J. Embryol. exp. Morph, 83, Supplement, 313-327 (1984)
Printed in Great Britain © The Company of Biologists Limited 1984
313
Cell behaviour in a polygonal cell sheet*
ByH. HONDA 1 , R. KODAMA 2 , T. TAKEUCHI 2 ,
H. YAMANAKA 1 , K. WATANABE 3 , AND G. EGUCHI 2
^anebo Institute for Cancer Research, Tomobuchicho 1-5-90, Osaka 534
2
National Institute for Basic Biology, Okazaki 444, Japan.
3
Hiroshima University, Nakaku, Hiroshima 730, Japan.
TABLE OF CONTENTS
Summary
Introduction
Materials and Methods
Cell monolayers
Electron microscopy
Computation
The boundary shortening procedure
Motility defined by a motility area ratio
Motility defined by the displaced distance of the centre of gravity of polygons
Results
Discussion
References
SUMMARY
Cell monolayers on culture dishes were divided into two groups: tensile monolayers and
non-tensile ones. In the development of an epithelium, a non-tensile cell monolayer turns into
a tightly bound tensile one. Detection of these states was carried out by using the boundary
shortening procedure, a computer-based geometrical method to show how much the
polygonal cell boundary contracts.
Non-tensile monolayers were divided further into two groups according to their motility: a
fluctuating monolayer in which cells move laterally, and a stable monolayer in which cells are
immobilized. Quantitative determination of cell motility was performed by analysing timelapse cellular patterns.
These computer-based geometrical analyses enabled us to divide monolayers into three
groups: tensile stable monolayers, non-tensile stable monolayers andfluctuatingmonolayers,
and this study therefore gives an insight into the way in which changing conformations of cells
may be assayed.
INTRODUCTION
Cell monolayers, which consist of one-cell-thick sheets of cells are found in
development as well as three-dimensional, multilayered cell aggregates. Cells in
* Supported in part by grants from the Japan Ministry of Education, Science and Culture.
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H. HONDA AND OTHERS
a monolayer are confined to the interface between a substratum and the medium
because their mechanism of movement requires a solid substratum but not the
exposed surface of neighbouring cells (Abercrombie & Heaysman, 1953, 1954;
Di Pasquale & Bell, 1974; Garrod & Steinberg, 1975; Timpe, Martz & Steinberg,
1978).
Some cell monolayers are epithelium-like in nature. A cell in an epitheliumlike monolayer has continuous tight contacts (tight junctions, belt desmosomes
or septate desmosomes) against neighbouring cells running around the periphery
of the cell just below the apical surface (Crawford, Cloney & Cahn, 1972;
Middleton & Pegrum, 1976; Eguchi, 1977; Crawford, 1979; Dan-Sohkawa &
Fujisawa, 1980; Kodama, Honda & Eguchi, 1981). The epithelium-like nature
of cell monolayers has been elucidated by using a geometrical analysis based on
a boundary shortening (BS) model of cells in a tissue (Honda & Eguchi, 1980;
Honda, 1983). The geometrical analysis has also been able to detect transitions
between the epithelial and the non-epithelial states in the early development of
starfish embryos (Honda, Dan-Sohkawa & Watanabe, 1983) and in the wound
healing process of a corneal endothelium (Honda, Ogita, Higuchi & Kani, 1982;
Honda, 1983).
Non-epithelial cell monolayers seem to be divided further into two groups: a
fluctuating state in which cells move laterally, and a stable state in which cells are
immobilized. In the present report, the motility of cells in a monolayer is defined
by analysed time-lapse cellular patterns of monolayers in order to determine
whether a monolayer is in the fluctuating state or the stable one. Values of
motility of several cell sheets are obtained and these values are discussed with
respect to junctions between neighbouring cells.
