Plant Physiol. (1998) 116: 1515-1526
Analysis of Cell Division and Elongation Underlying the
Developmental Acceleration of Root Growth in Arabidopsis
thaliana1
Gerrit T.S. Beemster and
Tobias I. Baskin*
Division of Biological Sciences, University of Missouri, Columbia,
Missouri 65211-7400
 |
ABSTRACT |
To investigate the relation between
cell division and expansion in the regulation of organ growth rate, we
used Arabidopsis thaliana primary roots grown vertically
at 20°C with an elongation rate that increased steadily during the
first 14 d after germination. We measured spatial profiles of
longitudinal velocity and cell length and calculated parameters of cell
expansion and division, including rates of local cell production (cells
mm
1 h1) and cell division (cells
cell1 h1). Data were obtained for the root
cortex and also for the two types of epidermal cell, trichoblasts and
atrichoblasts. Accelerating root elongation was caused by an
increasingly longer growth zone, while maximal strain rates remained
unchanged. The enlargement of the growth zone and, hence, the
accelerating root elongation rate, were accompanied by a nearly
proportionally increased cell production. This increased production was
caused by increasingly numerous dividing cells, whereas their rates of
division remained approximately constant. Additionally, the spatial
profile of cell division rate was essentially constant. The meristem
was longer than generally assumed, extending well into the region where
cells elongated rapidly. In the two epidermal cell types, meristem
length and cell division rate were both very similar to that of
cortical cells, and differences in cell length between the two
epidermal cell types originated at the apex of the meristem. These
results highlight the importance of controlling the number of dividing cells, both to generate tissues with different cell lengths and to
regulate the rate of organ enlargement.
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INTRODUCTION |
A central question in plant physiology is how plants regulate
their growth rate. The growth rate of a plant organ changes with
development and as the plant responds to stimuli. Growth rate is
regulated by the combined activity of two linked processes, expansion
and cell production. Although organ growth rate is determined by
expansion directly, growth rate is also influenced by cell production,
through the determination of how many cells are expanding at a given
time. Conversely, expansion may partially regulate cell production,
because it displaces cells from the meristem and because it is required
for continued cell division. Studies of the regulation of growth rate
have rarely measured expansion in the meristem, and studies that
measure cell division rates have rarely quantified expansion
concurrently. To understand how plants regulate the growth of their
organs, we need to quantify expansion throughout the growth zone as
well as cell production.
The rate of cell production by a meristem has two distinct components:
the number of dividing cells and their rate of division. The number of
dividing cells is determined by their size and by the size of the
meristem, whereas the rate of cell division is determined by the
regulation of the cell cycle. Therefore, an equivalent change in cell
production could be caused by distinct mechanisms. Increases in the
number of dividing cells could be caused by prolonging the expression
of cell cycle machinery, whereas increases in the rate of division
could be caused by enhancing the passage through cell cycle
checkpoints. It is not known to what extent plants regulate cell
production by either type of mechanism.
We have addressed the relationship between cell production and
expansion in the root of Arabidopsis thaliana. We used a
kinematic method that allows production and expansion rates to be
quantified under identical conditions, even on the same roots, and
quantifies the number of dividing cells as well as rates of cell
division. A kinematic approach is ideally applied to A. thaliana roots because their diameter is constant over the growth
zone, except for the very apical region, and cortical and epidermal
cells occur in only a single tier each (Dolan et al., 1993
). Moreover,
cell length can be measured in living roots by using Nomarski
microscopy, thereby avoiding fixation, embedding, sectioning, and the
attendant shrinkage (Baskin et al., 1995).
Kinematic methods were pioneered decades ago (Goodwin and Stepka, 1945;
Erickson and Sax, 1956; Hejnowicz, 1956), but although these methods
have been used often to measure rates of expansion, they have seldom
been used for measurements of division. Instead, investigators have
relied on other methods for quantifying cell division rates, including
mitotic index, rate of accumulation of metaphase cells after colchicine
application, and the fraction of labeled mitoses after application of a
pulse of tritiated thymidine. All of these methods were developed for
homogeneous cell cultures. In organs, they have serious pitfalls and
have produced contradictory results (Green and Bauer, 1977; Webster and
Macleod, 1980). By contrast, these pitfalls are avoided by kinematic
methods (Sacks et al., 1997). For quantifying cell production, the
kinematic approach was set on a stronger mathematical foundation by the introduction of the continuity equation (Silk and Erickson, 1979; Gandar, 1980; Silk, 1984), which allows the production of cells to be
treated analogously to the production of any substance, such as
sucrose. Only in the last few years has there been a renewed use of
kinematics for quantifying cell division rates (Ben-Haj-Salah and
Tardieu, 1995; Beemster et al., 1996; Sacks et al., 1997).
The primary root of A. thaliana, like that of many other
species, grows more rapidly with time from germination (Baskin et al.,
1995). This acceleration happens naturally (without exogenous hormones)
and is large, with rates doubling over several days. Therefore, we have
chosen this system to investigate how growing organs coordinate cell
production and expansion. In an earlier study of accelerating growth in
the A. thaliana root, the increasing growth rate was found
to be accompanied by increased cell production, which was argued to
explain the enhanced elongation (Baskin et al., 1995). However, that
study measured expansion indirectly and did not measure rates of cell
division. For the increasing growth rate of the root, the aim of the
present study was to resolve the contributions from expansion and cell
production. Our results show that accelerating root elongation rates
are accompanied by increased cell production in the meristem, with
little change in cellular expansion rates. These results suggest that
the number of growing cells regulates root growth rate
directly.
