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plants
Article
Structure and Biomechanics during Xylem Vessel
Transdifferentiation in
Arabidopsis thaliana
Eleftheria Roumeli
1,2,
*
,†
, Leah Ginsberg
2,†
, Robin McDonald
2
, Giada Spigolon
3
,
Rodinde Hendrickx
2
, Misato Ohtani
4,5
, Taku Demura
5
, Guruswami Ravichandran
2
and Chiara Daraio
2
1
Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195, USA
2
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA;
lginsber@caltech.edu (L.G.); robinmcd@caltech.edu (R.M.); rodindehendrickx@hotmail.com (R.H.);
ravi@caltech.edu (G.R.); daraio@caltech.edu (C.D.)
3
Biological Imaging Facility, California Institute of Technology, Pasadena, CA 91125, USA; giadas@caltech.edu
4
Department of Integrated Biosciences, Graduate School of Frontier Sciences, The University of Tokyo,
Kashiwa 277-8562, Japan; misato@edu.k.u-tokyo.ac.jp
5
Graduate School of Biological Sciences, Nara Institute of Science and Technology, Ikoma 630-0192, Japan;
demura@bs.naist.jp
*
Correspondence: eroumeli@uw.edu
These authors contributed equally to this work.
Received: 27 October 2020; Accepted: 3 December 2020; Published: 5 December 2020



Abstract:
Individual plant cells are the building blocks for all plantae and artificially constructed
plant biomaterials, like biocomposites. Secondary cell walls (SCWs) are a key component for
mediating mechanical strength and stiffness in both living vascular plants and biocomposite materials.
In this paper, we study the structure and biomechanics of cultured plant cells during the cellular
developmental stages associated with SCW formation. We use a model culture system that induces
transdifferentiation of
Arabidopsis thaliana
cells to xylem vessel elements, upon treatment with
dexamethasone (DEX). We group the transdifferentiation process into three distinct stages, based on
morphological observations of the cell walls. The first stage includes cells with only a primary cell
wall (PCW), the second covers cells that have formed a SCW, and the third stage includes cells
with a ruptured tonoplast and partially or fully degraded PCW. We adopt a multi-scale approach to
study the mechanical properties of cells in these three stages. We perform large-scale indentations
with a micro-compression system in three different osmotic conditions. Atomic force microscopy
(AFM) nanoscale indentations in water allow us to isolate the cell wall response. We propose a
spring-based model to deconvolve the competing stiffness contributions from turgor pressure, PCW,
SCW and cytoplasm in the stiffness of differentiating cells. Prior to triggering differentiation, cells in
hypotonic pressure conditions are significantly stiffer than cells in isotonic or hypertonic conditions,
highlighting the dominant role of turgor pressure. Plasmolyzed cells with a SCW reach similar levels
of stiffness as cells with maximum turgor pressure. The stiffness of the PCW in all of these conditions
is lower than the stiffness of the fully-formed SCW. Our results provide the first experimental
characterization of the mechanics of SCW formation at single cell level.
Keywords:
plant biomechanics; turgor pressure; micro-compression; AFM;
Arabidopsis thaliana
;
differentiation
1. Introduction
Plantae and plant-based materials are specialized conglomerates of plant cells. Therefore, studying
the mechanical properties of single cells and resolving further sub-cellular contributions provides a
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basis for further analysis of the heterogeneous tissue and plant-level biomechanics. In vascular plant
tissues, the micro-structure and composition of secondary cell wall (SCW) governs, to a large extent,
the mechanical properties of the entire tissue [
1
,
2
]. Thus, it is of paramount importance to investigate
the mechanical properties of the SCW, especially during the initial stages of formation, which has not
been explored to date.
Plant cells have two key structural elements that collectively govern their mechanical properties:
the cell wall and the cytoskeleton. The key structural component of the cell wall is cellulose, which has
a Young’s modulus (
E
=
110
–220 GPa) comparable to that of high performance engineering materials
like carbon fiber or steel [
3
]. Cellulose is immersed in an amorphous matrix of softer biopolymers,
hemicellulose, pectin, proteins and lignin, giving rise to a complex heterogeneous multilayered cell
wall structure [
4
]. The support provided to plant cells by the cell wall allows them to hold water at
high pressures (
p
=
0.3
–1.0 MPa), mainly through swelling of the vacuole [
5
]. This phenomenon in
plants is known as turgor pressure, and it is essential to the structural integrity and rigidity of the
cell. Additional structural support is provided to the cell by the cytoskeleton, largely through actin
filaments (
E
=
1.0–4.0 kPa) and microtubules (
E
=
1.1–1.3 GPa) [6–8].
