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Article

# The Cell Wall PAC (Proline-Rich, Arabinogalactan Proteins, Conserved Cysteines) Domain-Proteins Are Conserved in the Green Lineage

Huan Nguyen-Kim<sup>1,†</sup>, Hélène San Clemente<sup>1,†</sup>, Josef Laimer<sup>2</sup>, Peter Lackner<sup>2</sup>,
Gabriele Gadermaier<sup>2</sup>, Christophe Dunand<sup>1</sup> and Elisabeth Jamet<sup>1,*</sup>

Received: 17 January 2020; Accepted: 1 April 2020; Published: 3 April 2020

**Abstract:** Plant cell wall proteins play major roles during plant development and in response to environmental cues. A bioinformatic search for functional domains has allowed identifying the PAC domain (Proline-rich, Arabinogalactan proteins, conserved Cysteines) in several proteins (PDPs) identified in cell wall proteomes. This domain is assumed to interact with pectic polysaccharides and O-glycans and to contribute to non-covalent molecular scaffolds facilitating the remodeling of polysaccharidic networks during rapid cell expansion. In this work, the characteristics of the PAC domain are described in detail, including six conserved Cys residues, their spacing, and the predicted secondary structures. Modeling has been performed based on the crystal structure of a *Plantago lanceolata* PAC domain. The presence of β-sheets is assumed to ensure the correct folding of the PAC domain as a β-barrel with loop regions. We show that PDPs are present in early divergent organisms from the green lineage and in all land plants. PAC domains are associated with other types of domains: Histidine-rich, extensin, Proline-rich, or yet uncharacterized. The earliest divergent organisms having PDPs are Bryophytes. Like the complexity of the cell walls, the number and complexity of PDPs steadily increase during the evolution of the green lineage. The association of PAC domains with other domains suggests a neo-functionalization and different types of interactions with cell wall polymers

**Keywords:** cell wall; evolution; green lineage; modeling; PAC domain; phylogeny; plant

## 1. Introduction

Plant cell walls are composite structures mainly made of polysaccharides and proteins. Cellulose microfibrils and hemicelluloses form intricate networks, which are embedded in a pectin matrix [1]. Although present in minor amounts, the cell wall proteins (CWPs) play critical roles in polysaccharides organization and remodeling processes during growth and upon environmental stresses [2,3]. Cell wall proteomics has revealed the great diversity of CWPs and allowed the discovery of unexpected CWP families [4]. The combination of genetics and biochemistry approaches has allowed demonstrating the roles of CWPs in polysaccharide metabolism, biosynthesis of lipid-rich cell wall layers, lignin monomer polymerization, but also in signaling and ROS homeostasis maintenance [5-8].

Among the newly described CWPs families, the importance of the PAC (Proline-rich Arabinogalactan protein and Conserved Cysteines) domain containing-protein (PDP) family could

<footnote n="1">¹ Laboratoire de Recherche en Sciences Végétales, Université de Toulouse, CNRS, UPS, 31320 Auzeville Tolosane, France; huanqnu@gmail.com (H.N-K.); sancle@lrsv.ups-tlse.fr (H.S.C.); dunand@lrsv.ups-tlse.fr (C.D.)</footnote>

<footnote n="2">² Paris-Lodron-University of Salzburg, Department of Biosciences, 5020 Salzburg, Austria; josef.laimer@sbg.ac.at (J.L.); peter.lackner@sbg.ac.at (P.L.); gabriele.gadermaier@sbg.ac.at (G.G.)</footnote>

<footnote>* Correspondence: jamet@lrsv.ups-tlse.fr; Tel.: +33-(0)5-3432-3830</footnote>

<footnote>† These two authors equally contributed to the work.</footnote>
be stressed because of their presence in many cell wall proteomes (see WallProtDB, www.polebio.lrv.ups-tlse.fr/WallProtDB/, query with "Ole e1 allergen domain" as a keyword). The name of the PDP family was initially proposed by Baldwin et al. [9], who described them as a sub-family of non-classical arabinogalactan proteins (AGPs) containing both an AGP domain and a C-terminal domain containing six Cysteines residues (named Cys 1 to Cys 6 herein). Later on, a domain partly describing the PAC domain has been proposed in the Pfam database (PF01190, http://pfam.xfam.org/). The firstly described member of this family was a protein from *Nicotiana alata* named AGPNa3 [10]. Then, several proteins very close to AGPNa3 were studied, for a review, see [11]. As examples, the following ones can be mentioned: *Daucus carota* DcAGP1 [12]; *Arabidopsis thaliana* AtAGP30 [13], and AtAGP31 (At1g28290) [14]; *Capsicum annuum* CaPRP1 [15]; *Gossypium hirsutum* GhAGP31 [16]; and *Petunia hybrida* PhPRP1 [17]. More recently, it appeared that the PAC domain could also be found alone, located at the N-terminus of the mature protein or associated with different types of domains, such as a Histidine-rich region, an O-glycosylated Proline/Hydroxyproline-rich domain, or an extensin domain [18,19].

Functional studies on several of the *A. thaliana* PDPs have shown their diverse roles during plant development. *PRPL1* (*Proline-Rich Protein-Like*, At5g05500) has a trichoblast-specific expression and plays roles in root hair elongation, as shown by the reduction in length of root hairs in the *prpl1* mutant [20]. Plants lacking *FOCL1* (*Fused Outer Cutiular Ledge 1*, At2g16630) produce stomata without a cuticular ledge, and thus, *focl1* mutants display drought tolerance [21]. *AtAGP30* (*At2g33790*) is involved in root regeneration in vitro and in the timing of seed germination [13]. *AtAGP30* is expressed in root atrichoblasts under the control of ABA signaling [22]. *AtAGP31* is expressed in vascular tissues and repressed by methyl jasmonate at the transcriptional level [14]. *AtAGP31* has also been shown to accumulate in actively growing etiolated hypocotyls [23]. In vitro interactions have been demonstrated between its PAC domain and galactans or the Gal-Ara-rich O-glycans of its Proline/Hydroxyproline rich domain [11]. These studies have led to the assumption that *AtAGP31* could be involved in cell wall non-covalent protein/polysaccharide networks playing roles during quick cell elongation [11].

Recently, the crystal structure of the PAC domain of an allergenic protein from *Plantago lanceolata* containing an N-terminal PAC domain (Pla 1 1 as a member of the Ole e 1-like protein family, PDP code 4Z8W) has been determined, highlighting the importance of β-sheets in its secondary structure [24]. In particular, the structure revealed a seven-stranded β-barrel with four loop regions. Three intramolecular disulfide bonds were found between (i) β 1b and β 6 strands (Cys 1-Cys 5), (ii) β 2 and β 5 strands (Cys 3-Cys 4), and the (iii) C-terminus and loop C-terminal of β 2 strand (Cys 2-Cys 6), thus forming a closed branched loop. A detailed characterization of allergens of the same protein family allowed proposing that they share the same core structure, whereas loop regions can be heterogeneous.

In this article, we aim at giving an evolutive overview of the PDPs throughout the green lineage, from Bryophytes to late divergent plants, such as monocots and dicots. We first define more precisely the PAC domain characteristics in order to retrieve PAC domain sequences from available genomic or RNA-seq databases using a tailor-made bioinformatic script. Since the conservation of the primary amino acid sequences of PAC domains was rather low, and since the presence of β-sheets seemed to be essential for domain folding, bona fide PAC domains were selected according to their secondary structure conservation, and protein alignment was done using a software taking into account secondary structures. Modeling of tertiary structures was done based on the available crystal structure of the Pla 1 1 PAC domain. Finally, we could draw a phylogenic tree and sort the PAC domains according to their association with other domains. We could also investigate the occurrence of PAC domains in ancestor organisms.
## 2. Results and Discussion

### 2.1. Characteristics of the PAC Domain and Search for New PDP Candidates

The overall strategy used for this study is summarized in Figure 1. As a first step and in order to obtain a better definition of a PAC domain, orthologous sequences have been identified in the *A. thaliana* genome using that of the AtAGP31 PAC domain. Altogether, 14 candidate sequences were identified and manually checked for the presence of the six conserved Cys residues: At1g29140, At1g78040, At3g09925, At4g08685, At4g18596, At5g45880, At5g54855, AtAGP31, At5g05500 (PRPL1), At5g15790, At2g34790 (AtAGP30), At2g34700, At4g18596, and At2g16630 (FOCL1). These sequences were then used to identify additional PDPs by sequence similarity in eight other angiosperm genomes: *Amborella trichopoda*, *Brachypodium distachyon*, *Oryza sativa*, *Sorghum bicolor*, *Populus trichocarpa*, *Eucalyptus grandis*, *Linum usitatissimum*, and *Gossypium raimondii*. About 50 putative PDPs were collected and manually checked for the presence of the six conserved Cys residues. From this first data mining step, it appeared that the level of conservation of the amino acid sequences of the PAC domains could be low. In particular, except between the two first conserved Cys residues (Cys 1 and Cys 2), the spacing between Cys residues could be variable. Thus, the usual homology-based mining was not sufficient, and an alternative strategy was necessary to obtain exhaustive results for each plant. The alignment of angiosperms PAC domains has allowed calculating the range of spacing between the conserved Cys residues. Then, a tailor-made script based on several points detailed in Table 1 has been set up to search for additional PDPs in the same genomes or in other genomics or transcriptomics databases. However, the prediction of a signal peptide for protein secretion could not be made systematically for the proteins translated from transcriptomics data because the sequences could be incomplete. Furthermore, when genomic sequences were available, the presence of an intron between the sequences encoding, on the one hand, Cys 1 and Cys 2, and on the other hand, Cys 3 to Cys 6 was searched for to support the PAC domain identification.

<table><caption>**Table 1.** Five features of a bona fide PAC domain.</caption><tr><td>1.</td><td>Present in a protein with a predicted signal peptide</td></tr><tr><td>2.</td><td>Presence of six Cys residues downstream a Glycine residue and with a defined spacing <sup>1</sup>:<br/>Gly (3) Cys 1 (2) Cys 2 (10,50) Cys 3 (20,50) Cys 4 (8,20) Cys 5 (25,60) Cys 6</td></tr><tr><td>3.</td><td>Prediction of β-sheets according to the crystal structure of the <i>Plantago lanceolata</i><br/>(www.rcsb.org/structure/4Z8W) PAC domain protein</td></tr><tr><td>4.</td><td>Possibly associated to AGP, extensin, X(Proline<sub>n≥2</sub>) X-rich, Histidine-rich, or W-W domains</td></tr><tr><td>5.</td><td>No prediction of additional functional domains</td></tr></table>

Using this script, sequences encoding PAC domains have been searched for in 78 plant species belonging to the green lineage from Bryophytes (*Bryophyta*, *Marchantiophyta* and *Anthocerotophyta*) to late divergent plants. Altogether, about 450 putative PAC domain sequences were collected (S1–S4).

Three additional criteria have then been used to select bona fide PAC domain proteins. The first one was the number of conserved Cys residues. Indeed, we have found putative PAC domains showing the expected characteristics, but containing only five Cys residues, or containing more Cys residues, up to nine (S1,S5). Although some of them had sequences very similar to those of six Cys-containing PAC domains (S5), we have decided to dismiss them in case of a lack or an excess of Cys residues, which would modify the folding of the domain by generating disulfide bridges different from the expected ones. The second exclusion criterion was the absence of predicted β-sheets. Indeed, the crystal structure of the Pla I 1 PAC domain has allowed highlighting the importance of these β-sheets in its secondary structure [24]. Some proteins with large predicted α-helices and/or no predicted β-sheets have been dismissed with regard to this criterion, especially in Bryophytes, Equisetales, and Alismatales (S1,S6). The third criterion was the presence of associated predicted functional domains suggesting intracellular

<footnote n="1">¹ The number of amino acids between two successive Cys residues is indicated between brackets.</footnote>
functions like aldehyde dehydrogenase domain (PF00171, *Tetraphis pellucida* HVBQ_2004216) or JmjC and JmjN domains of transcription factors (PF02373 and PF02375, *Pallavicinia lyelli* YFGP_2007785) (S3). In most of these latter cases, it was not possible to predict the sub-cellular localization of the proteins because they resulted from the translation of incomplete contigs obtained from RNA-seq data.

<figure><img src="image_121.png" /><figcaption>**Figure 1.** Pipeline for Proline-rich Arabinogalactan protein and Conserved Cys (PAC) domain protein identification and phylogeny. The name of the bioinformatics programs and resources used at each step are indicated in brackets.</figcaption></figure>

## 2.2. *The Number and the Diversity of PAC Domain Proteins Increase Along the Green Lineage*

The PDPs have been classified according to the domains associated with the PAC domain. Four types were distinguished (Figure 2). Type 1 corresponds to proteins only containing a PAC domain. The corresponding genes could exhibit either no intron or one intron between the sequences encoding Cys 1 and Cys 2 and those encoding Cys 3 to Cys 6. Type 2 includes proteins with an N-terminal PAC domain, which could be associated to (i) a Proline-rich domain or (ii) a well-conserved domain of unknown function usually encoded by a specific exon and starting with the following amino acid motif: Tryptophane-X8-Tryptophane (W-W domain) (S7). As an example, At2g16630 (FOCL1) is a type 2-PAC domain protein with a W-W domain at the C-terminus. Type 3 encompasses proteins with a C-terminal PAC domain. The PAC domain could be associated with a Histidine stretch, a Proline-rich domain, and/or an AGP domain. For example, AtAGP30 and AtAGP31 are type 3-PAC domain-proteins. Finally, type 4 corresponds to proteins containing central PAC domains flanked by two extensin domains. Although a few proteins with Serine-(Proline)₄ motifs typical of extensins at their C-terminus were
found in *Anthocerophyta* and Lycopodiales, the first bona fide type 4-PDP was found in Psilotales. There is no such PDP in *A. thaliana*.

<figure><img src="image_122.png" /><figcaption>**Figure 2.** Classification of PAC domain proteins according to the location of the PAC domain and associated domains. **Type 1.** Proteins containing the PAC domain alone. **Type 2.** Proteins containing the PAC domain at their N-terminus together with another (several other) domain(s). **Type 3.** Proteins containing the PAC domain at their C-terminus together with another (several other) domain(s). **Type 4.** Proteins containing the PAC domain in a central position flanked by two domains with extensin motifs (Serine-(Proline)~n≥2~).</figcaption></figure>

In Bryophytes and Anthocerotophyta, only one to three PAC domain proteins were found for each species (S1). The number of PDPs was higher in Psilotales and Equisetales as well as in all the plant families, which have appeared later in the green lineage. Eleven PDPs are present in *Amborella trichopoda*, which is considered as an ancestor common to angiosperms [25]. The highest numbers of PDPs, i.e., between 17 and 23, were found in Poales, *Brachypodium distachyon*, *Sorghum bicolor*, *Zea mays*, and *Oryza sativa*, as well as in *Linum usitatissimum*, *Populus trichocarpa*, and *Gossypium raimondii*. In Poales like *B. distachyon* and *O. sativa*, the genes encoding PDPs could be found in tandem (Figure 3). The PAC domains of these genes could show a high degree of identity (more than 85%), supporting the recent tandem duplication events [26]. In addition, PAC domains with various numbers of Cys residues were also found in Poales (S1). The functionality of those PAC domains has not yet been established.

