Plant cells exhibit a great diversity in size and shape. Meristematic cells are usually isodiametric and then differentiate by developing distinct forms to acquire specific functions. This is easily noticeable in cells such as tip-growing root hairs or multi-lobed pavement cells. In contrast with animal cells, plant cells have the particularity of being tightly connected to each other by their surrounding walls located outside of the plasma membrane. Cell walls are dynamic structures that act as an exoskeleton by participating in the establishment and maintenance of cell shape and by protecting the cell content from biological, chemical and biophysical sources of aggression. Large plants such as trees are able to resist external forces due to the strength given by their cell walls. Moreover, cell walls play a significant role in processes such as cell adhesion, intercellular communication and water movement. Plant cell walls are classified into two groups: primary and secondary walls. The latter are usually present in specialized, non-growing cells and are beyond the scope of this review.

Primary cell walls (around 100–1000 nm thick in young growing cells) are essentially made of glucan-based cellulose microfibrils (CMFs) embedded in a highly hydrated matrix composed of pectins, hemicelluloses, structural proteins, and proteoglycans. The cell wall has to be fairly rigid, to provide support and protection, but also extensible, to allow cell expansion, which is driven by a strong intracellular turgor pressure. A strictly regulated balance between wall rigidity and flexibility is, therefore, imperative to regulate the differential growth that results in such a diversity of cell sizes and shapes. The plant hormone auxin is identified as a stimulator of cell elongation, as it increases cell wall extensibility. Specifically, auxin regulates cell wall properties by initiating wall loosening. The close link between hormonal action and cell wall synthesis and deposition has been investigated for many years, but much of the details still need to be clarified.

Plant cell walls are highly heterogeneous and cell wall composites vary among different species and cell types. Walls are very dynamic and their composition changes even within the same cell over time. Nonetheless, the key polysaccharides are usually present and their structure, biosynthesis, and interaction are summarized in this chapter.

Cell walls consist of different polymers including CMFs, which are embedded in components such as non-cellulosic polysaccharides and structural proteins. CMFs are the largest cell wall polysaccharides, composed of (1,4)-β-D-glucan parallel arrays assembled into long cylinders. Due to their stiff and load-bearing properties, CMFs are resistant to tensional forces. CMFs determine the direction of cell expansion. Indeed, their deposition and alignment define cell growth anisotropy, as shown by the characterization of cellulose-deficient Arabidopsis mutants, in which cell elongation is drastically reduced. Cellulose synthesis takes place beneath the cell wall at the plasma membrane via large rosette complexes made of CESAs and certainly other components such as KOR1, the function of which remains elusive. The CMF patterning of the wall is mediated via cortical microtubules (cMT) and CESAs at the plasma membrane, with the orientation of CMFs within the wall following the pattern given by the cMTs.

CMFs are embedded in a matrix of hemicelluloses and pectins composed of various carbohydrates that display complex glyosidic linkages. In dicotyledons such as Arabidopsis, pectins and hemicellulose xyloglucans (XyGs) are the most abundant cell wall components. XyGs are found mainly in primary cell walls and are thought to participate in cell wall extension during cell elongation. XyGs are composed of (110,113)-β-D- glucan chains, with side chains consisting of galactose, fucose, and xylose residues.151 XyGs influence wall extensibility and stiffness, as cell walls in an Arabidopsis double xyloglucan xylosyltransferases mutant (xxt1 xxt2) are softer and weaker than walls in the wild type. Mannans and heteromannans are hemicelluloses that are abundant in mosses, lycophytes, and in the secondary cell walls of gymnosperms. Other hemicelluloses such as xylans, heteroxylans, and (1,3;1,4)-β-D- glucans are highly represented in monocotyledons (cereals and grasses) and in secondary cell walls.

Pectins play an important role in the regulation of wall properties, because they control wall porosity and hydration, which causes wall swelling and influences wall thickness. Moreover, pectins adjust wall extensibility by influencing the alignment of CMFs and form the middle lamella, an adhesive compartment between two adjacent cell walls. Pectins are composed of highly heterogeneous polysaccharides, among which four main elements can be distinguished: homogalacturonan (HG), rhamnogalacturonan I (RGI), rhamnogalacturonan II (RGII), and xylogalacturonan (XGA). HG often contains highly methylesterified galacturonic acid residues, while RGI is more complex and is composed of alternating galacturonic acid and rhamnose with galactose, arabinose, or arabinogalactans forming side chains. A common feature of RGII is the presence of borate esters between RGII-specific sugar residues.

Non-cellulosic cell wall components are synthesized in the Golgi apparatus, packed into vesicles and trafficked along actin filaments (AFs) to the wall. The walls of actively growing cells display a porous structure, which allows polysaccharide to move relatively to each other (such as sliding) within the wall. Polysaccharide synthesis is carried out by synthases, which catalyze the polymerization of sugar residues, and glycosyltransferases, which connect the monosaccharides and short oligosaccharides to the polymer chains.