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MATERIALS AND METHODS |
Seeds of Arabidopsis thaliana L. (Heynh), ecotype
Columbia, were stored at 4°C. At d 0, they were surface sterilized
with 15% household bleach and plated on agar-solidified, modified
Hoagland solution in 90 × 90 mm2 square
tissue culture plates, which were then placed vertically in a growth
chamber under constant conditions (20°C, 80 µmol of light
m2 s1; Baskin and
Wilson, 1997).
Velocity and Longitudinal Strain Rates
On d 6, 8, and 10, three roots on each of five different plates
were selected for similar length and growth rate (estimated by eye from
marks on the bottom of the plate indicating the position of the root
tip on previous days). Under a dissecting microscope, graphite
particles (Mr. Zip, extra fine, A.G.S. Co., Muskegon, MI) were
sprinkled on the upper surface of roots with an eyelash mounted on an
applicator. After 1 h, the root with the least tendency to rotate
was selected from the marked roots on each plate and was used for
subsequent observations of particle positions. A plate was removed from
the growth chamber and placed vertically on a horizontally oriented
compound microscope fitted with a ×10 objective and a charge-coupled
device camera (C2400, Hamamatsu Co., Hamamatsu, Japan). A series of
overlapping images was recorded on videotape in S-VHS format with the
time stamped on each image by a time-date generator and the plate was
returned to the growth chamber. On a given day, five roots were
followed, and five or six observations were made of each root at
intervals of about 1 h. Subsequently, images from the videotape
were captured with an Apple Macintosh 7100/66 computer equipped with a
frame grabber board (LG3, Scion Corp., Frederick, MD), and composite
images of individual roots were created for each observation time. All image processing and analyses were done with the public domain NIH
Image program (version 1.60; National Institutes of Health; available
at http://rsb.info.nih.gov/nih-image/).
The position of individual particles relative to the tip of the root
was measured in each pair of images. Velocities of displacement (v[x]; µm h1) were
then calculated as:
|
(1)
|
where xi,t is the ith
particle at time t, and x = 0.5 *
(xi,1 + xi,2).
Subsequently, values of x were adjusted to represent distance from the quiescent center by subtracting the length of the
root cap (see below). For observations made on a given day, we were
unable to detect a significant change in the velocity profile over the
observation interval (5-6 h). Therefore, the resulting four to five
velocity data sets obtained for each root were combined and then
smoothed and interpolated into 25-µm spaced points.
The smoothing procedure fitted a series of overlapping, independent
polynomials to the data. First, a given number of data points was
selected symmetrically around the first desired x and the
parameters of a third-degree polynomial fitted to this interval were
used to calculate v(x). The value of x
was then increased by 25 µm and the process was repeated. For
positions at the beginning and end of the series, the data were not
symmetric around x but contained the same number of points.
The data thus obtained were not smooth enough to permit meaningful
differentiation required for subsequent calculations. Therefore, a
second step was introduced, in which the equally spaced data obtained
from step 1 were smoothed further using a similar procedure. This
second step was repeated until the change in velocity between
successive iterations became smaller than 1 µm
h1 for all points of the data set. To adjust
for differences in numbers of observations between individual roots,
the number of data points for step 1 was defined as the number of
points between the tip of the root and the location where velocity
started to increase rapidly (Fig. 2, inset; between 50 and 120 points),
and the length of this root segment defined the interval for step 2 (250-450 µm). The smoothing procedure was relatively insensitive to
the interval's length. The smoothing algorithm was implemented as a
macro for the program ProFit (version 5.0, QuantumSoft, Zürich, Switzerland).
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| Figure 2.
Spatial profiles of longitudinal velocity and
strain rate of A. thaliana roots on d 6 and 10. Data
from each root were smoothed and interpolated as described in
``Materials and Methods''; symbols are means ± se
(when larger than the symbol) of 10 roots. A, Velocity; the inset shows raw data points for a single d 10 root. The final velocity on d 6 was
241 ± 6 µm h1 and on d 10 it was 445 ± 12 µm h1. B, Strain rate; symbols on the x
axis and the vertical dashed lines mark the basal terminus of the
meristem averaged from individual roots.
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|
From the smoothed data, the length of the growth zone was determined as
the distance between the quiescent center and the first position where
the increase in velocity between successive positions was less than or
equal to 0. Final velocity, which equals the rate at which the root
elongated, was found by averaging the velocity over all points basal to
the end of the growth zone. We used the final round of fitted
polynomials to calculate strain rates (r[x]; % h1), the derivative of velocity with respect to
distance along the root:
|
(2)
|
Analysis of Cell Length
Directly after video recording, the plates were stored at 4°C to
minimize further growth. Individual roots were mounted in the nutrient
solution within chambers, which prevented deformation of the root and
which could be flipped over to allow cells in both halves of the root
to be observed. The roots were viewed under Nomarski optics (Zeiss
Axioplan) with a ×40, 0.9-numerical aperature objective. A series of
overlapping images of cortical and epidermal cell files from several
focal planes were captured using a charge-coupled device camera
(VI-470; Optronics Engineering, Goleta, CA) fitted to the microscope
and connected to a 486 PC running Image1/AT software (Universal
Imaging, West Chester, PA). The series of images continued until cell
length exceeded the width of the video image (when average cell size
was approximately 100 µm). Composite images were created and used to
measure the length of every cell in each cortical and epidermal cell
file that could be followed over most of its length. The position of each cell was defined by its midpoint. The length of the root cap was
determined separately on images through the median plane, as the
distance between the tip of the root and the basal margin of the
quiescent center.
