacturonides released from the cell wall by a fungal pectate lyase (Voxeur et al. 2019). Such patterns are the hallmarks of specific PME activities, which remain to be characterized.

PMEs are encoded by large gene families (66 members in Arabidopsis thaliana) and, in vascular plants, PME activity can be modulated by endogenous proteinaceous PME inhibitors (PMEIs), which are encoded by equally large families (71 in A. thaliana) [START_REF] Wolf | Homogalacturonan methyl-esterification and plant development[END_REF]Wang et al. 2013). In addition, demethylation exposes the HG to the activity of endogenous polygalacturonases (PGs) and pectate lyases (PLs), which require demethylated substrates [START_REF] Hocq | Connecting homogalacturonan-type pectin remodeling to acid growth[END_REF]. The few plant PMEs that have been studied so far have neutral to basic pH optima and processive activities, generating blockwise charge patterns. At least some of these PMEs can loose processivity in certain conditions (low pH [START_REF] Hocq | Arabidopsis AtPME2 has a pH-dependent processivity and control cell wall mechanical properties[END_REF] or in the presence of Ca 2+ (Vincent et al.

2013)) thus generating non-clustered patterns. It will be interesting to see to what extent

HG charge and substitution patterns can govern interactions with cell wall proteins. A recent study [START_REF] Francoz | Pectin Demethylesterification generates platforms that anchor peroxidases to remodel plant cell wall domains[END_REF]) revealed that a specific PMEI (PMEI6) is required for the generation of a binding site for a cell wall peroxidase (PRX36), presumably by altering the activity of an unknown PME, at a specific location within the outer cell wall of the Arabidopsis seed coat. At this specific location, the peroxidase changes the cell wall properties generating brittle spots that selectively rupture upon hydration, facilitating the release of the seed mucilage. Many other cell wall proteins have basic surfaces and bind to pectins as shown in vitro [START_REF] Carpin | Identification of a Ca 2+ -pectate binding site on an apoplastic peroxidase[END_REF][START_REF] Jamet | Isolation of plant cell wall proteins. In 2D PAGE: Sample preparation and fractionation[END_REF] and in vivo [START_REF] Wang | Cellulose-pectin spatial contacts are inherent to never-dried Arabidopsis primary cell walls: evidence from solid-state nuclear magnetic resonance[END_REF]. This is expected to contribute not only to the nanoscale distribution of cell wall modifying activities, but also to the formation of polyelectrolyte complexes that may also locally impact the hydration, porosity and rheology of cell walls. For instance, the interaction with basic extensins induced the dehydration of pectin layers in vitro (Valentin et al. 2010). Similar effects can be expected from the interaction with other polycations such as endogenous polyamines [START_REF] Messiaen | Polyamines and pectins. II. Modulation of pecticsignal transduction[END_REF] or chitosan present in the walls of endophytic [START_REF] Noorifar | Chitin deacetylases are required for Epichloë festucae endophytic cell wall remodeling during establishment of a mutualistic symbiotic interaction with Lolium perenne[END_REF] or pathogenic fungi [START_REF] Baker | Chitosan, the deacetylated form of chitin, is necessary for cell wall integrity in Cryptococcus neoformans[END_REF].

Tip growth

Tip growth is mainly studied in pollen tubes and root hairs. As such, there is much literature dealing with discoveries in both cell systems. It has been known since 1897 that growing pollen tubes contain moving granular protoplasm [START_REF] Potter | Streaming movements of the protoplasm in pollen of flowers[END_REF]. Years later, [START_REF] Castle | The topography of tip growth in a plant cell[END_REF]) concluded that the apical regions of tip growing cells may have the highest relative elemental rates of elongation known. Following this, the oldest models of tip growth zone activities were developed by [START_REF] Green | Morphogenesis of the cell and organ axis-biophysical models[END_REF], while in the same period electrophysiological experiments showed that calcium enters the growing pollen tube tip, with other positive ions, mainly protons, leaving at the more basal region [START_REF] Weisenseel | Large electrical currents traverse growing pollen tubes[END_REF]. The importance of calcium was backed up with the visualization of an internal Ca 2+ -gradient in pollen tubes [START_REF] Jaffe | Calcium accumulations within the growing tips of pollen tubes[END_REF]) and the observations that raising calcium in the tubes leads to growth arrest, but not of cell wall buildup, resulting in a thicker cell wall [START_REF] Picton | Evidence for the role of Ca 2+ ions in tip extension in pollen tubes[END_REF] while its deprivation or the use of a calcium-channel blocker results in localized swelling at the tube tip [START_REF] Reiss | Nifedipine-sensitive calcium channels are involved in polar growth of Lily pollen tubes[END_REF]. Later on [START_REF] Li | Distribution of unesterified and esterified pectins in cell walls of pollen tubes of flowering plants[END_REF]) observed a periodically arranged pattern of esterified and unesterified pectin in pollen tubes, which was linked to growth velocity fluctuations by [START_REF] Pierson | Tiplocalized calcium entry fluctuates during pollen tube growth[END_REF]. Further correlations between the oscillations of pollen tube growth, and those of calcium-ions and protons were described by [START_REF] Pierson | Tiplocalized calcium entry fluctuates during pollen tube growth[END_REF][START_REF] Feijó | Growing pollen tubes possess a constitutive alkaline band in the clear zone and a growth-dependent acidic tip[END_REF], respectively. In the early years of the 21st century, localized cell wall remodeling by expansin and XTH in tip-growing root hairs was shown by [START_REF] Baluška | Root hair formation: F-actin-dependent tip growth is initiated by local assembly of profilin-supported F-actin meshworks accumulated within expansinenriched bulges[END_REF] and Vissenberg et al. (2001), while the discovery that Rapid Alkalinization Factors (RALFs) regulate extracellular pH and growth of root hairs [START_REF] Wu | NaRALF, a peptide signal essential for the regulation of root hair tip apoplastic pH in Nicotiana attenuata, is required for root hair development and plant growth in native soils[END_REF]) opened up the findings that members of the Catharanthus roseus superfamily of receptor-like kinases (RLKs) control cell wall integrity at the pollen tube tip [START_REF] Boisson-Dernier | Disruption of the pollen-expressed FERONIA homologs ANXUR1 and ANXUR2 triggers pollen tube discharge[END_REF]) and in root hairs [START_REF] Duan | FERONIA receptor-like kinase regulates RHO GTPase signaling of root hair development[END_REF]. Only in 2018, [START_REF] Schoenaers | The auxinregulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth[END_REF] made a link between cell wall integrity sensing by one of these RLKs, ERULUS (ERU), and the oscillations of cell wall pectin methylesterification grade and the resulting growth of root hairs.

