Cell behaviour in a polygonal cell sheet* · The BS procedure is briefly as follows: we consider a polygonal cellular pat-tern, which is a surface view of a cell monolayer. Two arbitrary

J. Embryol. exp. Morph, 83, Supplement, 313-327 (1984) 3 1 3Printed in Great Britain © The Company of Biologists Limited 1984

Cell behaviour in a polygonal cell sheet*

ByH. HONDA1, R. KODAMA2, T. TAKEUCHI2,H. YAMANAKA1, K. WATANABE3, AND G. EGUCHI2

^anebo Institute for Cancer Research, Tomobuchicho 1-5-90, Osaka 5342National Institute for Basic Biology, Okazaki 444, Japan.

3Hiroshima University, Nakaku, Hiroshima 730, Japan.

TABLE OF CONTENTSSummaryIntroductionMaterials and Methods

Cell monolayersElectron microscopyComputationThe boundary shortening procedureMotility defined by a motility area ratioMotility defined by the displaced distance of the centre of gravity of polygons

ResultsDiscussionReferences

SUMMARY

Cell monolayers on culture dishes were divided into two groups: tensile monolayers andnon-tensile ones. In the development of an epithelium, a non-tensile cell monolayer turns intoa tightly bound tensile one. Detection of these states was carried out by using the boundaryshortening procedure, a computer-based geometrical method to show how much thepolygonal cell boundary contracts.

Non-tensile monolayers were divided further into two groups according to their motility: afluctuating monolayer in which cells move laterally, and a stable monolayer in which cells areimmobilized. Quantitative determination of cell motility was performed by analysing time-lapse cellular patterns.

These computer-based geometrical analyses enabled us to divide monolayers into threegroups: tensile stable monolayers, non-tensile stable monolayers and fluctuating monolayers,and this study therefore gives an insight into the way in which changing conformations of cellsmay be assayed.

INTRODUCTION

Cell monolayers, which consist of one-cell-thick sheets of cells are found indevelopment as well as three-dimensional, multilayered cell aggregates. Cells in

* Supported in part by grants from the Japan Ministry of Education, Science and Culture.

314 H. HONDA AND OTHERS

a monolayer are confined to the interface between a substratum and the mediumbecause their mechanism of movement requires a solid substratum but not theexposed 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 epithelium-like monolayer has continuous tight contacts (tight junctions, belt desmosomesor septate desmosomes) against neighbouring cells running around the peripheryof 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 natureof cell monolayers has been elucidated by using a geometrical analysis based ona boundary shortening (BS) model of cells in a tissue (Honda & Eguchi, 1980;Honda, 1983). The geometrical analysis has also been able to detect transitionsbetween the epithelial and the non-epithelial states in the early development ofstarfish embryos (Honda, Dan-Sohkawa & Watanabe, 1983) and in the woundhealing process of a corneal endothelium (Honda, Ogita, Higuchi & Kani, 1982;Honda, 1983).

Non-epithelial cell monolayers seem to be divided further into two groups: afluctuating state in which cells move laterally, and a stable state in which cells areimmobilized. In the present report, the motility of cells in a monolayer is definedby analysed time-lapse cellular patterns of monolayers in order to determinewhether a monolayer is in the fluctuating state or the stable one. Values ofmotility of several cell sheets are obtained and these values are discussed withrespect to junctions between neighbouring cells.

MATERIALS AND METHODS

Cell monolayers

Retinal pigment cells (which are epithelial) were obtained from 8-day-oldembryos of White Leghorn chicken, as described previously (Eguchi & Okada,1973), and were cultured in a 6 cm plastic culture dish with Eagle's minimumessential medium (MEM) supplemented with 8 % foetal calf serum (FCS). Theywere transferred to secondary culture at cell density of 1 x 106 cells per dish andwere photographed two weeks after passage.

Cartilage cells (which are not epithelial) were obtained from the mesoderm oflimb 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 plasticculture dish. BGJb medium with 10 % FCS was used. The cells were transferredto tertiary culture at a cell density of 5 x 105 cells per dish and photographed oneweek after passage.

FL line cells had been derived from normal human amnion tissue were cul-tured in a 6 cm plastic culture dish with Eagle's MEM supplemented with 10 %

Cell behaviour in a cell monolayer 315

FCS. They were transferred to the culture at a cell density of 1 x 105 cells per dishand were photographed six days after the passage.