Cell lengths from all files of a given cell type were combined for each
root and then smoothed and interpolated with the same procedure as used
for the velocity data. The number of data points used to define the
interval for step 1 was determined as the number of cells between the
inflection point where cell length started to increase (Fig. 3) and the
most basal data point and ranged from 15 to 40. The length of the
interval used for step 2 was defined as the distance between the same
inflection point and the quiescent center and ranged between 250 and
550 µm. The iteration in step 2 was repeated until the change in cell
length between successive iterations became smaller than 0.5 µm for
all positions.
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| Figure 3.
Spatial profiles of cell length and cell flux of
cortical cells on d 6 and 10. Symbols are means ± se
(when larger than the symbol) of 10 roots. A, Cell length; symbols on
the x axis and vertical dashed lines indicate the
average length of the meristem for individual roots, and the horizontal
dashed line indicates the cell length at the end of the meristem
averaged over all roots. Data from each root were smoothed and
interpolated as described in ``Materials and Methods''. B, Cell flux;
the final cell flux was 1.68 ± 0.09 cells h1 on d 6 and 2.55 ± 0.18 cells h1 on d 10 (mean ± se).
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Analysis of Cell Division
Cell flux (F[x]; cells
h1), the rate at which cells flow past a
particular position x, was calculated from:
|
(3)
|
The increase in F(x) is proportional to
local rates of cell production. This relationship is explicit in the
continuity equation (Silk and Erickson, 1979; Gandar, 1980; Silk,
1984), which we used to calculate local cell production rates
(P[x]; cells µm1
h1):
|
(4)
|
where 
(x) is cell density, the inverse of cell
length. The term 
F/x was calculated directly from the
cell flux profile of each root, using five-point, second-degree
differentiation formulas (Erickson, 1976). The term
(x)/t, which
equals 0 for all x under steady-state conditions, cannot be
calculated for individual roots, since cell length for each root was
observed only once. Therefore, this term was calculated for each of the three observation days from densities averaged over all roots, using
three-point, second-degree differentiation formulas (Erickson, 1976).
Cell division rates (D[x]; cell
cell1 h1) were
calculated from P(x) by correcting for cell
length using:
|
(5)
|
In contrast to terminology used recently by Sacks et al. (1997),
we call P, the direct result of the continuity equation, a
"cell production rate." By doing so, we adhere to the terminology proposed earlier by Gandar (1980) and avoid confusing this parameter with a "cell division rate." The rate of cell division is widely understood as being on a per cell basis and inversely proportional to cell cycle duration.
The position of the end of the division zone was determined for
individual roots as the location where P(x) first
became 0 or negative. In a few roots, P(x)
stabilized at small but positive values, and the end of the division
zone of these roots was taken as the position where
P(x) became approximately constant. The cell flux
at this position was defined as "final cell flux"
(Ff) and represents the total rate of cell
production for each file.
The cumulative number of cells per file, n(x),
was calculated from cell density data using:
![n(x) = 25 × <LIM><OP>∑</OP><LL>25</LL><UL>x</UL></LIM> <FR><NU>(&rgr;[x] + &rgr;[x − 25])</NU><DE>2</DE></FR>](/content/vol116/issue4/fulltext/1515/img006.gif)
|
(6)
|
with x = 25, 50, 75... . . The profile of
n was then used to determine cell numbers for defined
regions of the root.
Average cell division rate for the whole of the meristem
(
; h1) was
calculated for each root from the final cell flux and the number of
dividing cells (Ndiv):
|
(7)
|
Given the exponential nature of the cell division process, the
average cell cycle duration (
c; h)
can be calculated from Ndiv and
Ff (Green, 1976; Webster and Macleod, 1980;
Ivanov, 1994) as:
|
(8)
|
Temporal (Lagrangian) Quantification
Because root growth is not steady in A. thaliana
seedling roots (see ``Results''), we cannot easily transform the
spatial (Eulerian) data into temporal (Lagrangian) data expressing the
development of a material element as it moves through the growth zone
(Silk, 1984). However, the time it takes for a cell to move through the elongation zone (Tel) is relatively short,
so the number of cells in the elongation zone
(Nel) and the flux of cells through that zone (Ff) do not change much during this
period. Therefore, Tel can be estimated
from:
|
(9)
|
A true residence time for individual cells in the meristem cannot
be calculated because each cell exists only from its formation until it
undergoes cytokinesis. For the majority of cells, residence time would
therefore equal cell cycle duration. However, if the average cell cycle
duration in the meristem is approximately constant over time, we can
calculate residence time of the most basal transverse wall in the file
by assuming it was formed by a division of the most apical cell in the
file. Accordingly, residence time in the meristem
(Tdiv; h) is directly proportional to the
number of division cycles it takes to form all cells in the meristem
and was calculated as:
|
(10)
|
Tests of the Curve-Fitting Procedure
Various methods have been used to smooth and interpolate cell
length and velocity data. One approach is to fit a logistic function to
the data (Barlow et al., 1991; Morris and Silk, 1992). Although these
functions fit this type of data approximately, there is no reason to
expect an exact fit, and they may deviate systematically from the true
distribution. Therefore, a nonparametric smoothing method is
preferable. A method commonly used for this type of problem is cubic
(
) splines. To test curve-fitting procedures, we used a function to
generate simulated data sets and compared the real solution, obtained
analytically from the function, to the approximation from curve
fitting. The function used was a modified logistic function (Morris and
Silk, 1992) with parameters adjusted to resemble d 10 plants. Real data
were simulated by adding random "noise" having the same variance as
the original cell length or velocity data. Splines were fitted to the
simulated data using procedure "TRANSREG" of the SAS statistical
package (SAS Institute, Cary, NC), with one knot for the cell length
and nine knots for the velocity data giving optimal results.