MATERIALS AND METHODS
Cell monolayers
Retinal pigment cells (which are epithelial) were obtained from 8-day-old
embryos of White Leghorn chicken, as described previously (Eguchi & Okada,
1973), and were cultured in a 6 cm plastic culture dish with Eagle's minimum
essential medium (MEM) supplemented with 8 % foetal calf serum (FCS). They
were transferred to secondary culture at cell density of 1 x 106 cells per dish and
were photographed two weeks after passage.
Cartilage cells (which are not epithelial) were obtained from the mesoderm of
limb buds of 4-day-old chick embryo as described by Kodama & Eguchi, (1982)
with the modification that cells were cultured as a monolayer in a 6 cm plastic
culture dish. BGJb medium with 10 % FCS was used. The cells were transferred
to tertiary culture at a cell density of 5 x 105 cells per dish and photographed one
week after passage.
FL line cells had been derived from normal human amnion tissue were cultured in a 6 cm plastic culture dish with Eagle's MEM supplemented with 10 %
Cell behaviour in a cell monolayer
315
5
FCS. They were transferred to the culture at a cell density of 1 x 10 cells per dish
and were photographed six days after the passage.
KB line cells which had been derived from an epidermoid carcinoma in the
mouth of an adult male Caucasian were cultured in a 3-5 cm plastic culture dish
with Eagle's MEM supplemented with 6 % FCS. They were transferred to the
culture at cell density of l-5x 105 cells per dish and were photographed three days
after the passage.
An inverted microscope with phase-contrast optics was used for taking serial
photographs. Analyses were performed by using regions of microphotographs
which did not include dividing cells.
Electron microscopy
For transmission electron microscopy (TEM), cells cultured on a plastic culture
dish were washed twice with prewarmed Dulbecco's phosphate-buffered saline,
fixed with 2 % glutaraldehyde in serum-free Eagle's MEM at 37 °C, and then
transferred into the refrigerator. After an hour, fixative was substituted with 2 %
glutaraldehyde in 0-1 M-sodium cacodylate buffer pH 7-4 and the preparation was
left for one more hour at 4 °C. Post fixation was with 2 % OsO4 in 0-1 M-s-collidine
buffer pH 7-4, followed by staining en bloc with 2 % uranyl acetate. The material
was then dehydrated through absolute ethanol and was finally embedded in Epon.
Sections were stained with uranyl acetate and lead citrate, and observed using a
JEM 100-C transmission electron microscope (JEOL).
For scanning electron microscopy (SEM), cells cultured on glass plates
(5x5 mm) were washed and fixed by the same method as above. They were
dehydrated and substituted with n-amyl acetate, and were then dried by the
critical-point-drying technique, coated with gold and were then observed using
a JSM-F7 scanning electron microscope (JEOL).
Computation
Calculation, simulation, and drawings were carried out on by microcomputer
with disc store (P652 and Das 604, Olivetti) and an XY-plotter (WX535,
Watanabe-sokuki, Tokyo). Image analysis was carried out by an image analyser
(Kontron IBAS2).
The boundary shortening procedure
We have devised a boundary shortening (BS) procedure by which we can
quantitatively predict how much the cell boundary contracts in a cell monolayer.
It has been elucidated that the boundary length of epithelial cell monolayers
contracts so that the sheet is tensile (Honda & Eguchi, 1980; Honda, 1983). The
BS procedure will be used here to determine whether a sheet has epithelial
nature or not.
The BS procedure is briefly as follows: we consider a polygonal cellular pattern, which is a surface view of a cell monolayer. Two arbitrary vertices (P and
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H. HONDA AND OTHERS
Q in Fig. 1) linked with each other by a side were chosen in a polygonal pattern,
and they were moved so as to maintain a constant area for each polygon as shown
can be
in Fig. 1. The length of the five sides, AP'+BP'+P'Q'+QfC+Q'D
calculated from the position P' (which moves along the line containing P and is
parallel with AB). P', on the other hand, is sequentially moved away from P by
small distances (positive or negative) and isfixedat a point where the total length
of the five sides is locally minimized. This is the elemental step of the boundary
shortening procedure.