Beside polysaccharides, the cell wall contains various structural (non-enzymatic) proteins, which regulate its formation and growth. Among these structural proteins, EXTs and AGPs are well-characterized as regulating wall expansion [171,172]. EXPs are defined as wall-loosening proteins, enhancing wall expansion in acidic pH [173] and will later be discussed in the context of auxin-mediated cell wall expansion. Other structural glycoproteins, EXTs, are required for cell wall assembly [174– 177], as the EXT3-defective Arabidopsis mutant root-, shoot-, hypocotyl-defective (rsh) presents defective wall formation [111,178]. AGPs play a role in plant protection against pathogens, and, additionally, an increased amount of AGPs can be observed in wounded plants [170,179]. AGPs are known to specifically control pollen tube growth [170] but are also thought to regulate overall plant development [180].

Cell wall physical properties are maintained through the interactions among its polysaccharides [112,181]. A new model displaying the interactions between different cell wall polymers has been recently presented, in which “biochemical hotspots” crosslink different polysaccharides [116,7182]. These hotspots are present between CMFs and XyGs, but also among different CMFs, connecting them to each other [116,182–184]. This interesting model updates the previous theory, which was based on the wall being composed of separated CMFs, which could be cross-linked to either XyGs, in order to reinforce the wall, and/ or pectins, in order to soften the wall [114,185].

Crosslinking of CMFs with XyGs increases wall mechanical resistance [186–191]. XyGs are important for the separation of CMFs, as the XyG-deficient xxt1 xxt2 mutant is characterized by tightly compact CMFs [116,152]. XyG-CMF interactions are modulated by XTHs, which either catalyze the linkage of the XyGs to cellulose (strengthening the wall) or hydrolyze the breaking of the link of XyGs with CMFs (loosening the wall) [192–199]. During cell development, pectins are regularly delivered and inserted into the wall matrix, which suggests that their presence and abundance might regulate wall extensibility. Pectins can either enhance wall expansion by promoting movement of the CMFs or maintain CMFs in non- growing cell wall zones [200–205]. Moreover, different pectin domains crosslink to each other via calcium and boron bonds [110,156,158]. These connections are modified by PMEs, which regulate the crosslinking of pectins to calcium ions. Methyl- esterification (addition of methyl groups) decreases the ability of HGs to form crosslinks with calcium ions, causing softening of the wall. Accordingly, de-methyl-esterification (removal of the methyl groups) increases HG capacity to crosslink to calcium ions, which causes wall stiffening, compaction and enhanced adhesion [206,207]. Intriguingly, auxin has been shown to reduce the stiffness of the cell wall through demethylesterification of pectins in the shoot apex leading to organ outgrowth [208]. On the other hand, RGII chains are connected to each other through borate diester bonds, influencing wall hydration and thickness [156]. Arabinans and arabinogalactans are known to induce cell wall swelling, decreasing its stiffness while increasing its extensibility [209,210]. In summary, the cell wall is composed of a range of different polysaccharides, whose abundance and interactions determine its properties and regulate cell growth. Water accumulation in the vacuole induces high turgor pressure, which drives plant cell growth. This strong tensile stress presses against the plasma membrane, leading to the stretching of the cell wall polysaccharides. The wall needs to be moderately rigid to oppose this turgor pressure, to avoid breaking. However, the wall also has to adapt its composition by modifying and constantly adding polysaccharides to allow cell extension [116,168,211,212].

Cell wall expansion and overall cell growth is regulated via several factors, including plant hormones. Among them, auxin plays a vital role in controlling plant growth and development via promotion of cell division (proliferation), growth (expansion, elongation), and differentiation [124,125,213–217]. Enlargement of the cell occurs prior to cell division, however, no changes are observed in the vacuole size at this stage. On the other hand, cell expansion includes vacuole extension and is defined as a turgor-driven increase in cell size, which is controlled by the cell wall capacity to extend. Cell expansion is related to an increased ploidy level (endoreduplication), cellular vacuolization, and differentiation [215,218]. Almost four decades ago, auxin or indole-3-acetic acid (IAA) was implicated for the first time in cell wall loosening and cell expansion via modifications of cell wall composition. IAA causes pectin polymerization and increases pectin viscosity and XyG depolymerization [219].

In this second part, we discuss the auxin role during cell expansion and its direct link to the changes occurring in the cell wall [220]. Auxin activates the expression of cell wall- related genes and stimulates the synthesis of proton pumps, which leads to apoplast acidification [215]. Auxin also activates plasma membrane (PM) H+-ATPases through upregulating the phosphorylation of the penultimate of threonine of PM H+- ATPases, leading to apoplast acidification [221]. In an acidic environment, wall-loosening proteins are active and cause wall enlargement. The changes in the wall trigger the cell to activate calcium channels, which pump calcium into the wall and increase the pH, causing growth cessation. Finally, auxin acts on the cytoskeleton (AFs and cMTs) through RHO OF PLANTS (ROP) GUANOSINE-5′-TRIPHOSPHATASES (GTPases) and promotes trafficking of vesicles containing new cell wall material [222–225].

