Tetsuhiro Asada*
Department of Biological Science, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043 Japan
*Corresponding author: E-mail, [email protected]; Fax, +81-72-723-2061.
(Received December 7, 2012; Accepted March 11, 2013)
The plane of symmetric plant cell division tends to be selected so that the new cross-wall halving the cell volume has
the least possible area, and several cases of such selection are
best represented by a recently formulated model which promotes the view that the strength of the least area tendency
is the only criterion for selecting the plane. To test this
model, the present study examined the divisions of two
types of shape-standardized tobacco BY-2 cell, oblatespheroidal (os) cells prepared from protoplasts and sphericylindrical (sc) cells with unusual double-wall structures prepared from plasmolyzed cells. Measurements of cell shape
parameters and division angles revealed that both cell types
most frequently divide nearly along their short axes. While os
cells did not exhibit any other division angle bias, sc cell
division was characterized by another bias which made the
frequency of longitudinal divisions secondarily high. The
geometry of sc cells barely allows the longitudinal crosswalls to have locally minimum areas. Nevertheless, a comparison of detected and hypothetical standard divisions
indicates that the frequency of longitudinal sc cell division
can be significantly higher than that predicted when the
longitudinal cross-walls are assumed to have locally minimum areas smaller than their original areas. These results
suggest that, even in isolated plant cell types, the strength of
the least area tendency is not the only criterion for selecting
the division plane. The possibility that there is another basic,
though often hidden, criterion is discussed.
Keywords: Cell division plane Cell wall Cytokinesis Mechanical stress Symmetric division Tobacco BY-2 cells.
Abbreviations: mLS, modified Linsmaier and Skoog’s
medium; os cell, oblate-spheroidal cell; sc cell, spheri-cylindrical cell.
Introduction
In most plant tissues, each cell division event is completed by a
specific form of cytokinesis accompanied by the addition of a
new cross-wall, which inevitably fixes the relative positions of
the daughter cells (Gunning 1982). Due to this, regulation of the
cell arrangement in plant tissues largely depends on division
plane selection in each cell. As has been shown for epidermal
cells of land plants that divide symmetrically, the plane of cell
division is determined before mitosis, independently of the
position and orientation of the mitotic spindle (Ota 1961,
Palevitz and Hepler 1974a, Palevitz and Hepler 1974b).
A common structure that makes the division plane premitotically predictable in a variety of land plant cells is the
pre-prophase band of microtubules, which is transiently
formed in the region where the new cross-wall will meet the
parental cell wall (Mineyuki 1999). Clarification of the pre-mitotic processes which regulate selection of the plane of cell
division is a major issue concerning the mechanism of tissue
formation in plants, and various studies have been conducted
on this (Wada and Murata 1991, Smith 2001, Rasmussen et al.
2011).
An important basis for addressing this issue has been provided by discoveries of basic rules regarding selection of the
plane of cell division and, according to the literature (Sinnott
1960, Lloyd 1991, Lynch and Lintilhac 1997), there are three
classical division rules, all of which were initially described in
the middle to late 19th century. One rule discovered by
Hofmeister (1863) is that the plane of division is perpendicular
to the cell’s elongation axis. Sachs’s rule (1878) is that the plane
of division meets the mother cell wall nearly at right angles. The
other rule which was discovered through examining the geometrical similarity between masses of plant cells and soap bubbles (Errera 1888), often called Errera’s rule, is widely interpreted
as showing that, in the absence of tissue-level polarity, the plane
of symmetric division halving the cell is selected so that the new
cross-wall will have the least surface area. While a modeling
study indicates that Errera’s least area rule is essential for generating cell arrangements comparable with those seen in plant
tissues (Sahlin and Jönsson 2010), exceptions to this rule, such
as the fact that identically shaped cells of the same tissue can
often divide along completely different planes, are known.
Considering this, and based on new findings from experiments
Rapid Paper
Division of Shape-Standardized Tobacco Cells Reveals a
Limit to the Occurrence of Single-Criterion-Based
Selection of the Plane of Symmetric Division
Plant Cell Physiol. 54(6): 827–837 (2013) doi:10.1093/pcp/pct044, available online at www.pcp.oxfordjournals.org
! The Author 2013. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists.
All rights reserved. For permissions, please email: [email protected]
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Fig. 1 Preparation of sc cells. (A) Changes in shape of the protoplasts
of two gel-embedded BY-2 cells which were induced by applying
hypertonic medium containing 0.45 M mannitol onto the gel (left),
and those later induced by applying standard culture medium (right).
Photographs taken at 7.5 min intervals are shown in each row. Note
that the first treatment was not sufficient for inducing convex plasmolysis and yielded protoplast parts stretched to the partitioning cell
wall, indicated by arrows, and that the stretched parts were retracted
as the protoplasts started to swell in medium containing a lowered
concentration of mannitol. (B) A calcofluor-stained sc cell cultured for
2 d after protoplast shaping that involved treatments for inducing
protoplast shrinkage and swelling comparable with those shown in
A. Photographs were taken under white (left) and UV (right) light. The
insert shows a higher magnification of the encircled region. Note that
the new cell surface and original cell wall are distinguishable. Scale
bars, 40 mm.
using soap films, Besson and Dumais (2011) recently modified
the least area rule by introducing the concept of competition
between candidate division planes, and succeeded in formulating a probabilistic version that explains the symmetric divisions
of several cell types chosen from a green alga, a fern and two
seed plants. Characteristically, the new rule postulates that a
division plane is selected from its candidates with a probability
that increases inversely with the new surface area to be added,
and that candidate division planes adopt locally defined minimum area configurations, ensuring a significant right angle
tendency. Thus, if the same rule has a sufficiently wide coverage,
it would be appropriate to understand that the strength of the
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least area tendency is the only significant criterion for selection
of the plane of symmetric division in plant cells.