<figure><img src="image_123.png" /><figcaption>**Figure 3.** Examples of domain containing-protein (PDP) genes organized in tandem in the *B. distachyon* and *O. sativa* genomes. The orientation of the genes is indicated by arrows. The names of the genes are abbreviated, e.g., 20970 stands for *Bradi3g20970*, and 5750 for *O. sativa* *LOC_Os10g5750*. Genes sharing more than 85% identity in their PAC domain coding sequences at the amino acid level are represented with arrows of the same color.</figcaption></figure>
The different types of PDPs are unevenly distributed within the different plant species (Figure 4). Only type 1- and type 2-PDPs were found in all plant families. Among the type 1-PDPs, one sub-type should be distinguished. It corresponds to highly conserved sequences throughout the green lineage since Lycopodiales with an overall percentage of identity ranging from 60% to 88% and a percentage of similarity from 69% to 92%. For comparison, the percentage of identity and of similarity between two PAC domain sequences can be rather low (15.4% and 20.7%, respectively). Among the type 2-PDPs, those including a C-terminal W-W domain are present in nearly all plant families from Bryophytes to Brassicales. They could appear as ancestors of PDPs. Type 3- and type 4-PDPs seem to have appeared more recently in the evolution of the green lineage since the most ancient type 3- and type 4-proteins were found in *A. trichopoda* and in Psilotales, respectively. Of course, one cannot exclude that some PDPs are missing in this collection since only a few complete genomes are available for plants from Psilotales to Amborellales.

<figure><img src="image_124.png" /><figcaption>**Figure 4.** Distribution of the different types of PAC domains within the plant families. The different types of PAC domains are represented in Figure 2. Among type 1-PAC domains, those having a highly conserved amino acid sequence are distinguished (1'). Among type 2-PAC domains, those that are associated to a C-terminal W-W domain are highlighted (2').</figcaption></figure>

## 2.3. A Possible Origin for the PAC Domain

We have performed an extensive search of PAC domain sequences in the available databases dedicated to ancestors of the green lineage using both the script described above and BLAST queries using several PAC domains in case the spacing between Cys residues would be slightly different. Mining was done in the following families: Stramenopiles (Synura petersenii), Cryptophyta (Chroomonas sp), Chlorophyta (Asteromonas gracilis, Chlamydomonas rheinardtii, Nephroselmis olivacea, Volvox carteri, Scenedesmus dimorphus, Scherffelia dubia), Streptophyta (Chara braunii, Coleochaete orbicularis, Klebsormidium flaccidum, Mesotaenium caldariorum, Penium margaritaceum) (S4). In many cases, the proteins were incomplete either at their N-termini and it was not possible to predict a signal peptide, or at their C-termini, and they could not be classified. Whenever possible, the presence of predicted functional domains associated to the putative PAC domains was checked, and the proteins comprising functional domains associated to intracellular functions were not retained.

We could only find PAC domain-related sequences in *Chlorophyta*: 10 proteins were found in *C. rheinardtii* and one in *V. carteri*, which both belong to Chlamydomonales. The Glycine residue located upstream the first Cys residue was always missing, and the PAC domains were associated with Proline-rich motifs of two types: either Serine-(Proline)ₙ or (Proline)ₙ and up to three of them could be found in a given protein. However, the secondary structures of these domains were predicted to be
α-helices. In *C. rheinardtii*, the GP1 and GP2 proteins, which both have Serine-(Proline)ₙ motifs, were described as proteins rich in Hydroxyproline residues forming the insoluble glycoprotein framework of the cell wall [27,28]. Furthermore, in *C. orbicularis*, we could find another interesting PAC domain candidate, which was associated to Proline-rich motifs but contained seven Cys residues. The highest level of identity/similarity was found with two PAC domains of *Musa acuminata*: GSMUA_Achr4T17330 (45%/51%) and GSMUA_Achr7T01790.1 (39%/50%). The highest level of identity/similarity with a *Marchantiophyta* PAC domain was found with the *Conocephalum conicum* PAC domain ILBQ_2004952 (30%/46%) and the *M. polymorpha* Mapoly0014s0128 PAC domain (33%/45%). Altogether, the sequence showing the highest level of identity to bona fide PAC domains was found in *C. orbicularis*. This is consistent with the assumption that the Coleochaetales could be one of the ancestors of the green lineage [29].

## 2.4. *Three-Dimensional-Modeling of PAC Domain Proteins*

Three-dimensional-models were calculated for 41 bona fide and 9 putative PAC domains, based on the crystal structure of the *P. lanceolata* PAC domain [24]. The sequence identities between the template and the PAC domains varied between 9.6% and 30.4% (median 15.9%). A sequence identity of 30% is generally seen as a lower limit for reliable models predicted by homology modeling algorithms, but the assumption of disulfide bridges somewhat lowers this limit. However, the low sequence similarities were still an issue. In addition, in 6 out of the 50 PAC domains, the 3D-modeling software I-Tasser was not able to find conformations enabling the formation of the three disulfide bridges between the predefined Cys residues (S8). In all these cases, either the proteins were predicted to have α-helices, or they were missing the Glycine residue upstream Cys 1.

For the bona fide PAC domains, it was possible to propose relevant 3D-models fitting with the typical structure experimentally demonstrated for the *P. lanceolata* PAC domain [24]. Four selected PAC domains from different plants are shown in Figure 5: an *Anthocerophyta* (*Anthoceros formosa*), chosen as an ancestral plant, *A. trichopoda* as the common ancestor to flowering plants, and two higher plants, *Oropetium thomaeum* and *A. thaliana*. All four 3-D models show the expected parallel β-sheets forming a β-barrel and the three disulfide bridges. They also contain loop regions as the *P. lanceolata* PAC domains. The 3D-structure of bona fide PAC domains seems to have been conserved through the evolution of the green lineage. However, the *C. orbicularis* protein, which was assumed to be an ancestor of the PDPs in the green lineage, only had three β-sheets, but the three disulfide bridges were at the predefined positions (S8).

The PAC domains that have been considered apart because of the prediction of α-helices showed completely different 3D-structures (S8). They exhibited less β-sheets or only α-helices, and as mentioned above, the three disulfide bridges were not at the expected positions. The 3-D modeling, thus, brought an additional criterion to confirm bona fide PAC domains. Interestingly, such a β-barrel structure has already been described for a mannose-binding lectin family of red algae, the *Oscillatoria Agardhii* Agglutinin-Homolog (OAAH) mannose-binding lectin family [30]. In this case, two β-barrels associate perpendicularly to build up the complete 3D-structure of the molecule, and the interaction with cell wall polymers occurs at two crevices symmetrically located at its two ends [31]. This role would be consistent with the finding that the PAC domain of AtAGP31 can interact with cell wall polysaccharides and O-glycans in vitro [11].
<figure><img src="image_125.png" /><figcaption>**Figure 5.** 3D-modeling of four PAC domains. (A) A representative PAC domain of Bryophytes: IQJU_2004004_Anthoceros_formosae. (B) A PAC domain of *A. trichopoda*: AmTr_v1.0_068.122. (C) A representative PAC domain of the *O. thomaeum* monocot: Oropetium_11363A. (D) A representative PAC domain of the *A. thaliana* dicot: At1g28290. The N-terminus (N-ter) and the C-terminus (C-ter) of the proteins are indicated in blue and red, respectively. Blue ribbons represent β-sheets. The three disulfide bridges are drawn in yellow, and the names of the Cys residues involved are indicated.</figcaption></figure>

To test the role of the conserved Cys residues and, therefore, that of disulfide bridges in 3D-structure stability, in silico mutation experiments have been performed. Possible 5 Cys-PAC domain variants have been tested for the *P. lanceolata* PAC domain, and for each of the eight A. trichopoda PAC domains, which were considered as representative of the eight phylogenic clades (see below). Each Cys residue has been replaced by a Ser residue, and the change in stability was determined by MAESTRO (S11). In all cases, positive values of the ddG parameter indicating changes in unfolding free energy were found, indicating destabilization of the 3D-structure. Altogether, it seems that the conserved Cys residues are critical for the stability of the β-barrel. This could indicate that the domains lacking one Cys residue could be impaired in their biological activity or more sensitive to changes in their physiological environment. The presence of a seventh or even an eighth Cys residue could have different consequences depending on the position(s) of the additional Cys residue(s). Such residue(s) could be involved in different disulfide bridges or not. Only experimental work could allow showing any change in the biological activity of the PAC domain.

## 2.5. Phylogenetic Analyses Reveal the Presence of a Few Clades Grouping the PAC Domain Proteins According to Their Associated Domains

Based on all the criteria described above, 300 PAC domains have been selected for the building of phylogenetic trees (S1,S2). They have been chosen from plant families representative of the green lineage from Bryophytes to Brassicales based on a phylogenetic tree established using plastid gene sequences [32]. When several species were available for a given plant family, only one or a few of them were selected to represent it. For each plant family, the PAC domains sequences were analyzed for their percentage of identity, and the most representative plant species was retained. When the
sets of PAC domain sequences were too different between plants of the same family, several species
could be maintained. In addition, only PAC domains showing less than 85% of identity inside a
given plant species were conserved. As a first step, the sequences were aligned according to their
predicted secondary structure. Such a strategy was used in previous studies where the conservation
of the primary sequences of the proteins was not sufficient to ensure relevant alignments [33–35].
The PROMALS3D software was used, and the resulting alignment was introduced in the MEGA7
software to build up a maximum likelihood tree using 500 bootstraps. Due to the low level of
conservation between amino acid sequences and especially between the PAC domain sequences of the
older lineages, we have decided to build up two independent trees to avoid bias due to long-branch
attraction: the first one (Tree I) including plants from Bryophytes to *A. trichopoda*, and the second one
și (Tree II) from *A. trichopoda* to Brassicales.

Regarding Tree I, it is difficult to define clades grouping all the PAC domain sequences because
most of the bootstrap values were low (S9). We only considered clades corresponding to bootstrap
values higher than 30. We could define seven clades grouping 71% of the retrieved PAC domains, six of
them containing one *A. trichopoda* PAC domain: clade A (AmTr.v1.0.061.7, mostly type 1-PAC domains);
clade B (AmTr.v1.0.066.9, type 4-PAC domains); clade C (AmTr.v1.0.062.88, type 1-PAC domains, highly
conserved sequences); clade D (AmTr.v1.0.041.161, type 2 W-W domains); clade E (AmTr.v1.000047,
type 2-PAC domains); clade J (AmTr.v1.0.041.169, type 2-PAC domains); and clade K (Equisetum sp
PAC domains). The distribution of the PAC domain sequences of the other species was not clear.
PAC domains of Bryophytes were represented in clades A, D, and E, whereas a *Tmesipteris parva*
(Psilotale) PAC domain was found in clade B, and a *Phylloglossum drummondii* (Lycopodiale) PAC
domain in clades C, and J. Of course, one cannot exclude that PAC domains of plants, which have
divergent earlier than Amborellales are still missing since only a limited number of fully sequenced
genomes are available. Despite the presence of the key Cys residues and of conserved 3D-structure,
the large evolutive distance existing between Bryophytes and *A. trichopoda* together with a relaxed
selective pressure could explain the low sequence identity observed between sequences of Tree I.
Indeed, whereas terrestrialization is assumed to have occurred 450 MYA [36], the age of angiosperms
emergence was estimated to be between 169-199 MYA [37]. Based on the putative interaction with cell
wall polysaccharides and O-glycans, the PAC domain sequence variability could be correlated with the
variability of the cell wall composition from Bryophytes to angiosperms [38].

In Tree II, the PAC domains were distributed into 10 clades with high confidence bootstrap values
(from 72 to 100) with the exception of clade H (28) (Figure 6, S9). An *A. trichopoda* PAC domain was
found in each of them. Four clades were specific to higher plants, each of them, respectively, comprised
the following *A. trichopoda* PAC domains: AmTr.v1.0.047.45 (clade F); AmTr.v1.0.068.122 (clade G);
AmTr.v1.0.153.4 (clade H); and AmTr.v1.0.019.72 (clade I). Monocot and dicots were represented in
all the clades, but clade J comprised a high number of grass PAC domains originating from gene
duplication (see above). Interestingly, although the tree has been built up with PAC domains only, they
grouped according to their association to other domains: type 1-PAC domains were found in clades A,
C, F, H, and I; type 2-PAC domains were grouped in clades D, E, and J, with type 2 W-W domains
in clade D; type 3-PAC domains were found in clade G with the exception of three of them in clade
H with short Proline-rich motifs at their N-terminus; and type 4-PAC domains were only found in
clade D. Thus, it seems that there is a link between the amino acid composition of PAC domains, their
secondary structure, and the associated domains. Finally, it seems that all the PAC domains of higher
plants have a counterpart in *A. trichopoda*, meaning that the modern multi-domain structures of the
PDPs found in the ten angiosperm clades preceded the emergence of angiosperms.
<figure><img src="image_126.png" /><figcaption>**Figure 6.** Phylogenetic Tree II. Tree II was built up using 196 PAC domains sequences from *A. trichopoda* to *A. thaliana*. Ten clades (A to I) were defined according to significant bootstrap values (higher than 72, with the exception of clade B). The type of PDPs (e.g., Type 1 is 1, see Figure 2) found in each clade indicated between brackets. The name of the *A. trichopoda* PDP found in each clade is indicated and highlighted with a red star.</figcaption></figure>
## 2.6. Conserved Amino Acids Motifs Inside Clades

A search for conserved amino acid motifs was done for the PAC domains of each clade of Tree II. The most significant results were found for clades A, B, D, E, G, H, and I (Figure 7). In each clade, the most conserved motifs were detected at the N-terminus of the PAC domain. This was consistent with the definition of the pollen Ole e 1 motif in the Pfam and Prosite databases (PF01190 and PS00925, respectively). However, the consensus defined for the PS00925 domain only exactly fitted with that of clade A PAC domains ([EQT]-G-x-V-Y-C-D-[TNP]-C-R). Furthermore, the most conserved PAC domains were found in the C clade (Figure 8). Their degree of conservation in the green lineage from Lycopodiales to Brassicales is impressive. Finally, the C-terminal W-W domain present in all the proteins belonging to clade D was also very well conserved from the Bryophytes to the Brassicales with common motifs mostly located in its N-terminus half (S10).

<figure><img src="image_127.png" /><figcaption>**Figure 7.** The most conserved motifs of PAC domains inside clades A, B, D, E, G, H, I in PDPs of *A. trichopoda* plant families appeared subsequently. The number of PAC domains in each clade is indicated as well as the score of the conserved motif according to the MEME software.</figcaption></figure>

<figure><img src="image_128.png" /><figcaption>**Figure 8.** The most conserved PAC domains from clade C. The comparisons have been made between 18 PAC domain sequences from Lycopodiales to Brassicales.</figcaption></figure>

The combination of sequence conservation with the accessibility of conserved residues on the protein surface shall hint to functional important sites while conserved residues located in the protein core are more likely important for maintaining the fold. Also, conserved residues in the loop regions
may have a functional role, although they are less accessible in the static 3D-structural model as loops are often flexible and may move considerably. We, therefore, defined a representative 3D-model for each clade and obtained the solvent accessibility and secondary structure for each residue and aligned this information with the sequence profiles (S12). Indeed, many of the conserved sites are inaccessible to the solvent and located within or close to the β-sheets and, thus, are expected to maintain the fold. Candidates for the functional role are, for example, in clade A a Phe-x-Thr pattern (profile position 11-13); in clade B, a cluster of basic residues at position 18-22; in clade D, the conserved charged residues Lys and Asp at position 9 and 10; or in clade H, the amino acids Lys and Arg at position 35. The reliability of such assumptions depends on the quality of the structural models. We calculated a model quality score with MAESTRO and related the scores of the models to scores of experimentally determined structures (S13). The scores of the models are in the range of the modeling template structure (PDB code 4Z8W), indicating that none of the models should be largely wrong.

The conservation of motifs in PAC domains suggests common biological activities. It is possible to infer that their interactions with cell wall polysaccharides or O-glycans assumed from in vitro studies have been conserved and that the distribution of PDPs in the different plant families reflects differences in cell wall polysaccharides. Regarding the W-W C-terminal domain of the clade D PAC domains, its role remains to be unraveled. It is encoded by a distinct exon and could originate from exon shuffling [39].

