Annals of Botany 87: 693±698, 2001
doi:10.1006/anbo.2001.1392, available online at http://www.idealibrary.com on
S H O R T CO M M U N I CAT I O N
Image Analysis of Maize Root CapsÐEstimating Cell Numbers from
2-D Longitudinal Sections
A . G . B E N G O U G H * {, M . I I J I M A { and P. W. B A R LOW }
{Soil-Plant Dynamics Unit, Scottish Crop Research Institute, Dundee DD2 5DA, UK, {Graduate School of
Bioagricultural Sciences, Nagoya University, Chikusa, Nagoya 464-8601, Japan and }IACR-Long Ashton, Long
Ashton Research Station, Department of Agricultural Sciences, University of Bristol, Long Ashton, Bristol BS41 9AF,
UK
Received: 10 October 2000 Returned for revision: 14 November 2000 Accepted: 24 January 2001
The cap of the primary root of maize produces several thousand border cells that are shed from the outside of the cap
each day. Border cell production is important in the penetration of soil by roots, and in in¯uencing the activity of
both bene®cial and pathogenic organisms in the rhizosphere. To improve understanding of the dynamics of border
cell production, it is desirable to know the number of cells in di€erent parts of the root cap. An image analysis
procedure was used to quantify cell dimensions and locations in the median longitudinal section of maize (Zea mays
L.) root caps. Calculations based on root symmetry were then used to estimate the number of cells in 3-dimensions.
Our estimation procedure was tested initially using regular arrays of identical square and hexagonal shapes to
represent cells. It was then tested using two di€erent tissues showing analogous arrays: a transverse section through
the maize root cap junction, and a transverse section through a barley root. Good linear correlations were obtained
between the number of cells estimated and the number of cells actually counted in the microscope. The numbers of
cells in the whole maize root cap (8870 + 390) were then estimated from longitudinal sections. These numbers of cap
cells agreed with values that had been estimated for maize by other methods. In the ®rst tier of the cap meristem, tentimes more meristematic cells were located in the cap ¯anks (4500 cells) than were present in the columella portion.
Similarly, only 7 % of cells in the outermost layer of the root were associated with the columella region of the cap, a
fraction which compared well with previous measurements of sloughed cells extracted from rhizosphere sand. This
present technique can be applied to estimate the numbers of cells in any cylindrically symmetrical tissue from two# 2001 Annals of Botany Company
dimensional sections.
Key words: Anatomy, border cells, cell production, image analysis, maize, rhizosphere, root cap, sloughing,
stereology, Zea mays L.
I N T RO D U C T I O N
Border cells, produced in large numbers by cell detachment
from the outside of root caps, are achieving increasing
recognition for their possible roles in plant defence and in
providing a low-friction coating for roots penetrating soil or
other physically resistant media (Bengough and McKenzie,
1997; Hawes, 1998). In short-term experiments it was found
that although the rate of border cell loss from the root cap
of maize increased in compacted sand, as compared with
loose sand (Iijima et al., 2000), the size of the root cap
decreased. To understand better the dynamics of the root
cap tissue and its component cells, estimates of cell
production in the cap meristem are needed, together with
the total number of cells in the root cap. The cell
production rate can be calculated from the number of
dividing cells in the meristem, coupled with their rate of
division. Meristematic and other cells of the root cap are
conveniently imaged in median longitudinal sections
prepared for microscopy. Therefore, to calculate the total
* For correspondence. Fax
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numbers of cells produced or sloughed o€, it is necessary to
derive an estimate of the numbers which are present in the
three-dimensional tissue from the two-dimensional microscope images.