Like in Chara, pectin insertion thus also appears to drive the expansion of tip-growing pollen tubes and root hairs. In such cells, growth is restricted to the extreme apex and depends on the fusion of vesicles containing new cell wall material with the apical plasma membrane [START_REF] Bove | Magnitude and direction of vesicle dynamics in growing pollen tubes using spatiotemporal image correlation spectroscopy and fluorescence recovery after photobleaching[END_REF][START_REF] Ketelaar | Rates of exocytosis and endocytosis in Arabidopsis root hairs and pollen tubes[END_REF][START_REF] Balcerowicz | Cell fate determination and the switch from diffuse growth to planar polarity in Arabidopsis root epidermal cells[END_REF]. This results in polar growth that is highly responsive to local changes in the cell's environment [START_REF] Schoenaers | Molecular mechanisms regulating root hair tip growth: a comparison with pollen tubes[END_REF].

Valuable insights into growth mechanisms in these cells came from the observation of growth rate oscillations, which, as detailed below, are accompanied by oscillations with the same temporal or spatial frequency as a number of other cellular parameters [START_REF] Kroeger | The pollen tube paradigm revisited[END_REF][START_REF] Damineli | Oscillatory signatures underlie growth regimes in Arabidopsis pollen tubes: computational methods to estimate tip location, periodicity, and synchronization in growing Cells[END_REF]). These include exocytosis rate, cell wall modification and thickness, Rho-like GTPase (ROP) activity, apical F-actin presence, cytoplasmic pH and calcium gradients, apoplastic pH and Reactive Oxygen Species (ROS) levels [START_REF] Hepler | Polarized growth in higher plants[END_REF][START_REF] Hwang | Pollen-tube tip growth requires a balance of lateral propagation and global inhibition of Rho-Family GTPase activity[END_REF][START_REF] Yan | Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes[END_REF][START_REF] Schoenaers | Molecular mechanisms regulating root hair tip growth: a comparison with pollen tubes[END_REF]. Such oscillations are also reflected in the periodic cell wall deposition patterns that were reported in tobacco pollen tubes [START_REF] Geitmann | Ultrastructural immunolocalization of periodic pectin depositions in the cell wall of Nicotiana tabacum pollen tubes[END_REF][START_REF] Derksen | Wall architecture with high porosity is established at the tip and maintained in growing pollen tubes of Nicotiana tabacum[END_REF][START_REF] Mckenna | Exocytosis precedes and predicts the increase in growth in oscillating pollen tubes[END_REF] monitored PME-GFP levels in the cell wall of pollen tubes, as a marker for exocytosis. They concluded that exocytosis oscillates with the growth rate, where peaks in exocytosis precede periodic growth bursts. (A critical note here is that GFP is less fluorescent at lower pH [START_REF] Kneen | Green Fluorescent Protein as a noninvasive intracellular pH indicator[END_REF]), hence PME-GFP fluorescence oscillations might also reflect apoplastic pH oscillations). Cell wall thickness was also shown to oscillate, also with its maxima preceding the growth rate maxima (Figure 4A). Interestingly, variations in the amount of deposited cell wall material correlated with the extent of the subsequent growth rate increases. This suggested that cell wall deposition determines the elongation rate of these cells [START_REF] Mckenna | Exocytosis precedes and predicts the increase in growth in oscillating pollen tubes[END_REF]) (Figure 4B), in contrast to the above mentioned "biomechanical hotspot" model for diffusely growing cells, in which cell wall deposition somehow passively follows cell wall relaxation. A role for cytosolic calcium oscillations in the control of oscillations in exocytosis, cell wall thickness and growth rate was explored in a model by [START_REF] Kroeger | Model for calcium dependent oscillatory growth in pollen tubes[END_REF].

The fusion of vesicles with the plasma membrane is controlled by members of the syntaxin family of soluble N-ethyl-maleimide sensitive factor attachment protein receptors (SNAREs; (Rodriguez-Furlán et al. 2016)), the exocyst complex [START_REF] Hála | An exocyst complex functions in plant cell growth in Arabidopsis and Tobacco[END_REF]) and in part by members of the plant ROP family. ROP activity oscillates in pollen tubes with the same frequency as tip growth oscillations [START_REF] Hwang | Pollen-tube tip growth requires a balance of lateral propagation and global inhibition of Rho-Family GTPase activity[END_REF], and its apical location depends on the action of ROP1 ENHANCERs (RENs), proteins that are located sub-apically and help to remove ROPs from the plasma membrane using clathrin-mediated endocytosis [START_REF] Li | The REN4 rheostat dynamically coordinates the apical and lateral domains of Arabidopsis pollen tubes[END_REF]). ROPs interact with diverse effectors and mediate actin dynamics, microtubule organization (and thus vesicle trafficking, reviewed in [START_REF] Nibau | RAC/ROP GTPases: 'hubs' for signal integration and diversification in plants[END_REF][START_REF] Yalovsky | Regulation of membrane trafficking, cytoskeleton dynamics, and cell polarity by ROP/RAC GTPases[END_REF]), ROS production [START_REF] Carol | A RhoGDP dissociation inhibitor spatially regulates growth in root hair cells[END_REF]) and the formation of a tip-focused Ca 2+ gradient [START_REF] Li | Control of pollen tube tip growth by a Rop GTPase-dependent pathway that leads to tip-localized calcium influx[END_REF], and are therefore considered as 'hubs' for signal integration during tip growth.

The requirement of pectin deposition for proper tip growth was suggested by the observation that root hair growth was inhibited in mutants (for two distinct UDP-GalA biosynthetic enzymes) with reduced pectin levels [START_REF] Pang | Comparative proteomics indicates that biosynthesis of pectic precursors is important for cotton fiber and Arabidopsis root hair elongation[END_REF] or in WT upon pectate lyase treatment [START_REF] Park | A role for CSLD3 during cell-wall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF]. Next to deposition, PME-driven pectin modification (see Box 2) is also critical for pollen tube and root hair growth. In pollen tubes, PME activity is essential for growth, as shown by the curved, irregularly shaped and stunted pollen tubes with reduced elongation rates upon inactivation of PPME1 or VANGUARD1 (VGD1), which both encode pollen-specific PMEs (Tian et al. 2006;[START_REF] Jiang | VANGUARD1 encodes a pectin methylesterase that enhances pollen tube growth in the Arabidopsis style and transmitting tract[END_REF]. The involvement of PME activity in proper tip growth of pollen tubes was modeled using Finite Element Modeling (FEM) and also experimentally validated [START_REF] Fayant | Finite Element Model of polar growth in pollen tubes[END_REF]. In root hairs, genetic validation for a role of PME activity in elongation awaits the identification of pme-mutants with a root hair phenotype, but [START_REF] Schoenaers | The auxinregulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth[END_REF] were already able to show that inhibiting PME activity with a catechin extract also affected root hair growth. Interestingly PME activity also appears to oscillate in the tip of growing root hairs [START_REF] Schoenaers | The auxinregulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth[END_REF] or pollen tubes [START_REF] Rounds | Propidium iodide competes with Ca 2+ to label pectin in pollen tubes and Arabidopsis root hairs[END_REF]. This was shown by the oscillations in the staining intensity of propidium iodide, a dye that binds to anionic pectin. These oscillations may mirror oscillations in PME activity, which, given the high pH optimum of the bulk of PME activity [START_REF] Hocq | Connecting homogalacturonan-type pectin remodeling to acid growth[END_REF], is expected to be controlled by the oscillations in surface pH, reported for pollen tubes [START_REF] Hepler | Ions and pollen tube growth[END_REF]) and root hairs [START_REF] Monshausen | Oscillations in extracellular pH and reactive oxygen species modulate tip growth of Arabidopsis root hairs[END_REF] (Box 2).