## 3. Materials and Methods

### 3.1. Databases

The sequences used in this study have been retrieved from different databases, such as Orchidstra 2.0 ([40] http://orchidstra2.abrc.sinica.edu.tw/orchidstra2/orchid_blast.php), genome annotation Databases ([41], http://genome.microbedb.jp/blast/blast_search/klebsormidium/genes), Phytozome ([42], https://phytozome.jgi.doe.gov/pz/portal.html), OneKP ([43], https://db.cngb.org/onekp/) (see S1). When necessary, nucleotide sequences have been translated into amino acid sequences using EMBOSS transeq ([44], https://www.ebi.ac.uk/Tools/st/emboss_transeq/).

### 3.2. Comparisons and Alignment of PAC Domains

The BLAST (https://blast.ncbi.nlm.nih.gov/Blast.cgi) program has been used for sequence comparison. Similarities between PAC domain sequences have been calculated using either Blast2seq (https://blast.ncbi.nlm.nih.gov/Blast.cgi) or needle (http://www.bioinformatics.nl/cgi-bin/emboss/needle). The sub-cellular localization of proteins has been predicted with TargetP-2.0 ([45], http://www.cbs.dtu.dk/services/TargetP/) and the presence of β-sheets and/or α-helices using SABLE ([46], http://sable.cchmc.org/) and NetSurfP ([47], http://www.cbs.dtu.dk/services/NetSurfP/). The selected PAC domains starting at the Gly amino acid located three amino acids upstream of Cys 1 and ending at Cys 6 have been aligned using PROMALS3D ([48], http://prodata.swmed.edu/promals3d/promals3d.php) to take into account the prediction of α-sheets. The phylogeny has been calculated using MEGA7 ([49], https://www.megasoftware.net/) with the maximum likelihood option and 500 bootstraps. The presence of the PROSITE (PS00925, [50], https://prosite.expasy.org/) and Pfam (PF01190, [51], http://pfam.xfam.org/) domains have been checked in the retrieved sequences. Inside clades, conserved motifs have been identified using MEME ([52], http://meme-suite.org/tools/meme) or WebLogo3 ([53], http://weblogo.threeplusone.com/).

### 3.3. Three-Dimensional Modeling

For a subset of PAC domains, models were generated utilizing MODELLER [54] and I-Tasser [55]. Thereby, disulfide bridges were defined beforehand based on alignments with PDB entry 4Z8W corresponding to the *P. lanceolata* PAC domain [24]. Subsequently, these models were scored with
MAESTRO [56], DOPE [57], and ProSA 2003 [58]. Then the top-scoring models were relaxed with Rosetta [59], and finally, the relaxed models were scored with the same three methods.

We consistently used PAC domains from *A. trichopoda* as representative models for each clade. The relative solvent accessibility of these models was calculated by an adaptation of the Geometry library algorithm [60]. The secondary structure assignment was obtained by DSSP [61,62].

Both MODELLER and I-Tasser depend on template structures. MODELLER is a homology-modeling tool, which assumes significant sequence similarity between target and template structures in order to create a reliable alignment between them. Loops and sidechains are modeled with respect to the target sequence. The overall fold, however, is largely determined by the template structure. I-Tasser is a fold-recognition approach, where sequence similarity between target and template does not play a major role. Moreover, I-Tasser uses structural fragments rather than complete protein (domain) folds, from which the overall fold is built. The final model is not determined by a single template. As such, it should be better applicable for PAC domain sequences with low similarity to the Pla I 1 PAC domain.

**4. Conclusions**

This study has allowed better defining PDPs by combining amino acid sequences features, secondary structures, and 3D-modeling. This protein family has appeared early during the evolution of the green lineage. It has, however, not been possible to identify with certainty a PAC domain ancestor in the presumed precursor organisms of the green lineage even if the *C. orbicularis* PAC domain appeared as a possible candidate. The association of the PAC domain with Pro-rich sequences seemed to be an ancient event, the most ancient sequence carrying both a PAC domain and a Proline-rich domain being found in Bryophytes, and those carrying both a PAC domain and extensin domains in Psilotales. Despite a great amino acid variability between PAC domains, the tertiary β-barrel structure strengthened by three disulfide bridges has been conserved in all bona fide PAC domains. Finally, the subset of PAC domains belonging to Clade C is intriguing. Their very high level of conservation at the amino acid sequence level suggests that they play critical roles in plant cell walls. Defining the specificity of interaction of the different PAC domains with other cell wall polymers will be one of the next challenges to fully unravel the roles of PDPs in the cell wall architecture.

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/21/7/2488/s1 S1 Number of PAC domain and PAC domain-related proteins in different plants from Bryophytes to Brassicales; S2 Amino acid sequences of PAC domain proteins in the green lineage; S3 Some examples of PAC domain-related proteins containing predicted functional domains suggesting intracellular functions; S4 Amino acid sequences of PAC domain-related proteins in ancestors to the green lineage; S5 Amino acid sequences of putative PAC domains with only five Cys residues, more than six Cys residues, or no Gly residue upstream Cys 1; S6 Amino acid sequences of putative PAC domains with six Cys residues, but predicted α-helices; S7 Amino acid sequences of the PAC and W-W domains of Type 2-PDPs including a C-terminal W-W domain; S8 Top-scoring 3D-models of PAC domains and the corresponding scores. Some PAC domain 3D-models; S9 Expanded phylogenetic trees of PAC domains from Bryophytes to *A. trichopoda* (Tree I) and from *A. trichopoda* to Brassicales (Tree II); S10 The conserved W-W domain from PAC domains belonging to clade D from Bryophytes to Brassicales PDPs; S11 *In silico* mutagenesis experiment to test the stability of the 3D-structure of a set of PAC domains mutagenized on one of the six conserved Cys residues; S12 Solvent accessibility and secondary structure for each residue and alignment of this information with the conserved sequence profiles of PAC domains; S13 MAESTRO scores for PAC domain models in relation to MAESTRO scores for experimentally-determined structures taken from the PDB database.

**Author Contributions:** Conceptualization, E.J. and C.D.; methodology, E.J., C.D., G.G., J.L., P.L., and H.S.C.; validation, J.L., G.G., P.L., and E.J.; investigation, H.N.-K.; data curation, H.N.-K., E.J., H.S.C.; writing—original draft preparation, E.J.; writing—review and editing, all authors.; visualization, G.G., J.L., P.L. and E.J.; supervision, E.J.; project administration, E.J.; funding acquisition, E.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors are thankful to Université Paul Sabatier-Toulouse III (France) and CNRS for supporting their research work. HNG-K has been granted by the Vietnamese Ministry of Education and Training for his PhD work. This work was also supported by the French Laboratory of Excellence project entitled "TULIP" (ANR-10-LABX-41; ANR-11-IDEX-0002-02). JL is supported by the Austrian Science Fund (FWF, grant P30042).

**Conflicts of Interest:** The authors declare no conflict of interest.
Abbreviations

PAC Proline-rich, Arabinogalactan protein, conserved Cysteines

PDP PAC Domain Protein

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Review

# Phyllotaxis Turns Over a New Leaf—A New Hypothesis

Derek T. A. Lamport <fnref n="1" />,*, Li Tan <fnref n="2" />, Michael Held <fnref n="3" /> and Marcia J. Kieliszewski <fnref n="3" />

Received: 1 November 2019; Accepted: 5 February 2020; Published: 9 February 2020

**Abstract:** Phyllotaxis describes the periodic arrangement of plant organs most conspicuously floral. Oscillators generally underlie periodic phenomena. A hypothetical algorithm generates phyllotaxis regulated by the Hechtian growth oscillator of the stem apical meristem (SAM) protoderm. The oscillator integrates biochemical and mechanical force that regulate morphogenetic gradients of three ionic species, auxin, protons and Ca<fnref n="2" />⁺. Hechtian adhesion between cell wall and plasma membrane transduces wall stress that opens Ca<fnref n="2" />⁺ channels and reorients auxin efflux “PIN” proteins; they control the auxin-activated proton pump that dissociates Ca<fnref n="2" />⁺ bound by periplasmic arabinogalactan proteins (AGP-Ca<fnref n="2" />⁺) hence the source of cytosolic Ca<fnref n="2" />⁺ waves that activate exocytosis of wall precursors, AGPs and PIN proteins essential for morphogenesis. This novel approach identifies the critical determinants of an algorithm that generates phyllotaxis spiral and Fibonaccian symmetry: these determinants in order of their relative contribution are: (1) size of the apical meristem and the AGP-Ca<fnref n="2" />⁺ capacitor; (2) proton pump activity; (3) auxin efflux proteins; (4) Ca<fnref n="2" />⁺ channel activity; (5) Hechtian adhesion that mediates the cell wall stress vector. Arguably, AGPs and the AGP-Ca<fnref n="2" />⁺ capacitor plays a decisive role in phyllotaxis periodicity and its evolutionary origins.

**Keywords:** Phyllotaxis; arabinogalactan proteins; auxin; calcium signaling; acid growth; Hechtian oscillator; plasma membrane ion fluxes

## 1. Introduction

Agnes Arber [1] in “The Natural Philosophy of Plant Form” comprehensively described the development of plant morphology from the ancient philosophers—Plato, Aristotle and Theophrastus—to the more recent Cambridge botanical tradition that extends from William Turner, Nehemiah Grew and “Robin” Hill to the present. William Turner (1508–68), father of English botany, published the first herbal in English (1551) as a Fellow of Pembroke College; Nehemiah Grew (1641–1712), another Pembroke graduate, father of plant anatomy published “The Anatomy of Plants” (1682) depicted in the exquisite stained-glass windows of the college library. Finally, the Hill reaction demonstrated the photolysis of water as the source of atmospheric oxygen and established molecular botany as a new level of scientific enquiry. Arber’s historical perspective may help resolve some long-standing problems of plant morphogenesis. Thus, Arber [1] presented “The mechanism of plant morphology” and an insightful approach to the pivotal role of the cell wall and the stress–strain of cell expansion that results in “form conditioned by pressure” where “even a minor [cell wall] alteration may be associated with striking changes in the external form.” In Northcote’s laboratory, those ideas catalyzed the first Ph.D. dissertation devoted to the primary cell wall and the discovery of cell wall proteins as a new field of study. These hydroxyproline-rich glycoproteins, especially the arabinogalactan proteins (AGPs), are involved in a hypothetical Hechtian growth oscillator. It involves transduction of the wall

<footnote n="1">1 School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QG, UK</footnote>

<footnote n="2">2 Complex Carbohydrate Research Center, University of Georgia, Athens, GA 30602, USA; tan@ccrc.uga.edu</footnote>

<footnote n="3">3 Department of Chemistry and Biochemistry, Ohio University, Athens, OH 45701, USA; held@ohio.edu (M.H.); kielisze@ohio.edu (M.J.K.)</footnote>

<footnote>* Correspondence: derekt.a.lamport@googlemail.com; Tel.: +44-1273486430</footnote>
stress-strain to the plasma membrane where an auxin-activated proton pump dissociates AGP-Ca²⁺. Elevated cytosolic Ca²⁺-activates exocytosis thus regulating plant growth. Discussion of the Hechtian Oscillator vis-a-vis the role of the primary cell wall in plant morphogenesis [2] suggests extrapolating the oscillator to phyllotaxis based on the premise that presence of the oscillator components implies the presence of a functional Hechtian Oscillator. Indeed, recent work suggests the mechanotransduction of stress relocates auxin efflux PIN proteins that generate new protoderm primordia. However, the precise biochemical mechanisms involved in stress transduction and the role of auxin and calcium homeostasis remain to be elucidated. Here, we invoke Hechtian adhesion and AGPs as essential components that lead us to propose a novel biochemical algorithm for floral phyllotaxis and an explanation of its strong tendency towards a periodic series first described by Fibonacci (1170–1240). This approach contrasts with many previous studies with an overwhelming mathematical bias. Indeed, many observations in Nature involve periodicity and the probable underlying oscillations

Oscillatory plant growth, known since Darwin [3], was subsequently confirmed by rapid tip growth of pollen tubes and root hairs [4]. Plant morphogenesis also involves periodicity strikingly displayed by the pattern of leaves and floral organs [5] that often appear as Fibonacci spirals typified by whorls of 3, 5, 8, 13, 21 and 34 petals [6]. Hypothetically, such periodicity depends on an underlying oscillator such as the recently formulated Hechtian growth oscillator [2,7] that involves auxin-driven Ca²⁺ release from arabinogalactan proteins (AGPs) of the cell surface; this hypothesis accounts for the origin of oscillations in molecular detail absent from previous models of tip growth [8]. Here, we extrapolate the Hechtian Oscillator to the challenging problem of phyllotaxis and the generation of primordia in the protoderm, the outermost cell layer of the stem apical meristem SAM. Earlier work emphasized physical factors and a mathematical approach was comprehensively reviewed in [6,9,10]. However, more recent work emphasizes a cell wall stress vector generated by rapid cell expansion in the protoderm that re-orientates auxin efflux PIN proteins of neighboring cells and thus directs auxin transport (and the inferred generation of Ca²⁺ waves) that regulate growth and differentiation (e.g., [11–14]). The present paper complements these and more recent models of [15] but with the notable exception of [16]; none consider a possible role for cell surface AGPs. However, "Nature keeps some of her secrets longer than others" [17]. That includes the elusive molecular function of classical AGPs [18–20]. Identified some fifty years ago [21–23], AGPs remained "A Great Puzzle" until the recent demonstration that AGP glycomodules bind Ca²⁺ specifically [24]. They form a cell surface AGP-Ca²⁺ capacitor that involves the interaction of three essential ions auxin, H⁺ and Ca²⁺. These "morphogens" of the Ca²⁺ signal transduction pathway (Figure 1) interact and thus regulate cell expansion and growth.

The pathway begins with the transduction of the cell wall stress vector to the plasma membrane, via AGP57C [25] as the likely molecular basis of Hechtian adhesion between the cell wall and the plasma membrane. Further transmission of a biochemical signal to the cytoplasm involves stretch-activated proton and Ca²⁺ ion fluxes of the plasma membrane generated by the Hechtian growth oscillator [7]. The cytoplasmic response to Ca²⁺ influx presumably involves exocytosis of wall plasticizers and precursors including redirection/reorientation of auxin efflux PIN proteins, eponymously named after their mutant pin-shaped phenotype. These auxin transport proteins channel auxin flow away from slow expansion towards rapid expansion thus generating auxin waves with maxima corresponding to the periodicity of nascent primordia. Turing's classic paper [26] postulated only two morphogens sufficed to generate spiral phyllotactic periodicity. The sections below expand on Turing's original suggestion with recent experimental evidence. Turing's insight was much closer to reality than the "two interacting morphogens" he envisaged.
<figure><img src="image_132.png" /><figcaption>**Figure 1.** (a) The Hechtian Oscillator ion fluxes regulate growth. Depicts a simplified version of the Hechtian Oscillator in [2]. This figure shows stills from the animation in Supplemental Data. Membrane and ion fluxes are analogous to a molecular "pin-ball machine." KEY: protons: red, Ca²⁺ ions: yellow, auxin: green, stretch-activated Ca²⁺ channels; Ca²⁺ trickle initiates proton pump activity; (b) **Phase I. Quiescent**: [7s] Proton pump minimally active; Ca²⁺ channels closed with minimal Ca²⁺ influx. **Phase II. Activation**: [6s] Turgor increases cell expansion and thus wall stress that increases demand for auxin and opens stretch-activated Ca²⁺ channels; Ca²⁺ trickle initiates auxin binding by the proton pump, initiating low-level oscillator activity leading to Phase III. **Phase III. Fully Activated**: [12s] high auxin levels fully activate proton pump. Proton extrusion dissociates periplasmic glycomodule AGP-Ca²⁺. Entry via Ca²⁺ channels generates cytosolic Ca²⁺ waves that activate: exocytosis of: cell wall precursors, wall plasticizers and redirect auxin efflux "PIN" proteins. **Phase IV**: [9s] Returns to Quiescent state: Stress relaxation closes Ca²⁺ channels. Auxin dissociates from proton pump; cytosolic Ca²⁺ recycles to recharge glycomodules and determine phyllotaxis periodicity as follows.</figcaption></figure>

The ingenuity of Mother Nature exceeds our human imagination by involving three interacting ions, auxin, protons and Ca²⁺ (Figure 1) as the master regulator of plant growth. Although ion accumulation studied for more than 80 years [27] has generally assumed the relative immobility of
Ca²⁺ ionically bound to the cell wall, non-intuitively Ca²⁺ bound by cell surface AGPs now appears to be the major source of dynamic cytosolic Ca²⁺. Counter-intuitively, the mechanism for the release of dynamic Ca²⁺ from ionically bound AGP-Ca²⁺ is not obvious. However, the paired glucuronic carboxyls of AGP glycomodules explain the remarkable stoichiometric Ca²⁺-binding properties of periplasmic AGP-Ca²⁺; its dissociation by an auxin-activated proton pump predicts an essential role of AGPs in Ca²⁺ homeostasis [24].