KB line cells which had been derived from an epidermoid carcinoma in themouth of an adult male Caucasian were cultured in a 3-5 cm plastic culture dishwith Eagle's MEM supplemented with 6 % FCS. They were transferred to theculture at cell density of l-5x 105 cells per dish and were photographed three daysafter the passage.

An inverted microscope with phase-contrast optics was used for taking serialphotographs. Analyses were performed by using regions of microphotographswhich did not include dividing cells.

Electron microscopy

For transmission electron microscopy (TEM), cells cultured on a plastic culturedish were washed twice with prewarmed Dulbecco's phosphate-buffered saline,fixed with 2 % glutaraldehyde in serum-free Eagle's MEM at 37 °C, and thentransferred 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 wasleft for one more hour at 4 °C. Post fixation was with 2 % OsO4 in 0-1 M-s-collidinebuffer pH 7-4, followed by staining en bloc with 2 % uranyl acetate. The materialwas then dehydrated through absolute ethanol and was finally embedded in Epon.Sections were stained with uranyl acetate and lead citrate, and observed using aJEM 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 weredehydrated and substituted with n-amyl acetate, and were then dried by thecritical-point-drying technique, coated with gold and were then observed usinga JSM-F7 scanning electron microscope (JEOL).

Computation

Calculation, simulation, and drawings were carried out on by microcomputerwith 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 canquantitatively predict how much the cell boundary contracts in a cell monolayer.It has been elucidated that the boundary length of epithelial cell monolayerscontracts so that the sheet is tensile (Honda & Eguchi, 1980; Honda, 1983). TheBS procedure will be used here to determine whether a sheet has epithelialnature or not.

The BS procedure is briefly as follows: we consider a polygonal cellular pat-tern, which is a surface view of a cell monolayer. Two arbitrary vertices (P and


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 shownin Fig. 1. The length of the five sides, AP'+BP'+P'Q'+QfC+Q'D can becalculated from the position P' (which moves along the line containing P and isparallel with AB). P', on the other hand, is sequentially moved away from P bysmall distances (positive or negative) and is fixed at a point where the total lengthof the five sides is locally minimized. This is the elemental step of the boundaryshortening procedure.

All information on a given pattern (x-, y-coordinates of vertices, fixed terminalpoints, and their connection relations) were stored on computer disc. A side wasselected by using a random number procedure on which the elemental step ofboundary shortening procedure would be performed. The elemental steps wererepeated 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 sideare displaced while maintaining a constant area for each domain, so that the lengthof AP'+BP'+P'Q'+Q'C+Q'D becomes a minimum. PP' and QQ' are parallelwith AB and CD, respectively. When P moves to P', Q is forced to move to Q' soas to maintain a constant area for two respective polygons (polygon APQC andpolygon BPQD).

Cell behaviour in a cell monolayer 317a polygonal pattern (the total boundary length) ceased to decrease. The wholeprocedure is called the BS procedure.

In order to quantitatively work out the amount of boundary shortening, an svalue is defined as the ratio of percentage of decrease of the total boundarylength of the final pattern to the initial total boundary length. The s value in-dicates 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 thecell sheet is likely to be in tension. The cell sheet is considered to be epithelium-like in nature. A large s value means that the cell sheet is not in tension and doesnot show an epithelium-like nature.

Motility defined by a motility area ratio

Some polygonal patterns of cell monolayers show movement: for instance, amonolayer of KB cells have been photographed at 1 h intervals. Three patternsfrom serial photographs may be seen overlaid in (Fig. 2). A traced area of movingpolygonal sides is shown stippled in this Figure. The motility area of cells in amonolayer is defined by the ratio in percentage terms of the stippled area to thetotal 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. Allcentres 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 aresuperposed. 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 (shownby thin line) is the motility area.

EMB 83S


quantified as follow: positioning of two patterns is determined so that 2(r/-r,j2

is minimum, where r, and r/are position vectors of the centres of gravity of thei-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 whosearea equals the average area of all polygons. As will be shown in the Resultssection, there is a remarkable linear relationship between the motility area andthe motility centre.

RESULTS

Cell monolayers attaining confluence on culture dishes were maintained bychanging the medium every two days. Most of the photomicrographs were seri-ally taken every hour. Single photographs of retinal pigment, cartilage, FL andKB cells are shown in Fig. 3.