In line with this, the activity of most other cell wall modifying enzymes is also highly pHdependent. The activity of expansins is promoted in an acidic environment [START_REF] Mcqueen-Mason | Two endogenous proteins that induce cell wall extension in plants[END_REF]), whereas recombinantly-produced XG endo-transglycosylasehydrolases (XTHs) show widely diverging pH optima [START_REF] Maris | Enzymic characterization of two recombinant xyloglucan endotransglucosylase/hydrolase (XTH) proteins of Arabidopsis and their effect on root growth and cell wall extension[END_REF][START_REF] Maris | Characterization of five recombinant xyloglucan endotransglucosylase/hydrolase (XTH) proteins of Arabidopsis reveals specific enzymatic properties[END_REF].

Recombinant pectate lyases have alkaline pH optima [START_REF] Ali | Structural insights into the loss of catalytic competence in pectate lyase activity at low pH[END_REF], while polygalacturonases are more active at acidic pH [START_REF] Hocq | Connecting homogalacturonan-type pectin remodeling to acid growth[END_REF]. In this respect, it needs to be mentioned that in alkaline conditions, PME activity on methylesterified pectin generates protons, and hence contributes to cell wall acidification [START_REF] Moustacas | Pectin methylesterase: metal ions and plant cell wall extension. The role of metal ions in plant cell wall extension[END_REF], in concert with plasma membrane-localised H + -ATPases (AHAs). In pollen tubes, AHAs are specifically localized in the shank and they have been shown to be the drivers for cytosolic pH oscillations [START_REF] Hoffmann | Plasmamembrane H + -ATPases sustain pollen tube growth and fertilization[END_REF]. Indeed, mutants in AHAs show reduced H + and anion fluxes around the pollen tube tip, slower cytosolic pH oscillations, shallower cytosolic pH gradients and reduced growth rates. Root hair and pollen tube elongation therefore seem to be in line with the acid growth theory (Box 3) [START_REF] Rayle | The acid growth theory of auxin-induced cell elongation is alive and well[END_REF], where cell wall pH oscillations cause periodic activation of PMEs at high pH in antiphase with the activation of expansins at low pH [START_REF] Cosgrove | Loosening of plant cell walls by expansins[END_REF].

Based on the calcium-pectate exchange mechanism previously proposed for Chara, [START_REF] Rojas | Chemically mediated mechanical expansion of the pollen tube cell wall[END_REF]) developed a computational model for pollen tube growth (Figure 4C). This model posits that cell wall deposition promotes cell elongation and that cell elongation inhibits cell wall deposition through a negative feedback loop. It also implies that cell expansion ceases when all available pectin is incorporated into the loadbearing cell wall layer and no new material is available. This model was able to predict pollen tube shape, trajectories of cell wall material at the growing surface and even growth oscillations, which occur above a certain elongation rate, where cell expansion outruns cell wall deposition. The model clearly indicates that in the case of tip-growing cells, wall expansion is limited by deposition and/or insertion of material. Evidently, turgor pressure provides the driving force for growth also in this model [START_REF] Kroeger | Regulator or driving force? The role of turgor pressure in oscillatory plant cell growth[END_REF][START_REF] Dumais | Mechanics and hydraulics of pollen tube growth[END_REF].

The calcium-pectate exchange model does not address the role in tip growth of cellulose-XG remodeling described in the biomechanical hotspot model. As discussed below, however, this cannot be ignored given the strong root hair growth phenotypes of mutants for cellulose or XG synthesis or expansins.

Cellulose deposition is essential for maintaining cell wall integrity as shown by the growth inhibition and/or rupture of root hairs treated with a cellulase or the cellulose synthesis inhibitor 2,6-dichlorobenzonitrile (DCB) [START_REF] Park | A role for CSLD3 during cell-wall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF]. Mutant analysis and localization experiments suggest that proteins other than those involved in cellulose synthesis in primary walls (CESA1, CESA3 and CESA6) synthesize cellulose at the root hair tip [START_REF] Endler | Cellulose synthases and synthesis in Arabidopsis[END_REF][START_REF] Park | A role for CSLD3 during cell-wall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF]. CELLULOSE SYNTHASE LIKE (CSL)D2 and CSLD3 (KOJAK) are likely candidates. Indeed their mutants produce abnormal root hairs that rupture early [START_REF] Favery | KOJAK encodes a cellulose synthase-like protein required for root hair cell morphogenesis in Arabidopsis[END_REF] or late [START_REF] Bernal | Functional analysis of the cellulose synthase-like genes CSLD1, CSLD2, and CSLD4 in tip-growing Arabidopsis cells[END_REF] during development or which show a swollen base, wavy growth or occasional branches. Evidence for a role of CSLD3 in cellulose synthesis came from the observation that a chimeric gene encoding CSLD3 with the catalytic domain of CESA6 complemented the csld3/kjk root hair phenotype [START_REF] Galway | Root hair-specific disruption of cellulose and xyloglucan in AtCSLD3 mutants, and factors affecting the post-rupture resumption of mutant root hair growth[END_REF][START_REF] Park | A role for CSLD3 during cell-wall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF].

In addition, recent data confirmed that CSLD3 is indeed a UDP-glucose-dependent (1-4)-β-glucan synthase that can be purified as higher-order complexes with similar ultrastructural features as those formed by CESA6 proteins [START_REF] Yang | Biochemical and genetic analysis identify CSLD3 as a beta-1,4glucan synthase that functions during plant cell wall synthesis[END_REF]. The fact that CSLDs are active where plasma membrane-associated cortical microtubules are generally absent (in the root hair tip or at the new cell plate), suggests that they contribute to the production of cellulose structures different from the long microfibrils generated by microtubule-associated cellulose synthase complexes. It will be interesting to see whether the shorter disordered cellulose-like fibrils that can be observed in the tip of growing root hairs are produced by CLSD complexes [START_REF] Akkerman | Texture of cellulose microfibrils of root hair cell walls of Arabidopsis thaliana, Medicago truncatula, and Vicia sativa[END_REF]Newcomb and Bonnet 1965).