There has been much study of this estimation process
at the sub-cellular level and in non-symmetrical tissues
(e.g. many animal tissues), giving rise to the longestablished science of stereology (e.g. Steer, 1981). Some
plant tissues have particular properties of symmetry that
are not present in the bulk of tissues studied using
stereological techniques. This potentially allows geometric
calculations to be used in estimating cell numbers from
appropriate sections. In the past, botanists have used such
calculations, but without detailed consideration of the
underlying assumptions (e.g. Clowes, 1976). With the wide
accessibility of image analysis techniques, and high
performance computer processing, there is now considerable potential to perform such calculations much faster and
more easily than was previously possible.
In this paper a semi-automated technique is described for
measuring cell sizes and location in root caps using image
analysis. Simple geometry is used to estimate cell numbers
# 2001 Annals of Botany Company
694
Bengough et al.ÐImage Analysis of Maize Root Caps
using the symmetrical properties of the root cap. Also
discussed are the assumptions involved in the calculations,
as well as some of the technical problems overcome in
deriving the cell number estimates.
M AT E R I A L S A N D M E T H O D S
materialsÐcross-sections of maize root caps prepared just
distal to the junction with the root proper junction and of
barley seminal rootsÐwere used to check our cell number
estimate.
Image analysis
Section preparation
The primary roots of maize seedlings were grown as
described in Iijima et al. (2000), ®xed in formalin acetic
alcohol (FAA), and embedded in paran wax. Longitudinal
sections 8 mm thick were cut through the root cap using a
microtome, and the sections stained by Feulgen's reaction to
stain nuclei and counterstained with 0.25 % Fast Green to
stain cell walls. An image of the median section was then
captured using a Zeiss Axioplan 2 binocular microscope
with a digital camera. The median longitudinal sections were
analysed for six seminal root tips grown on moistened
blotting paper at 19 8C for 64 h. Two additional test
Images of the median sections were analysed using
KS3000 software (Image Associates Ltd., Thame, Oxfordshire, UK). Initially, a skeleton outline of cell locations was
produced. From this outline, the geometric centres of
gravity of the root cap cells were calculated and the maximum and minimum feret dimensions of each cell measured
(Fig. 1), the feret being the distance separating two parallel
lines just touching the sides of the cells. The most accurate
means of producing a skeleton outline was to trace the cell
walls by hand, using a ®bre-tipped pen onto a clear acetate
sheet placed on a printed picture of the root cap section.
Hand-tracing the cell wall outlines ensured that intercellular
binary image of cells traced from micrograph
and scanned in using desktop scanner
dimensions, areas, and co-ordinates of centres
of gravity of cells obtained using KS300 image
analysis package
max feret
min feret =
d
centres of gravity of cells rotated
and translated in spreadsheet to centre
about origin of
d
x-y axes
numbers of cells calculated according
to eqn (3). The number of cells, of
2πr
kd, that fit into a circle of radius
r, is calculated for each cell visible in the
dimension
r
two-dimensional section.
F I G . 1. Procedure for digitizing and measuring root cap cells.
Bengough et al.ÐImage Analysis of Maize Root Caps
air-spaces were identi®ed and not classi®ed as small cells.
The image was then captured using a desktop scanner,
digitally ®ltered to remove a small amount of `noise' (small
clusters of isolated black pixels introduced by the scanning
process) and analysed for cell dimensions and locations.
The central cell in the ®rst tier of the cap meristem and
the central cell in the apex of the root cap were used to
specify the axis of symmetry of the root cap. The geometric
cell centre of gravity co-ordinates were rotated and
translated, so that the axis of symmetry of the root cap
was vertically oriented with the apex of the root cap at the
co-ordinate origin. The new co-ordinates (x2, y2), were
related to the original co-ordinates (x1, y1) by the equations:
x2 ˆ …x1 ÿ xc † cos y ‡ …y1 ÿ yc † sin y
y2 ˆ …x1 ÿ xc † cos y-…y1 ÿ yc † sin y
…1†
…2†
where y is the angle of rotation required to align the axis of
symmetry vertically, and (xc, yc) are the co-ordinates of the
tip of the root cap, about which the new origin is centred.