Recent advances in instrumentation are the impetus for the resurgence in research focused on the
mechanics of cell growth [
9
11
]. Experimental methods, protocols and mechanical models of plant cells
vary, contributing to results that span orders of magnitude [
9
]. Still, newly designed experiments have
the potential to achieve an unprecedented spatial resolution and therefore to decouple the mechanical
contributions from each structural element of a cell in the overall mechanical performance of plant cells
and tissues. For example, Routier-Kierzkowska et al. designed an experimental apparatus which they
termed as cellular force microscope and used it to create stiffness maps of onion epidermis peels [
12
].
The results of this new experiment in combination with finite-element simulations revealed that turgor
pressure caused the observed stiffening on top of inflated cells. Braybrook and Peaucelle performed
AFM indentations on plasmolyzed Arabidopsis tissues, which ensured the isolation of the response of
the cell wall from any contribution due to turgor pressure [
13
]. By measuring the response from the
plasmolyzed tissue, they were able to demonstrate that auxin leads to wall acidification in preparation
for cell expansion.
This cell wall loosening behavior in preparation for elongation was first observed by Radoti ́c et al.
who performed AFM indentation measurements on suspension-cultured Arabidopsis cells and
observed that the cell wall stiffness at the beginning and end of cell growth was almost an order
of magnitude lower than during the exponential growth phase [
14
]. The mechanism behind this
cell wall loosening in preparation for elongation has been explained by Cosgrove in a subsequent
review [4].
Even though many are working towards a defined micromechanical model, the exact contribution
of the cell wall(s) and cytoplasmic components on the effective stiffness of the system during growth
and differentiation remains elusive. Using a novel protocol to characterize the rheology of isolated
Arabidopsis protoplasts, Durand-Smet et al. found that the elastic modulus of the protoplast was about
three orders of magnitude lower than plant cells with a cell wall [
8
]. In the same work, plant cells were
treated with a microtubule destabilizing drug, which reduced the elastic modulus of the protoplast
to half of its original value, demonstrating that MTs contribute to the overall stiffness of the cell.
Sampathkumar et al. used live-imaging of
Arabidopsis thaliana
(Arabidopsis) plants, particularly in
epithelial cells, and a mechanistic model to find that there is a direct correlation between microtubule
(MT) organization and geometry-derived mechanical stresses [
15
]. Apparently, the maximum stress in
the cell wall is found in areas with highest cellulose concentration, which is driven by the MTs in the
cytoplasm. Taken together, the results of Durand-Smet et al. and Sampathkumar et al. show that MTs
contribute to the overall stiffness of cells intrinsically, and through an interaction with the cell wall.
Here, in order to understand the mechanical contributions of the subcellular components, like the cell
wall(s) and cytoplasm, throughout the transdifferentiation process, we propose a robust multi-scale
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mechanics assay that includes nano-indentation to capture cell wall properties, chemical treatments to
control osmotic conditions and micro-indentation to evaluate global cell properties.
We choose to focus on xylem vessel element differentiation, which is one of the most extensively
used systems to study SCW development and thickening [
16
,
17
]. Xylem vessel elements develop
a precisely patterned SCW beneath the primary cell wall (PCW) giving rise to an entangled
multilayered heterostructure.
The deposition of SCW in xylem vessel elements is intricately
linked to programmed cell death (PCD), and both processes are happening concurrently during
differentiation [
18
]. Therefore, quantifying the mechanical contributions of the cell wall(s) and
cytoplasm during differentiation of xylem vessel elements is a convoluted problem, and one that
has not yet been solved. Our multi-scale biomechanical assay is designed to capture mechanical
contributions from the PCW, the SCW, their potential coupled effects, as well as the cytoskeleton at
various turgor pressures and osmotic conditions.
Early in vitro SCW induction systems for
Zinnia elegans
facilitated physiological, biochemical,
and molecular studies that elucidated the tracheary element (TE) differentiation mechanism [
19
21
].
The Demura group introduced the post-translational induction system of VASCULAR-RELATED
NAC-DOMAIN7 (VND7) genes which induces transdifferentiation of various types of plant cells into
xylem vessel elements upon treatment with a glucocorticoid, such as dexamethasone (DEX) [
16
,
17
].
The induction system has been demonstrated successfully in Arabidopsis plants and cell cultures,
as well as
Populus tremula x tremuloides
plantlets, and
Nicotiana tabacum
cell cultures [
16
]. The system
causes the activation of transcriptional activity of VND7 to induce ectopic transdifferentiation of
Arabidopsis cultured cells into protoxylem vessel-like cells [16].
In this study, we use the VND7 system in Arabidopsis suspension-culture cells because it is a
robust model with a high efficiency in transdifferentiation and uniformity in cell culture. To decouple
the effects of cell wall stress, cytoskeleton rearrangement, and turgor pressure on observed cell stiffness,
we test transgenic Arabidopsis cells in an extensive multi-scale biomechanical assay. To validate the
cell wall stiffness decoupled from turgor pressure, we perform AFM indentations [
22
]. We propose
a mechanistic spring model to represent the stiffness of the cell in compression, which allows the
decoupling of stiffness contributions from the cell wall(s) and cytoplasm.