To assess the coverage of Besson and Dumais’s division rule
and acquire further insight into the default mechanism of division plane selection in plant cells, the present study examined
the divisions of two types of shape-standardized tobacco BY-2
cell, oblate spheroidal (os) cells and spheri-cylindrical (sc) cells,
both of which are distinct in shape from those of plant tissues
previously used for testing the new rule. Os cells are identical to
the deformed cells first observed by Lynch and Lintilhac (1997),
and, in the present study, they were prepared by culturing gelembedded wall-regenerating protoplasts in an original loading
apparatus for axial compression of the gels with pressures <1%
of the turgor pressure determined for normal BY-2 cells (Sano
et al. 2007). The study of Lynch and Lintilhac clearly showed
that those cells preferentially divide along their short axes, although data from this study are insufficient for testing the
probabilistic least area rule. Sc cells comprise a newly introduced cell type with shapes determined by putting semi-spherical caps onto both the termini of cylinders, and were prepared
by appropriately plasmolyzing cylindrical BY-2 cells and culturing the plasmolyzed cells in hypertonic medium (Fig. 1). A
specific feature of sc cells is that each cell with regenerated
walls is enclosed in a cylindrical cage of the original cell wall,
which plays a key role in artificially shaping the inner cell
(Fig. 1B). If the criterion for selecting the plane of symmetric
division comes only from the strength of the least area tendency, normal plant cells with round shapes similar to those of
os or sc cells would be least likely to divide along their long axis.
Results
Division of os cells
Protoplasts prepared from proliferating tobacco BY-2 cells were
embedded in agarose gels, cultured under a vertically applied
load for 2 d, and images of os cell-derived cell pairs contained in
the gels were taken (e.g. Fig. 2A, left). The mean ± SD (n = 307)
of the values for the cell pair’s longest diameter was
43.5 ± 6.4 mm, whereas that for the cell pair’s shortest diameter
was 38.1 ± 6.2 mm. The mean value for the shape-determining
ratio s, denoting the cell pair’s longest divided by shortest diameter was 1.15 (Fig. 2B, left). The mean rate of the cell pairs with
cross-walls positioned at 75–90 to the long axis was significantly greater than that of the cell pairs belonging to any of the
other five division angle groups (Fig. 2C, left). The mean percentage did not differ significantly among the division angle
groups other than in the 75–90 group.
Cell pairs with cross-walls observed as sharp and straight
lines were selected, and the lengths of the cross-walls were
measured. The mean value for the cross-wall length was more
or less equivalent to that for the cell pair’s shortest diameter,
not only for the members of the 75–90 division angle group
but also for those of the other five groups (data not shown).
This was due to the limited cell deformation and slight but
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Two-criteria theory for symmetric division control
Fig. 2 Geometry of cell pairs derived from os cells (left) and those derived from sc cells (right). (A) Example of the fluorescence signal
distribution in a calcofluor-stained cell pair and obtained values for the cell pair’s geometrical parameters. , tentatively determined angle
of the cross-wall with respect to the cell’s long axis; D for os cells and L for sc cells, cell length measured along the long axis; h for os cells and w for
sc cells, cell length measured along the short axis; s, shape-determining ratio denoting D/h or L/w. (B) Frequency distribution of s. Distinguished
data sets were obtained from the indicated numbers of cell pairs observed in independent experiments. The sc cells used for obtaining one data
set (white) were prepared with media containing a higher concentration of mannitol (see the Materials and Methods). (C) Frequency distribution of a. Values are the mean obtained by analyzing the three independent data sets from the cell pair populations distinguished in A. Error
bars indicate standard deviations. (D) Averages of s and the cross-wall length lcw divided by h of os cell-derived cell pairs and those of s and lcw/w
of sc cell-derived cell pairs. The data shown in D were obtained from selected cell images suitable for measuring the cross-wall length. The
numbers of os cell-derived cell pairs used for analyzing the 0–15, 15–30, 30–45, 45–60, 60–75 and 75–90 division angle groups were 10, 8, 7, 9, 9
and 24, respectively, and those of sc cell-derived cell pairs used for analyzing the same division angle groups were 17, 10, 6, 9, 10, and 41,
respectively. Error bars indicate standard errors. Different lower case letters in C and D indicate significant differences among mean values at
P < 0.05.
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T. Asada
frequent reduction in the division symmetry. The mean values
for s and the cross-wall length divided by the shortest diameter
also did not differ significantly among the division angle groups
(Fig. 2D, left).