## 2. Hechtian Adhesion

The Profound implications of Hecht [28] and many other's observations are becoming clear. Numerous papers emphasize Hechtian strands of plasmolyzed cells but ignore the corollary, strong adhesion between the wall and plasma membrane of turgid cells which until recently has remained a scientific mystery. However, in plasmolyzed pollen tubes [7] and root hair tips [29] (Figure 2), a high density of Hechtian strands correlates rapid tip growth with Hechtian adhesion arguably mediated by AGP57C [25]. This suggests its essential role in transduction of the wall stress vector that initiates oscillations and cytosolic Ca²⁺ waves as hypothesized by the Hechtian Oscillator (Figure 1) [7].

<figure><img src="image_133.png" /><figcaption>**Figure 2.** Hechtian strands in root hairs (arrow head) towards the very tip after labeling wheat root hairs with a membrane selective non-permeable fluorescent styryl dye, FM1-43. Reprinted with permission from [29].</figcaption></figure>

## 3. Is the Hechtian Oscillator Just an Hypothesis? Direct Evidence

The correlation between Hechtian adhesion and tip growth also implies that transduction of the wall stress vector with concomitant activation of the proton pump releases Ca²⁺ from a tip-localized AGP-Ca²⁺ capacitor, hence a source of the tip-focused Ca²⁺ influx. Although initially an inference, direct experimental evidence was described most recently by De Vriese et al. [30]: Tobacco BY-2 cells expressing the bioluminescent Ca²⁺ sensor aequorin responded immediately to addition of the auxin analog 2,4-D, "the luminescent signal rapidly increased and reached a maximum after 90 s." Thus, direct evidence confirms a major prediction of the Hechtian Oscillator hypothesis that connects activation of the proton pump and proton extrusion with rapidly increased cytosolic Ca²⁺ (Figure 1).

The Hechtian Oscillator exemplifies the pollen tube paradigm of rapid tip growth in particular [2,7]. The rapidly growing cell wall transmits its stress-strain status via Hechtian adhesion to the plasma membrane. The role of Hechtian adhesion in stress transduction, inexplicably overlooked for more than a hundred years, also explains how a periplasmic AGP-Ca²⁺ capacitor, as a major component of the oscillator and its auxin-activated proton pump, can regulate plant growth in general. The biochemical physiological and ecological properties of the Hechtian Oscillator also avoid the vagaries of a variable external Ca²⁺ supply; it guarantees immediate access to Ca²⁺ while recycling cytosolic Ca²⁺ replenishes the AGP-Ca²⁺ capacitor. Such efficient use of Ca²⁺ may ensure the survival of calcifuge species in Ca²⁺-deficient habitats where over-expression of AGPs also observed under salt
stress [31] may enhance the ability to scavenge Ca²⁺. Marine plants such as Zostera (Eelgrass) support that hypothesis. Recent characterization of their AGPs shows an elevated glucuronic acid content suggestive of enhanced Ca²⁺ binding in high salt [32].

### 4. Auxin Activity Is a Proxy for the Hechtian Oscillator

Heisler et al. [13] concluded that in the shoot apical meristem of Arabidopsis, "cycles of auxin build-up and depletion accompany, and may direct, different stages of primordium development," further confirmed by a more recent study of Arabidopsis embryogenesis [33]. Auxin waves indicate the presence of an auxin-activated proton pump an essential component of the Hechtian Oscillator. Therefore, auxin activity itself can be taken as a proxy for an active Hechtian Oscillator, consistent with the well-known association of auxin with cell expansion.

Thus, H⁺ dissociation of periplasmic AGP-Ca²⁺ [24] is the inferred source of cytosolic Ca²⁺ that activates exocytosis in the AGP-rich protoderm. Indeed, ubiquitous distribution of AGPs throughout the Plant Kingdom [34,35] implies an absolute requirement for AGPs. Lethal knockouts of genes encoding pollen AGPs [36] confirm their essential global role. Indeed, AGPs are closely associated with morphogenesis even at the very earliest stages such as microspore embryogenesis [37]. Therefore we hypothesize that a biological oscillator generates oscillatory growth and contributes to primordia periodicity; phyllotaxis is a test case of the Hechtian Oscillator and its general applicability is developed in the following sections.

### 5. A Molecular Pin-Ball Machine Regulates Ion Fluxes at the Plasma Membrane

Auxin activates plasma membrane H⁺-ATPase proton pump by increasing its phosphorylation which increases the rate of proton extrusion [38]. The extent of ATPase phosphorylation [39] exerts fine gain control of the proton pump over a wide range. Hydrolysis of a single ATP molecule fuels the extrusion of about three protons by an H⁺-ATPase "turbo-molecular" proton pump. The molecular pathway involves successive glutamate protonation and deprotonation from the cytoplasmic side to the periplasm and cell wall (Figure 3) [39] and initial extremely fast lateral proton diffusion on the plasma membrane surface [40].

d

<figure><img src="image_134.png" /><figcaption>**Figure 3.** The proton pump pathway. Sequential protonation and deprotonation of the c-ring involve ATP-hydrolysis-driven rotation that causes protonation of a Glu residue at the cytoplasmic half-channel with subsequent deprotonation of a Glu residue at a luminal half-channel. Reprinted with permission from [39].</figcaption></figure>

Proton extrusion and a concomitantly low wall pH associated with cell extension so-called "acid growth" [41] exemplify Lord Rutherford's dictum that "No experimental result is ever wrong." A widely accepted (textbook) explanation invokes low pH-dependent wall loosening "enzymes" and expansins all of unknown specificity [42] but ignores the dissociation of AGP-Ca²⁺ that provides an alternative reinterpretation of "acid growth" based on a visual analogy of the plasma membrane depicted as a metaphorical "molecular pin-ball machine" in (Supplemental Data) that regulates three ion fluxes, H⁺, Ca²⁺ and auxin (anions at neutral pH, neutral at low pH). When activated by auxin, the proton pump shoots fast protons into the periplasm where they dislodge Ca²⁺ ions from the periplasmic AGP
glycomodules; i.e., proton efflux generates Ca²⁺ influx. Thus, free Ca²⁺ ions then enter the cytosol via stretch-activated Ca²⁺ channels. The rapid increase of cytosolic Ca²⁺ [30] activates exocytosis of putative wall plasticizers, namely AGPs and AGP peptides [7] (Figure 1). Regulation of Ca²⁺ homeostasis is thus the major function of the proton pump rather than the regulation of wall pH.

## 6. Transduction of the Stress Vector through the Protoderm

Primordia are initiated in a "generative annulus" [6]. This thin band of protodermal cells encircles the outermost cell layer of the stem apical meristem (SAM) protoderm where its powerful morphogenetic properties are triggered by the incipient primordia. These most rapidly expanding cells transmit the stress vector to neighboring cells via their anticlinal walls [14,43–45]. Such stress relocates the auxin efflux "PIN" proteins so their polarization in the protoderm results in auxin transport towards incipient primordia. The physical basis of stress transduction depends on Hechtian adhesion while its co-localized auxin efflux "PIN" proteins were shown by immunocytochemistry [45]. Such polarized localization of auxin efflux proteins, e.g., PIN1 in the protoderm [33], suggested a crucial role for auxin transport in the generation of primordia [46]. It was concluded that "PIN directs auxin to the sites where young primordia are being formed." Rapid relocation of PIN1 is evidently of huge significance, although the precise mechanism remains obscure. Two components not previously considered essential for primordia formation involve Hechtian adhesion and AGPs. They mediate transduction of the cell wall stress vector, as follows:

## 7. Stress, PIN Protein Redirection and Auxin Waves

"Symmetries control distribution in space" [47] begs the question: What is the origin of symmetry, and how is it broken? This centuries' old debate gradually developed from "vital force" and the equally unfalsifiable "morphic resonance" to Spemann's organizer, morphogenetic fields, Waddington's "evocators" and Turing's morphogen gradients to current concepts of homeobox genes and a plethora of cognate transcription factors. They illustrate the complexity of animal morphogenesis compared with the sublime sessile simplicity of plants and the view here that auxin gradients control proton and Ca²⁺ fluxes that are predominant regulators of growth and differentiation.

Auxin transport involves diffusion facilitated by auxin efflux, eponymous "PIN" proteins essential to the generation of auxin waves that break the perfect symmetry of the protoderm as follows:

Morphogenesis frequently involves auxin waves [48]. That includes phyllotaxis [5] where a recent theoretical biophysical model involving complex linear wave equations predicts auxin waves that specify the site of new primordia [16]. Those authors noted that: "*The role of auxin transport in phyllotaxis must be universal*" and also inferred that "*electromechanical feedbacks apparently involve the Ca²⁺ and H⁺ ions.*" Recent direct experimental evidence [7,24] explains how the cell wall stress vector and transcytosis relocate PIN proteins and thus together with AGP-Ca²⁺ generate the auxin and Ca²⁺ waves that initiate primordia formation.

Rapidly expanding cells of the protoderm transmit the stress vector via anticlinal walls towards slower cell expansion (Figure 4). The biophysical basis of stress transduction arguably involves Hechtian adhesion between the wall and plasma membrane as described for the growth of pollen tubes and epidermal cells of root tips [45]. Hechtian adhesion is also evident in the protoderm: for example, Figure 1A of [49] shows a Hechtian strand formation in protodermal areas. Hechtian adhesion is virtually universal and thus also present in actively growing tissue like the protoderm! Furthermore, auxin waves are also evidence of an active Hechtian Oscillator based on Hechtian adhesion.

Transmission of the stress vector relocates PIN auxin efflux proteins to the stressed anticlinal walls of stressed cells [45]. Thus, auxin moves against its concentration gradient towards cells with the highest auxin levels therefore depleting the auxin of less rapidly expanding cells. Channeling auxin towards stress generators, i.e., the most rapidly expanding cells, presumably initiates primordia when auxin reaches a critical threshold level [15]. Attenuation of the stress vector by intervening distal cells depleted of their auxin slows their expansion until a boundary "tipping point" of minimum cell
expansion appears (Figure 4) where the stress vector reverses its direction with concomitant reversal of PIN protein polarity [45]. Thus, a new auxin gradient increases towards a new stress vector initiated by cell expansion of a newly formed primordium. Hence, auxin waves appear as peaks that coincide with new primordia separated by auxin troughs; these repeat what is in essence an autocatalytic cycle (Figure 5):

<figure><img src="image_135.png" /><figcaption>**Figure 4.** Stress in arabinogalactan proteins (AGP)-rich protoderm generates primordia. This hypothetical scheme illustrates the possible origin of auxin waves in phyllotaxis [6]. Five-fold rotational symmetry predominates as the phenotype in dicot floral phyllotaxis. A plausible biochemical algorithm generates auxin waves and new primordia: Rapid cell expansion creates the stress vector (red arrows) that orientates PIN proteins; these channel auxin (green arrows) towards rapidly expanding cells to form incipient primordia and deplete auxin from sites of slow expansion until reaching a “tipping point” (lowest auxin level, slowest cell expansion, minimal stress) where PIN proteins reverse their orientation. Auxin maxima and minima generate regions of rapid expansion at auxin peaks corresponding to incipient primordia P1 to P5 separated by slowest growth at auxin troughs or “tipping points.” Precise spacing of growth peaks corresponds to the frequency of auxin waves controlled by three primary determinants, proton pump, auxin flux and AGP-Ca²⁺ capacitor size.</figcaption></figure>

We propose that the generation of successive auxin waves varying in amplitude and frequency depends on the response of the proton pump and cell surface AGP. Indeed, there is an increasingly clear correlation between enhanced AGP expression and tissue morphogenesis.

Membrane-bound PIN proteins recycle rapidly via transcytosis; for example, the relocalization of PIN7 occurs within two minutes after the gravity stimulus [50]. Arguably, the mechanism involves Hechtian adhesion that transmits wall stress directly to the plasma membrane rather than indirect transmission via “statoliths.” During rapid tip growth of pollen tubes and root hairs, Hechtian adhesion predominates at the growing tip where wall stress–strain is most apparent and exocytosis is maximal. This correlation suggests that the stress vector relocates Hechtian adhesion sites at a malleable cell wall and this, in turn, directs the exocytosis of wall precursors including auxin efflux PIN proteins (cf. Figure 4). Thus, auxin waves and cytosolic Ca²⁺ [51] generated by transmission of the cell wall stress vector depend on two additional factors, transcytosis and cell wall rheology.
<figure><img src="image_136.png" /><figcaption>**Figure 5.** The auxin autocatalytic cycle. While Turing proposed a model based on the interaction between simple diffusion gradients of two morphogens, we suggest the interaction of three ions: PIN proteins boost the uphill diffusion of auxin against the concentration gradient while protons the fastest diffusing ions, dissociate AGP-Ca²⁺ thus enhancing exocytosis of PIN proteins (and Ca²⁺ channels) that propagate the Ca²⁺ message. This is summarized by the canalization theory [12] in which “small local differences in auxin concentration are amplified by a self-reinforcing accumulation mechanism, resulting in local auxin elevation and auxin depletion in the surrounding tissue.”</figcaption></figure>

## 8. Cell Wall Rheology

Transmission of the stress vector from rapidly expanding cells of incipient primordia involves plasticity of the anticlinal cell walls. Although Anton Heyn [52] identified wall plasticity as a crucial determinant of cell expansion, even after eighty years the biochemical basis of the Heyn paradigm remains debatable. Despite Heyn's emphasis on plasticity, cleavage of covalent cell wall crosslinks remain the predominant but elusive explanation [53]. Most synthetic plastics depend on plasticizers like phthalates, small molecules that disrupt the alignment of linear polymer chains but do not cleave covalent bonds. Analogous plasticizers of pectins include classical AGPs but their molecular size precludes simple diffusion through a pectic matrix. However, the much smaller diffusible AGP peptides upregulated by auxin [54] are also potential plasticizers; significantly their glucuronic acid content [55] indicates Ca²⁺-binding capacity similar to the much larger non-diffusible classical AGPs typified by LeAGP1 that transit the wall by extrusion rather than diffusion [31]. Thus small AGP peptides diffusing though the wall can compete for Ca²⁺ crosslinks and thus favor a pectic gel-sol transition with a concomitant increased wall plasticity. Pectin methyl esterases have also been invoked [56]; Cosgrove [57] notes “localized deesterification of homogalacturonan as a signature event in the auxin-induced patterning of the shoot apical meristem ... this correlation of de-esterified pectin with softer meristem regions is perplexing” but consistent with electrostatic repulsion of ionized pectic carboxylates their Ca²⁺ depleted and scavenged by AGPs and AGP peptides with a higher affinity for Ca²⁺. However, Altartouri et al. [58] represent the prevailing view that Ca²⁺ crosslinkage of de-esterified pectin decreases wall plasticity. This implicitly assumes sufficient free Ca²⁺ for pectin crosslinking but ignores AGP-Ca²⁺ homeostasis that determines the availability of both free and bound apoplastic Ca²⁺.