Xyloglucan is also essential for root hair growth. Indeed, mutants for XG 6-XYLOSYLTRANSFERASES (XXTs) (xxt1/xxt2, xxt1/xxt2/xxt5) lack detectable XG and have short root hairs with swollen bases [START_REF] Cavalier | Disrupting two Arabidopsis thaliana xylosyltransferase genes results in plants deficient in xyloglucan, a major primary cell wall component[END_REF][START_REF] Cavalier | Disrupting two Arabidopsis thaliana xylosyltransferase genes results in plants deficient in xyloglucan, a major primary cell wall component[END_REF].

Disruption of the synthesis of a GalA-containing XG (in the ROOT HAIR SPECIFIC8/ XYLOGLUCAN-SPECIFIC GALACTURONOSYLTRANSFERASE1 (RHS8/XUT1) mutant) results in shorter root hairs [START_REF] Peña | A galacturonic acid-containing xyloglucan is involved in Arabidopsis root hair tip growth[END_REF], which, however, do not rupture.

The same is true for root hairs treated with a xyloglucanase [START_REF] Park | A role for CSLD3 during cell-wall synthesis in apical plasma membranes of tip-growing root-hair cells[END_REF].

Expansins are also required for normal root hair growth as shown by the shorter root hair phenotypes of RNAi lines for EXPANSIN A7 (EXPA7) in Arabidopsis [START_REF] Liao | Root hair-specific EXPANSIN A7 is required for root hair elongation in Arabidopsis[END_REF], or an OsEXPA17 mutant in rice (ZhiMing et al. 2011). In addition, application of expansin to growing root hairs triggered, at low concentrations, radial swelling of the tip and transient growth inhibition or, at higher concentrations, bursting [START_REF] Cosgrove | The growing world of expansins[END_REF].

XTHs act on the same cellulose/XG network. Although XG endotransglycosylase activity (XET) was observed at the tip and in the shank of root hairs (Vissenberg et al. 2000(Vissenberg et al. , 2001(Vissenberg et al. , 2003)), no xth mutants with a detectable root hair phenotype have been described so far, possibly due to redundancy.

Another critical oscillating parameter during root hair growth is the production of ROS in the apoplast. Indeed, mutations in ROOT HAIR DEFECTIVE (RHD2) encoding a plasma membrane NADPH oxidase, strongly decreased ROS accumulation and caused stunted roots with no or very short root hairs [START_REF] Foreman | Reactive oxygen species produced by NADPH oxidase regulate plant cell growth[END_REF]. Different interpretations of this phenotype have been formulated. [START_REF] Foreman | Reactive oxygen species produced by NADPH oxidase regulate plant cell growth[END_REF] proposed that extracellular ROS is required for the activation hyperpolarization-activated Ca 2+channels in the plasma membrane, which form the cytoplasmic calcium gradient that is required for root hair growth and acts in the negative feedback regulation of ROP activity [START_REF] Yan | Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes[END_REF]. [START_REF] Monshausen | Oscillations in extracellular pH and reactive oxygen species modulate tip growth of Arabidopsis root hairs[END_REF] proposed an alternative interpretation, in which the lack of root hairs in rhd2 is the result of premature bursting due to reduced apoplastic ROS levels. In this view, cell wall expansion in root hairs reflects a balancing act between growth-promoting (e.g. acid growth) and growthrestricting activities, where apoplastic ROS promotes wall strengthening through oxidative cross-linking of cell wall extensins [START_REF] Schnabelrauch | Isolation of pI 4.6 extensin peroxidase from tomato cell suspension cultures and identification of Val-Tyr-Lys as putative intermolecular cross-link site[END_REF]Velasquez et al. 2011). Support for this view comes from the observation that growth at higher pH, which slows down cell expansion, restored root hair growth in the rhd2 mutant [START_REF] Monshausen | Oscillations in extracellular pH and reactive oxygen species modulate tip growth of Arabidopsis root hairs[END_REF]). The essential role for extensins (Velasquez et al. 2011;2015a,b;[START_REF] Draeger | Arabidopsis leucine-rich repeat extensin (LRX) proteins modify cell wall composition and influence plant growth[END_REF][START_REF] Møller | Identification and evolution of a plant cell wall specific glycoprotein glycosyl transferase, ExAD[END_REF]) but also of other structural proteins such as PRP1, PRP3 [START_REF] Bernhardt | Expression of AtPRP3, a proline-rich structural cell wall protein from Arabidopsis, is regulated by cell-type-specific developmental pathways involved in root hair formation[END_REF], PRPL1 [START_REF] Boron | Proline-rich protein-like PRPL1 controls elongation of root hairs in Arabidopsis thaliana[END_REF] and AGPs [START_REF] Mollet | Arabinogalactan proteins, pollen tube growth, and the reversible effects of Yariv phenylglycoside[END_REF][START_REF] Marzec | Arabinogalactan proteins are involved in root hair development in Barley[END_REF] in cell wall assembly of root hairs was shown by genetic and pharmacological studies.

Together, these observations show that understanding tip growth requires integration of the growth-promoting "calcium-pectate exchange" and "biomechanical hotspot" models but also growth-restricting activities involving oxidative cross-linking of cell wall proteins.

Given the importance and highly dynamic character of the cell wall at the growing root hair and pollen tube tip, the status of the cell wall must be constantly monitored to prevent (premature in case of the pollen tubes) bursting of the cell. This information on cell wall status must therefore feed back to the growth-controlling processes. RLKs of the Catharanthus roseus subfamily (CrRLK1Ls), such as FERONIA (FER) [START_REF] Duan | FERONIA receptor-like kinase regulates RHO GTPase signaling of root hair development[END_REF] and ERULUS (ERU) [START_REF] Schoenaers | The auxinregulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth[END_REF], were suggested to function in the perception of cell wall status in root hairs by binding to specific cell wall ligands, and they are indeed related to growth control through activity changes of the apical plasma membrane-localized ROPs [START_REF] Molendijk | Arabidopsis thaliana Rop GTPases are localized to tips of root hairs and control polar growth[END_REF][START_REF] Jones | The Arabidopsis Rop2 GTPase is a positive regulator of both root hair initiation and tip growth[END_REF]. Our current understanding states that ligand-bound RLKs activate ROPs, which then initiate NADPH-oxidase-dependent ROS production, leading to changes in calcium-channel activity and changes in the cell wall [START_REF] Duan | FERONIA receptor-like kinase regulates RHO GTPase signaling of root hair development[END_REF]. It would be interesting to see which ligands serve as cell wall status indicators, and whether vesicle fusion and new cell wall deposition are controlled by RLK activation, especially in the light of the abovementioned calcium-pectate exchange model to explain tip growth, where RLKs could act in the control of wall deposition and expansion [START_REF] Rojas | Chemically mediated mechanical expansion of the pollen tube cell wall[END_REF][START_REF] Dumais | Mechanics and hydraulics of pollen tube growth[END_REF]. [START_REF] Schoenaers | The auxinregulated CrRLK1L kinase ERULUS controls cell wall composition during root hair tip growth[END_REF] have indeed shown that ERU is involved in the control of cell wall PME activity dynamics, since eru root hairs have elevated PME activity levels, reflected in increased de-methylesterified pectin abundance and in propidium iodide fluorescence intensity oscillations with a lower frequency and higher amplitude.