All information on a given pattern (x-, y-coordinates of vertices, fixed terminal
points, and their connection relations) were stored on computer disc. A side was
selected by using a random number procedure on which the elemental step of
boundary shortening procedure would be performed. The elemental steps were
repeated on several thousand random numbers until the total length of sides in
Fig. 1. An elemental step of the BS procedure. Vertices P and Q linked by a side
are displaced while maintaining a constant area for each domain, so that the length
of AP'+BP'+P'Q'+Q'C+Q'D becomes a minimum. PP' and QQ' are parallel
with AB and CD, respectively. When P moves to P', Q is forced to move to Q' so
as to maintain a constant area for two respective polygons (polygon APQC and
polygon BPQD).
Cell behaviour in a cell monolayer
317
a polygonal pattern (the total boundary length) ceased to decrease. The whole
procedure is called the BS procedure.
In order to quantitatively work out the amount of boundary shortening, an s
value is defined as the ratio of percentage of decrease of the total boundary
length of the final pattern to the initial total boundary length. The s value indicates the degree of lack of boundary shortening of the given pattern. That is,
a small s value suggests that a contractile system is under operation and that the
cell sheet is likely to be in tension. The cell sheet is considered to be epitheliumlike in nature. A large s value means that the cell sheet is not in tension and does
not show an epithelium-like nature.
Motility defined by a motility area ratio
Some polygonal patterns of cell monolayers show movement: for instance, a
monolayer of KB cells have been photographed at 1 h intervals. Three patterns
from serial photographs may be seen overlaid in (Fig. 2). A traced area of moving
polygonal sides is shown stippled in this Figure. The motility area of cells in a
monolayer is defined by the ratio in percentage terms of the stippled area to the
total area of the polygonal pattern.
Motility defined by the displaced distance of the centre of gravity of the polygons
The motility of cells in a monolayer has also been defined in another way. All
centres of gravity of polygons are determined by using an image analyser.
Difference of the distribution of centres between two serial patterns has been
Fig. 2. Procedure to obtain the motility area. Three serial polygonal patterns are
superposed. The traced area of moving sides of polygons is designated by stipple.
The ratio in percentage of this area to the total area of a polygonal pattern (shown
by thin line) is the motility area.
EMB 83S
318
H. HONDA AND OTHERS
quantified as follow: positioning of two patterns is determined so that 2(r/-r,j 2
is minimum, where r, and r/are position vectors of the centres of gravity of the
i-th cell in two serial patterns. The motility centre is defined as lOOxSIr,-—r,-l/
(N-Rave) where N is total cell number and Rave is a diameter of the circle whose
area equals the average area of all polygons. As will be shown in the Results
section, there is a remarkable linear relationship between the motility area and
the motility centre.
RESULTS
Cell monolayers attaining confluence on culture dishes were maintained by
changing the medium every two days. Most of the photomicrographs were serially taken every hour. Single photographs of retinal pigment, cartilage, FL and
KB cells are shown in Fig. 3.
The polygonal patterns traced from these photographs were analysed using the
BS procedure to compute how much the cell boundary contracts (Fig. 4; Table
1). The pattern of the retinal pigment has a small s value (s = 0-527), whereas the
cartilage cell's pattern has a large s value (s = 1-33). These data are confirmation
of the previous results (Honda & Eguchi, 1980). That is, the monolayer of
pigment cells is epithelial, but the monolayer of cartilage cells is not epithelial.
Established line cells such as FL and KB cells have large s values showing that
they are not epithelial.
Fig. 5 shows patterns of serial three polygonal patterns in superposition. The
traced motility area of polygons is designated by the solid areas. A percentage
ratio of this area to the total area of polygonal pattern, was obtained and is shown
in Table 1. Retinal pigment and cartilage cells are rather more stable than FL and
KB cells.