Fine control of pectin rheology by small diffusible AGP peptides has not previously been considered. Similar reasoning may apply to some monocots where glucuronoxylans largely replace pectin [59]. Finally, we can only agree that: “Cell expansion thus appears to be intimately linked to these wall sensor pathways in ways we are only beginning to fathom.” [57].

## 9. A Phyllotaxis Algorithm

“While progress has been made, there are many fascinating challenges in phyllotaxis still open for the curious mind to explore. The story is far from over. While careful experiments are crucial to continued progress, it does not require elaborate experiments for ordinary folk to enjoy the wonderful architectures seen near the
meristems of plants" [6]. Summarizing much recent work: "Key results stem from the observed facts that phyllotactic patterns are naturally produced by instabilities, connected to both the distribution of the growth hormone auxin and to the local stress-strain fields." Although those "instabilities" remain undefined, phyllotaxis per se is remarkably stable but with exceptions described by Arber [1] in several species. For example, a completely dimerous flower of Iris on a shoot also bearing a normal trimerous flower, and Potentilla flowers with three, four, five or six petals and concluded that "phyllotaxis depends upon the rhythmic development of primordia at the growing apex." Somewhat ahead of its time, eighty years ago, the insightful observation was made: "it seems reasonable to suppose that these variations are associated with internal chemical oscillations" with a final intuitive leap to "Physico-chemical factors...one such factor has been so universal as to affect the whole of the Plant Kingdom; this is the development of a cell wall encasing each unit of the plant body." "The challenge now is to describe how the stem apical meristem generates phyllotactic patterns de novo" [12]. The historical emphasis on mathematical approaches based on optimal packing shows that Fibonacci patterns can arise naturally in many pattern-forming systems but this is not obviously connected with the biochemical mechanisms involved in patterning. Both approaches achieve optimal packing but in quite different ways. All the components of the Hechtian Oscillator are present. Thus, a dynamic algorithm involving protoderm biochemistry and mechanotransduction is now feasible as a working hypothesis.

Protoderm cell expansion generates new primordia (N). For example in a floral phyllotaxis, *N* is a function of the stem apical meristem (SAM) size and the magnitude of major variables that define the symmetry and periodicity of new primordia. To sustain their growth, rapidly expanding cells demand auxin by generating the cell wall stress vector (CW<sub>sv</sub>) that redirects PIN proteins thus channeling auxin towards these incipient primordia (Figure 4). A resulting auxin gradient then appears as waves in the annulus, a narrow band of morphogenetic cells surrounding the outer protoderm (SAMP<sub>a</sub>) with auxin maxima and minima corresponding to future primordia and boundary tipping points, respectively. Generally, increasing the magnitude of a variable increases auxin transport towards a primordium hence rapidly depleting distal cells. Reversal of PIN protein orientation then generates a new primordium. Thus, an increased auxin depletion rate increases the number of new primordia. However, they also depend on Ca<sup>2+</sup> availability determined by the expression of AGPs. We predict that AGPs strongly expressed in the protoderm will increase the periodicity of primordia while weaker expression will decrease it. Thus, to that extent, the algorithm is semi-quantitative and dependent on strong expression of AGPs in the protoderm of Arabidopsis meristems [60], Euphorbia embryonic cultures [61] and during somatic embryogenesis of Arabidopsis [62]. The novel suggestion that AGPs play a decisive role as crucial determinants of phyllotaxis periodicity (Figure 6) depends on a complex function of a hypothetical algorithm derived from the foregoing considerations:

<figure><img src="image_137.png" /><figcaption>**Figure 6.** Major variables of the phyllotaxis algorithm.</figcaption></figure>
Stem apical meristem protoderm SAMP<sub>a</sub> generates N new primordia as a function of an equation comprised of the following variables:

1. AGP-Ca<sup>2+</sup> capacitor: AGP<sub>c</sub>;

2. Stem apical meristem protoderm annulus radius: SAMP<sub>a</sub>;

3. PP proton pump activity: PP;

4. Auxin efflux activity: A<sub>efflux</sub> (hence auxin levels: A<sub>ux</sub>);

5. Ca<sup>2+</sup> channels: C<sub>ch</sub>;

6. Exocytosis is a complex variable regulated by Ca<sup>2+</sup> influx;

7. Hechtian adhesion: H<sub>ad</sub>;

8. Cell wall stress vector: CW<sub>sv</sub>;

$$ \frac{\text{SAMP}_a}{\text{AGP}^{-1} + (\text{PP} \cdot \text{A}_{\text{ux}})^{-1} + (\text{C}_{\text{ch}}^{-1} + \text{CW}_{\text{sv}})^{-1} + \text{H}_{\text{ad}}^{-1}} $$

The cell wall stress CW<sub>sv</sub> vector determines auxin, proton and Ca<sup>2+</sup> ion fluxes involving four phases of the Hechtian Oscillator proton pump that regulate cell expansion.

**Phase I. Quiescent:** Minimal cell wall stress corresponds to minimal Ca<sup>2+</sup> influx and minimal activity of the oscillator.

**Phase II. Activation:** Cell expansion increases wall stress, demand for auxin and opens Ca<sup>2+</sup> channels; entry of Ca<sup>2+</sup> initiates auxin binding to the proton pump and initial oscillator activation leading to Phase III.

**Phase III. Maximum Activation:** Occurs at the high auxin levels supplied by redirected auxin efflux PIN proteins; accelerated proton extrusion dissociates glycomodule AGP-Ca<sup>2+</sup> and supplies the Ca<sup>2+</sup> channels thus generating cytosolic Ca<sup>2+</sup>waves that activate exocytosis, notably of wall precursors and plasticizers but also enabling dynamic redirection of PIN proteins. Addition of precursors reinforce the wall and slow its expansion, leading to Phase IV:

**Phase IV. Return to quiescent phase:** Stress relaxation of reinforced wall closes Ca<sup>2+</sup> channels.

Cytosolic Ca<sup>2+</sup> recycles via AGP precursors and Ca<sup>2+</sup>transporters replenish periplasmic AGP-Ca<sup>2+</sup>

When attenuation of the stress vector reaches a tipping point of minimal oscillator activity and least rapid cell expansion, distant cells expand more rapidly and now exert a new stress vector in an opposing direction thus generating a new primordium that contributes to phyllotactic symmetry.

SAMP<sub>a</sub> stem apical meristem protoderm generates new primordia as a function of the activity of five major variables or determinants shown in the speculative graph taking petal phyllotaxis as an example ranging from 3 to 34 petals. It assumes that the cell wall stress vector CW<sub>sv</sub> is essentially constant for a given SAMP<sub>a</sub>.

Protoderm AGP content (activity) is the primary determinant based on the simple hypothesis that size of the AGP-Ca<sup>2+</sup> capacitor determines the periodicity of primordia initiation (cf. Figure 4) where a large capacitor generates more primordia. The graph correlates the Fibonacci series with AGP expression and activity of other factors particularly the proton pump not previously connected with phyllotaxis. Other determinants illustrate an inferred hierarchy based on the size of their relative input to the Hechtian growth oscillator.

The beguiling simplicity of the above plot inferred largely from biochemical observations is in strong contrast to previous complex formulations based largely on mathematical/geometrical logic.

## 10. Evolutionary Origin of Angiosperm Phyllotaxis

The evolutionary history of the stem apical meristem from a relatively simple arrangement of apical cells in the Bryophytes and ferns culminates in the morphogenetic protoderm of the angiosperms. Here, we conjecture that hybridization may solve the riddle of Fibonacci phyllotaxis and its evolutionary origins.
Strong AGP expression predicts numerous closely spaced primordia (Figure 4) that generate floral phyllotaxis, arguably determined by the amplitude of the Ca²⁺ signal that depends on the AGP-Ca²⁺ capacitor size, proton flux and Ca²⁺ channel status. Thus, cells of the protoderm with a large AGP-Ca²⁺ capacitor will increase cytosolic Ca²⁺ rapidly and therefore generate numerous primordia within a shorter range than in a protoderm with weaker AGP expression and therefore with more cells between primordia. For example, lower activity of the proton pump and a smaller AGP-Ca²⁺ capacitor increase spacing between primordia. Unlike the animal kingdom, plants have an enormous propensity for polyploidy and hybridization that we suggest provides a simple biochemical explanation for an evolutionary origin of the well-known Fibonacci series of floral organs exemplified by the 3, 5, 8, 13, 21 and 34 petals (Figure 6), e.g., *Ranunculus ficaria* (13), *Erigeron canadensis* (21). Can hybridization between contiguous members of the series generate a Fibonacci sequence? If so, how? Consider a hybrid expressing the sum of AGPs from both parents! If AGPs play a dominant role in defining phyllotaxis, then a hybrid of two-fold and threefold symmetry, with a corresponding increased size of the AGP-Ca²⁺ capacitor, would generate the most common five-fold symmetry, and so on for subsequent members of the series (Figure 6). Thompson [17] viewed the Fibonacci series not as the cause but merely "*a consequence of optimal space filling in systems adding new units at a pole.*" Thus, we infer that hybridization generates floral Fibonacci phyllotaxis and accounts for the evolutionary origin of a discrete series rather than a smooth arithmetic progression. This suggestion has the merit of simplicity based on Occam's Razor in contrast to all preceding mathematical conjectures [9] and is supported by the Hechtian Oscillator as a predictive paradigm.

## 11. D'Arcy Thompson, Alan Turing and Peter Mitchell Revisited

Thompson's classical "Growth and Form" [17] exemplified a purely descriptive mathematical approach that collated a huge corpus of biophysical observations rather than hypothesis-driven experiments. On the other hand, Turing [26] combined a mathematical with a physical-chemical approach. Thus, while a Turing self-replicating machine aptly fits cell replication, Turing postulated that ontogeny based on biological parsimony might involve the diffusion of only two chemical morphogens that would suffice to create morphogenetic gradients. Those ideas preceded the biochemical insights of Mitchell (Mitchell [63], experimentalist par excellence who questioned conventional wisdom and proposed the versatile chemiosmotic proton pump). A universal energy transduction machine couples proton gradients across lipid membranes to generate ATP that energizes all life. In reverse, it consumes ATP and pumps protons. This vectorial chemical system differs fundamentally from conventionally scalar chemical ones as explained by Mitchell [64]: "*It was obviously my hope that the chemiosmotic rationale of vectorial metabolism and biological energy transfer might one day come to be generally accepted, and I have done my best to argue in favour of that state of affairs for more than twenty years ... was it not the great Max Planck who remarked that a new scientific idea does not triumph by convincing its opponents, but rather because its opponents eventually die?*" Although Mitchell's unconventional ideas were initially rejected, they were finally recognized. Their universal applicability has become apparent more recently. In simple photoautotrophs, light-driven proton gradients involve bacteriorhodopsin [65], while in more advanced eukaryotes, an electron transport chain generates mitochondrial proton gradients. Proton pumps and their regulation are thus at the epicenter of plant growth that, stripped to its bare essentials, depend on three morphogen gradients, auxin, protons and Ca²⁺ rather than just two.

However, these gradients do not arise by simple diffusion but are regulated by auxin efflux "PIN" proteins whose discovery began with Rubery and Sheldrake's [66] classic experiments in the laboratory of Northcote [67]. PIN proteins control auxin gradients and auxin levels that activate the proton pump while the cell wall stress vector opens Ca²⁺ channels that generate cytosolic Ca²⁺ gradients. Thus, the Hechtian growth oscillator is an extrapolation of Mitchell's chemiosmosis that unifies physics and chemistry in a minimalist approach to regulating plant growth. Indeed, precursors to life surely involve proton gradients as a basis of prebiotic energy transduction and the universal proton pump of exoplanet life in the habitable zone.
**Supplementary Materials:** The following are available online at http://www.mdpi.com/1422-0067/21/3/1145/s1.

**Author Contributions:** D.T.A.L., L.T., M.H. and M.J.K. have made major contributions over many years to the chemistry of hydroxyproline-rich glycoproteins which combined with insightful discussions led directly to this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We gratefully acknowledge our home Academic institutions for the past many years of support that has made this and previous work possible. We are indeed greatly indebted to our colleague Ben Coleman for the Supplemental Data animation of the Hechtian Oscillator ion fluxes.

**Conflicts of Interest:** The authors declare no conflict of interest.

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Concept Paper

# The Role of the Primary Cell Wall in Plant Morphogenesis

Derek T. A. Lamport <fnref n="1" />,*, Li Tan <fnref n="2" />, Michael Held <fnref n="3" /> and Marcia J. Kieliszewski <fnref n="3" />

Received: 12 June 2018; Accepted: 4 September 2018; Published: 9 September 2018

**Abstract:** Morphogenesis remains a riddle, wrapped in a mystery, inside an enigma. It remains a formidable problem viewed from many different perspectives of morphology, genetics, and computational modelling. We propose a biochemical reductionist approach that shows how both internal and external physical forces contribute to plant morphogenesis via mechanical stress-strain transduction from the primary cell wall tethered to the plasma membrane by a specific arabinogalactan protein (AGP). The resulting stress vector, with direction defined by Hechtian adhesion sites, has a magnitude of a few piconewtons amplified by a hypothetical Hechtian growth oscillator. This paradigm shift involves stress-activated plasma membrane Ca<fnref n="2" />⁺ channels and auxin-activated H⁺-ATPase. The proton pump dissociates periplasmic AGP-glycomodules that bind Ca<fnref n="2" />⁺. Thus, as the immediate source of cytosolic Ca<fnref n="2" />⁺, an AGP-Ca<fnref n="2" />⁺ capacitor directs the vectorial exocytosis of cell wall precursors and auxin efflux (PIN) proteins. In toto, these components comprise the Hechtian oscillator and also the gravisensor. Thus, interdependent auxin and Ca<fnref n="2" />⁺ morphogen gradients account for the predominance of AGPs. The size and location of a cell surface AGP-Ca<fnref n="2" />⁺ capacitor is essential to differentiation and explains AGP correlation with all stages of morphogenetic patterning from embryogenesis to root and shoot. Finally, the evolutionary origins of the Hechtian oscillator in the unicellular Chlorophyceon algae reflect the ubiquitous role of chemiosmotic proton pumps that preceded DNA at the dawn of life.

**Keywords:** morphogenesis; cell wall protein; hechtian oscillator; calcium signaling; H⁺-ATPase

## 1. Introduction

"If questions are to be asked about life processes, how can one fail to enquire into what is perhaps the most striking feature of life, morphogenesis? Morphogenesis is the end product of cell differentiation. Cell shape is one aspect of the more general problem of differentiation. Consider the primary cell wall, how it grows, and there is evidence enough for the primary wall playing a decisive role in influencing the shape of a cell. Therefore, the primary cell wall must be studied, but how?" (Lamport 1963) [1].