Diffuse cell expansion

In contrast to the extremely polarized expansion in tip growing cells, the growth of cells embedded in tissues is considered "diffuse", i.e. not restricted to specific subcellular locations. The distinction between tip growth and diffuse growth, however, is not always that clear [START_REF] Geitmann | Mechanics and modeling of plant cell growth[END_REF]. Indeed, the "diffuse" growth pattern can be either homogeneous or non-homogeneous, referred to as "homotropic" and "heterotropic" respectively. In the latter case, local foci with increased growth rate, reminiscent of tip growth, create irregular deformation patterns, underlying the large variety of cell shapes that can be found in plants (Figure 5). One well-studied example of heterotropic growth is that of the formation of the lobes of puzzle-shape pavement cells in the epidermis of Arabidopsis leaves or cotyledons (Figure 5A). In these cells, the appearance of inhomogeneities in cell wall deformation patterns depends, like in root hairs and pollen tubes, on ROP signaling modules, which not only promote the formation of specific membrane domains that locally organize the cytoskeleton and secretory events [START_REF] Liu | Two expansin genes, AtEXPA4 and AtEXPB5, are redundantly required for pollen tube growth and AtEXPA4 is involved in primary root elongation in Arabidopsis thaliana[END_REF]), but also other processes crucial for growth, such as protein translation (through TARGET OF RAPAMYCIN (TOR) signaling upon activation by the plant hormone auxin) [START_REF] Schepetilnikov | GTPase ROP2 binds and promotes activation of target of rapamycin, TOR, in response to auxin[END_REF].

This raises the question of how the position of these ROP domains is determined. A recent elegant study, also building upon data presented by [START_REF] Bidhendi | Mechanical stress initiates and sustains the morphogenesis of wavy leaf epidermal cells[END_REF], showed that stress patterns may provide initial positional cues [START_REF] Belteton | Real-time conversion of tissue-scale mechanical forces into an interdigitated growth pattern[END_REF].

They first used a 3D FEM model, elaborated from the observed geometry of a few epidermal cells, to show that, in developing pavement cells (Figure 5A), highest stress is found along the anticlinal (perpendicular to the surface) cell walls. Next, using time lapse imaging, the authors showed that the symmetry breaking event underlying lobe initiation was preceded by the local and transient formation of transfacial cortical microtubule bundles, facing both anticlinal and external periclinal (parallel to the surface) cell walls in the cell located at the convex site of the future lobe (Figure 5B).

Using the 3D FEM model, the site of the transfacial microtubule accumulation could be predicted from the local maxima of the mechanical stress patterns, which are the resultant of the mechanical anisotropy of the walls of the cell and the anisotropy of the supracellular stress patterns within the organ (Box 1). It has been shown that cortical (i.e. right below the plasma membrane) microtubules align with maximum stress patterns through a so far unknown mechanism [START_REF] Hamant | Are microtubules stress sensors?[END_REF]). These microtubules in turn guide the trajectories of the cellulose synthase complexes, which move in the plasma membrane while depositing stiff microfibrils. The latter reinforce the cell wall along the stress patterns thus changing the anisotropy in wall mechanics and overall stress patterns and, as a result, the orientation of surface deformation [START_REF] Hamant | Developmental patterning by mechanical signals in Arabidopsis[END_REF][START_REF] Mirabet | the role of mechanical forces in plant morphogenesis[END_REF]. Consistent with this, also in pavement cells, the microtubule bundles facing the anticlinal walls co-localized with GFP-tagged cellulose synthase complexes. The authors proposed a model in which the cellulose microfibrils deposited in the anticlinal wall of the cell at the convex side of the future lobe, create a "patch of anisotropic wall". The subsequent local anisotropic cell wall deformation, perpendicular to the microfibril orientation, would then drive lobe formation [START_REF] Belteton | Real-time conversion of tissue-scale mechanical forces into an interdigitated growth pattern[END_REF].

This study provides a nice example of how mechanical stress patterns, predicted from a geometrical model, may provide initial positional cues for local cell wall deformation patterns, which may be sharpened and reinforced by ROP-mediated feedback signaling. The study, however, also points to inconsistencies in current models for diffuse cell expansion, in particular how turgor-driven cell wall relaxation can lead to lobe formation given that adjacent cells most likely have comparable turgor pressures. This is even more striking for the formation of furrows in cells in which cell adhesion was prevented (by treatment with low doses of pectinases, removing the middle lamella, or in mutants with reduced cell adhesion). These furrows consist of closely opposed walls from the same cell connected by a widened bulb at the apex, that grow into the cell (Verger et al. 2018;[START_REF] Belteton | Real-time conversion of tissue-scale mechanical forces into an interdigitated growth pattern[END_REF]. The driving force for such ingrowths cannot be the turgor, but reflects an intrinsic capacity of the cell wall to increase its surface. A similar conclusion was drawn from the study of natural cell wall ingrowths observed in a number of cell types (Borowska-Wykret and Kwiatkowska 2018) (Figure 5C,D). The authors proposed a model in which ingrowth initiation is driven by the swelling of the matrix between the oriented microfibrils in the anticlinal cell walls, selectively on the convex side of the lobe. Finally, turgor-driven cell wall expansion is also an unlikely mechanism for the formation of Rhizobium infection threads [START_REF] Rae | Structure and growth of infection threads in the legume symbiosis with Rhizobium leguminosarum[END_REF] or fungal infection structures that progress against the turgor pressure of the host cell (Huckelhoven 2007). Here again the driving force for cell wall deformation appears to come from the insertion and expansion of cell wall material.

A potential molecular mechanism for turgor-independent cell wall deformation was suggested by a recent study on Arabidopsis pavement cells [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]). This study used super-resolution microscopy with anti-HG antibodies to reveal that HG, instead of forming an amorphous gel, can show a striking degree of organization, at least in anticlinal cell walls. Indeed, the epitopes for a subset of these antibodies (2F4, LM20 and LM19) formed filaments parallelling the cellulose microfibrils. Stacked parallel chains of HG are expected to form semi-crystalline fibrils, such as those that have been reported previously (Figure 3). Interestingly, other anti-HG antibodies (JIM7) did not reveal such filaments [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF]. This indicates that first, the observed filaments were not artifactual and second, different HG populations with a distinct mesoscale organisation must exist in the same cell wall. The study also showed a higher proportion of low/high DM HG in the wall on the convex side of the lobe. Given the abovementioned increased distance between polymers in crystals of low DM HG relative to those of high DM HG, the authors proposed a mechanism in which HG demethylesterification induces a phase transition causing the cell wall to swell. Since this occurred preferentially on one side of the cell wall, a lobe was expected to form. Indeed, lobe formation could be simulated with a FEM model based on this mechanism. The causality between PME activity, the HG phase transition and lobe formation was suggested by the inhibition of all these events by the inducible overexpression of a PMEI in transgenic Arabidopsis. In addition, inducible overexpression of a PME promoted the accumulation of low DM HG on both sides of the wall, increased the distance between fibrils observed by SEM and promoted cell expansion while preventing lobe formation. The latter was expected given the lack of asymmetry in the connected opposing cell walls.