Arabidopsis seedling hypocotyls elongate exclusively by cell expansion, making this organ a model system in which to investigate the contribution of auxin signaling to cell elongation [220,226]. Auxin acts through the TIR1/AFB nuclear auxin receptor family, the degradation of the transcriptional regulators AUX/IAAs and the ARFs, which mediate different transcriptional responses [226,227]. TIR1/AFBs are part of the Skp1/Cullin/F-box (SCF) complex, which promotes degradation of AUX/IAAs, which otherwise repress auxin-mediated transcription [228] through the interactions with ARFs in the absence of auxin. Once the concentration of auxin increases, the hormone mediates the linkage of TIR1/AFBs with AUX/ IAAs and the degradation of the latter through proteasomal activity [229–232]. Different Arabidopsis AUX/IAA mutants such as auxin resistant/indole-3-acetic acid inducible (axr2/ iaa7, axr5/iaa1, axr3/iaa17) or short hypocotyl/indole-3- acetic acid inducible (shy2/iaa3) display cell expansion defects [215,233,234], indicating that auxin induces cell expansion through the degradation of AUX/IAAs. ARFs are transcription factors that bind to the promoters of auxin-responsive genes [231,235–237]. Among the 22 ARFs in Arabidopsis, ARF7 has been shown to positively regulate the expression of EXP8 [238], thus playing an essential role in extensive cell growth [239].

Auxin is known to induce acid growth (Fig. 48), which is defined as the loosening of the walls at low pH, leading to an increase in wall extensibility and rapid cell elongation [123,125,249– 254], through the TIR/AFB signaling machinery [255]. Auxin stimulates the activity of plasma membrane H+-ATPase proton pumps [256,257] (Fig. 48(Aa)), which pump out protons (H+) to the wall matrix, leading to apoplast acidification (pH 4.5–6) [124,247,254,258]. This process induces the hyperpolarization of the plasma membrane and is regulated by the auxin-inducible SAUR proteins [257]. Activation of potassium channels occurs and potassium ions are pumped into the cytosol (Fig. 48(Ab)). The increasing concentration of potassium in the cytosol stimulates water uptake, which generates tensile stress, forcing the cell wall to extend [215,259,260]. Auxin not only stimulates the activity of proton pumps and potassium channels [259– 261], but also induces the expression of genes encoding these proteins [259–263]. Note that auxin-sensitive proton pumps are mostly located in the epidermis [123,264], which is thought to be limiting for growth and is essential for shaping plant organs [263–266]. Moreover, different cells display distinct abilities to perceive acid growth; for instance, mature cells are less sensitive to acidic pH and extend less than young cells [267,268].

Auxin-induced acidic pH is required to activate EXPs (Fig. 48(Ac)), which are specific, non-enzymatic wall-loosening proteins. EXPs were identified as inducing the relaxation of the walls in actively expanding hypocotyl cells of Cucumis sativa [173,269–271]. EXPs disintegrate polysaccharide networks by cutting and loosening connections between CMFs and non- cellulosic polysaccharides such as XyGs [270,272,273]. As a result, CMFs slide and move apart, promoting wall loosening, hydration and swelling. Interestingly, in plants exposed to gravitropic and light stimuli, EXP-encoding genes (EXP1 and EXP8) are upregulated in elongating cells. This was observed before plant morphological changes appear, suggesting that auxin stimulates EXP expression, leading to the wall property changes [215,237].

As the most external cell compartment, the cell wall is by necessity involved in plant cell growth. This has been demonstrated by analyzing different cell wall deficient mutants that display various growth defects. Indeed, the cell wall is a very dynamic cell composite, which is characterized by complex polysaccharide interactions and various modifications during cell development. Moreover, plant cells grow symplastically, and they need to adjust their growth to the neighboring cells. Changes within the wall occur during turgor-driven cell growth, which is mediated via acidification of the wall and loosening of the connections between different cell wall polysaccharides. Acidic growth has been shown to be promoted by auxin, which activates structural proteins and enzymes such as EXPs, XTHs, and PMEs, modifying the interactions between different cell wall polymers. Furthermore, progress in molecular biology has allowed us to connect auxin with the activation of the acidifying proteins (proton pumps, [330]) and numerous genes that are related to wall biosynthesis and modification. In summary, auxin plays a major role in regulating cell expansion through the activation of cell wall synthesis and modification-related genes. However, it still remains elusive as to how auxin regulates the modifications in the wall over time. Further development of in muro detection methods, which follow cell wall changes over cell development, will undoubtedly provide more clues about the temporal regulation of cell wall expansion and cell elongation by this master hormone.