In 1952, Turing proposed that "morphogens acting together and diffusing through a tissue is adequate to account for morphogenesis." His classic paper [2] described simple reaction-diffusion systems in mathematical detail, no doubt inspired by classic texts such as D'Arcy Thompson's [3] "On Growth and Form" (1917), Wardlaw's "Phylogeny and Morphogenesis" [4] and probably Joseph Needham [5]. However, despite the appealing simplicity of the theologian William of Occam (1287-1347) and his razor "entia non sunt multiplicanda praeter necessitatem", the devil is in the biochemical details where "angels fear to tread". Turing invoked Graham's law of diffusion to infer the existence of morphogen gradients (that includes hormones) and the drift to equilibria analogous

<footnote n="1">¹ School of Life Sciences, University of Sussex, Falmer, Brighton BN1 9QG, UK</footnote>

<footnote n="2">² Complex Carbohydrate Research Center, University of Georgia, Athens, GA 30602, USA; tan@ccrc.uga.edu</footnote>

<footnote n="3">³ Department of Chemistry and Biochemistry, Ohio University, Athens, OH 45701, USA; held@ohio.edu (M.H.); kielisze@ohio.edu (M.J.K.)</footnote>

<footnote>* Correspondence: lamportd@msu.edu; Tel.: +44-012-7348-6430</footnote>
to an electronic oscillator, an idea that we recently developed as the Hechtian growth oscillator [6]. Despite Turing’s profound insight and subsequent progress, the problem of plant morphogenesis remains a huge challenge far exceeding the original formulation of simple diffusion. Here, we describe the origin of auxin, H⁺, and Ca²⁺ gradients and how their interaction creates morphogenetic patterns. We therefore approach the formidable problem of plant morphogenesis from an empirical biochemical perspective based on the dynamic role of AGPs (arabinogalactan glycoproteins) in a novel Hechtian growth oscillator. A cell surface AGP-Ca²⁺ capacitor is a crucial component that depends on the complex carbohydrate chemistry of classical AGPs [7,8] that chelate Ca²⁺ by paired glucuronic carboxyl groups of numerous small glycomodules. Not surprisingly, after their initial discovery as an arabinogalactan polysaccharide [9] and as a hydroxyproline-rich arabinogalactan polysaccharide protein complex [10], it has taken 60 years since the founder event [11] to unravel the structural basis for the proposed central role of AGPs in plant biology as a cell surface Ca²⁺ capacitor [12]. The role of AGPs emerged as an essential component of the Hechtian oscillator when we correlated tip-focussed cytosolic Ca²⁺ and tip-localised AGPs with Hechtian adhesion and rapid tip growth of pollen tubes [6].

Here, we extrapolate these recent results to morphogenesis and propose two new avenues: Firstly, we propose the avenue of cell walls and mechanoperception involving Hechtian transduction as described in detail here but not considered by Turing; secondly, we propose postulated chemical morphogen gradients [2] identified here as auxin and Ca²⁺. We propose that mechanotransduction generates both gradients, although each has a different biochemical origin; thus, auxin gradients originate from biosynthesis and transport by tissue-specific auxin efflux PIN proteins. On the other hand, cytosolic Ca²⁺ gradients originate from Ca²⁺ stored in a cell surface AGP-Ca²⁺ capacitor [12]. AGPs are essential components of the Hechtian growth oscillator that amplifies the magnitude and direction of stress vectors regulating plant growth [6]; that explains why plants have heavily invested in AGPs [13] and why this investment is so highly diversified [14]. Many AGPs are developmentally regulated and tissue-specific [15–18]. While the significance of a large pool of dynamic Ca²⁺ at the periplasmic cell surface seems inescapable to us, the role of AGPs in Ca²⁺ gradient formation in tissues is less obvious because it depends on a membrane-bound H⁺-ATPase that dissociates AGP-Ca²⁺. That shows the close link between auxin and Ca²⁺ signalling with the primal proton pump. Paired glucuronic carboxyls of AGP glycomodules bind Ca²⁺ tightly [12] (analogous to Ca²⁺ chelation by dicarboxylic acids). This effectively scavenges less tightly bound Ca²⁺ of pectin and also free Ca²⁺ in the transpiration stream. Thus, abundant cell surface AGP-Ca²⁺ acting as a Ca²⁺ sink would enable both cells and tissues to compete for Ca²⁺, so that Ca²⁺ supply meets demand where it is greatest, such as in meristem primordia. The “choice” of Ca²⁺ as a universal signalling ion can be ascribed to the size (0.9 Å) of its ionic radius; thus, Ca²⁺ sheds water more rapidly and is therefore more reactive than other divalent ions—notably Mg²⁺ [19]—of similar charge but with a smaller ionic radius (0.65 Å) that binds the water of hydration more strongly than Ca²⁺.

The following five sections of this essay show how morphogenetic patterns originate, involving (1) cell wall mechanotransduction and the developmental sequence, (2) the embryogenesis of the fertilised egg cell, (3) roots, (4) shoots, and finally (5) the evolution of morphogenesis.

Most models of morphogenesis, particularly computer-generated models, generally favour a genetic perspective with an emphasis on signalling cascades. However, they ignore two “unknown unknown” missing pieces of the morphogenetic puzzle, identified here as Hechtian mechanotransduction and the AGP-Ca²⁺ capacitor.

## 2. Cell Wall Mechanotransduction

Hecht's classical observations of adhesion between wall and plasma membrane in plasmolysed cells [20] and its significance to cell signalling have been overlooked for more than a century with few exceptions [21]. This seems inexplicable and is most likely because the emphasis has been exclusively on signalling molecules rather than a physical connection. Widespread Hechtian adhesion, which is prominent particularly during rapid tip growth, after plasmolysis (Figure 1) suggested the presence of
specific tethers that transduce the stress–strain status of the wall to plasma membrane receptors that
can respond to piconewton (10⁻¹² N) forces (Table 1).

<figure><img src="image_141.png" /><figcaption>**Figure 1.** Hechtian strand occurrence: from algae to chloroplast guard cells. (A) Closterium desmid in 12% sucrose: reprinted from [22], Scale bar = 2.1 µm; (B) *Penium margaritaceum*: reprinted from [23], Scale bar = 2 µm; (C). Ginkgo cells plasmolysed in 0.3 M NaCl reprinted from [24], Scale bar is 10 µm; Arrows in (A–C) show location of Hechtian strands. (D1–3) Guard cell H⁺-ATPase and its translocator PATROL (proton ATPase translocation control) in *Arabidopsis*. The plasma membrane ATPase AHA1 and its translocator PATROL1 co-localise at the tips of Hechtian strands in plasmolyzed guard cells transformed with GFP-PATROL1 (D1) and RFP-AHA1 (D2) merged in (D3). Enlarged images of the region enclosed in the yellow square are not shown here. Reprinted from [25], Scale bars = 5 µm.</figcaption></figure>

However, the Hechtian transduction hypothesis creates three dilemmas:

1. How does it distinguish between the huge forces (mega Pascal range) exerted on the membrane by osmotic pressure and the minute piconewton forces that activate Ca²⁺ channels and ATPases?

2. How does it provide a directional signal in response to anisotropic stress? [26]

3. Why does the wall need strong adhesion to the plasma membrane although turgor pressure ensures it? Is the elusive mechanosensor a Boojum or a Snark?

Hechtian adhesion must satisfy several criteria: minimally, it must involve strong, stable and specific interactions with both the cell wall and plasma membrane. Several candidates frequently suggested such as wall-associated kinases and integrins lack hard data and can be eliminated. For example, integrins recognise the RGD motif of the mammalian extracellular matrix but are absent from plants. Other possible candidates include formins and many AGPs anchored securely to the plasma membrane [27–30] by a C-terminal GPI-lipid double tail of long-chain fatty acids that requires a force of ~350 piconewtons to detach from the membrane [31], compared with changes in molecular conformation that are sensitive to far fewer piconewtons [32,33].

At-AGP57C (At3g45230) is covalently linked to pectic RG-I homogalacturonan [34] and is also likely anchored to the plasma membrane by its predicted GPI signal sequence. This identifies a putative Hechtian adhesion site of crucial significance that would enable the instant transmission of the wall
stress-strain status and its rate-determining pectin rheology to enable the rapid tip growth of root hairs and pollen tubes.

Wall stress and strain is thus focussed at the molecular level on Ca²⁺ channels and H⁺-ATPase; both membrane components are stretch-activated by just a few piconewtons.

<table><caption>**Table 1.** Piconewton forces crucial to biochemical function and Hechtian adhesion.</caption><thead><tr><td>System</td><td>Action</td><td>Adhesion Strength pN</td><td>References</td></tr></thead><tbody><tr><td>Integrin-RGD binding</td><td>Binding</td><td>~10</td><td>[35]</td></tr><tr><td>GPI-proteins</td><td>Adhesion</td><td>103–350 pN</td><td>[31]</td></tr><tr><td>Protein e.g., talin</td><td>Unfolding</td><td>5 pN</td><td>[32]</td></tr><tr><td>Cation channels</td><td>Open</td><td>4 pN (to open)</td><td>[36]</td></tr></tbody></table>

Piezo proteins responsive to mechanical force are well-documented in animal systems [33]. Finally, Hechtian stress-strain transduction and exocytosis comprise the novel Hechtian oscillator [6], an exquisitely designed high gain biological amplifier (Figure 2) that translates piconewton forces [37] into tropisms, with wide ramifications in plant biology.

<figure><img src="image_142.png" /><figcaption>**Figure 2.** The Hechtian growth oscillator. Regulators of the plasma membrane H⁺-ATPase reflect its two major roles: 1. It maintains negative inner membrane potential and enhances anion exit and cation entry; 2. It dissociates AGP-Ca²⁺ as a source of cytosolic Ca²⁺. Green arrows indicate upregulation or red represent downregulation, with exceptions where the mechanism remains to be elucidated. Auxin activates H⁺-ATPase. cf. Figure 3: Plasma membrane H⁺-ATPase regulation is central to plant biology [38]; the effects of high steady state auxin levels on root cell elongation in Brachypodium [39]; auxin-driven morphogenetic patterns depend on unidirectional fluxes [40]; the evolution of auxin signaling and PIN proteins [41]; what initiates auxin biosynthesis remains unknown [42]; auxin activates the plasma membrane H⁺-ATPase via phosphorylation [38]. Abscisic acid negative regulation: decreases steady-state levels of phosphorylated H⁺-ATPase possibly by promoting dephosphorylation via a protein phosphatase [43] and suppresses hypocotyl elongation in Arabidopsis [43]; abscisic acid stress signalling evolved in algal progenitors [44]. Blue light: the blue light photoreceptor pigment phototropin increases cytosolic Ca²⁺ [45]. Brassinosteroids: Increase cytosolic Ca²⁺ via increased auxin</figcaption></figure>
levels [46]. Cytokinins enhance cell division by unknown mechanisms. Ethylene upregulates auxin biosynthesis in the Arabidopsis root apex and inhibits root cell expansion [47]; thus, anthranilate synthase mutants yield ethylene-insensitive root growth phenotypes. Ethylene specifically inhibits the most rapid growth phase of expanding cells—normally the root hair initiation zone but ethylene moves it much closer to the tip. Auxin and ethylene act synergistically to control root elongation, root hair formation, lateral root formation and hypocotyl elongation [48]. Ethylene modulates root elongation through altering auxin transport: Ethylene binds to receptor proteins such as ETR1 and EIN2 controlling transcription factor EIN3 that targets ERF1, the ethylene response factor that regulates diverse genes, most likely tissue-specific. In shoots, auxin moves from the apex to the base [49]. PIN1 mutants decrease auxin transport in inflorescences while PIN2, PIN3, and PIN7 mutants decrease polar auxin transport in roots. In roots, auxin moves rootward via PIN1, PIN3, and PIN7 in the central cylinder and shootward in the outer cell layers via PIN2 which mediates gravitropism. Ethylene-induced auxin synthesis involves the α and β subunits of anthranilate synthase [47]. Fusicoccin: The fungal toxin fusicoccin fills a cavity in the interaction surface between PM H⁺-ATPase and 14-3-3 proteins to form a tight bridge that activates the ATPase irreversibly [38]. Gibberellins increase cytosolic Ca²⁺ via a DELLA-independent signalling pathway [50]. Gravity: in root gravitropism, auxin regulates root curvature via apoplastic pH and a Ca²⁺-dependent signalling pathway [51]; PIN proteins responsible for polar auxin transport and gravitropism reviewed in [42]; in microgravity, cucumber seedling PIN protein distribution is parallel to the minor root axis. However, a 1 g force re-aligns PIN1 to the lower side of the endodermis thus facilitating auxin transport from the upper side of the root to the lower side. Similarly, PIN3 and PIN7 of the gravity sensing columella also re-align to the lower side [52]. Nitric oxide: high apical levels of reactive oxygen species (ROS) in *Arabidopsis* root hairs suggest possible activation of a Ca²⁺ channel that modulates root hair-tip growth [53]. Red light: the elevation of auxin levels is well established as an early event, in response to response to prolonged shade. During an initial triggering phase, phytochrome interacting factors (PIFs) bind to the promoters of auxin synthesis genes and generate a burst of auxin that promotes growth [54]. ROS: NADPH oxidase generates active oxygen species that activate Ca²⁺ channels and regulate cell expansion and root morphogenesis [55].

Although osmotic pressure is equally distributed at the plasma membrane, wall pressure exerts an equal and opposite force. However, a direct covalent connection between pectin and the plasma membrane would enable instant transmission of the wall stress–strain status by fibrous macromolecules.

Two extreme examples, stomata and pollen tubes, demonstrate the efficacy of Hechtian adhesion: the stomatal guard cell wall elasticity transmits stress while the rapid tip growth of a pollen tube involves wall plasticity; when stretched, it transmits strain arguably via AGP57C [34] or its homologous GPI-anchored classical AGPs, supporting a vital role for the Hechtian growth oscillator in morphogenesis as discussed in subsequent sections.

The pollen tube tip has the simplest primary cell wall—almost exclusively pectin and with fast tip growth—so is an ideal system to test hypotheses involving the Hechtian transduction of wall stress–strain. Pectin rheology is deceptively simple and depends largely on the degree of methyl esterification of pectic polygalacturonic acid residues, in contrast to AGP glucuronic acid, which is never esterified. Highly methyl-esterified pectins form gels, while de-esterification followed by Ca²⁺ crosslinking forms much stronger gels. A frequently cited pectic paradigm [56] assumes sufficient available free Ca²⁺ for crosslinking but ignores the regulation of Ca²⁺ in muro by AGPs which, with their demonstrated higher affinity for Ca²⁺, compete for pectic Ca²⁺. Such competition effectively strips Ca²⁺ from pectin. The concomitant electrostatic repulsion of negatively charged pectic carboxylates explains the increase in wall plasticity by pectin methylesterase [57]. This effect, not previously considered, may also explain the role of the small diffusible “AGP peptides” [58] that possess two arabinogalactan glycomodules, presumably with paired glucuronic acid residues that bind Ca²⁺. Significantly, small AGP peptides are upregulated by auxin [39], suggesting another subtle level of control over plasticity of the pectin-rich primary cell walls.
Driven by turgor pressure, cells expand in a direction orthogonal (i.e., at right angles) to the direction of stress that strains the pectic matrix; the concomitant Hechtian transduction of pectic strain initiates Ca²⁺ oscillations and exocytosis (Figure 2). The stress vector also causes the orthogonal orientation of microtubules and cellulose deposition [26] that reinforce the pectic matrix. As noted above, pectin rheology depends on its methyl esterification status regulated by pectin methyl esterase [59], the availability of free Ca²⁺ and borate crosslinking of the RG-II pectic component. Crosslinking of the cellulosic component (notably absent from pollen tube tips) may also be regulated by expansin [60,61].

Such complexity explains why the molecular basis of cell wall plasticity remains recalcitrant since first described [62]. “The difficulty lies not in the new ideas, but in escaping from the old ones” (John Maynard Keynes). Many are Boojums—hypotheses that postulate non-existent entities are not falsifiable and should disappear: for example, the widely accepted effect of low pH on wall loosening by activating enzymic cleavage of load-bearing covalent crosslinks. However, both crosslinks and enzymes remain unidentified. In the absence of an alternative viable unifying hypothesis, the Hechtian oscillator emphasises the role of Ca²⁺ in the exocytosis of wall plasticisers as detailed in [6] rather than covalent bond cleavage. Plant cells share a wall with neighbours and can therefore use Hechtian adhesion to sense which wall is being highly stressed by a rapidly expanding neighbour cell. Such stressed cells respond by the rapid reorientation of auxin efflux PIN proteins to direct auxin efflux towards their rapidly expanding neighbour [26]. Cells also compete for available Ca²⁺ by increasing the size of their cell surface AGP-Ca²⁺ capacitor; this can increase the amplitude of Ca²⁺ oscillations, thereby enhancing exocytosis.