2. Results and Discussion
2.1. Morphological Observations of the VND7-Inducible Arabidopsis Cells
The VND7-inducible Arabidopsis cells were stained and observed under a laser scanning
confocal microscope at various stages of their differentiation. We document that transdifferentiation
of VND7-inducible cells follows the same general stages as TE differentiation seen in other plant
systems [
19
21
]. Common morphological observations during differentiation of TEs in
Zinnia elegans
,
Populus deltoides
and Arabidopsis, in the order that they occur, are: (i) the differentiating cell expands
and becomes highly vacuolated and the nucleus is confined, pushing against the cell wall and marking
the initiation of PCD; (ii) the cytoskeleton rearranges as the cell produces vesicles which have been
associated with substance exchange between the cytoplasm and cell wall for SCW deposition; (iii)
tonoplast ruptures as SCW is deposited and starts thickening; (iv) following SCW thickening, in planta,
PCW perforation is observed [
18
,
23
25
]. From the transmitted and confocal fluorescent images,
as well as optical microscopy images (see Figure A1A–C), we can robustly identify three distinct
stages of cell transdifferentiation based on the cell wall(s) and cytoplasm, as presented in Figure 1A–F.
Specifically, in the VND7 system we study in this work, we classify the stages as follows: (i) Stage 0:
cells prior to induction of transdifferentiation (prior to adding DEX in the solution), having only a
PCW developed and visible. (ii) Stage 1: cells having been induced (exposed to DEX for a minimum
of 24 h) and having only a PCW developed. (iii) Stage 2: cells having been induced (exposed to
DEX for a minimum of 24 h) and having an intact PCW and a SCW developed. The cytoplasmic
contents of these cells are visible and still inside the cell. In our observations, cytoplasm retraction
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and detachment from the cell wall happens soon after SCW deposition. (iv) Stage 3: cells having been
induced (exposed to DEX for a minimum of 48 h) having a thickened SCW, and partially perforated
PCW. With or without perforated PCW, in stage 3 the majority of cytoplasmic contents are removed
from the cells (indicating the tonoplast rupture). Using the confocal fluorescent images, we compile
three-dimensional reconstructions for each identifiable stage of transdifferentiation, presented in
Figure 1G–I, which allow the evaluation of the PCW thickness, as well as visualization of the bundled
SCW thickenings.
Figure 1.
Transmitted, fluorescent, and 3D reconstructions of confocal images of the elongated
VND7-inducible cells in the 3 stages of transdifferentiation. (
A
,
D
,
G
) Living cells which have only
developed a PCW are identified as stage 1. The PCW is under stress from the internal turgor pressure.
(
B
,
E
,
H
) Cells in stage 2 have both a PCW and the beginnings of a SCW. In this stage, the PCW
has possibly begun hydrolyzing, and thin spiral bundles of SCW can be distinguished. The spiral
patterning is characteristic of protoxylem vessels. (
C
,
F
,
I
) In stage 3, SCW thickening is observed;
PCD has progressed; the tonoplast has ruptured and cytoplasmic contents have been removed from
the cell. All scale bars are 20
μ
m.
From confocal and additional light microscopy images (data not presented here), we discern two
equally represented shapes in the cell population, based on their aspect ratio: rounded and elongated.
Elongated cells have a mean aspect ratio of approximately 2:1, whereas rounded cells have a mean
aspect ratio of approximately 1:1. Even though the microscopy images denote that approximately half
of the population of cells are rounded, and half are elongated, we observe that rounded cells tend to
be tightly clustered, while elongated cells are found more likely in an isolated state or located on the
edges of large clusters. For that reason, all mechanical data in the following sections are measured from
elongated cells, and we will focus on the morphology of those cells in this section. For all dimensions
and feature sizes of both rounded and elongated cells, see Tables A1 and A2. The principal dimensions
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and feature sizes of elongated cells, along with an illustrative example are shown in Table 1 and
Figure 2, respectively.
Figure 2.
Illustration of measured principal dimensions and feature sizes of elongated VND7-inducible
cells from confocal fluorescent microscopy image. Scale bar is 20
μ
m.
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Table 1.
Measured principal dimensions and feature sizes of elongated VND7-inducible cells in the 3
stages of transdifferentiation. Length (
L
), width (
w
), and thickness (
t
) of SCW bundles are measured
using image processing. Volume (
V
) is calculated from measured length and width, assuming cells are
cylindrical in shape. The density of SCW bundles (
ρ
) is calculated by counting the number of bundles
observed in a particular cell, and dividing by the cross-sectional area in the image.