The splines and our method both seemed to fit velocity (not shown) and
cell length data (Fig. 1A) well. However,
when a derivative was examined (e.g. strain rate), the results from the
spline fit deviated from the function's derivative more than the
results of our method (Fig. 1B); when two simulated data sets were
combined as required to calculate cell production rates, the results of the spline fit deviated notably from the analytical solution (Fig. 1C).
We repeated this test twice on different simulated data sets with
similar results.
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| Figure 1.
Comparison of curve fitting with cubic ()
splines and repeated partial polynomials. A modified logistic function
(Morris and Silk, 1992) was fitted to the velocity and cell length data of a d 10 plant, and random noise, with variance equal to that of the
actual data, was added to generate simulated data sets. Each data set
was smoothed and interpolated using cubic splines or repeated partial
polynomials, and strain rates and cell division parameters were
calculated as described in ``Materials and Methods''. A, Cell length; B, strain rate; C, cell production rate. In B and C, the solid line
plots the analytical solution of the function.
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Statistical Analysis
The experiment was repeated twice, for a total of 10 replicate
plants per observation day. Statistical significance of differences between d 6, 8, and 10 for all parameters was determined by
multivariate analysis of variance with Statistica (PC version 5.1, StatSoft, Inc., Tulsa, OK).
| |
RESULTS |
We analyzed cell division and expansion in the longitudinal
direction only, simplifying the root as a single file for each cell
type under study. This assumption is reasonable because in the A. thaliana root lateral expansion and formative divisions are
restricted to the very apical part of the growth zone (Dolan et al.,
1993). We measured velocity and cell length as a function of position
along the root axis and used these data to calculate spatial profiles
of expansion and cell division. Because velocity and cell length
profiles were measured on the same root, all of the required
calculations were made on an individual root basis, which allowed us to
estimate the variability between roots for all parameters.
Velocity and Strain Rate Profiles
Measurements of velocity as a function of position often showed a
relatively sharp transition, from a shallow rate of increase near the
apex to a steeper rate more basally (Fig.
2A, inset). This prominent transition
was absent from the averages over 10 roots (Fig. 2A), because the
transition occurred at different locations for individual roots. The
final velocity (i.e. overall root elongation rate) on d 10 was nearly
twice that of d 6, reflecting a 16.6% increase per day, similar to
that reported by Baskin et al. (1995). These average final velocities
were about 10% less than elongation rates of unmarked roots on the
same plates, as determined by marks on the bottom of the plate at the
position of the root tip on each day.
Increased root growth rates arose primarily from an increase in the
longitudinal extent of the growth zone, whereas both the shape of the
strain rate profile and maximal strain rates remained the same (Fig.
2B). Note that strain rates did not decrease to 0 at the apex; instead,
in the apical few hundred micrometers, strain rates remained
approximately constant, at about 4% h1.
Between d 6 and 10, the average length of the growth zone, defined as
the distance between the quiescent center and the position where strain
rate first reached 0, nearly doubled (Table
I). Thus, the increasing root velocity
was caused by an enlarging growth zone, without increased maximal
strain rate.
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Table I.
Spatial and temporal dimensions of the growth zone
and its components for cortical cells in A. thaliana roots
Data are the means ± se of 10 roots. Delineation of
growth zone and meristem length is described in "Materials and
Methods," and the length of the zone of rapid elongation was defined
as their difference. The number of cells within each zone, and their residence time, was calculated as described in ``Materials and Methods''. Significance denotes the overall significance of the
difference between days, determined by multivariate analysis of
variance.
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Cell Flux
In the apical region of the growth zone, the profile of cortical
cell length was gently concave downward, which is typical of root
tissues, and with time the extent of the region of small cells
increased (Fig. 3A). The flux of cells at
a given position, i.e. the number of cells passing that position per
time, can be calculated by dividing that position's velocity by cell
length (Eq. 3). Because velocity increased with distance from the
quiescent center and cell length remained approximately constant, cell
flux increased in the apical part of the growth zone until reaching a
plateau (Fig. 3B). The maximal cell flux, which equals the total production rate of cells per file, increased significantly between d 6 and 10.
The increase in total cell production rate was slightly less than the
increase in root elongation rate (1.6-fold for cell flux versus
1.8-fold for root elongation rate). This indicates that the extent of
cellular elongation also increased, even though maximal strain rates
did not increase (Fig. 2B). This increased elongation predicts that
final cell length would have increased somewhat (by 1.2-fold), which is
similar to the value previously found (Baskin et al., 1995). Therefore,
during the developmental acceleration of root elongation rate, greater
cell flux increased the number of elongating cells, but there was only
a small change in the elongation of individual cells.