Consider the primary receptors of force transduction. What are they, and how do they propagate tension to the cell interior? Stretch-activated Ca²⁺ channels [63] and auxin-activated H⁺-ATPase [64] control Ca²⁺ influx as follows: the plasma membrane ATPase [38,65] is similar to the mitochondrial ATP synthase: a rotary nanomachine fuelled by the proton motive force that generates ATP. However, in reverse, fuelled by cytosolic ATP, it becomes a molecular turbine rotating at up to ~8000 rpm, ejecting proton jets that pump about three protons into the periplasm for each ATP molecule hydrolysed [66].

<figure><img src="image_143.png" /></figure>

**Figure 3.** Posttranslational regulation of the PM H⁺-ATPase alternates between two states: reprinted from [38]. Red = downregulated pumps hydrolyze ATP with low efficiency, hence the low transport of H⁺. Green = upregulated pumps with high ATPase efficiency, and high H⁺ transport rates. C-terminal regulatory domains control transition between the two states. The phosphorylation (P) of the C-terminal penultimate threonine residue (Thr-947 in pump AHA2) creates a binding site for a 14-3-3 protein that stabilises the pump. The binding of lysophosphatidylcholine (Lyso-PC) and phosphorylation at Thr-881 also activates the PM H⁺-ATPase independently of phosphorylation and 14-3-3 protein binding. It is not known whether phosphorylation at Thr-881 in the C-terminal domain interferes with or depends on 14-3-3 binding (as indicated by the question mark). Phosphorylation at Ser-899 or Ser-931 inactivates the pump. Phosphorylation at Ser-931 blocks the binding of 14-3-3 protein, but is not known for Ser-899. Only well-characterized regulatory events are shown.
These powerful proton jets dissociate the AGP-Ca²⁺ of the cell surface capacitor that supplies the Ca²⁺ channels. The evidence [6] for this is a 100% correlation between tip-localised AGPs and “tip-focussed” cytosolic Ca²⁺ during the rapid tip growth of pollen tubes.

How Ca²⁺ fluxes translate into morphogenesis depends on the local wall plasticity that determines the direction and magnitude of the wall stress vector; its amplification depends on the size of the AGP-Ca²⁺ capacitor (Figure 2) and its obvious abundance at metabolically active sites [67]. Arguably, the stress vector also determines the anisotropic location of Hechtian adhesion sites that activate the local vectorial exocytosis of wall precursors and dynamic reorientation of auxin efflux (PIN) proteins. Mechanical stress causes auxin efflux carrier localisation at the plasma membrane adjacent to the most stressed or strained walls cells and thus directs auxin toward neighbours that are rapidly expanding [68]. Counterintuitively, “the net flow of auxin in shoot tips is up the auxin gradient such that any cell directs its auxin toward neighbouring cells that have a higher auxin concentration” [26]. Auxin flux against the concentration gradient towards regions of active expansion growth, although an apparent contravention of the Second Law of Thermodynamics, is pithily summarised by Mathew’s Law: “To him that hath shall be given. And to him that hath not shall be taken away”.

Plant cells exploit a “thermodynamic loophole” based on their ability to trap ionised auxin in the cytosol (pH 7.4) where it cannot freely permeate the plasma membrane. However, in the wall at ~pH 5, auxin is protonated and thus freely permeates the plasma membrane of adjacent cells. Thus, auxin wins the Sysiphean uphill struggle.

The regulation of the oscillator at several biochemical levels involves Ca²⁺ channel activity and the plasma membrane H⁺-ATPase (Figure 2). The proximity of a large or small AGP-Ca²⁺ capacitor and its dissociation by ATPase proton pump thus creates dual gradients of auxin and Ca²⁺; coincidentally, two interacting morphogens required for the creation of “Turing patterns” [2]. By connecting these gradients, both dependent on the proton motive force, the Hechtian oscillator emerges as a master regulator of plant growth; this paradigm shift demands the reappraisal of the acid growth hypothesis [69] that depends on the widely accepted activation of wall-loosening enzymes. However, alternative explanations for a low wall pH include the PIN-directed auxin transport of protonated auxin and increased plasticity of deprotonated pectin. Finally, the release of Ca²⁺ from AGP-Ca²⁺ by a proton pump [12] is an extrapolation of Mitchell’s original chemiosmotic hypothesis [70].

### 3. Embryogenesis

The above description of stress-dependent auxin and Ca²⁺ gradients shows how polarity can arise at the earliest stages of embryogenesis, particularly with an AGP-Ca²⁺ sink as a source of dynamic cytosolic Ca²⁺, while tissue tensions determine the orientation of auxin efflux proteins and cellulose deposition. Organogenesis then follows similar biochemical and biomechanical rules. Every budding botanist sees sliced celery stalks curl because internal tissues are under compression and outer tissues under tension. This simple principle applies during embryogenesis as the stress vector changes from the internal meristem (compression) to the outer protoderm (tension). The concomitant rearrangement of auxin efflux proteins in the protoderm under tension results in lateral auxin export from its apex outwards, with consequential slow growth and anisotropy at the torpedo stage that splits the tissue into the two cotyledons [71] (Figure 4).

Angiosperm double fertilisation results in a triploid endosperm and a diploid zygote that elongates and establishes the shoot–root hierarchy with an initial asymmetric division into a small apical cell that becomes the proembryo; the large vacuolated basal cell divides by transverse divisions to produce the suspensor, a short file of cells that act as an “umbilicus” connecting the embryo with maternal tissues. The hypophysis is a remarkable pivotal apical cell of the suspensor, and as the precursor to the embryonic root, it demarcates the crucial zone between shoot and root. Thus, many auxin mutants result in a defective hypophysis and rootless seedlings. Presumably, a simplified morphogenetic programme of hypophysis silences most major shoot programmes and defines the
fate of future cells in the root as a "partial shoot" [72] characterised by the root tip meristem, xylem, phloem, pericycle and lateral roots.

<figure><img src="image_144.png" /></figure>

**Figure 4.** Embryogenesis in Arabidopsis: Cell lineages, PIN protein localization, and auxin response maxima (reprinted from [71]). Auxin response maxima and PIN protein localization follow a regular cell division pattern. Thin lines show lineages between stages: PIN protein localization is shown as follows: red (PIN1), blue (PIN4), and green (PIN7), and DR5 reporter is pink. (A) After the division of the zygote, one and two-cell embryos express PIN7 in the basal daughter cell (bc), and the apical cell (ac) expresses the DR5 reporter. After two more cell-divisions, all proembryo (pe) cells express PIN1 and DR5 reporter. Basal suspensor (sus) cells express PIN7 localized on the proembryo side. At the globular stage, central lower cells of the proembryo establish basal PIN1 polarity while PIN1 localizes apically in outer protoderm (pd) cells. At the same time, PIN7 polarity reverses in suspensor cells and PIN4 is activated in the uppermost suspensor cell that now expresses the DR5 reporter and is specified as hypophysis (hyp). During the transition stage, the PIN1 polarity at the flanks of the apical embryo half converges in adjacent cells, accompanied by the appearance of new DR5 maxima. These sites mark the initiation of the cotyledons; (B) The torpedo stage shows discrete regions of the embryo: RAM (root apical meristem), green, root apical meristem (white, future quiescent centre); hypo, blue, hypocotyl; Cot, yellow, cotyledons; and SAM (shoot apical meristem), red, the shoot apical meristem.

Plant cells are generally totipotent, and single cultured cells can regenerate an entire plant [73,74]. While cell lineage does not necessarily determine cell fate, the aphorism of Hans Driesch that "the fate of a cell is a function of its position" implies that both its lineage [75] and position [76] are pertinent. Indeed, "morphogen" gradients evident as auxin and AGP-Ca²⁺ are highly correlated with the earliest stages of embryogenesis including the polarised haploid egg cell that yields a zygote with polarised AGP distribution increasing at the later two-cell stage and onwards [77]. Auxin biosynthesis evidenced by the DR5 reporter is similarly localized, particularly at the 2-cell, 8-cell and globular stages in *Arabidopsis* [71]. Auxin distribution depends on auxin efflux carriers which are initially inferred [78] and subsequently identified at the genomic level by "PIN" mutants that have phenocopied inhibitors of auxin transport [79]. Unlike the anisotropic protoderm, the early growth of meristematic tissue is isotropic. Variations in the local growth of the meristem arise possibly because cell surface AGPs compete for limited Ca²⁺; combined with tissue tensions, this leads to boundary regions which are low in Ca²⁺. These peripheral anisotropic regions, particularly in the ectoderm, result in tge rearrangement of auxin efflux proteins with consequent auxin depletion in boundary zones between the meristem, hence the origin of new primordia and phyllotaxis; i.e. auxin peaks generate a spiral phyllotactic pattern.

Much work over more than 25 years (Table 2) reveals a remarkable family of tissue-specific auxin efflux (PIN) proteins that ensure a regulated supply of auxin during embryogenesis and the
ensuing stages of morphogenesis. However, until now, the signals that initiate PIN protein localisation remain unknown; the Hechtian transduction proposed here is the best candidate based on considerable supporting evidence.

<table><caption>**Table 2.** The PIN Ffamily of auxin efflux proteins.</caption><thead><tr><td>Auxin Efflux Protein</td><td>Major Location or Function</td><td>Efflux Orientation</td><td>References</td></tr></thead><tbody><tr><td>PIN 1</td><td>Outer protoderm and lower cells of proembryo</td><td>Rootward</td><td>[71]</td></tr><tr><td>PIN 2</td><td>Root epidermis and lateral root cap; regulates gravitropism</td><td>Shootward</td><td>[26]<br>[42]</td></tr><tr><td>PIN 3</td><td>Gravitropism</td><td>Rootward</td><td>[26]</td></tr><tr><td>PIN 4</td><td>Hypophysis</td><td></td><td>[71]</td></tr><tr><td>PIN 5</td><td>ER</td><td>Cytosol</td><td>[42]</td></tr><tr><td>PIN 6</td><td>ER</td><td>Cytosol</td><td>[42]</td></tr><tr><td>PIN 7</td><td>Suspensor</td><td>Apical towards embryo<br>Rootward</td><td>[80]</td></tr><tr><td>PIN 8</td><td>ER</td><td>cytosol</td><td>[42]</td></tr></tbody></table>

The Hechtian growth oscillator generates morphogenetic patterns; arguably, these depend on localised adhesion sites that result in vectorial exocytosis of wall precursors. This includes auxin efflux PIN proteins directed to the sites of the highest strain in expanding cells, [26] thus ensuring a supply of auxin for their continued growth. AGPs specifically localised in the suspensor [81] (Figure 4 in reference [81]) (6 to 9 cells in *Arabidopsis*) with apically polarised PIN4 and PIN7 auxin efflux proteins [80] highlight its active role as an "umbilicus" supplying auxin and nutrients from maternal tissues to the embryo.

Stress also predicts the plane of cell division marked by the preprophase band of microtubules [82] as putative mitosis stabilisers [83] and the appearance of the cell plate templated by extensin self-assembling amphiphiles; [84] hydroxyproline-rich glycoproteins central to plant growth once again cooperate with biomechanical forces. Elegant laser ablation experiments alter the orientation of PIN proteins in the apical meristem [26]. These classic experiments [16,26,85] show that tissue biomechanics create stress vectors that reorientate tissue-specific auxin efflux PIN proteins. We infer that specific Hechtian adhesion is the "missing link" that connects biomechanical stress vectors with auxin action and PIN reorientation: a chemically defined covalent connection between cell wall pectin and a known plasma membrane such as AGP57C likely transduces stress that dissociates AGP-Ca²⁺, thus increasing cytosolic Ca²⁺ that triggers vectored exocytosis. We infer that Hechtian adhesion and AGPs amplify both the direction and magnitude of stress vectors resulting in growth orientation. Not surprisingly, mutants of Gal31 are lethal [86], possibly by disrupting the 1-6-linked galactose sidechain of the AGP-Ca²⁺ glycomodule [87].

## 4. Roots

The morphogenesis of root xylem tissues begins with the specific expression of the JIM13 AGP epitope in a single metaxylem initial just above four central cells of the quiescent centre [88]. The how and why have been dominated by the speculative idea of AGPs as signalling molecules per se. Thus, a role for AGPs in Ca²⁺-signalling was unexpected yet surprisingly close to reality, with AGP-Ca²⁺ belatedly seen here as the major dynamic source of Ca²⁺ regulated by auxin. Significantly, transformed plants that overproduce auxin show excessive xylem and phloem development [89] and bushy phenotypes [90].

Mechanical stress patterns involved in root morphogenesis have yet to be modelled. Nevertheless, a recent comprehensive experimental approach [91] correlated gravitropism with the epidermal
location of auxin efflux protein PIN2 which was dramatically co-localised with Hechtian adhesion sites between the plasma membrane and the cell wall (Figure 5).

<figure><img src="image_145.png" /><figcaption>**Figure 5.** PIN proteins maintain their polarity at the cell wall of plasmolysed cells. Plasmolysis shows that apical (PIN2-GFP and PIN1-GFP-3) and basal (PIN1-GFP-2) proteins remain attached to the cell wall by their polar domains. (A–D) Note—yellow arrowheads = nonpolar PIN-GFP signal at the plasma membrane. HS = Hechtian strands with PIN-GFP-connections to the wall. White arrowheads = a strong persistent PIN-GFP signal at the cell wall–plasma membrane interface. Scale bars = 10 µm. Reprinted from Figure 4 of [91].</figcaption></figure>

The presence of the cell wall is essential for gravity perception [91]. These observations connect gravitropism with a rapid increase of cytosolic Ca²⁺ [51] and the following conclusion [91]: “Thus, the identified tight link between the cell wall and cell polarity provides the conceptual possibility for regulation of signal fluxes and, ultimately, plant development via signaling from the extracellular matrix.” Such evidence suggests that auxin-based mechanoperception and subsequent root morphogenesis involve the Hechtian growth oscillator. This fundamental phenomenon supersedes textbook dogma and hypotheses in highly contentious and confusing fields [49,92–94] that struggle to disentangle cause from effect. As a prime example, consider the challenge to identify the gravity sensor. Although quite unknown, it may involve critical components of the Hechtian oscillator as “the very earliest stages of gravitropic bending depend on auxin-stimulated Ca²⁺ influx” [41,51]. Nevertheless, the Cholodny–Went explanation of auxin redistribution remains unquestioned dogma [95]: “The ability of roots to reorient their growth in response to changes in the gravity vector is dependent on the asymmetric redistribution of auxin at the root tip” [41]. This demands a biochemical explanation.

The root–shoot paradox: root tip gravitropism increases auxin at the lower side that decreases growth while less auxin at the upper side increases growth. However, in shoots, a similar auxin distribution in response to gravity reverses the direction of growth. We resolve this paradox by asking: How does auxin inhibit growth at the lower side of the root? Extensin peroxidase [96] provides the answer: crosslinked extensin decreases the rate of cell extension ([97] cf. [47]) via di-isodityrosine formation [98,99]. Presumably, programmed cells of the root tip respond to high levels of auxin simply by enhancing the enzymic crosslinking of wall proteins. Thus, extensins and AGPs, as the Yin and Yang of cell extension, may illustrate yet again the ingenious parsimony of nature that involves these hydroxyproline-rich glycoproteins as both negative and positive regulators of cell extension.