Dimension
Mean
±
SE
L
stage 1
(
μ
m)
60.4
±
2.4
L
stage 2
(
μ
m)
56.4
±
4.9
L
stage 3
(
μ
m)
61.6
±
3.7
w
stage 1
(
μ
m)
30.7
±
1.0
w
stage 2
(
μ
m)
31.2
±
2.8
w
stage 3
(
μ
m)
34.7
±
1.6
V
stage 1
(
μ
m
3
)
44,700
±
2100
V
stage 2
(
μ
m
3
)
43,100
±
5300
V
stage 3
(
μ
m
3
)
58,300
±
4100
ρ
stage 2
(#/
μ
m
2
)
0.056
±
0.005
ρ
stage 3
(#/
μ
m
2
)
0.060
±
0.004
t
stage 2
(
μ
m)
1.05
±
0.01
t
stage 3
(
μ
m)
1.45
±
0.01
Confocal imaging reveals a PCW in stage 1 (thickness 580
±
10 nm (Mean
±
Standard Error)),
while bundles of SCW in spiral patterns are observed in stages 2 and 3 of transdifferentiation. In stage 2,
the early SCW bundles are deposited, and the cell begins to undergo PCD. In stage 3, as PCD progresses,
the SCW bundles are thickened further, the tonoplast ruptures, contents of the cytoplasm are degraded
and removed from the cell, and the PCW is at least partially hydrolyzed [
2
]. (See Figure A2 for partial
PCW perforation at stage 3). During the last stage of differentiation, the SCW bundles thicken by
approximately 40%. The bundle density does not change notably between stages 2 and 3.
2.2. Biomechanics of Differentiating VND7-Inducible Arabidopsis Cells
All reported mechanical data in the following sections are measured from elongated cells in an
isolated state. In the mechanical testing we add stage 0 to the differentiation stages, which describes
transgenic cells prior to exposure to DEX, reflecting cells in their state before transdifferentiation
is induced. There is no observable difference between stages 0 and 1 using the confocal or light
microscope, but it has been reported that from stage 0 to 1, the MT and actin filaments reorganize
the cytoplasmic fibrillar network into a bundled conformation that will later guide the spiral
SCW patterning [
26
,
27
]. In fact, the MT-rearrangement in particular has been visualized in the
VND7-inducible system and has been reported in literature [28].
The elongated cells were compressed using a micro-compression tool that covered most of their
top surface area. We propose a spring model to describe the overall cell stiffness, as pictured in Figure 3.
The pictured model has two springs in series, one which represents the stiffness of the cell wall, and the
other represents the stiffness of the cytoplasm. The combined stiffness of these two springs is given by
the following equation:
k
total
=
k
CW
k
cyto
k
CW
+
k
cyto
(1)
A direct result of using this model is that the overall stiffness must be less than the stiffness of
either constituent springs. In the following sections we will use this proposed model to deconvolute
the stiffness contributions from the cell wall(s) and cytoplasm. The result is a ranking of the stiffness
contributions from the cell wall(s) and cytoplasm in each stage of differentiation. It is important to
note that this ranking depends on the validity of the assumptions outlined in the following paragraph.
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Figure 3.
Proposed series spring model to analyze cell stiffness from micro-compression testing.
The total stiffness measured by the micro-compression tool is the equivalent stiffness for the two
springs in series, given by Equation (1), and it must be less than the intrinsic stiffness of either
constituent spring in the series. For a given overall stiffness,
k
total
, the included plot illustrates the
relationship between the stiffness of the two springs,
k
CW
and
k
cyto
.
In using this simplified model, we assume that the cell wall and cytoplasm behave as linear elastic
materials at small indentation depths, and we ignore any nonlinear effects like adhesion, viscosity,
or plasticity. For shallow indentations, the effects from stress at the boundaries of the cell also become
negligible [
29
]. This simplified one-dimensional model allows us to quantify the relative stiffness
contributions of each component. Stiffness is not an intrinsic material property, like Young’s modulus
which is independent of the shape and dimensions of the material, since by definition stiffness is a
function of both the material and it’s geometry. To relate spring stiffness to Young’s modulus would
require a three-dimensional model which captures the structural mechanics of a pressurized cell with
a heterogeneous membrane undergoing large deformations. Due to the lack of such a model in the
current literature, we adopt this one-dimensional spring model, which allows us to decouple the
relative contributions from the cytoplasm and cell wall(s), although we cannot yet directly obtain
intrinsic material properties for either component. See Figure A3 for the specific spring models used to
represent cells in each stage of transdifferentiation, and in each solution with different osmolarity.