It should be noted that lobe formation occurs during the expansion of the entire cell.

This requires differential expansion rates across an already expanding wall. If we assume that the expansion of the straight walls is also, at least in part, driven by pectin insertion and swelling, lobe formation could arise from enhanced activation of PME activity on the convex side or, perhaps more likely, from the inhibition of demethylesterification on the concave side. It will therefore be interesting to see whether the local cell wall pH differs between the two opposing cell walls at the concave and convex sides, since it would affect the activities of PMEs and other growth regulators.

Together, the study of lobe and furrow formation suggests a turgor-independent driving force for cell wall deformation based on the conversion of chemical energy into mechanical energy associated with the de-methylesterification of HG.

New food for thought

In summary, three models for cell expansion are currently being proposed in different contexts: (i) the biomechanical hotspot model for acid growth in diffusely growing cells, (ii) the Ca 2+ -pectate cross-link exchange model for Chara and tip-growing cells and (iii) the expanding pectin filament model for lobe formation in pavement cells. The question is whether these models explain cell expansion only in certain cell wall types or whether they are part of an integrated processing system in which overlapping, synergistic or antagonistic chemo-mechanical phenomena and control points might modulate cell wall expansion, with some aspects becoming dominant in some cell types/developmental stages/environmental conditions and others being completely absent in other instances.

The above discussions showed that the latter possibility is the more likely one. Indeed, we discussed the requirement for XG-cellulose cross-link removal in tip-growing root hairs, in addition to Ca 2+ -pectate cross-link exchange. Inversely, in diffusely growing cells, genetic evidence showed a key growth-promoting role for pectin demethylesterification in a variety of contexts [START_REF] Peaucelle | Arabidopsis phyllotaxis is controlled by the methyl-esterification status of cell-wall pectins[END_REF][START_REF] Peaucelle | Pectininduced changes in cell wall mechanics underlie organ initiation in Arabidopsis[END_REF][START_REF] Peaucelle | The control of growth symmetry breaking in the arabidopsis hypocotyl[END_REF][START_REF] Andres-Robin | Evidence for the regulation of gynoecium morphogenesis by ETTIN via cell wall dynamics[END_REF][START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF][START_REF] Wachsman | Cell wall remodeling and vesicle trafficking mediate the root clock in Arabidopsis[END_REF][START_REF] Jonsson | Mechanochemical feedback mediates tissue bending required for seedling emergence[END_REF][START_REF] Stefanowicz | Plasmodiophora brassicae-triggered cell enlargement and loss of cellular integrity in root systems are mediated by pectin demethylation[END_REF], suggesting that Ca 2+ -pectate exchange and/or pectin swelling also occurs in these cells, although more complex scenarios involving signaling or PMEdependent cell wall acidification impinging on cellulose-XG remodeling cannot be excluded. In pavement cells, FEM modeling showed that cell wall deformation driven by swelling pectins would create additional stresses in particular in external periclinal cell walls [START_REF] Haas | Pectin homogalacturonan nanofilament expansion drives morphogenesis in plant epidermal cells[END_REF], and perhaps also between younger and older cell wall layers, which would require relaxation for instance through XG-cellulose cross-link removal.

Finally, pectin swelling upon de-methylesterification might also contribute to turgordriven expansion. For instance, cell wall swelling was observed in Arabidopsis root epidermis cells upon auxin or brassinosteroid treatment [START_REF] Elgass | Novel application of fluorescence lifetime and fluorescence microscopy enables quantitative access to subcellular dynamics in plant cells[END_REF]).

The study of tip growth showed the importance of the surface pH and ROS oscillations that contribute to expansion and cross-linking cycles leading to the formation of periodic cell wall deposition patterns. Similar processes could explain the deposition of layered cell walls of diffusely growing cells, although such oscillations would be more difficult to observe.

The observation of oriented HG chains and pectin fibrils raises the question how the HG chains can reach their uni-axial orientation. Is this through interaction with similarly oriented cellulose? Pectin-cellulose interactions have indeed been observed in muro using solid-state NMR on never-dried cell wall preparations [START_REF] Wang | Cellulose-pectin spatial contacts are inherent to never-dried Arabidopsis primary cell walls: evidence from solid-state nuclear magnetic resonance[END_REF]. Also, fractionation studies revealed a pectin fraction strongly bound to the cellulosic residue.

Interestingly, this fraction and not the chelator-extractable pectin fraction had disappeared in a seedling lethal mutant for the GalA transferase GAUT1 (Mohnen in this book), suggesting the existence of a specialized biosynthetic pathway. How pectin is bound to cellulose is not known, but it may be through xylan [START_REF] Ralet | Enzymatcally and chemically de-esterified lime pectins: physico-chemical characterisation, polyelectrolyte behaviour and calcium binding properties[END_REF], arabinan or galactan side chains (Zykwinska et al. 2005) of RG-I or even through covalent links that have been observed between HG and XG (Stratilová et al. 2020) or cellulose [START_REF] Broxterman | Interactions between pectin and cellulose in primary plant cell walls[END_REF] respectively. Alternative orientating mechanisms are not excluded, such as self-assembly through a nematic crystalline phase [START_REF] Sanchez | Spontaneous motion in hierarchically assembled active matter[END_REF][START_REF] Saw | Biological tissues act as active nematic liquid crystals[END_REF] or perhaps through exocytosis by vesicular-tubular structures reminiscent of those observed in neurons or in suberizing plant cells (De Bellis et al. 2021).

Finally, the presence of uni-axially oriented HG filaments, the swelling of which contributes to the growth direction of single-layered anticlinal cell walls, corresponds more to a growth mechanism by intussusception than chemorheological growth. The above-mentioned statement of [START_REF] Bonner | Studies on the growth hormone of plants. V. The relation of cell elongation to cell wall formation[END_REF][START_REF] Bonner | Studies on the growth hormone of plants. V. The relation of cell elongation to cell wall formation[END_REF] C) More detailed view on the events explained in B) happening at the pollen tube tip (from [START_REF] Rojas | Chemically mediated mechanical expansion of the pollen tube cell wall[END_REF], with permission). Load-bearing cross-links are altering positions in the wall, from the old pectin located more in the outer cell wall to the newly incorporated pectins more to the inner side of the wall. The model is based on 3 key concepts: 1) cross-link dissociation allows turgor pressure to stretch (and thin) the cell wall, 2) newly deposited methylesterified and uncross-linked pectin serves as a reservoir of material that waits to be incorporated into the cross-linked network by dissociating existing cross-links, after being de-methylesterified by PMEs, and 3) cross-links reform at the same rate as they are broken, but in a relaxed state. Step 1: The growth cycle begins with the deposition of secretory vesicles.