Cell Division
The increased rates of cell production by the meristem could be
due to either increased size of the meristem or increased rates of cell
production per unit length of the meristem. Local cell production rates
in the meristem can be calculated from the local increase in the cell
flux profile added to the local rate of change in cell density, as
expressed by the continuity equation (Eq. 4; Silk and Erickson, 1979;
Gandar, 1980; Silk, 1984). Except for the most apical 100 µm, cell
production rates were higher on d 10 than on d 6 throughout the
division zone (Fig. 4A). Both maximal
cell production rate and the extent of the region of cell production
increased. The average length of the meristem, determined for
individual roots as the position where cell production rates first
reached 0, increased by 62% from d 6 to 10 (Table I). As a consequence
of the increasing length of both parts of the growth zone, the number
of cells in the meristem and zone of rapid elongation steadily
increased (Table I).
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| Figure 4.
Spatial profiles of cell production rate and cell
division rate in cortical cells on d 6 and 10. Cell production and
division rates were calculated for each root as described in
``Materials and Methods''; symbols are means ± se
(when larger than the symbol) of 10 roots.
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Cell production rates per unit length may be significant
physiologically (Ben-Haj-Salah and Tardieu, 1995; Sacks et al., 1997); for example, these rates might reflect the abundance of a regulatory factor with an activity proportional to its concentration. However, cell division is naturally considered on a per cell basis, because a
cell can be produced only by another cell and not by an arbitrary length of meristem. A rate of cell division per cell can be calculated as an average for the entire meristem by dividing total cell flux by
the number of cells in the meristem (Eq. 7). Also, local rates of cell
division per cell can be calculated by correcting local cell production
rates for differences in cell length (Eq. 5). The average rate of cell
division was constant from d 6 through 10 (Table
II). Consequently, the average cell cycle
duration, calculated as the inverse of cell division rate and corrected for the exponential nature of the cell division process (Eq. 8), was
also constant (Table II). The cell cycle averaged 18.6 ± 0.7 h (mean ± se, n = 30), which is
shorter than the 20 to 25 h previously reported for cortical cells
in A. thaliana by other methods (Fujie et al., 1993; Baskin
et al., 1995).
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Table II.
Average cell division rate and cell cycle duration
of cortical cells
Average cell division rate () and cell cycle
duration ( c) over the whole of the
meristem at 6, 8, and 10 d after sowing (mean ± se; n = 10). Average cell division rate was
calculated as the total cell production in the meristem, i.e. final
flux, divided by the number of cells in the meristem; the average cell cycle duration was calculated as the inverse of average division rate
multiplied by ln(2) (see ``Materials and Methods''). Significance
denotes the overall significance of the difference between days,
determined by multivariate analysis of variance.
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Although rates of cell production increased over time throughout most
of the meristem (Fig. 4A), this was not reflected in parallel increases
in cell division rates, which instead remained approximately constant
throughout the meristem (Fig. 4B). For the basal part of the curve
shown for d 10, the large ses resulted from large values of
cell length in this region amplifying small deviations from 0 of the
calculated local cell production rates, as well as from differences
among roots in the location where cell production rates decreased
rather abruptly to 0. Evidently, cell production was increased entirely
by the increased number of dividing cells.
Surprisingly, when the extent of the division zone was compared with
the spatial profile of expansion (Fig. 2B), cell division activity
continued until strain rates almost reached their maximum. Similarly,
cell division continued well beyond the location where cell length
started to increase. The average size at which cells left the meristem
was 39.5 ± 4.1 µm (mean ± se,
n = 30) and varied little with time, despite the fact
that this length was reached at different distances from the quiescent
center (Fig. 3A).
Temporal Analysis of Cell Expansion and Division
Thus far, we have focused on spatial aspects of cell expansion and
division, quantifying these processes with respect to position along
the root axis. However, the spatial distribution of cell expansion and
division could be a reflection of the temporal regulation of these
processes. For example, the size of the meristem could be regulated by
the number of times a given cell is allowed to divide; similarly, the
size of the elongation zone could be regulated by cells rapidly
elongating for a set amount of time. It is therefore important to
determine both spatial (Eulerian) and temporal (Lagrangian) aspects of
cell division and expansion (Silk, 1984).
For the zone of rapid elongation, despite its enlargement over time
(Fig. 2), residence time did not increase significantly (Table I),
which along with the similar maximal strain rates indicates that the
elongation behavior of a cell as it moved through the zone did not
change. Actually, the extent of cellular elongation was expected to
have increased because of the predicted increase in final cell length.
If the increased cellular elongation were due to only increased
residence time in the zone of rapid elongation, then the magnitude of
the expected increase would be only 0.7 h, which is too small to
have been detected (Table I) and could easily have been missed. For the
meristem, we used Equation 10 to calculate residence time because
average cell cycle duration was essentially constant over time. On
successive days, a cell wall formed by division of the most apical cell
took progressively longer to migrate through the meristem (Table I). In
other words, as the meristem developed, cells continued dividing for
longer periods. Prolonging cell division could be the regulatory event that increased the total rate of cell production and increased the
growth rate of the root.