Division of sc cells
Plasmolyzed cells consisting of protoplasts with spheri-cylindrical shapes and enclosing original cell walls were obtained
from stationary phase tobacco BY-2 cells, cultured in hypertonic medium containing aphidicolin for 2 d and then in
medium not containing aphidicolin for 1 d, and images of sc
cell-derived cell pairs were taken (e.g. Fig. 2A, right). The
mean ± SD (n = 300) of the values for the cell pair’s length
measured along the longitudinal axis was 63.0 ± 13.0 mm,
whereas that for the cell pair’s width was 41.3 ± 6.7 mm. The
mean value for the shape-determining ratio s denoting the cell
pair’s length divided by width was 1.55 (Fig. 2B, right). The
mean rate of the cell pairs with cross-walls positioned at
75–90 to the long axis was significantly greater than that of
the cell pairs belonging to any of the other five groups, and that
of the cell pairs with cross-walls positioned at 0–15 tended to
be secondarily high and greater than that of the cell pairs belonging to any of the four oblique division groups (Fig. 2C,
right). The difference between the mean rates of the cell pairs
of the 0–15 division angle group and those belonging to either
of the 30–45 and 45–60 groups was not statistically significant
when analyzed for all cell pairs (Fig. 2C, right). However, it was
judged to be significant when analyzed for selected cell pairs
with s values <1.60 (short sc cells; Fig. 2C, right).
The mean values for both the cross-wall length and cell pair’s
width were significantly greater in the 0–15 than in the 75–90
division angle group, and tended to be greater than in the most
oblique division group (data not shown). The mean ratio of the
cross-wall length to the cell pair’s width determined for the
0–15 division angle group was significantly greater than that
for the 75–90 group, which was almost 1 and the lowest value,
and tended to be greater than that for the most oblique division group (Fig. 2D, right). These data suggested that longitudinal sc cell division represents a marked departure from
Errera’s rule. The mean s value for the 0–15 division angle
group was significantly smaller than that for the 75–90
group, and also tended to be smaller than that for the most
oblique division group (Fig. 2D, right), being consistent with
the result that a tendency to divide longitudinally was more
marked for short than for all observed sc cells (Fig. 2C, right).
Cell wall configurations in sc cell-derived cell
pairs
The division planes selected in sc cells can be classified into
types I, II and III according to how many cell wall parts, out of
the three, provide the sites at which each cross-wall meets the
parental cell wall (Fig. 3A). Every cross-wall type includes one
subtype with a part of the cross-wall located in close proximity
to one of the two boundaries between the round and
830
cylindrical cellular parts (Fig. 3, Ib, IIb and IIIb) and another
subtype with two cross-wall parts separately located in close
proximity to each boundary (Fig. 3, Ibb, IIbb and IIIbb). The
latter subtypes of types I, II and III are closely related to each
other.
The rates of cell pairs with type-I, -II and -III cross-walls in a
population of those with s values ranging from 1.2 to 1.6
(n = 138) were 43.5, 16.7 and 39.8%, respectively. The cell
pairs with cross-walls connecting the two boundary regions
comprised less than about 10% of each population of the cell
pairs with type-I, -II or -III cross-walls, and all of them belonged
to oblique division groups (Fig. 3C). All cell pairs with type-I
cross-walls belonged to the 45–60, 60–75 and 75–90 division
angle groups; in contrast, most of those with type-III cross walls
(89.1%) belonged to the 0–15, 15–30 and 30–45 division angle
groups (Fig. 3C). Importantly, the type-III cross-wall was found
in >90% of the members of the latter three groups and all
members of the 0–15 and 15–30 division angle groups.
Thus, it appears that differences in the selection frequency
among differently positioned type-III division planes account
for the sc cell-specific division angle bias.
Relative areas of the longitudinal cross-walls of sc
cell-derived cell pairs
As predicted for typically shaped sc cells (Fig. 4A), oblique
cross-walls connecting the two boundary regions have the
smallest surface areas in flat type-III cross-walls passing through
the cell center, and the smaller the angle of a type-III cross-wall
to the longitudinal axis, the larger its surface area. A factor that
can make the area of a longitudinal type-III cross-wall smaller
than that of the oblique one is its displacement away from the
cell center, i.e. a reduction of division symmetry, such as that
associated with one of the cross-wall subtypes (Fig. 3, IIIb).
Slight symmetry reductions may allow longitudinal type-III
cross-walls to retain areas significantly larger than those of oblique cross-walls connecting the two boundaries between the
round and cylindrical cellular parts, referred to here as bb-plates
(Fig. 4A). The positions of such longitudinal cross-walls are still
near to those of oblique type-III cross-walls with smaller areas
and, therefore, these positions would not correspond to local
area minima. However, when symmetry reduction is so marked
that the longitudinal cross-walls have areas smaller than those
of the bb-plates, these cross-walls should be counted as having
locally minimum areas, because their areas are smaller than
those of nearby oblique cross-walls. If the longitudinal crosswalls of sc cell-derived cell pairs have locally minimum areas
due to their displacement, the bimodal angular frequency distribution obtained for sc cell division (Fig. 2C, right) could be
explained in accordance with the theory that the strength of
the least area tendency is the only criterion for selecting the
plane of symmetric division.
To compare the surface areas of the longitudinal cross-walls
of sc cell-derived cell pairs with those of the bb-plates, the ratio
of the cross-wall’s surface area to its maximum possible area,
Plant Cell Physiol. 54(6): 827–837 (2013) doi:10.1093/pcp/pct044 ! The Author 2013.