Step 2: Nascent pectin is initially unincorporated with the load-bearing network.

Step 3: The nascent pectin is then de-esterified by the enzyme pectin methylesterase.

Step 6: Expansion downregulates deposition.

Step 5: This reaction integrates the nascent pectin into the loadbearing network and allows turgor-driven expansion.

Step 4: A cross-link is a calcium ion bound to two pectin residues. A new cross-link forms when a de-esterified residue draws he calcium ion from an exisiting one, thereby dissociating it.

Figure legends Figure 1 :

 legends1 Figure legends

Figure 2 :

 2 Figure 2: Phase separation in ionized polymer gels (Adapted from Tanaka et al.

Figure 3 :

 3 Figure 3: Visualization of fibrillar pectin.

Figure 4 :

 4 Figure 4: Calcium-pectate exchange model to explain tip growth.

Figure 5 :

 5 Figure 5: Lobe formation in pavement cells and ingrowth development in pine

Acknowledgements

The authors acknowledge the financial support by the University of Antwerp (BOF-DOCPRO4) and the Research Foundation Flanders (FWO Post-doc fellowship) to KV and ANR project ANR-20-CE11-0008, HOMEOWALL to HH. The IJPB benefits from the support of Saclay Plant Sciences-SPS (ANR-17-EUR-0007).


Pierre Hornych

Thomas Gabet

Fabienne Mai Lan Nguyen

Fabienne Anfosso-Lédée

Patrick Duprat

Anfosso Lédée

Evaluation of a solution for electric supply of vehicles by the road, at laboratory and full scale

Keywords: Electric Road System, Full scale testing, Mechanical behavior, Thermal behavior, Bonding

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Electric Road Systems (ERS) are mainly developed to decarbonize road freight transport on long distances. This is why this type of infrastructure will be installed on highways and main roads. The ERS developed by Alstom, a ground-based feeding system, is based on a technical solution used in railways, for power supply of catenaryless tramways. In the railway solution, the feeding rails are integrated inside the track slab.

In this project for road application, the goal is to adapt the ERS to heavy goods vehicles, by installing a mobile current collector underneath the vehicle, which will allow to collect the electric current from the feeding track while driving. The main challenge in this ERS development is the integration of the feeding track inside the road pavement. To accept this type of infrastructure, the road authorities want to be certain that it will not damage the road pavement, that it will be safe for the users and that it will not impact the maintenance works. The integration in the road pavement and the interface with the vehicle are shown on figure 1. The objectives of the study presented in this paper were to find the best solution for ERS integration in the road, and to validate that it will not affect the mechanical durability of the road structure. For this purpose, laboratory tests were first performed to select an appropriate joint material for integrating the ERS in a bituminous pavement, and to verify its bonding strength, and its resistance to mechanical and thermal loading. Then, a full-scale test was performed to validate the durability of the selected solution under wheel loading.

Laboratory testing

The installation of the electric rail system (ERS) in an asphalt pavement required to find appropriate solutions to ensure a good bonding between the asphalt materials and the rubber support of the steel rails. For that purpose, it was decided to assess several possible bonding materials. It was decided to test the resistance of the asphalt/bond/rubber assembly according to both mechanical and thermal loadings, in order to simulate pavement loading conditions. For that purpose, laboratory tests were first carried out on small slabs of asphalt concretes in which rubber blocks were incorporated, simulating the electric rail system. Two types of tests were performed : wheel tracking tests, which consisted in submitting the slab to bi-directional wheel loading, at controlled temperatures (20, 40, and 60 °C); thermal loading, which consisted in subjecting the slab to cyclic temperature variations, from +20 °C to + 60°C, and from -20°C to +20°C.

Wheel tracking tests

The wheel tracking tests were performed using the French large wheel tracking apparatus (standard NF-EN 12697-22). This apparatus allows to test simultaneously 2 samples, of 500 x180 x 100 mm, under the loading of a wheel with a contact pressure of 600 kPa, and a loading rate of 1 cycle/second. It should be noted that this test is a qualification test for materials, carried under very severe loading and temperature conditions, not meant to represent the effective field conditions. For the project, it was decided to perform the tests at 3 different temperatures, 20 °C, 40 °C, 60°C. The temperature of 60 °C, used in the standard, represents an extreme temperature seldom reached in pavement surface layers in Europe.

An asphalt concrete of AC10 type with a 30/50 pen grade bitumen, typical of wearing courses used on French highways, was chosen for the tests. The asphalt concrete slabs were manufactured, using a laboratory plate compactor. Then each slab was sawn, to incorporate the rubber elements, either in the center of the slab, or on one side, as shown on figure 2. This allowed to apply the wheel loads on the rubber rail, or on the joint between the rubber rail and the asphalt material. The interface between the asphalt concrete and the ERS support was filled with an elastomeric resin.

The wheel tracking test procedure included 3 load sequences, of 30000 load cycles each, at increasing temperatures (20 °C, 40°C and 60°C), during which the rutting of the specimens was measured. The tests presented here were performed with an elastomeric resin used for sealing of rail track joints, and with the two positions of the rubber element. Figure 3 shows the specimen with the rubber on the side. Rut depths were measured on each specimen at 15 different positions (see figure 3) The sample with the centered rubber element gave very good results. The rutting value did not exceed 0.5 mm at 60°C after 30 000 cycles, which is very low. Indeed, the maximum permissible rut depth for this asphalt concrete at 60 °C is 10 mm after 30 000 cycles. The sample with the rubber element on the side presented more rutting. Figure 4 presents rut depths measurements obtained on the slab with the rubber element on the side, during the test at 60 °C. The final average rut depths reached 3.4 mm on the joint, and 9,3 mm on the asphalt material (with a local maximum value of 12,7 mm). These results were considered good, as the average rutting didn't exceed the maximum permissible value of 10 mm. It should be mentioned again that this temperature of 60°C is extreme, and that the effective number of vehicles passing on the interface will in reality be very low.

Thermal cycling tests

Another possible deterioration mechanism of the embedded ERS is thermal cracking, due to the different thermal expansion coefficients of the asphalt concrete and rubber. Firstly, in order to evaluate the risk of such thermal cracking, finite element simulations were carried out. A simplified, thermo-elastic behavior was considered, with an elastic modulus of 20 000 MPa for the asphalt material and 1000 MPa for the rubber, and thermal expansion coefficients of 30 µε/K and 110 µε/K respectively. A 600 mm x 200 mm x 120 mm slab, with an embedded rubber element (representing a laboratory specimen) was simulated and subjected to a temperature decrease of 40°C (from 20°C to -20°C).