For the micro-indentation tests, we extract cells from their normal growth conditions (in growth
media) at different time points before and after exposure to DEX, from 24 h to several days,
evaluate their morphology in an optical microscope (see Figure A1A–C) and identify their stage
of transdifferentiation. Testing of cells at different time points after exposure to DEX allows us to
capture them at each of the four identified differentiation stages. We confirm the stage of differentiation
and cell morphology through the optical microscope embedded in the micro-mechanical testing system
(see Figure A1D–F). After the extraction from normal growth conditions, we treat the cells in three
different osmotic conditions and maintain them during the mechanical testing, which is conducted in
solution. We refer to the testing conditions as hypertonic, when cells are in sorbitol, isotonic, when cells
are in growth media, and hypotonic, when cells are in deionized water. See Table A3 for details on
the calculation of the osmotic pressure in each solution. In hypertonic conditions, the cells are visibly
plasmolyzed as evident from optical microscopy images after the first minute of exposure to sorbitol
(See Figure A4). We note that the plasmolysis is evident for cells in stages 0–2 when the cytoplasm is
still inside the cells. In isotonic and hypotonic conditions, the cell physiology as studied by optical
microscopy is the same as in their normal growth conditions (cells are turgid, cytoplasm pushing
against the cell wall). While we refer to cells treated with growth media as being in an isotonic
condition, they are turgid, and the turgor pressure drives their growth and development. We use the
term isotonic in a relative sense, as compared to the high osmotic pressure differential in hypotonic
conditions. In the case of deionized water-suspended cells, the higher osmotic pressure (see Table A3)
causes higher stress on the cell walls [
30
]. In Figure 4 the initial effective stiffness values for the overall
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cell in each stage of differentiation, are presented grouped by osmolarity of solution. Underneath each
category is a graphical illustration of the morphology of the cells. The initial effective stiffness is
measured from the first 1
μ
m of indentation data after contact. This depth of indentation ensures
that we capture some contribution to the overall stiffness from turgor pressure and/or the cytoplasm,
since the measured (hydrated) PCW and SCW thicknesses are both close to 1
μ
m [
11
]. See Figure A5
for an alternative grouping of the stiffness measurements by stage and osmolarity of solution.
Figure 4.
Panel showing the stiffness in 4 stages of transdifferentation in 3 types of solutions with
different osmolarity: (
A
) sorbitol; (
B
) growth medium; (
C
) water. Note the difference in scale on
the y-axis in (
C
) from the extreme stiffness of cells in hypotonic conditions before induction of
differentiation. Bottom line graphically represents the morphology of the cells in each condition
and stage. Stars indicate significant differences in distribution according to the nonparametric
Kolmogorov-Smirnov test. *
p
< 0.1, **
p
< 0.05, ***
p
< 0.01. (Data shown correspond to
2 < n < 35
.
Each indentation test on an individual cell is represented by a point in the plot.)
2.2.1. Hypertonic Condition
In hypertonic conditions, i.e., the sorbitol condition (Figure 4A), water flows out of the vacuole
and across the cell membrane, as the cell is plasmolyzed. The relief of turgor pressure allows for
isolation of the mechanical response of the cell wall [
9
,
31
]. So, in these conditions we model the
stiffness response of the cell as a single spring which represents the cell wall(s). When uninduced cells
(stage 0) are placed in hypertonic conditions, the measured stiffness (
k
hyper,stage 0
=
0.59
±
0.06
N/m
)
corresponds to that of unstressed PCW.
k
hyper, stage 0
=
k
hyper,PCW
(2)
After DEX exposure, but before the formation of the SCW begins, we do not expect to see a
difference in the stiffness of the PCW. Indeed, we do not detect any statistically significant difference
in stiffness between stages 0 and 1 in hypertonic conditions (
k
hyper,stage 1
=
0.69
±
0.17 N/m).
k
hyper, stage 1
=
k
hyper,PCW
(3)
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In stage 2, the PCW is expanded and modified to allow space for the deposition of the SCW [
25
].
The coupled stiffness of the thin SCW bundles and the modified PCW interact in a way that produces a
significant increase on the cellular effective stiffness (
k
hyper,stage 2
=
4.71
±
2.31
N/m
); this value is over
five times the value observed in the prior stages, and more than double the addition of the isolated
PCW stiffness and isolated SCW stiffness from stages 0 and 3. We propose two possible reasons for the
observed increase in stiffness.
The presence of sorbitol may cause an increase of the cell wall stiffness through enhanced
molecular interactions between the polysaccharide chains of the PCW and SCW. We hypothesize
that in the presence of sorbitol, a polyalcohol with six hydroxyl groups per molecule, these side
groups can interact with the available surface hydroxyl groups of the various polysaccharide chains
(i.e., cellulose, hemicellulose, pectin) in the PCW and SCW. These polysaccharides are present on each
cell wall in different amounts and configurations, and the interactions between them are a topic of
active investigations [
32
]. The introduction of sorbitol may therefore contribute additional hydrogen
bonding between the PCW and SCW, supporting our micro-indentation experimental observations.