Two-criteria theory for symmetric division control
Fig. 3 Cell wall configurations in sc cell-derived cell pairs. (A) Schematic illustrations to explain how observed cross-walls were classified
according to their relative position. Each dotted line represents the boundary between the cell’s round and cylindrical parts. Gray indicates
the cellular part including the site at which the cross-wall meets the parental cell wall. (B) Example of the recorded fluorescence signal
distribution in a calcofluor-stained cell pair. Scale bar, 10 mm (C) Frequency distribution of angle a obtained for each cross-wall type and
subtype formed in the cell pairs with s values ranging from 1.2 to 1.6 (n = 138). Cell pairs were chosen from those used for obtaining the data
shown in Fig. 1.
and that of the bb-plate’s surface area to the maximum possible
area, were estimated for all members of the 0–15 division angle
group. The data revealed that the mean value for the estimated
relative area of the longitudinal cross-wall is significantly greater
than that of the bb-plate regardless of the cell pair’s s value
(Fig. 4B). The rate of cell pairs with longitudinal cross-walls
whose areas are estimated to be smaller than those of their
bb-plates was 4.7% (n = 43). These results indicate that the longitudinal cross-walls of sc cell-derived cell pairs barely have locally minimum areas. The estimated surface area of the crosswall relative to its maximum possible area tended to be smaller
than 1 (Fig. 4B), suggesting that the longitudinal cross-walls
barely have globally maximum areas.
Comparison of detected and hypothetical
standard divisions
According to Besson and Dumais (2011; Prusinkiewicz 2011),
the pairwise probability pij of a plant cell dividing with a new
cross-wall i instead of another j having a larger area can be
expressed as:
1
pij ¼ 1+eij
ð1Þ
where b is an experimentally obtained constant (average: 20.6),
and dij is the relative area difference between the candidate
cross-walls. dij is expressed as dij = (Aj Ai)/A, where A is the
mean cell area, and Ai and Aj are the areas of the walls i and j,
respectively. Importantly, the cross-walls counted as competing
candidates are limited to those with locally defined minimum
areas. Another expression of pij is pij = Pi/(Pi + Pj), where Pi and
Pj are the probability of observing the formation of the new
cross-wall i and j, respectively, among all candidate cross-walls;
the pairwise probability of observing the formation of the cross
wall j instead of i is given by pji = Pj/(Pi + Pj) or by pji = 1 – pij.
These lead to the following predictions regarding the selection
of a cross-wall a not corresponding to a local minimum:
(i) When the cross-wall a has an area the size of the cross-wall j, the
experimentally obtained pairwise probability of observing the
formation of the cross wall a instead of i, Pa/(Pi + Pa), will be
smaller than the theoretical pairwise probability pai, calculated
with an equation derived from Equation 1.
(ii) When there is another possible cross-wall b with an area larger
than that of i but smaller than that of j or a, the experimentally
obtained pairwise probability Pa/(Pi + Pa) will be smaller than
the theoretical pairwise probability pbi, calculated with an equation derived from Equation 1.
Whether or not the selections in os and sc cells of the crosswalls nearly parallel to the cell’s long axes correspond to the
selection of the new cross wall a described in the first prediction
was tested. To prepare equations for calculating the pairwise
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T. Asada
Fig. 4 Estimation and comparison of the relative surface areas of the cross-walls of sc cell-derived cell pairs. (A) The relative surface areas of
hypothetical cross-walls rotating with respect to the long axis by angle a in typically shaped sc cells with s values of 1.2, 1.4 and 1.6. All
hypothetical cross-walls are flat and pass through the cell center. The position bb indicates that of bb-plates. The illustration shown on the left
explains cross-wall positions. (B) The relative surface areas of longitudinal cross-walls (Acw/AL0, top) and bb-plates (Abb/AL0, top) and their ratio
(Acw/Abb, bottom) estimated for sc cell-derived cell pairs belonging to the 0–15 division angle group with s values ranging from 1.0 to 1.4, 1.2 to
1.6 and from 1.4 to 1.8. AL0 denotes the surface area of a flat cross-wall positioned parallel to the cell’s long axis and passing through the cell
center, Abb, that of a bb-plate, and Acw, that of an observed longitudinal cross-wall (left). The estimation of Acw/AL0 involved considering both the
effects of the cross-wall’s inclination by angle a and its displacement away from the cell center by distance dsr (left), as described in the Materials
and Methods. Values are the mean, and error bars indicate standard deviations. The numbers of the analyzed cell pairs with s values ranging from
1.0 to 1.4, 1.2 to 1.6, and from 1.4 to 1.8 were 29, 28 and 13, respectively. Asterisks indicate significant differences at P < 0.01 (Student’s t-test).
probability, pos1, of an os cell-derived cell pair having a crosswall with an area equal to the globally maximum area instead of
another with the globally minimum area and its counterpart for
predicting sc cell division, psc1, the mean cell area was defined as
A = (3/4V)2/3p1/3, where V is the cell volume.