Using the KS3000 software, we measured the maximum and
minimum feret dimensions of each cell, and the co-ordinates
of the geometric centre of gravity of each cell in every image.
Estimating cell numbers
Assumptions. It was assumed that the minimum feret
dimension equals the width of the cell, as was generally the
case in the micrograph tracings of the longitudinal sections,
and that the cells are arranged in circular rings with
cylindrical symmetry (see Fig. 1). However, for the small
meristem cells, the measured width corresponded to the
maximum feret dimension (i.e. the cells had not started to
elongate). To account for this orientation e€ect, cells with
an area less than 180 mm2 were given a value of d equal to
the maximum feret dimension. About 90 % of meristem
cells in the ®rst four tiers had areas smaller than 180 mm2.
The number of cells in each ring is simply the circumference of the ring of cells divided by the circumferential
width of each cell. The total number of cells, N, in the root
cap is the sum of the numbers of cells in all of the rings
[eqn (3)]:
Nˆ
n X
2pri
i
di k
First, the technique was used to estimate cell numbers in
2-D cross-sections from data relating to the number of cell
walls intersecting a 1-D line through the centre of the
transverse section. This line represented, in e€ect, a small
region of the median longitudinal section through the root
cap, which was being used to calculate the total number of
cells in three dimensions. Thus, if the technique works for
the 1-D to 2-D estimation procedure, it should integrate
correctly for the 2-D to 3-D case, which is the summing
together of all regions of the longitudinal section. However,
this extrapolation to 3-D depends on the width of the cells
(especially those measured as the feret dimensions) being
similar in all directions, i.e. the cells being cylindrical.
The estimation procedure was tested using tiled arrays of
uniform shapes to represent cells, and on cells from two
plant tissues with approximate cylindrical symmetry.
The procedure was tested initially for uniform square
cells arranged on a regular grid, uniform hexagonal cells
arranged on a hexagonal grid, maize cap meristem
cells within a cross-section cut at the root-cap junction,
and cortical cells in a cross-section of a barley root (see
Fig. 2 caption for more details). Lines corresponding to
simulated `median sections' through the arrangements of
plant cells were drawn randomly, and the intersections with
the cell walls used to calculate the co-ordinates of the
geometric centres and the diameters of each cell. The
estimated number of cells within each of the concentric
rings of cells was then calculated using eqn (3) and plotted
against the actual number of cells counted in each ring on
the two-dimensional cell map (or cross-section).
Estimating cell numbers in root caps. The numbers of cells
present in various parts of a root cap (Fig. 3A) were
estimated by applying eqn (3) to the cell location and
dimension data from median longitudinal sections of the six
maize root caps. Cell number was estimated in cells located
in the ®rst four tiers of the cap meristem, and in the
outermost layer of the root cap cells. Meristematic or mature
cells occupying the cap columella were identi®ed separately
from those comprising the ¯ank portion of the root cap.
R E S ULT S
…3†
where n is the number of cells visible in the section, ri is the
distance of the cell centre of gravity from the axis of
symmetry, di is the appropriate feret dimension and k is a
correction factor due to the likelihood that a random
longitudinal section through a cell will underestimate the
maximum diameter of the cell. Theoretically, k equals 1.27
for perfect cylinders (Steer, 1984). In this paper we initially
set k equal to 1, and then graphically assessed the value of k
that gave the best correlation between estimated and actual
cell numbers.
Veri®cation of the estimation procedure. The procedure
developed for estimating cell numbers in three dimensions
(3-D) from 2-D sections was tested in a stepwise fashion.
695
Cell numbers estimated
Test sections. The number of cells estimated in the square
and hexagonal grids using eqn (3), with k ˆ 1, was linearly
related to the number of cells present (Fig. 2A). The dashed
lines in Fig. 2A±C have gradients of 1.0 and 1.27. The
goodness-of-®t of the data to these lines indicates the best k
value for the cell shapes, sizes and packing arrangement.