Two kinds of KB cell monolayers, low and high density of cells, were compared: values of motility area were 30-7 and 31-1, respectively, showing little
difference. The value of the motility area of a region in a FL cell monolayer
which was close to a free edge of the sheet was 22-4 similar to the value of a
central region in a monolayered colony (23-5) where the cells attained complete
confluency (Table 1).
Motility centres were also obtained from all these monolayers: all of the
centres of gravity of polygons in two serial patterns were obtained by an image
analyser. The two patterns were fixed by the method as described in Materials
and Methods and were superposed. Then, displacement of the centre of gravity
of each polygon between the two serial patterns was obtained. The results are
presented in Fig. 6, where scale of displacement is enlarged three times for clear
elucidation.
Correlation between the motility area and the motility centres is shown in Fig.
7, where the correlation coefficient may be seen to be 0-971. This shows a
remarkable linear relationship between them.
Cell behaviour in a cell monolayer
Fig. 3. Microphotographs of cellular patterns of monolayers. (A) Retinal pigment
cells from chick embryos. (B) Cartilage cells from chick embryos. (C) FL line cells.
(D) KB line cells. Bar = 50jum. Stars are for cell identification.
319
320
H. HONDA AND
OTHERS
0-552
Fig. 4. The BS procedure of cellular patterns of retinal pigment (A), cartilage (B),
FL (C) and KB (D) cells. Solid line, patterns of actual monolayers. Dotted line,
patterns after the BS procedure. Solid circles, fixed points during the procedure.
Numerals are s values. Bar = 50jum. Stars are for cell identification (see Fig. 3).
Cell behaviour in a cell monolayer
321
Fig. 5. Patterns in superposition of three serial polygonal patterns. (A) Patterns of
retinal pigment cell photographed at O-O*1,1 -5h and 2-5h. (B) Patterns of cartilage cells
photographed at O-O*1, l-5h and 2-5h. (C) Patterns of FL cells photographed at 0-0\
l-0h and 2-0\ (D) Patterns of KB cells photographed at 0-0h, l-0h and 2-0h. Solid
area, traced region of moving sides of polygons during 2-0 or 2-5 h. Thin line, total
area of polygonal patterns. Numerals are values of the motility area. Bar = 50/im.
Stars are for cell identification (see Fig. 3).
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H. HONDA AND OTHERS
5-03
Fig. 6. Displacement of the centre of gravity of polygons during 1 h is shown by a line
in each cell. The length of lines is enlarged three times for clear elucidation.
Numerals are values of the motility centre. Scale bar at the bottom of respective
polygonal pattern = 50 jum.
323
Cell behaviour in a cell monolayer
Table 1. The s values and the motility values of cell monolayers
Cell monolayer
s value*
Motility (area)
Motility (centre)
Retinal pigment
Cartilage
FL
0-527
1-33
0-98
l-69t
KB
1-99
15-7
11-6
23-5
22-4t
30-7
31-11
5-03
3-61
7-15
7-33f
10-3
8-70±
* the average value of two serial patterns.
t a pattern of the monolayer close to an edge of the sheet.
$ a pattern of the monolayer of high cell density.
KB*/
100 yS
yS
O
FL
50
0-971
10
1
i
20
30
Motility (area)
Fig. 7. Relationship between the motility area and the motility centre. Correlation
coefficient = 0-971. RP, C, FL, KB indicate data of monolayers of retinal pigment,
cartilage, FL, and KB cells respectively. Open circles of FL and KB indicate a
monolayer close to an edge of the sheet and a monolayer of high cell density,
respectively.
DISCUSSION
Cells in some monolayers are constantly moving. The movement is not
locomotion towards a definite direction, but is a kind of fluctuation. The movement can be quantified in two independent ways; by the motility area and the
motility centre. The two motilities are closely correlated as shown in Fig. 7.