Alternatively, the collapse of the cell in hypertonic conditions may cause buckling or folding of
the PCW over the SCW bundles. Cell wall buckling or folding would result in more amount of cell
wall material being compressed under the indenter, thereby justifying a higher stiffness. This apparent
stiffening in plasmolyzing conditions due to cell wall buckling has been suggested also for plant
tissue indentations [
31
]. Again, this phenomenon would exist in all stages, but would be enhanced
when the PCW is in contact with the spiral SCW. The gaps between the spiral SCW bundles provide
channels in between which the PCW could fold, giving the overall cell wall material a thicker and
more organized shape.
These two proposed mechanisms for stiffening are not mutually exclusive. The sorbitol may be
interacting with cellulose in the PCW as it buckles to provide an even further increase in stiffness
for the reorganized overall cell wall structure. In any case, the combined cell walls (CCWs) are the
material which provides stiffness to the cell in the hypertonic condition.
k
hyper, stage 2
=
k
hyper, CCW
(4)
As PCD proceeds, all contents of the cytoplasm are lost and the PCW is at least partially
hydrolyzed. At the end of transdifferentiation, the main remaining structural component of the
xylem vessel element is a thickened SCW. In the final stage, in all solutions, we attribute all the
measured stiffness to the thickened SCW (
k
hyper,stage 3
=
1.03
±
0.13 N/m).
k
hyper, stage 3
=
k
SCW
(5)
We measure a statistically significant higher stiffness in stage 3 when compared to stages 0 and 1
in hypertonic conditions. This result suggests that the fully developed SCW is stiffer than the PCW
before and after induction. We also measure a statistically significant lower stiffness in stage 3 when
compared to stage 2 in hypertonic conditions. The loss of the PCW as PCD proceeds eliminates the
stiffening that was observed in stage 2, through either (or both) chemical and physical interactions
explained in the paragraphs above.
2.2.2. Isotonic Condition
In isotonic conditions (Figure 4B), the cells are growing, so the turgor pressure is above the
osmotic pressure of the solution, but not as high as in the hypotonic condition discussed in the next
section (see Table A3). In growth media the cells are turgid, the cytoplasm pushes against the cell wall,
presenting a distinct morphological difference compared to the plasmolyzed cells which are shriveled
and have a retracted cytoplasm. As shown in literature, turgor pressure (from the vacuole and the
cytoplasm) provide additional mechanical stiffness to the cell underneath the cell wall [
11
,
33
,
34
].
They are represented by a new spring in our model connected in series to the cell wall(s). Before PCD is
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initiated, in stages 0 and 1, due to the presence of turgor pressure, we expect the stiffness of the PCW to
be higher than in the same stages in hypertonic conditions because it is stressed (
k
iso,PCW
>
k
hyper,PCW
).
In stage 0, before transdifferentiation is initiated, we observe the lowest stiffness among the cells
tested in isotonic solution (
k
iso,stage 0
=
0.82
±
0.52
N/m
). From our spring model, the overall stiffness
of the cell in isotonic conditions in stage 0 is
k
iso, stage 0
=
k
iso,PCW
(
k
n-b,iso
)
k
iso,PCW
+
k
n-b,iso
(6)
There is no statistically significant difference between the effective stiffness of cells in stage 0 in
hypertonic and isotonic conditions. For the effective spring constants in both of these models to be
equivalent, the two springs in series in the isotonic model must be stiffer than the single spring in the
hypertonic model (see plot in Figure 3). This implies that the PCW and the combined cytoplasm and
vacuole in isotonic conditions must be stiffer than the PCW in hypertonic conditions. In other words,
our model confirms that the PCW is stiffened through stress exerted from turgor pressure that exists in
isotonic conditions.
Upon induction of transdifferentiation, the effective stiffness of the cells increases significantly.
In stage 1, the model still contains 2 springs: one for the stressed PCW (
k
iso,PCW
), and one for
the bundled cytoplasm in isotonic conditions (
k
b,iso
). The mean effective stiffness in stage 1 is
k
iso,stage 1
=
2.40
±
0.52 N/m.
k
iso, stage 1
=
k
iso,PCW
(
k
b,iso
)
k
iso,PCW
+
k
b,iso
(7)
Assuming that there is no change in the PCW stiffness from stages 0 to 1, as observed in sorbitol
(Figure 4A), our model indicates that the cytoplasmic contribution in stage 0 must be less than in stage
1 in isotonic conditions (
k
n-b, iso
<
k
b, iso
).