The value of k is closest to 1 for the square shapes (Fig. 2A)
and the cross-sectional cellular arrays at the maize root cap
junction (Fig. 2B), about 1.15 for hexagonal shapes
(Fig. 2A), and 1.27 for the cross-sectional cellular arrays
in the barley root cortex (Fig. 2C). A value of k ˆ 1 was
therefore assumed in estimating the cell numbers in the
maize root caps. The degree of scatter of the points in Fig. 2
is greater for the plant tissue sections than for the polygonal
696
Bengough et al.ÐImage Analysis of Maize Root Caps
grids due to the natural variation in cell size and shape
within these tissues.
Estimated number of cells
100
A
80
60
40
k = 1.27
k = 1
20
Square
Hexagonal
0
0
20
40
60
80
100
Number of cells
Estimated number of cells
60
B
50
DISCUSSION
40
Cell numbers in the maize root cap
30
20
k = 1.27
10
k = 1
Maize cap
0
0
10
20
30
40
50
60
Number of cells
Estimated number of cells
Root caps. The mean number of cells in whole maize root
caps was estimated as 8870 + 390 (+s.e.). There were about
50 cells in each tier of the cap meristem that gave rise to the
columella, whereas there were up to 500 cells in each layer
of the ¯anking portion of the cap meristem (Fig. 3B). The
outermost layer of the root cap which would form the next
cohort of border cells was composed of approx. 1300 cells.
Only about 6 % of these cells were associated with the
columella region of the cap. The fact that they had been
generated by the central portion of the cap meristem implies
that 94 % of all border cells derive from the ¯ank meristem
surrounding the columella. The outermost columella cells
were more rounded, having a mean aspect ratio (taken as
equal to the maximum feret dimension divided by the
minimum feret dimension) of 1.90 + 0.04, as compared to a
mean aspect ratio of 3.25 + 0.05 for the outermost, more
elongated, ¯ank cells.
C
100
50
k = 1.27
k = 1
Barley cortex
0
0
50
100
Number of cells
F I G . 2. Veri®cation of the estimation procedure: cell numbers were
estimated in three situations. A, Arrays of square and hexagonal cells.
Two sets of points for the hexagonal cells indicate the extremes
according to where the intersecting lines are drawn. The points for the
square array indicate the result if the intersecting line is drawn
diagonally across the square cells or along their edges. B, Meristem
cells of the maize root cap in transverse section at the root cap junction.
C, Cortical cells of a barley root in transverse section. In the case of B
and C, ®ve replicate lines were drawn intersecting the centre of the root,
and the numbers of cells estimated using eqn (3). The estimated and
actual number of cells were compared in each of the eight concentric
rings of cells in the barley root cortexÐhence there are eight
corresponding data points in (C).
Cell numbers in simulated two-dimensional sections were
predicted reliably using our estimation procedure (Fig. 2).