Motility seems to be a reliable value which defines characteristics of monolayers
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H. HONDA AND OTHERS
Fig. 8. TEM of the monolayer of FL cells. Circles indicate spot desmosomes. (A)
Specimen sliced into a section parallel with the bottom surface of a culture dish.
X2000. (B) An enlarged view of parallel section. X6600. (C,D) Vertical section of
the contact between neighbouring cells, x 11000.
Cell behaviour in a cell monolayer
.'••T*'
U\M,
Fig. 9. Electron micrographs of the monolayer of KB cells. A circle indicates a spot
desmosome. (A), TEM of specimen sliced into a section parallel with the bottom
surface of a culture dish. X7600. (B) SEM of apical surface of a monolayer. x600.
(C,D) TEM of vertical sections of the contact between neighbouring cells, x 12 000.
326
H. HONDA AND OTHERS
because it does not vary depending on cell density nor location in a monolayer
(central or peripheral region in a monolayered colony).
Using the motility values in addition to the s values of the BS procedure, cell
monolayers are divided into three groups: stable and tensile monolayers (small
motility values and small s values), stable but non-tensile ones (small motility
values and large s values), and fluctuating ones (large motility values and large
rvalues).
Difference in motility can be attributed to the nature of the cell contacts. We
will consider retinal pigment cells, FL ones and KB ones only, as cartilage cells
do not contact each other directly, but rather with an intercellular matrix (Eguchi
& Okada, 1971). Retinal pigment cells in a monolayer have tight junctions and
belt desmosomes (junctional complex) between neighbouring cells, running
completely around the periphery of each cell. The junctional complex is
associated with microfilaments forming a band running around the cell periphery
(Eguchi, 1977). In contrast, FL cells in a monolayer do not have any continuous
junction between neighbouring cells (Fig. 8C,D), but some dispersed spot desmosomes (Fig. 8A, B, D). Most of the cell contacts are due to interdigitation of
microvilli. KB cells are similar to FL cells (Fig. 9), but spot desmosomes are quite
few. Space between the cells is wide and there are interdigitating micro villi
between them (Fig. 9A). Cell affinity seems to be weaker because even the most
careful sample preparation of critical-point-drying technique for SEM makes
large artificial spaces between cells (Fig. 9B). KB cells also do not have any
continuous junction between neighbouring cells (Fig. 9C,D).
Continuous junction between neighbouring cells such as tight junctions, belt
desmosomes and septate desmosomes are considered to reduce the numerical
value of cell motility. It is worthy to note that dispersed spot desmosomes do not
interfere cell fluctuation.
Transition of a tissue between tensile and non-tensile states have been found
in the early development of the starfish embryo (from a non-tensile state to a
tensile one: Honda, Dan-Sohkawa & Watanabe, 1983), and the wound injuring
and healing process in the corneal endothelium (from a tensile state to a nontensile one, and then to a tensile one: Honda et al. 1982). Transition between
states of high and low motility in situ is found to take place during morphogenesis
of the corneal endothelium where fibroblasts migrate on the surface of the
stroma, attain confluence, and form a stable monolayered sheet with junctional
complex (Nelson & Revel, 1975; Bard & Hay, 1975; Kodama, unpublished).
Cell movement in a monolayer might be also influenced by the nature of the
contact between the cell bottom and the surface of the culture dish. However,
we do not consider cell locomotion for a long distance in the present report, but
only cell fluctuation, where average position of a cell does not vary so greatly.
The motility value is affected more strongly by the nature of lateral contacts
between neighbouring cells than between the basal surface of the cell and the
underlying substratum.
Cell behaviour in a cell monolayer
327
We thank Ms Yoshiko Tanaka-Ohmura for techniques of electron microscopy, Ms Toshiko
Tada for cell culturing, Ms Kyoko Nagai for preparation of the manuscript, and Ms Yumiko
Ueura for drawing.
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