The relative area difference dos1 needed for calculating pos1 is
written as:
os1 ¼ s1=3 ðs 1Þ
dsc1 needed for calculating psc1 is written as:
ð2=3Þ sc1 ¼ 4ðs 1Þ= 3=2ðs 1=3Þ
832
ð2Þ
ð3Þ
Substituting these and b = 20 in equations derived from
Equation 1, the pairwise probabilities can be expressed as functions of s. The curves of dos1, dsc1, pos1 and psc1 are shown in
Fig. 5A. Using the prepared equations and cell models with
simplified shapes, the pairwise probability was calculated for
each observed cell pair, and the mean value (Fig. 5B, pos1
or psc1) was compared with that for the experimentally
obtained rate of members of the 0–15 division angle group
relative to that of the 0–15 and 75–90 groups (Fig. 5B,
P015 =½P015 +P7590 ). This analysis revealed that the two
mean values obtained for os cell-derived cell pairs do not significantly differ from each other (Fig. 5B, left), and that, in the
case of short sc cell-derived cell pairs, the mean value for the
Plant Cell Physiol. 54(6): 827–837 (2013) doi:10.1093/pcp/pct044 ! The Author 2013.
Two-criteria theory for symmetric division control
Substituting this and b = 20 in an equation derived from
Equation 1, the pairwise probability can be expressed as a function of s (Fig. 5A, right), as well as the relative area difference
(Fig. 5A, left). The mean value for the pairwise probability psc2
was calculated for short sc cell-derived cell pairs, and compared
with the above-mentioned mean value for the rate of members
of the 0–15 division angle group relative to that of the 0–15
and 75–90 groups, experimentally obtained for the same cell
pairs. This analysis revealed that the mean of the experimentally
obtained division frequency ratio is significantly greater than
that of the theoretical pairwise probability (Fig. 5B, right). This
result is contrary to the prediction of 2.
Discussion
Fig. 5 Comparison of detected and hypothetical standard divisions.
(A) The curves of the relative area differences dos1, dsc1 and dsc2 (left)
and the pairwise probabilities pos1, psc1 and psc2 (right). Each function
of s is shown or explained in the Results. The pairwise probabilities
were obtained for b = 20 using equations derived from Equation 1.
(B) The measured rate of members of the 0–15 division angle group
relative to that of the 0–15 and 75–90 groups [P0–15/(P0–15 + P75–90)]
and the theoretical pairwise probability pos1 obtained for os cells (left),
and the same division frequency ratio and theoretical pairwise probabilities psc1 and psc2 obtained for short sc cells (right). Values are the
mean obtained through three independent experiments, and each
mean value was calculated for >37 cell pairs. Error bars indicate
standard deviations. Different lower case letters indicate significant
differences among mean values at P < 0.05.
experimentally obtained division frequency ratio was significantly greater than that for the theoretical pairwise probability
(Fig. 5B, right). The result obtained for os cell division does not
exactly meet the prediction of 1, and the other for sc cell division is contrary to the same prediction.
Next, the second prediction was tested for the case where
the cross-walls a and b correspond to the longitudinal and bbsubtype cross-walls of sc cell-derived cell pairs, respectively. To
calculate the theoretical pairwise probability, psc2, of an sc cellderived cell pair having a cross-wall with an area the size of its
bb-plate instead of another with the globally minimum area,
the relative area difference needed for calculating it, dsc2, can be
expressed as:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
.
ð2=3Þ
1+ðs 1Þ2 1
sc2 ¼
3=2ðs 1=3Þ
ð4Þ
Tobacco BY-2 cells with os shapes most frequently divided
along their short axis (Fig. 2C, left), consistent with the findings
of a previous report (Lynch and Lintilhac 1997). While this
result is in agreement with the single-criterion theory that
the strength of the least area tendency is the only criterion
for selecting the symmetric division plane, another result
from comparing detected and hypothetical standard divisions
(Fig. 5B, left) was not exactly predictable according to Besson
and Dumais’s least area rule. The latter result can be interpreted
as predicting that the measured frequency of observing os cells
dividing parallel to the long axis would be higher than that of
normal plant cells with os shapes dividing parallel to the long
axis. In this context, it is noteworthy that, when retaining original spherical shapes, axially compressed BY-2 protoplasts tend
to divide perpendicular to the compression axis (Lynch and
Lintilhac 1997). Although this tendency was not clearly detected in the present study, os cells may have exhibited a tendency related to it so that these cells could more preferentially
divide along the long axis than uncompressed cells with os
shapes. An alternative explanation is that the mean value for
the pairwise probability pos1, which was obtained without considering the effects of symmetry reductions, is significantly
lower than its true value. In os cells more similar to a sphere
than sc cells (Fig. 2B), even a slight symmetry reduction can
make the relative area differences nearly zero, and calculation
not considering these effects tends to underestimate critically
the same pairwise probability. Therefore, the result would not
necessarily indicate a significant difference between the division
plane selections in os and normal plant cells.