Cell Production and Cell Division in Epidermal Cells
Results thus far have concerned division and expansion only in
cortical cells. For various species, tissues differ in the position of
the basal terminus of cell division (Rost and Baum, 1988), and they may
also differ in other parameters of cell division; however, to our
knowledge this has been studied only with nonkinematic methods. In
A. thaliana, the epidermis contains two cell types, which
are segregated in files. Cells in one type of file nearly always make
root hairs (trichoblasts) and cells in the other type rarely make hairs
(atrichoblasts; Dolan, 1996). The atrichoblasts are longer than
trichoblasts at maturity, which indicates that atrichoblast files
produce fewer cells than do trichoblast files (because the two types of
file must have the same longitudinal velocity at any given position).
To determine the basis for the lowered cell production of
atrichoblasts, as well as to compare both types of cells with cortical
cells, we measured the length of both types of epidermal cells in a
subset of the same roots used above. The length of trichoblasts was
similar to cortical cells throughout the apical part of the growth zone
(Fig. 5A); the small difference in the
first 75 µm from the quiescent center may reflect some (larger) root
cap cells being mistakenly measured as epidermal cells. However,
atrichoblasts were longer than the other cell types throughout the
meristem (Fig. 5A).
View larger version (30K):
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| Figure 5.
Spatial profiles of cell length and cell division
parameters of epidermal cells. A, Cell length; because trichoblast cell length was similar to that of cortical cells, data for these cells are
omitted from B to D for clarity. B, Cell flux; C, cell production rate;
D, cell division rate. Data for cortical cells were re-drawn from
Figures 3 and 4 and are shown for comparison. Data are for d 10. Symbols plot means ± se (when larger than the symbol)
for five roots.
|
|
Because trichoblasts had essentially the same cell length profiles as
cortical cells, they also had similar cell division characteristics;
however, atrichoblasts differed because they were larger than the other
cell types at all positions. In atrichoblasts, cell flux increased more
gradually and cell production rate was lower at all positions in the
meristem (Fig. 5, B and C); however, despite the difference in cell
production rate, the three cell types had rates of cell division that
were not significantly different (Fig. 5D). Also, the cell types all
ceased division at approximately the same distance from the quiescent
center (Fig. 5D). Therefore, the lesser cell production in atrichoblast
files resulted from there being fewer dividing cells per file, and this
lessened cell number resulted from the larger size of atrichoblasts,
not from slower divisions.
| |
DISCUSSION |
The primary root of A. thaliana exhibited accelerated
growth because the size of the growth zone increased. From d 6 to d 10, the root meristem produced cells more rapidly, but at all times the
newly produced cells elongated in very nearly the same way. We
hypothesize that the length of the zone of rapid elongation depends on
the number of cells moving through it. In this view, each cell is
endowed with a certain capacity for elongation; therefore, cell
production rate, by determining the number of cells elongating at a
given time, regulates root elongation rate directly.
Methodology
To measure the spatial profile of velocity, the time interval
between successive observations was 1 h. This is a relatively long
time for the determination of strain rates in roots; investigators often use an interval of 15 min. Our use of a longer period was necessary to determine accurately the low velocities in the meristem. The disadvantage of longer time intervals is a loss of accuracy, particularly at the basal end of the elongation zone, because of the
considerable displacement of each particle. However, for this work the
excess particle displacement was less than 20% of the length of the
growth zone, which has been modeled to affect the calculated strain
rate profiles negligibly (Peters and Bernstein, 1997).
The accelerating growth of A. thaliana roots presents a
technical challenge. To our knowledge, the data presented here are the
first published kinematic analyses of growth under non-steady-state conditions. At steady state, the term in Equation 4 expressing the
local time-dependent change in cell density equals 0, and observations
at a single time suffice for calculations (Sacks et al., 1997). We
evaluated this term from observations made on the 3rd d and it was
always less than 1 cell mm1
h1 and usually much less. Even though the
magnitude of the time-dependent change in cell density was small, we
included it in all of the results shown here; had it been omitted, the
results would not have been changed materially.
The difference between smoothing methods (Fig. 1) illustrates the
sensitivity of the calculations to sources of error. Therefore, we
considered other possible sources of systematic error (measurement error is trivial compared with the variability in cell length or
velocity). We found that potential misalignment of cell length and
velocity data (due to errors in calibration factors or measurement of
root cap length), the finite time that elapsed between the last
velocity observation and cell length determination, and the movement of
particles during the 1-h observation interval all had some effect on
the calculated distributions of cell production and division
rates. However, these effects were relatively small and did not
materially affect our conclusions.
Division in Epidermal Cells
To our knowledge, differences in cell division parameters between
trichoblasts and atrichoblasts have never been quantified before. We
found that, whereas trichoblasts closely resembled cortical cells,
atrichoblasts had lowered rates of cell production, extending up to the
most apical part of the meristem; moreover, the lowered production rate
was caused not by cells dividing more slowly but instead by their being
longer and, consequently, fewer. The regulation of root hair formation
in A. thaliana roots has been studied extensively, and many
of the involved loci have been identified. When the expression of such
loci has been studied, it has been found throughout the meristem, right
up to the initials (Galway et al., 1994; Masucci et al., 1996). Our
results show that the size divergence between the epidermal cell types
originated in the very apical part of the meristem and was perpetuated
by constant cell division rates; we suggest that epidermal cell fate is
regulated in part through regulating the size of the initial cells.