Figure 5 present the results of the calculations. As shown on this figure, the different thermal properties of the rubber and asphalt concrete lead to a higher contraction of the rubber element, thus generating in particular compressive stresses under the groove inside the AC material, and tensile stresses at the corner of the groove. Such tensile stress in the AC material may cause cracking, especially under repeated thermal cycles. On figure 5, the maximum tensile stresses generated are of the order of 0.2 MPa. Although these simulations are very simplified, and do not describe correctly the long-term viscoelastic behavior of the asphalt mix, it was concluded that a significant risk of thermal cracking exists. It was decided to perform laboratory thermal cycling tests to investigate this phenomenon.

Several thermal tests were performed to assess different types of interface and climate conditions. Only the results obtained with the thick interface filled with elastomeric resin are presented here (figure 6). The sample was submitted to 88 temperature cycles between -20°C and 20°C, at a rate of 2 cycles per day. This simulates a very cold climate. After 88 cycles, the sample presented no crack (see figure 6), in contrary to previous samples with other interface materials, not presented here. This was attributed to the high elasticity, low stiffness and good adhesion of the resin, which was able to resist to the high strain levels generated by the temperature cycles. After these tests, it was decided to retain the resin for full scale testing.

Experimental pavement section and test program

Due to the limitations of the laboratory tests, which cannot reproduce exactly field conditions, it was considered important to validate the behavior of electric road system by a full-scale test, carried out with the FABAC traffic simulator. This small linear traffic simulator has four wheel modules, driven by a chain and electric motor (see figures 7 and 8). Each wheel module can be equipped with single or dual wheels, and apply loads varying between 30 and 75 kN. The length of the loaded section is 2 m. The loading speed can vary between 1 and 5 km/h, and the maximum loading rate, under continuous operation, is 300 000 load cycles per week. The pavement section in which the electric supply rails were embedded was 20 m long and consisted of 3 asphalt layers: a 2.5 cm thin asphalt concrete wearing course, a 5 cm binder course and a 12 cm thick asphalt base course. It was built on a 30 cm thick granular subbase, with a bearing capacity of about 70 MPa.

The rails were placed at an angle of 7° with the wheel path of the FABAC machine, to simulate the loading of a vehicle crossing the rails when changing lane (see figure 9), which was considered as the worst loading situation. To install the electric supply rails in the pavement, a trench was first milled in the middle of the lane, then the bottom of the trench was filled with the elastomeric resin. The electric supply track was then put in place, and finally, the joints were filled with resin. The test program consisted in applying 500 000 load cycles, with dual wheels, loaded at 65 kN (French standard half-axle), and a loading speed of 3.6 km/h. This number of load cycles was selected to represent worst case conditions. On a road, loads will be applied on the rail only during overtaking or lane change maneuvers, and the number of loads applied at the same place will be much lower.

The test was performed in April 2019. Figure 10 shows the rails after installation in the pavement. The monitoring of the pavement included:

 Visual inspections of the pavement and rail system, to detect any deteriorations.  Measurements of transverse profile, before loading, and after 250 000 and 500 000 load cycles, at 3 different longitudinal positions.  Temperature measurements, at 4 different depths.  Benkelmann beam deflection measurements, at regular intervals, on the rails, at 3 different longitudinal positions.

Temperature measurements

During the whole test, temperatures were measured continuously (at 10 minutes intervals) at 4 different depths in the pavement structure (see figure 11). The FABAC machine is an outdoor equipment, with no temperature control system, and hence the temperatures depend on the local climatic conditions. During the test, the temperatures were mild, varying between 5°C and 26 °C at the surface, and between 7 °C and 21 °C at a depth of 5 cm (close to the bottom of the ERS rail).

Transversal profile measurements and visual inspections

Transverse profile measurements were made before the start of the test, and then at 250 000 and 500 000 load cycles, with a profilometer equipped with a laser displacement sensor, with a measuring accuracy of 1 mm. The profiles measured at mid-length of the rail (profile P2) are presented on figure 12. The metallic conductive segments are clearly visible on these profiles. The maximum rut depth after 500 000 load cycles reached approximately 6 mm, which is a satisfactory value, given the high number of loads applied, which largely exceeds the number of loads expected on a real road. On national road in France, the permissible rut depth level is typically 10 mm. Visual inspections were also made regularly during the test, and figure 13 shows a view of the test section after 500 000 load cycles. The observations showed that rutting developed mainly during the first 100 000 load cycles, and was mainly due to permanent deformations of the asphalt material. They also indicated no deterioration of the electric supply track, a good adhesion of the elastomer joint on the asphalt and rubber, and no cracking of the joint.

Deflection measurements

Deflections were measured approximately every 100 000 load cycles, at 2 different longitudinal positions, on the rubber element. The measurements were made in the middle of the wheel path, using a Benkelman beam. The results, presented on figure 14, indicate a slight increase of deflections during the first 100 000 cycles, and then no significant evolution during the rest of the test, except some variations due to temperature changes (the measured temperatures are indicated on figure 14). The deflection levels varied between 20 and 40 mm/100. They were lower than the deflection estimated by linear elastic calculations for this structure (54 mm/100 at a temperature of 12°C), which indicates a good stiffness of the experimental structure A technical solution for the insertion of the ERS system in a bituminous pavement was developed and tested. Standard or traditional tools for assessing the mechanical behavior and durability of asphalt pavements were adapted and successfully applied to select and validate the technical solution satisfying our requirements. The next step is now to build a 50-meter long full-scale test track, to validate the safety of the solution using test vehicles. In case of success, the final step before large-scale deployment on roads will be to build a demonstrator of a few kilometers on a circulated road.

Supply track

Elastomer joint

Fig. 1

 1 Fig. 1 Principle of the Electric Road System and integration of the track in the road pavement

Fig. 2

 2 Fig. 2 Slab configurations used for the laboratory wheel tracking tests (dimensions in mm) -In grey the rubber elements

Fig. 4

 4 Fig. 4 Rut depths measured during the wheel tracking test at 60 °C on the specimen with the rubber element on the side.

Fig. 5

 5 Fig. 5 On the left: Numerical model of the asphalt slab with the embedded rubber element. On the right: compressive/tensile stresses induced in the specimen by a temperature decrease of 40°C.

Fig. 6

 6 Fig. 6 View of the specimen with elastomeric resin after 88 temperature cycles

Fig. 7

 7 Fig. 7 Principle of the FABAC machine

Fig. 9

 9 Fig. 9 Positioning of the electric rails on the experimental pavement

Fig. 11

 11 Fig. 11 Temperature variations at different depths in the experimental pavement section

Fig. 12

 12 Fig.12Transverse profile measurements after 0, 250 000 and 500 000 load cycles.

Fig. 13

 13 Fig.13 View of the supply track after the accelerated loading test