The sc cell division is characterized not only by a division
angle bias which makes the frequency of divisions nearly perpendicular to the longitudinal axis the highest, but also by another which makes the frequency of longitudinal divisions
secondarily high (Fig. 2C). This could be explained in accordance with the single-criterion theory if the selected longitudinal
division planes correspond to local area minima. However, the
result from comparing the estimated relative surface areas of
the cross-walls (Fig. 4) indicates that the longitudinal crosswalls barely have locally minimum areas. Furthermore, the
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T. Asada
measured frequency of longitudinal sc cell division was even
significantly higher than that predicted when the selected longitudinal division planes were assumed to correspond to local
area minima (Fig. 5B, psc1). Therefore, it is reasonable to conclude that sc cell division is characterized by an extremely high
frequency of occurrence as division along the long axis, which is
not in agreement with the single-criterion theory. The measured frequency of longitudinal sc cell division was also even
significantly higher than that predicted when the selected longitudinal cross-walls were assumed to have locally minimum
areas the sizes of the bb-plates (Fig. 5B, psc2). This, when combined with the result indicating that the longitudinal crosswalls of sc cell-derived cell pairs have significantly larger areas
than the bb-plates (Fig. 4B), strongly suggests that the sc cellspecific division tendency represents a departure from the
probabilistic least area rule.
We can predict that oblique divisions of sc cells hardly exhibit the typical right angle tendency, namely the tendency to
follow Sachs’s rule strictly, unlike their longitudinal divisions.
Therefore, the data regarding the order of the division frequency from sc cells (Fig. 2C, right) could be explained if
there are two independent geometrical criteria which separately cause symmetric divisions to follow the least area and
right angle rules. However, the existence of the two geometrical
criteria would not be sufficient to account for all features of sc
cell division, especially the fact that it is predicted to be characterized by an unusually high frequency of occurrence as division along the long axis.
When exploring factors making sc cell division so unique, it
is noteworthy that sc cells are likely to have a double-wall
structure even in their cylindrical parts (Fig. 1B), and that the
apparent stimulation of longitudinal division was more clearly
detected in short than in all sc cells (Fig. 2C, right; Fig. 2D,
right). The field of mechanics (Flügge 1960) allows us to predict
that, in a plant cell with the spheri-cylindrical shape, the cell
walls of its central cylindrical part would be subjected to orthoradial stresses twice as strong as meridional stresses, as long as its
protoplast applies uniform outward pressure to the cell walls.
Unlike this imaginary sc cell, a real sc cell has enclosing outer
walls that can function as a ‘hoop’ for preventing the inner new
walls from being subjected to orthoradial stresses and, in its
central cylindrical part, the new cell walls may have orthoradial
stresses weaker than meridional stresses, unless the outer wall’s
secondary effect of weakening meridional stresses is not negligible. It is indeed predictable that the shorter the cylindrical
part of an sc cell, the smaller the secondary effect of outer walls.
It can also be predicted that real sc cells are continuously under
the outer wall’s hoop effect, since BY-2 protoplasts cultured in
hypertonic medium do not shrink but start to expand within a
few days as they have regenerated cell walls (Hasezawa and
Syono 1983). Therefore, it seems reasonable to hypothesize
that the apparent stimulation of longitudinal division in sc
cells involves the reversal of wall stress anisotropy, making meridional stresses dominant. The hypothesis proposes that, basically or in each isolated plant cell unit, the plane of symmetric
834
division also tends to be positioned parallel to the axis along
which dominant cell wall stresses arise, if any, while tending to
adopt an area-minimizing configuration. A prediction based on
this two-criteria theory is that the divisions of cells with no or
isotropic wall stresses would be the only case explicable in accordance with the single-criterion theory and probabilistic least
area rule.
According to Cooke and Paolillo (1980), apical cells of filamentous fern gametophytes have shapes represented as a
hemisphere subtended by a cylinder, which correspond to
half of the spheri-cylindrical shape, and their new cross-wall
occupies either the transverse or longitudinal plane in a way
strictly following the least area rule. The two-criteria theory
predicts that the division of cylindrical plant cells strictly follows
neither the least area nor the probabilistic least area rule due to
its greater tendency to occur as transverse divisions resulting
from dominant orthoradial stresses in the cell wall. Regarding
the apical cell division, however, transverse cross-walls are not
formed in the cell’s cylindrical part but in the terminal, round
part in which the parental cell walls are probably subjected to
almost isotropic stresses. Therefore, the reported data seem not
to contradict the two-criteria theory. Because the transverse
cross-walls selected in those apical cells hardly exhibit the typical right angle tendency, the same data can be regarded as
providing counter-evidence to the hypothesis that there is a
geometrical criterion which causes divisions to follow the right
angle rule strictly. As shown by Minc et al. (2011), cells with
shapes reminiscent of sc cells can be prepared from sea urchin
eggs using microchambers into which the eggs are placed, and
their division is characterized by a single division angle bias
which makes the frequency of division perpendicular to the
long axis the highest. Thus, at least for those animal cells, a
spheri-cylindrical cell geometry itself is not sufficient to lead
to a division tendency similar to that for sc cells. A bimodal
angular frequency distribution comparable with that for sc cell
division has been reported as characterizing the orientation of
the mitotic spindle in a human HeLa cell type, whose cortical
cue activities were spatially controlled with a fibronectincoated micropattern (Théry et al. 2007).