Spatial Profile of Cell Division Rate
The spatial distribution of cell division rate has been estimated
based on data from mitotic indices, tritiated-thymidine labeling, or
colchicine blocking. Given the disruptive nature of these methods and
their failure to account for the movement of cells during the labeling
interval (Green and Bauer, 1977; Webster and Macleod, 1980), the
results obtained, especially spatial aspects, must be interpreted with
care. Our data indicate that cell division rates are approximately
constant throughout the meristem (Fig. 4B). This agrees with kinematic
observations in roots of maize (Barlow, 1987), onion
(González-Fernández et al., 1968; Carmona and Cuadrado,
1986), and wheat (Hejnowicz, 1959) but is in contrast to other work on
maize roots (Erickson and Sax, 1956; Sacks et al., 1997) and timothy
grass (Goodwin and Avers, 1956; Hejnowicz, 1956; Erickson, 1961), which
showed a bell-shaped distribution of cell division rate. Environmental differences may explain the different cell division patterns; however,
another possibility is inadequate curve fitting. A bell-shaped curve
may have resulted from oversmoothing, which tends to eliminate abrupt
transitions; furthermore, most of the above study results had only a
few data points in the meristem, which exacerbates the difficulty of
curve fitting. Because we have many data points in the meristem and
used a gentle smoothing approach applied to individual roots, the
observed constancy of cell division rate is likely to be real. It
remains to be determined to what extent the spatial profile of
cell division rate can be affected by environmental conditions.
Proliferative Fraction
For years, scientists have debated the existence of a
proliferative (or growth) fraction. It has been argued, on the basis of
direct (Erickson, 1961; Bertaud and Gandar, 1985) and indirect (Balodis
and Ivanov, 1970; Clowes, 1976) observations, that toward the base of
the meristem an increasing proportion of cells leave the mitotic cycle,
while only the proliferative fraction continues to divide. Because
plant cells do not slide, a cell that stops dividing increases in
length relative to cells that continue dividing by a factor of
2n for each missed cycle. Consequently, if a
proportion of cells left the cell cycle, the distribution of relative
cell lengths found at the apical portion of the meristem would be
narrower than at more basal positions. The main argument against the
presence of cells that stop dividing much sooner than others is that
the predicted differences in cell size between cells have been rarely observed (Webster and Macleod, 1980).
To determine whether any cells had stopped dividing early, we compared
the distribution of cortical cell length in the apical part of the
meristem (between 100 and 200 µm from the quiescent center) with that
in the mature region of the root. In the apical part of the meristem,
the proportion of cells lying outside the 2-fold size range expected if
all cells divided exactly in half at the same length, was 17% (out of
673 cells from 5 roots), and in the mature region the proportion was
14% (out of 200 cells from 10 roots). That the proportion of cells
exceeding the 2-fold range was low indicates a fairly close
coordination of cell length and cell division. The similarity of the
proportion between the distal meristem and the mature region shows that
individual cells stopped dividing within one cell cycle of one another
and, therefore, that cortical cells in A. thaliana roots
continue to divide throughout the meristem (i.e. the proliferative
fraction equals 1).
Actually, this observation is reconcilable with direct observations
that some cells leave the cell cycle when they are near the center of
the meristem. Given the fact that the cell cycle duration was
approximately constant throughout the meristem, in one cell cycle the
entire basal half of the meristem becomes displaced into the zone of
rapid elongation (Ivanov, 1994). This means that cells originating from
a division basal to the center of the meristem will have left the
meristem before getting the chance to divide again. Direct observations
of such cells following that division will show them to be
nonproliferative, while adjacent cells will divide again.
Basal Terminus of the Meristem
Our results indicate that cell division in cortical and epidermal
cell files continues well into the region where cell length increases
rapidly (Fig. 3A) and where strain rates are severalfold higher than in
the apical part of the meristem (Fig. 2B). This result agrees fully
with data on the root meristems of timothy grass, wheat, and maize that
were obtained by kinematic approaches (Goodwin and Stepka, 1945;
Erickson and Sax, 1956; Goodwin and Avers, 1956; Hejnowicz, 1959; Sacks
et al., 1997). However, this result conflicts with delineation of the
meristem based on the distribution of mitoses seen in longitudinal
sections, which typically find that the meristem ends at a more apical
location, where cell lengths or strain rates are near their minimal
values (Luxová, 1980; Barlow et al., 1991; Ishikawa and Evans,
1995).
We believe that, compared with mitotic indices, the kinematic
determination of cell production delineates the basal terminus of the
meristem more reliably. Scoring mitotic frequency in sections is
difficult because as cell size increases, the frequency of nuclei
decreases, and therefore the number of sections required to sample
mitotic cells adequately at the basal end of the meristem becomes
large. It is also possible that, as cell expansion accelerates, the
duration of mitosis shortens, further reducing the frequency of mitotic
cells. This would shorten the time a rapidly elongating cell spends
without cortical microtubules, which are depolymerized during mitosis
but are needed to control the directionality of cell expansion.
Consistent with the terminus of the meristem defined kinematically,
mitoses have been found in regions of considerable cell length or high
strain rate (Jensen and Kavaljian, 1958; Rost and Baum, 1988).
Therefore, for many species, the meristem very likely extends to
regions where cells are relatively long and strain rates are high.
Physiologically, the basal portion of the meristem, where cell length
and strain rate rapidly increase, is of great interest. An important
role, distinct from other parts of the growth zone, is apparently
played by this region in response to many different stimuli
(Balu
ka et al., 1994; Ishikawa and Evans, 1995). This region was
first called the "postmitotic isodiametric growth zone," since
renamed "transition zone" (Baluka et al., 1996), and has been considered to be a region where cells recover from being mitotic
and prepare for their phase of rapid expansion. However, according to
our results as well as those in the literature (cited above), the basal
part of the meristem extends into a region where cells expand rapidly.