Even for cells that were shaped di€erently and packed with
imperfect cylindrical symmetry, the relative estimates of the
numbers of cells in each part of the sectioned tissue were
possible, though naturally subject to correspondingly large
random errors. Although this technique was applied to
study cell numbers in root caps of maize, the technique
could also be applied to estimate cells numbers in threedimensional tissues from median longitudinal sections of
any root or stem tissue where cylindrical symmetry is
present. The most time-consuming part of the procedure is
obtaining a clear skeleton outline of the cell walls for image
processing. Undoubtedly this will become easier with
advances in image processing techniques, but we found
that the most accurate and time-ecient procedure involved
tracing the images by hand onto acetate paper. Cell numbers
estimated in the whole root cap are in reasonable agreement
with the average 7900±12 080 cells estimated in maize
(`Golden Bantam') by Clowes (1976). In the present case,
the cell numbers ranged from 7800±10 600 (coecient of
variation of 11 %) compared to the 3900±20 900 cells found
in the 60 root caps examined by Clowes (1976). The
proportion of outer cap cells that were rounded (6 %) was
similar to the proportion (7 %) of rounded border cells
identi®ed by Iijima et al. (2000). The aspect ratios of the
rounded cells were 1.9 in both studies. The aspect ratios of
the elongated outer cells were signi®cantly smaller than
those of the elongated border cells [3.25 + 0.05 compared to
3.9 in Iijima et al. (2000)], probably indicating that cell
elongation continued during detachment of the border cells
and their residence in the rhizosphere. It is interesting to
note that cell numbers in the ¯anks of the root cap meristem
are up to ten-times greater than in the columella meristem
(Fig. 3). In studying total cap cell production rates, or
Bengough et al.ÐImage Analysis of Maize Root Caps
697
A
7
7
4
6
2
1
2
4
6
4
Key
1- columella portion of cap meristem
3
2- flank portion of cap meristem
3- root cap columella
4- root cap flank
5- outer layer of cap columella
6- outer layer of cap flank
5
7- root-cap junction
B
1500
Estimated number of cells in root cap
Columella
Flank
1000
500
0
Tier1
2
3
4
Outer cell layer
Cell location
F I G . 3. A, Numbered diagram indicating the di€erent regions of the root cap. B, Estimated mean numbers (+ s.e., n ˆ 6) of cells in particular
regions of the root cap of maize. Regions measured were the ®rst four tiers of the root cap meristem (1st tier is nearest root-cap junction) and in the
outermost cell layer of the cap (these cells will become the next cohort of border cells). The numbers of cells in the ¯ank and columella portions of
the root cap were identi®ed separately.
border cell production, it is therefore much more important
to estimate the cell doubling times in the ¯ank portion of the
cap meristem than in the more obvious central columella
region. Barlow et al. (2001) describe a pattern of cell division
in the cap meristem in detail. The regions considered were
columella and ¯ank meristem and the principles of the
model may be regarded as general for the caps of roots, such
as maize, with a closed meristem structure.
In conclusion, the mathematical procedure of transforming two-dimensional images into a three-dimensional
analogue gave realistic estimates of cell numbers in the
entire root cap of maize. The method should be applicable
to two-dimensional cross-sections of tissues that show
cylindrical symmetry. However, further work should be
performed to test the accuracy and reproducibility of the
technique on each tissue studied, although in some cases
(e.g. cells in speci®c zones of the tissues) it will be dicult to
validate the numerical estimates because the cells are
inaccessible. Comparisons of actual and estimated numbers
are valid for root caps and therefore suggest that the
mathematical technique may be reliable when employed in
other circumstances.
AC K N OW L E D G E M E N T S
We thank Monbusho and the GB-Sasakawa Foundation for
partly funding the visit to SCRI by Dr Iijima, and the Royal
Society for a collaborative research grant. The Scottish Crop
Research Institute and Institute of Arable Crops Research
receive grant-aided support from the Scottish Executive
698
Bengough et al.ÐImage Analysis of Maize Root Caps
Rural A€airs Department and Biotechnology and Biological Sciences Research Council of the UK respectively.
Thanks to J. McNicol of Biomathematics and Statistics
Scotland, and L. Deeks for helpful discussions.
L I T E R AT U R E C I T E D
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Bengough AG, McKenzie DM. 1997. Sloughing of root cap cells
decreases the frictional resistance to maize (Zea mays L.) root
growth. Journal of Experimental Botany 48: 885±893.
Clowes FAL. 1976. Cell production by root caps. New Phytologist 77:
399±407.
Hawes MC, Brigham LA, Wen F, Woo HH, Zhu Z. 1998. Function of
root border cells in plant health: Pioneers in the rhizosphere.
Annual Review of Phytopathology 36: 311±327.
Iijima M, Griths BS, Bengough AG. 2000. Sloughing of cap cells and
carbon exudation from maize seedling roots in compacted soil.
New Phytologist 145: 477±482.
Steer MW. 1981. Understanding cell structure. Cambridge: Cambridge
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