Plant surfaces have mechanical stresses dependent on the
presence of pressure from inner tissues, and the cells constituting the stretched epidermis tend to divide along the axis along
which dominant stresses are predicted (Green and Selker 1991,
Hamant et al. 2008). These and other data on cell division in
compressed inner tissues (Lintilhac and Vesecky 1984) suggest
that, in stretched or compressed plant tissues, mechanical stresses can constitute a contextual cue determining the plane of
symmetric division selected in each cell. However, to my knowledge, mechanical stress has never been hypothesized to be
involved in division plane selection in laterally isolated cylindrical cells, such as those of epidermal hairs (Ota 1961, Esau
1977) or early embryos (Esau 1977, Webb and Gunning 1991),
which are neither stretched nor compressed through neighboring cells but have cell walls probably subjected to orthoradial
stresses. This could be due to the fact that the maximal stresses
Plant Cell Physiol. 54(6): 827–837 (2013) doi:10.1093/pcp/pct044 ! The Author 2013.
Two-criteria theory for symmetric division control
arising in cell walls of isolated cylindrical cells are predicted to
be far weaker than those arising within plant surfaces (Selker
et al. 1992, Hamant et al. 2008). Testing the above-mentioned
two-criteria theory may be equivalent to exploring the possibility that such relatively weak wall stresses help elongating
but still short cylindrical cells to divide perpendicular to the
elongation axis following Hofmeister’s rule.
A difficulty encountered in discussing the criteria or source
of information for selecting the plane of symmetric division in
plant cells is that the definition of the ‘default’ of division plane
selection is currently ambiguous. The default selection should
be defined as that seen in cells which are not provided with any
spatial cue. However, defining the cue-free system itself is impracticable because our knowledge on possible cues is currently
limited. Among candidate plant cell types in which the default
of division plane selection might be seen, isolated cells are the
simplest. The present results suggest that, even in the simplest
system, the strength of the least area tendency is not the only
criterion for selecting the plane of symmetric division.
Combined with other techniques, the use of sc cells is expected
to facilitate the design of new experiments to clarify the premitotic processes which regulate division plane selection in
plant cells and test the two-criteria theory.
Materials and Methods
Plant cell line
All experiments were performed using tobacco BY-2 cells
(Nagata et al. 2004) derived from a seedling of Nicotiana tabacum L. cv. Bright Yellow-2. Cells were maintained by culture
using modified Linsmaier and Skoog’s medium (mLS), as
described previously (Nagata et al. 1981).
Preparation and culture of os cells
Os cells were prepared from cells of 3- or 4-day-old cultures,
namely those in the logarithmic phase of growth, which were
more suitable for protoplast isolation than stationary phase
cells, under sterile conditions. To isolate protoplasts, cells
were suspended in mLS supplemented with 1% (w/v)
Sumizyme (undiluted form; Shin-nihon kagaku kogyo), 0.1%
(w/v) pectolyase (Seishin Pharmaceutial), 1% (w/v) bovine albumin (fraction V; Sigma-Aldrich), 0.2 mM phenylmethylsulfonyl fluoride and 0.4 M mannitol, pH 5.5, and the obtained cell
suspension was gently agitated for 90 min at 30 C. Protoplasts
were collected by centrifugation, washed twice with 0.5 M mannitol solution, and suspended in mLS supplemented with 0.4 M
mannitol at a density of 4.7–7.7 105 ml1. To embed protoplasts, the suspension of protoplasts was mixed with an equal
volume of pre-heated mLS medium containing 3% (w/v) agarose LO3 (Takara) and 0.4 M mannitol, and the obtained mixture
was solidified in 2 mm deep molds made of silicon rubber spacers and glass slides. The gel sheets containing protoplasts were
hand-sectioned into square pieces of 10 10 mm, and the
pieces were suspended in mLS supplemented with 0.4 M
mannitol. After being placed on a 4 mm thick glass plate
which constituted the bottom of an original loading apparatus
(Supplementary Fig. S1), each gel piece was further cut into
four identical square pieces, which were then separated and
placed under a load of about 120 mN. The axially compressed
state was maintained for 2 d at 23 C in a humid chamber. The
loading system was calibrated with a load cell with a rated
capacity of 500 mN (LTS-50GA ; Kyowa Electronic Instruments).
Preparation and culture of sc cells
Sc cells were prepared from cells of 7-day-old cultures, namely
those in the stationary phase of growth, at room temperature
under sterile conditions. First, part of a cell culture was mixed
with 5 vols. of mLS supplemented with 30 mM propyzamide,
and the mixture was gently agitated for 1 h. To prepare plasmolyzed cells, part of the suspension of propyzamide-treated
cells was mixed with an equal volume of mLS supplemented
with 0.8 M mannitol, and the mixture was gently agitated for
20 min. Detachment of the plasma membrane from the cell wall
was enhanced by further mixing with the same volume of the
same medium and gently agitating the obtained cell suspension
for 1 h. Then, swelling of the protoplasts of plasmolyzed cells
was induced by mixing the cell suspension with an equal
volume of mLS, as the concentration of mannitol was reduced
from about 0.53 to 0.265 M. To ensure severe convex plasmolysis without allowing cell cycle progression, the cells were suspended in mLS supplemented with 0.45 M (0.66 M for one data
set) mannitol and 0.5 mg l1 aphidicolin, and the obtained cell
suspension was gently agitated for 3 h. Protoplast shapes were
finally adjusted by suspending cells in mLS supplemented with
0.3 M (0.4 M for one data set) mannitol and 0.5 mg l1 aphidicolin, and gently agitating the resultant cell suspension for 2 h.