Interestingly, the transition zone approximately coincides with the
location where cortical and epidermal cells are undergoing their final
round of cell division; the final cell division may represent a
specific developmental stage, during which cells possess distinctive
characteristics. We concur with the recent proposal to name this region
the transition zone but point out that the zone is a region where cells
are undergoing their final division as well as expanding rapidly.
Cell Production and the Regulation of Organ Growth Rate
Cell production sustains growth; additionally, we suggest that
cell production can regulate organ growth rate. The regulation of organ
growth rate has traditionally been viewed from two distinct perspectives. The first is a purely spatial perspective, in which the
position of the zone of rapid elongation and its size are considered to
be specified by positional controls acting on the process of expansion.
This view has been applied explicitly to morphogenesis (Cooke and Lu,
1992; Kaplan, 1992) and is commonly implicit in physiological studies
that characterize spatial profiles of expansion (Sharp et al., 1988).
The second perspective is cellular. Recognizing that the extent of the
zone of rapid elongation is determined by the trajectory of the cells
that move through it, the cellular view holds that the trajectory of
the cells is specified when the cell is formed, just prior to its
leaving the meristem. A model based on cells acting independently and
even stochastically has been used to predict successfully a variety of
organ level responses (Bradford and Trewavas, 1994). For root growth, a
doubled cell production with no other change, in the spatial view,
would halve the size of mature cells but would not change the size of the zone of rapid elongation or root elongation rate; in the cellular view, this would double the size of the zone of rapid elongation (and
root elongation rate), because it would double the number of cells
executing their set trajectories.
Spatial and cellular regulation are not incompatible and may both
apply; nevertheless, we believe that cellular regulation is more
important. The perspectives have not been distinguished by most studies
of organ growth rate because they have found effects on both cell
production and cellular elongation, so both processes were presumably
affected independently. However, similar to the developmental example
studied here in roots, there are several examples from studies of
leaves in which an applied stress reduced the growth of the organ and
the production of cells proportionally, without changing the elongation
of individual cells (Terry et al., 1971; Lecoeur et al., 1995; Beemster
et al., 1996). To explain these results on the leaf or the root, the
spatial view must posit cell production and spatial control change in
parallel, whereas the cellular view need posit a change in cell
production only.
Further support for the cellular view comes from studies in which organ
elongation is changed by treatments that should affect cell division
specifically. First, cell division has been inhibited with 
rays,
inhibitors of DNA synthesis, and by reducing the activity of the cell
cycle regulator Cdc2 kinase, and organ elongation was considerably
slowed (Foard and Haber, 1961; Barlow, 1969; Hemerly et al., 1995).
However, these inhibitions of cell division were extreme and for that
reason could have diminished elongation in response to some
physiological disruption. More telling are treatments that stimulate
cell production and increase organ elongation without affecting
cellular elongation as judged by the approximately constant size of
mature epidermal cells; this happened in roots of A. thaliana plants either mutant at the AXR1 locus
(Lincoln et al., 1990) or constitutively expressing a mitotic cyclin
gene in the meristem (Doerner et al., 1996). The latter example is compelling because there is no obvious reason why the continuously expressed cyclin in the meristem should alter spatial controls on
elongation. To explain these results, the spatial perspective must
invoke linkages between cell division and the spatial control of
elongation that are to date purely hypothetical, but the cellular perspective explains them easily by relating the changed organ growth
directly to the changed flux of cells.
Finally, the hypothesis that the behavior of the zone of rapid
elongation is controlled spatially predicts that cell production could
be changed without changing the elongation of the organ. To our
knowledge, no such example has been found. Note that the converse
finding, changed elongation without changed cell production, fits
either perspective because the changed elongation could result from
changing either spatial controls or the endowment of each cell
for elongation when it enters the zone of rapid elongation.
The number of examples in which division and expansion parameters have
both been fully quantified is small, but such documentation must take
place before the mechanisms that coordinate these processes can be
productively explored. In this paper, we have shown for A. thaliana roots how a kinematic method allows division and
expansion parameters of the whole growth zone to be measured
accurately, and we have explained most of the developmental increase in
elongation rate by increased cell production. It appears that cell
number and temporally programmed cell behavior play important roles in regulating the growth of plant organs.
| |
FOOTNOTES |
1
This work was supported by a postdoctoral
fellowship to G.T.S.B. from the University of Missouri Molecular
Biology Program, by the Cooperative States Research Service, U.S.
Department of Agriculture under agreement no. 92-37304-7868 (with
T.I.B.), and by grant no. 94ER20146 to T.I.B. from the U.S. Department
of Energy, which does not constitute endorsement by that department of
views expressed herein.
*
Corresponding author; e-mail
baskin{at}biosci.mbp.missouri.edu; fax
1-573-882-0123.
Received October 8, 1997;
accepted January 11, 1998.
| |
ACKNOWLEDGMENTS |
We thank Jan Wilson for excellent technical assistance, Prof.
Wendy Silk (University of California, Davis) for sharing results prior
to publication, which gave us helpful insights for the analysis performed here, and Prof. Robert Sharp for his revelatory comments concerning the manuscript.
| |
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Top
Abstract
Introduction