While the above approach to a complex problem is consistent with Occam’s razor, it contrasts with the complexity of recent papers that deal with the dynamic rearrangement of PIN proteins transporting auxin from both root tip and the shoot via xylem and root epidermis (Figure 6).
<figure><img src="image_146.png" /><figcaption>**Figure 6.** Reprinted with permission from Sato et al. [49]. Root gravitropism in *Arabidopsis*. (A) Gravity perception in *Arabidopsis thaliana*. At time point 0, roots grow vertically. After a 90° turn, the following events occur: (1) At 10 s, statoliths are still at the old bottom of the cell. After 3 min, statoliths move towards the new bottom of the cell to be uniformly distributed at 5 min [92]; (2) PIN3 and PIN7 relocalization is achieved 2 min after the gravity stimulus and, in consequence, a lateral auxin gradient is generated between the upper and lower side of the root (thin and thick orange arrows respectively) [100]; (3) the development of differential extracellular pH levels between the upper (acidic) and lower (alkaline) side of the gravistimulated root [51]; (B) Gravity signal transduction and transmission via auxin transport and redistribution. Black arrows show that AUX1 and PIN2 channel auxin from the shoot to the root tip. Blue arrows show how PIN4 distributes auxin efflux through the vascular tissue to the columella cells. PIN3 and PIN7 set up the auxin flow (green arrows), with an accumulation on the lower side of the root. PIN2 and AUX1 transport auxin through the lateral root cap to the epidermal cells in the elongation zone (orange arrows) where the actual growth response will occur.</figcaption></figure>

However, no convincing molecular mechanism has been offered for auxin-increased cell extension. Auxin has also not been successfully connected with Ca²⁺ signalling although [49] "auxin somehow activates cytosolic Ca²⁺ waves," the major source being the Hechtian oscillator via auxin-activated H⁺-ATPase dissociation of AGP-Ca²⁺ that releases Ca²⁺ to the cytosol via Ca²⁺ channels. How that translates into increased cell extension in the root tip elongation zone remains a conundrum, as discussed above. Although the prevalent statolith hypothesis is now textbook dogma, the precise molecular details of statolith mechanotransduction remain quite unknown. Mutants that lack amyloplast statoliths do not resolve the problem: while they decrease the gravitational response, they do not eliminate it [93]. Finally, both plasma membrane H⁺-ATPases [25] (~11 in *Arabidopsis*) and PIN proteins recycle in response to mechanotransduction, thus adding an additional level of complexity.

This raises the pertinent question: What is the biochemical source of signalling Ca²⁺ and its connection to auxin? Regions of high auxin biosynthesis, e.g., meristems, young primordia and reproductive organs, express YUCCA, a flavin mono-oxygenase that decarboxylates indole pyruvate to yield auxin [48]. Arguably, Hechtian adhesion and auxin-activated plasma membrane ATPase dissociate AGP-Ca²⁺ to provide Ca²⁺ that activates exocytosis enabling the gravity vector (9.8 N·kg⁻¹)
to redistribute auxin by recycling the auxin efflux PIN proteins. As the root tip derives its auxin from transport through central root tissues and also local biosynthesis (Figure 6), the columella is quite possibly the gravity sensor as it also contains the statoliths. However, that view is not consistent with the Hechtian oscillator and the Hechtian transduction of the gravity vector leading to auxin transport and its asymmetric redistribution by PIN1 and PIN3 auxin efflux proteins [26] cf. [41].

The Hechtian oscillator is also evident in mature root tissues such as the pericycle which expresses AGPs [101] and generates adventitious lateral roots and a specific extensin ([102] cf. [75]). Possibly, pericycle progenitor cell AGPs scavenge local Ca²⁺ that enhances exocytosis when stimulated by auxin supplied from root tip biosynthesis [103]. Similarly, root hair positioning is also correlated with AGP-reactive epidermal cells Figure 4A in [101], while defects in root tip auxin biosynthesis result in a shift of root hair emergence towards the shoot.

## 5. Shoots

Morphogenesis of the shoot involves phyllotaxis of leaves and flowers; a problem of formidable complexity recognised by Egyptian, Greek and Roman scholars since antiquity [104] up to the present. Numerous competing hypotheses largely based on mathematical formulations connect physical forces to growth, but with many biochemical unknowns. Recent significant experimental advances [26,68,85] closely connect the stress vectors of growing tissues with the reorientation of auxin efflux PIN proteins (Figure 7): exocytosis and endocytosis (transcytosis) rapidly redeploy PIN proteins to expanding walls that show the greatest stress or strain. This implies that stress-induced signals from the cell wall promote the accumulation of PIN1 (and thus export of auxin) at the nearest membrane of cells stressed by their rapid expansion as follows.

<figure><img src="image_147.png" /><figcaption>**Figure 7.** Stress vectors in the shoot apical meristem. The suggested changing meristem stress patterns cause auxin depletion in the boundary region as primordia form [26]. Note that the magnitude and direction of the stress vector are strongly anisotropic (red arrows) in the boundary region between the primordium and shoot apical meristem apex. Reprinted from [85] with permission from AAAS.</figcaption></figure>

Rapid PIN1 redeployment [105] raises the question of how cells perceive the mechanical signals that largely determine PIN1 polarity. In plants, the gap between biophysical stress and biochemical response is generally ignored. However, PIN protein recycling depends on Ca²⁺-directed vectorial exocytosis, and therefore shares essential components of the Hechtian growth oscillator that translate biophysical force into biochemistry. This connects the oscillator with the generation of new primordia; hypothetically, their regular spatial separation or phyllotaxis results from competing demands for auxin and Ca²⁺ morphogens, channelled to the most rapidly growing cells by PIN proteins and cell surface AGPs that scavenge Ca²⁺. This results in auxin depletion and slower growth in the boundary or “saddle region” between the apical meristem and primordia. Indeed, competition for auxin and Ca²⁺ may determine the angle of divergence between successive primordia and thus the creation of whorls [106], although the morphogenesis of flowering involving, for example, a protein florigen [107] and development of seeds is beyond the scope of this brief essay.
Auxin initiates phyllotaxis by transport against a concentration gradient to sites of primordia formation; these depend on the polarity of auxin efflux (PIN) proteins maintained by the cell wall [91,108]. However, the apical dominance of the shoot, although generally ascribed to the auxin inhibition of lateral bud growth, may actually depend on the absence of PIN polarity from dormant tissues. Arguably, the removal of the shoot apex restores PIN1 polarisation in the bud [109] via renewed axillary auxin transport that breaks dormancy. A role for the Hechtian growth oscillator in apical dominance seems likely and is consistent with the bushy phenotype of tomato plants over-expressing AGP LeAGP1 [110]. The size of the AGP-Ca²⁺ capacitor could determine the balance between the dormancy and active growth of axillary buds.

## 6. The Evolution of Morphogenesis

Phylogeny and morphogenesis are inextricably linked [111], and so our brief description can only attempt a broad-brush summary that reconciles old observations with new discoveries. Specifically, these relate wall stress-strain and Hechtian adhesion to the control of cytosolic Ca²⁺ by auxin. Thus, auxin efflux PIN proteins transport auxin to target sites, where the activation of H⁺-ATPase releases Ca²⁺ from AGP-Ca²⁺, triggering exocytosis. This paradigm shift can be traced back to the primordial soup and unifies the chemiosmotic proton motive force with auxin and Ca²⁺ signalling. By analogy with inscriptions on the Rosetta stone, once decoded, these three fundamental transport phenomena translate the same growth message into morphogenesis.

Morphogenesis begins with prebiotic synthesis from CH₄, CO₂, and water to yield HCHO [112], a precursor to simple sugars via the Butlerov (formose) reaction. The subsequent prebiotic generation of self-replicating molecules and self-assembling amphiphiles formed lipid membranes and nanobubble aerosols. Such semipermeable membrane-bounded protocells sequestered and concentrated reactants by chemiosmosis, most likely in Darwin's "warm little pond" (In a letter to J.D. Hooker 1871). Hence, the origin of Peter Mitchell's proton motive force [70], a universal phenomenon that precedes RNA-DNA replication and drives reactions that exploit the chemistry in a watery environment of planets in the "Goldilocks zone". The first simple prokaryotes were chemical machines; their further specialisation and morphological adaption led to unicellular eukaryotes, morphogenetic machines characterised by increasing structural adaptations and complexity, exemplified by the invention of chromosomes as Darlington's "little packets of predestination", internal membrane systems such as ER (endoplasmic reticulum), Golgi, and cell walls to protect the plasma membrane. Indeed, most major evolutionary advances from chemiosmotic energy transduction to cellular organelles appeared very early and remain as essential features of modern eukaryotic cells whose precise origins by endosymbiont capture [113] remain to be elucidated.

From the cell wall viewpoint, the unicellular flagellate *Chlamydomonas* provides the most striking example of evolutionary conservation and diversification, with a large complement of 182 different proteins related to hydroxyproline-rich extensins [114]. The *Chlamydomonas* wall is devoid of cellulose and consists almost entirely of glycoproteins that self-assemble as a crystal lattice [115], a remarkable precursor to their conserved self-assembly role in higher plants [84]. The leap to multicellular cooperation involved two distinct evolutionary lines: one line embedded cells in a hydroxyproline-rich glycoprotein (HRGP) protective matrix typified by volvocine algae; the other Chlorophycean line evolved silicified or calcified protective cell walls (Figure 8) typified by the calcareous plates of Coccolithophores, such as *Emiliana huxleyi* of the cretaceous that built the chalk hills and cliffs of the present era.

Static cell surface CaCO₃ coccoliths of Coccolithophores represented by *E. huxleyi* are the probable evolutionary precursor to dynamic cell surface AGP-Ca²⁺, hence Ca²⁺ signalling. Algae increased the tensile strength of a primary cell wall prototype by co-opting cellulose, thus enabling turgor pressure and the major evolutionary pathway to metaphytes. Indeed, the composition of algal pectin-rich cellulosic walls is remarkably similar to those defined as primary walls in the cambial tissues of higher plants [116]. That raises the question: When did the Hechtian oscillator emerge? Based on
the presence of Hechtian strands associated with rapid tip growth [6], we extrapolated Mitchell's original chemiosmotic hypothesis to include Ca²⁺ signalling. This implies incredible evolutionary conservation and an early origin of the Hechtian pscolerator in unicellular Chlorophycean algae such as Closterium [22] and Penium [23], as both exhibit tip growth with prominent Hechtian strands (Figure 1).

<figure><img src="image_148.png" /><figcaption>**Figure 8.** Chilly Brook chalk cliffs with *E. huxleyi*. Coccolithophores such as *E. huxleyi* (inset) constructed massive soft chalk deposits of calcium carbonate during the cretaceous period (145–65 MYA), now seen here from across the Chilly Brook water meadows dominated by *Ranunculus acris*, adjacent to the River Ouse in the South Downs National Park at Lewes, UK. This view encapsulates the entire evolutionary progression from the simplest unicellular protists such as *E. huxleyi* to advanced dicots such as *R. acris* at the pinnacle of alternation of generations, all dependent on calcium. (Photo: DTAL).</figcaption></figure>

Single cells remaining attached after cytokinesis evolved into simple linear filamentous algae as the first step towards multicellularity and its regulation. Although auxin is a key growth regulator in higher plants, it is evident as a biosynthetic pathway in the simplest unicellular chlorophytes [117]. However, auxin transport also involves efflux PIN proteins, and these first appear in filamentous algae—"living fossils" such as *Spirogyra* [117]—with anchoring rhizoids that differentiate only from terminal cells [118]. Thus, the PIN proteins and polarity of *Spirogyra* rhizoids, as well as stretch-activated Ca²⁺ channels, nicely represent the earliest evolutionary progression from marine via freshwater to land plants (Figure 9).

Further lateral cohesion between adjacent filaments forms a prototype thallus. Other "living fossils" include *Coleochaete* a prototype leafy liverwort (Hepaticae) that retains the fertilised diploid egg cell until "germination". *Coleochaete* cell walls are also significantly enriched in hydroxyproline-rich glycoproteins. Alkaline hydrolysis yields a hydroxyproline glycoside profile (Figure 10) dominated by small hydroxyproline heterooligosaccharides, similar to the profile of *Chlamydomonas*, but surprisingly different from the simple Hyp-arabinoside profile of higher plants.
<figure><img src="image_149.png" /><figcaption>**Figure 9.** Metaphyte origins. Progression from single cells to filaments that align, forming a flat thallus. The examples here are the biflagellate *Chlamydomonas*, *Spirogyra* and the red arrow points to *Coleochaete scutata*.</figcaption></figure>

<figure><img src="image_150.png" /><figcaption>**Figure 10.** *Coleochaete* hydroxyproline glycosides. Alkaline hydrolysates of *Coleochaete scutata* cell walls fractionated on a cation exchange column gave a Hyp-glycoside profile that appeared similar to the profile of cell walls isolated from higher plants. However, closer inspection and quantitative sugar analyses showed a striking difference; in higher plants, the Hyp-glycosides are simple arabinosides, whereas *Coleochaete* shows heterooligosaccharides of up to seven sugar residues that include galactose, glucose and arabinose, compositions remarkably similar to the profile of cell walls isolated from *Chlamydomonas* [119] but different from other members of the plant kingdom [120]. Presented at the 11th Cell Wall Meeting, Copenhagen [121].</figcaption></figure>

Although more popular notions suggest Chara or Nitella as a land plant precursor [122], that seems unlikely for several reasons; firstly, despite being invoked as a model system, their cell walls lack hydroxyproline-rich cell wall proteins; secondly, the relatively thick walls of Chara are rich in non-methyl esterified pectin; and finally, the large cells are coenocytes but remain locked in an evolutionary cul-de-sac.
Bryophytes initiate the gametophyte-sporophyte "alternation of generations" brilliantly elucidated by Hofmeister [123] (Figure 11).

<figure><img src="image_151.png" /><figcaption>**Figure 11.** The moss *Bryum capillare* exemplifies the alternation of generations. *Bryum capillare* with attached diploid sporophytes dependent on the haploid gametophyte generation. (Photo: DTAL).</figcaption></figure>

Further evolutionary development of the attached sporophyte (e.g., with stomata) culminated in its complete dominance in higher plants with their increasingly complex division into root, shoots and leaves. Root-like structures appeared as rhizoids in the Bryophytes, but true roots defined by their gravitropic response, endogenous branching, root hairs, and a protective root cap originate from the suspensor hypophysis during angiosperm embryogenesis. While sharing much in common with true shoots, roots clearly lack many shoot characteristics and have therefore been described as "partial shoots" [72] that evolved as an adaptation to a subterranean life [124].

The ultimate reduction of the gametophyte generation to just a few cells, namely pollen and the ovule as an integumented megasporangium, completes this brief summary based on a novel growth oscillator unifying other growth regulators that control Ca²⁺ release and exocytosis.

## 7. Postscript

Ion transport dominates this paper, which is greatly influenced (1955–1961) by personal acquaintance (DTAL) with the Cambridge pioneers who included Peter Mitchell (proton pump), David Keilin (cytochrome discovery) and Robert "Robin" Hill Reaction (photolysis of water). The cell wall protein was undoubtedly inspired by Fred Sanger in the adjacent lab (protein structure, 1958 Nobel Prize), and Joseph E. Varner [125] on his sabbatical leave acted as a "midwife to wall protein." H.A. Krebs was one of DTAL's BA examiners. Two years of National Service as a corporal radio instructor at the Royal Air Force Radio School Yatesbury (1953–1955) inspired thoughts about biological oscillators. Finally, the poet Alexander Pope (1688–1744) summarises the effect of the intellectual environment exemplified by Joseph Needham (morphogenesis) and Don Northcote (cell walls) in the Cambridge Department of Biochemistry: "As the twig is bent so is the tree inclined."

**Funding:** No current funding

**Acknowledgments:** Dedicated to the memory of Joseph E. Varner, mentor, friend and colleague.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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