Treating cells with propyzamide before inducing plasmolysis
and inserting a step where protoplasts of plasmolyzed cells
swell rapidly were found to be effective to detach the plasma
membrane smoothly from the cell wall and induce convex
plasmolysis. Then, 5–7 ml of the final sample of plasmolyzed
cells was transferred to a plastic dish with a diameter of 9 cm
and incubated for 2 d at 23 C in a humid chamber. After washing to remove aphidicolin, the cells were suspended in mLS
supplemented with 0.3 M (0.4 M for one data set) mannitol,
and the cell suspension was incubated for 12–18 h and used for
analysis. Replacement of solutions was carried out using sievelike tools made by covering one end of a plastic or glass cylinder
with a piece of nylon mesh sheet.
Observation of cells
To observe cell pairs derived from sc cells, cell suspensions were
mixed with equal volumes of mLS supplemented with 0.3 M
mannitol and 20 mg l1 calcofluor white II (Wako Chemicals),
and part of each mixture was transferred into wells made by
placing plastic membranes with holes in them onto glass slides.
For observing cell pairs derived from os cells, the agarose gels
containing the cells were hand-sectioned on a glass slide into
Plant Cell Physiol. 54(6): 827–837 (2013) doi:10.1093/pcp/pct044 ! The Author 2013.
835
T. Asada
vertical slices with a width of less than about 1 mm, and the
obtained gel slices were transferred into wells made by putting
silicon rubber sheets with holes in them onto glass slides and
filling them with mLS supplemented with 0.4 M mannitol and
10 mg l1 calcofluor white II. All samples were observed within
a few hours after being placed under coverslips under an epifluorescence microscope (BX-51; Olympus), and images were
recorded with a digital camera (DP-21; Olympus).
Analysis of cell images
Analyses of collected digital images were performed with the
programs Image J, developed and distributed by the National
Institute of Health of the USA, and Photoshop CS3 (Adobe).
Measurements of the cell length and width involved manual
operation to encircle the cell’s outline with the minimal size of
an ellipse or rectangle, through which the cell’s center and long
and short axes were defined. Cross-wall angle measurement
involved manually placing a straight line on the two diametrical
points where the new meets the older cell wall. Each dsr value
for calculating Acw/AL0 was obtained by measuring the distance
between the cell center and a straight line representing a crosswall position. The sc cell-derived cell pairs often had curved
cross-walls and, for such cross-walls, the distance dsr did not
often correspond to the shortest distance between the cell
center and cross-wall. The areas of sc cell-derived cell pairs
were measured with a tool of Image J, and the obtained
values were used as estimated AL0 values for obtaining Abb/AL0.
For sc cells with typical and simplified shapes determined by s
and sizes determined by w, the area Aa of a flat cross-wall
positioned at angle (with respect to the cell’s long axis and
passing through the cell center is:
ZP1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w2
A ¼ 4
sin2 x2 dx
2
ffi
ZP3 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w2 2
2
2
+4
1 ðs 1Þ sin x dx
2
ð5Þ
P2
Where P1, P2 and P3 are P1 = w(s 1)/(2 cos a),
P2 = w(s 1)tan asin a/2, P3 = wˇ(1 (s –1)2 sin2 a)/2, respectively. AL0 corresponding to Aa given for a = 0 is written as:
AL0 ¼ w2 s 1+
ð6Þ
4
The relative area sizes shown in Fig. 4A were obtained by
using Equations 5 and 6. The area A0 of a flat cross-wall positioned parallel to the cell’s long axis and displaced away from
the cell center by dsr is:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2ffi
w2 2dsr
2dsr
A¼
ð7Þ
1
+ w2 ðs 1Þ 1 2
w
w
836
Statistical analysis
All multiple comparison tests were performed with the software StatView, ver. 5.0J (SAS Instiute) according to the methods
of Tukey and Kramer or of Games and Howell
Supplementary data
Supplementary data are available at PCP online.
Funding
The Faculty of Biological Science, Graduate School of Science,
Osaka University [a special grant for research development].
Estimation of cross-wall size
0
Values for Acw/AL0 were obtained as estimates by multiplying Aa/AL0 by A0 /AL0. The approximation should result in an
overestimation of the rate of displacement-dependent area reduction. Each Aa and A0 value was obtained by substituting
measured parameter values in Equations 5 and 7, respectively.
The values were divided by the same cell’s AL0 value calculated
by substituting measured w and s values in Equation 6 to obtain
each A0 /AL0 and Aa/AL0 value. Values for Abb were also obtained
as estimates by using the equation Abb = w(l1 + l2)p/8, where l1
and l2 are the longest diameters of two bb-plates measured for
each cell pair. Each estimated Abb/AL0 value was the Abb value
for a cell pair divided by the area of the same cell pair. The
mean ± SD (n = 43) of the values for the ratio of AL0 estimated
with Equation 6 to that estimated from a cell pair’s area was
1.035 ± 0.039.
Acknowledgements
I thank Dr. Hiroki Yasuhara of Kansai University for his kind
assistance in maintaining tobacco BY-2 cells, and Dr. Toshio
Sano of Hosei University for his valuable discussion on turgor
pressure. I would also like to express my sincerest thanks to Dr.
Ykä Helariutta and his colleagues of the University of Helsinki
for their encouragement during my stay with them, where I
started to work on another project regarding division plane
selection prior to the present study, and to an anonymous
reviewer for invaluable comments.
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