As transdifferentiation proceeds to stage 2, a series of concurrent events influence the mechanical
behavior of the cells: (i) the PCW is modified (loosened to allow for elongation for the SCW deposition
and possibly entering the hydrolysis stage) (ii) the beginnings of SCW bundles are deposited, and (iii)
the anisotropic fibrillar cytoplasm starts detaching from the cell walls as the turgor pressure is reduced
as a result of the cell entering the PCD stage upon differentiation [
25
]. The stiffness of the new
CCW is represented in the spring model as
k
iso, CCW
, and the spring from the cytoplasm is removed,
since the cytoplasm is no longer in contact with the cell wall. These mechanisms act together to
determine the effective stiffness of the cell (
k
iso,stage 2
=
2.06
±
0.44
N/m
). The reduced turgor pressure,
loss of cytoplasmic contribution as the cell dies and the PCW loosening reduce the effective stiffness
of the system. The deposition of SCW increases the stiffness of the cell wall spring component,
and therefore the overall system. According to our experiments, the cells have the same stiffness in
stages 1 and 2. Thus, assuming that the cytoplasmic contribution is negligible at stage 2, the stressed
PCW of stage 1 must be stiffer than the CCW of stage 2 (
k
iso, CCW
<
k
iso,PCW
). This highlights the
significant effects of turgor pressure stiffening the PCW in stages 0 and 1.
k
iso, stage 2
=
k
iso, CCW
(8)
At the last stage of differentiation when the SCW is fully developed and thickened, the measured
effective stiffness (
k
iso,stage 3
=
1.78
±
0.97
N/m
) is not statistically significant from the overall
stiffnesses in stages 1 and 2. In order for cells in stage 3 to have the same overall stiffness as cells in
stage 1, each component of the springs in series in stage 1 must be stiffer than the single spring in stage
3 (
k
SCW
<
k
iso,PCW
). This highlights again the increased stiffness of a PCW under turgor pressure in
stages 0 and 1.
k
iso, stage 3
=
k
SCW
(9)
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2.2.3. Hypotonic Condition
In water (Figure 4C), before the DEX induction, we measure the absolute stiffest cell response
(
k
hypo, stage 0
=
7.37
±
1.58
N/m). This demonstrates that in hypotonic conditions, the high turgor
pressure increases the stiffness of cytoplasm and the PCW. This is in agreement with the findings of
Routier-Kierzkowska et al. and many others who have studied the effects of turgor pressure on cell
and tissue mechanics [12,33,35–37].
k
hypo, stage 0
=
k
hypo,PCW
(
k
n-b,hypo
)
k
hypo,PCW
+
k
n-b,hypo
(10)
According to the two-spring model, this means that both the stiffness of the PCW and the
cytoplasm in hypotonic conditions in stage 0 must be greater than any other directly measured stiffness.
As differentiation begins, the overall stiffness of the cell (
k
hypo, stage 1
=
1.89
±
0.48
N/m) is
drastically reduced.
k
hypo, stage 1
=
k
hypo*,PCW
(
k
b,hypo
)
k
hypo*,PCW
+
k
b,hypo
(11)
Assuming that there is no decrease in the cytoplasmic stiffness from stages 0 to 1, there must be
lower stress in the PCW in stage 1, which we will denote
k
hypo*,PCW
. We hypothesize that the stress
exerted on the cell wall is reduced as the cell prepares for SCW deposition (
k
hypo,PCW
>
k
hypo*,PCW
).
Loosening of the PCW to prepare for elongation prior to addition of PCW material has been previously
reported, and here we propose that this same mechanism governs SCW deposition [
4
]. This loosening
should be occurring in all osmotic conditions, but we propose that it is only distinguishable in
hypotonic conditions because in these conditions the PCW is under the highest amount of stress since
it is subjected to the highest turgor pressure. An alternative, or additional possible mechanism for this
observed weakening is an early hydrolysis of the PCW. Both of these possibilities are supported by
literature [
25
]. Our analysis could not distinguish the stiffness of the PCW in water stage 1 (
k
hypo*,PCW
)
from the stiffness of the PCW in growth medium at the same stage (
k
iso,PCW
).
As SCW is deposited, we measure that the effective stiffness at stage 2 is the lowest among all
stages in hypotonic treatment (
k
hypo, stage 2
=
0.71
±
0.14 N/m).
k
hypo, stage 2
=
k
hypo, CCW
(12)
As seen before, the balance between PCW modification (loosening/hydrolysis), early SCW
deposition, and loss of turgor and cytoplasmic contribution determines the overall system stiffness.
The effective stiffness of cells at stage 2 in hypotonic conditions is significantly lower than that of cells
at stage 2 in isotonic and hypertonic conditions (see Figure A5). This difference in stiffness between
water and other solutions in stage 2 supports the prior proposal that there is weakening of PCW due
to early hydrolysis in water.
Finally in the last stage the measured stiffness (
k
hypo, stage 3
=
1.12
±
0.15
N/m) corresponds solely
to the fully developed SCW.
k
hypo, stage 3
=
k
SCW
(13)
Our results indicate that the combined CW stiffness of stage 2 is weaker than the mature SCW
(
k
hypo, CCW
<
k
SCW
). As expected, we measure that the thickened SCW in any solution has the
same stiffness, which shows that the properties of the fully developed SCW are not affected by the
treatments. We have two cases of exceptionally high stiffness; uninduced cells in hypotonic conditions
and plasmolyzed cells in stage 2 of transdifferentiation. Besides these two exceptional cases, the SCW
alone is at least as stiff as any combined stiffnesses in any other case.
To summarize, the isolated CW stiffnesses can be ordered:
k
PCW
<
k
SCW
<
k
iso,PCW
,
k
hypo*,PCW
<
k
hypo,PCW
(14)
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Again, we see that turgor pressure governs the overall mechanical response of the cell to
compression through prestressing the PCW. We also confirm that the SCW bundles are stiffer than the
PCW material without any prestress.
The CCW stiffnesses can be ordered as follows:
k
hypo, CCW
<
k
iso, CCW
<
k
hyper, CCW
(15)
The proposed molecular mechanisms governing the stiffness of the CCW are the hydrolysis of the
PCW in water, and the stiffening of cellulose chains in the presence of sorbitol. Buckling or folding of
the PCW in hypertonic conditions may also act to further stiffen the CCW response.
Finally, the stiffness representing the cytoplasm can be constrained with two inequalities:
k
n-b, iso
<
k
b, iso
<
k
n-b,hypo
(16)
k
n-b, iso
<
k
b, hypo
(17)
See Figure A6 for a visual representation of the magnitude of each stiffness component. Our assay
allows us to directly assess, for the first time, the mechanical contributions of the cytoskeleton in the
effective stiffness of intact plant cells, highlighting their important role in the mechanics of the system.
2.3. AFM Analysis of Differentiating VND7-Inducible Arabidopsis Cells
AFM nano-indentation tests were conducted in water to evaluate cell wall indentation moduli
in each stage of differentiation, as shown in Figure 5. We use a spherical bead with a 1
μ
m diameter,
which is able to capture the response of a rather large representative area of the PCW, considering
the fact that cellulose fibrils are organized in bundles with 5–50 nm thickness [
3
]. The average
indentation depth for the force-controlled experiment is
79.5
±
3.9
nm (Mean
±
Standard Error),
which is less than 10% of the average thickness of the hydrated PCW or SCW bundles. Therefore,
the indentation depth is adequately shallow to assume that we can isolate the response of the cell
wall, even though the cells are turgid [
11
,
14
,
15
,
31
]. Young’s moduli measured from the PCW in
stage 1 in hypotonic conditions (
E
hypo, stage 1
=
372
±
51
kPa) is higher than in other stages of
differentiation, which is in agreement with our micro-indentation results. The Young’s moduli
measured from the CCW in stage 2 (
E
hypo, stage 2
=
192
±
13
kPa) is the lowest of the three stages,
again confirming our measurements from the micro-indentation test. Finally, the Young’s moduli
measured in stage 3
(
E
hypo, stage 3
=
271
±
15 kPa)
has an intermediate stiffness, which further validates
our micro-indentation results.
Measurements with AFM illustrate the extremely heterogeneous structure of the CW. In stage 1,
where the PCW is the only CW of the system, the indentation modulus is measured in a range of
58.7 to 1840 kPa as shown in the histogram and map inset of Figure 5B. This large distribution arises
from the heterogeneous, fibrillar structure of the PCW. The distribution of rigid cellulose fibrils in the
compliant heterogeneous matrix of polysaccharides, proteins and phenolic compounds, is causing
the local distribution of stiffness we observe with AFM. The high stress in the PCW in hypotonic
solution leads to a high stress in the fibres of the PCW, which amplifies the observed heterogeneous
stress distribution. In stage 2, the indentation modulus is measured in a range of 31.0 to 601 kPa
(Figure 5C). The higher number of measurements with low moduli in stage 2 illustrate the degradation
of the PCW, especially between SCW bundles, which was also suggested from the micro-compression
tests. The overlay of line scan measurements on images of the cell reveals that we observe the higher
moduli when testing over the combined early SCW bundles and PCW. In the example shown as an
inset in Figure 5C, we see a modulus of approximately 600 kPa over the SCW bundle, and moduli
around 300 kPa between the bundles. In stage 3, the indentation modulus is measured in a range of
5.6 to 676 kPa. The inset of Figure 5D shows a line scan over an area containing two SCW bundles.
The line scan shows that the moduli on top of the bundles is as high as 700 kPa, and between the