The polygonal patterns traced from these photographs were analysed using theBS procedure to compute how much the cell boundary contracts (Fig. 4; Table1). The pattern of the retinal pigment has a small s value (s = 0-527), whereas thecartilage cell's pattern has a large s value (s = 1-33). These data are confirmationof the previous results (Honda & Eguchi, 1980). That is, the monolayer ofpigment 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 thatthey are not epithelial.

Fig. 5 shows patterns of serial three polygonal patterns in superposition. Thetraced motility area of polygons is designated by the solid areas. A percentageratio of this area to the total area of polygonal pattern, was obtained and is shownin Table 1. Retinal pigment and cartilage cells are rather more stable than FL andKB cells.

Two kinds of KB cell monolayers, low and high density of cells, were com-pared: values of motility area were 30-7 and 31-1, respectively, showing littledifference. The value of the motility area of a region in a FL cell monolayerwhich was close to a free edge of the sheet was 22-4 similar to the value of acentral region in a monolayered colony (23-5) where the cells attained completeconfluency (Table 1).

Motility centres were also obtained from all these monolayers: all of thecentres of gravity of polygons in two serial patterns were obtained by an imageanalyser. The two patterns were fixed by the method as described in Materialsand Methods and were superposed. Then, displacement of the centre of gravityof each polygon between the two serial patterns was obtained. The results arepresented in Fig. 6, where scale of displacement is enlarged three times for clearelucidation.

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 aremarkable linear relationship between them.


Fig. 3. Microphotographs of cellular patterns of monolayers. (A) Retinal pigmentcells from chick embryos. (B) Cartilage cells from chick embryos. (C) FL line cells.(D) KB line cells. Bar = 50jum. Stars are for cell identification.

320 H . H O N D A A N D O T H E R S

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).


Fig. 5. Patterns in superposition of three serial polygonal patterns. (A) Patterns ofretinal pigment cell photographed at O-O*1,1 -5h and 2-5h. (B) Patterns of cartilage cellsphotographed 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. Solidarea, traced region of moving sides of polygons during 2-0 or 2-5 h. Thin line, totalarea of polygonal patterns. Numerals are values of the motility area. Bar = 50/im.Stars are for cell identification (see Fig. 3).


5-03

Fig. 6. Displacement of the centre of gravity of polygons during 1 h is shown by a linein 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 respectivepolygonal pattern = 50 jum.


Table 1. The s values and the motility values of cell monolayers

Cell monolayer

Retinal pigmentCartilageFL

KB

s value*

0-5271-330-98l-69t1-99

Motility (area)

15-711-623-522-4t30-731-11

Motility (centre)

5-033-617-157-33f

10-38-70±

* 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.

100

50

-

yS FL

1

KB*/

yS O

0-971

i

10 20

Motility (area)

30

Fig. 7. Relationship between the motility area and the motility centre. Correlationcoefficient = 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 amonolayer 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 notlocomotion towards a definite direction, but is a kind of fluctuation. The move-ment can be quantified in two independent ways; by the motility area and themotility centre. The two motilities are closely correlated as shown in Fig. 7.Motility seems to be a reliable value which defines characteristics of monolayers


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 ofthe contact between neighbouring cells, x 11000.

Cell behaviour in a cell monolayer

U\M,

. ' • • T * '

Fig. 9. Electron micrographs of the monolayer of KB cells. A circle indicates a spotdesmosome. (A), TEM of specimen sliced into a section parallel with the bottomsurface 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.


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, cellmonolayers are divided into three groups: stable and tensile monolayers (smallmotility values and small s values), stable but non-tensile ones (small motilityvalues and large s values), and fluctuating ones (large motility values and largervalues).

Difference in motility can be attributed to the nature of the cell contacts. Wewill consider retinal pigment cells, FL ones and KB ones only, as cartilage cellsdo not contact each other directly, but rather with an intercellular matrix (Eguchi& Okada, 1971). Retinal pigment cells in a monolayer have tight junctions andbelt desmosomes (junctional complex) between neighbouring cells, runningcompletely around the periphery of each cell. The junctional complex isassociated with microfilaments forming a band running around the cell periphery(Eguchi, 1977). In contrast, FL cells in a monolayer do not have any continuousjunction between neighbouring cells (Fig. 8C,D), but some dispersed spot des-mosomes (Fig. 8A, B, D). Most of the cell contacts are due to interdigitation ofmicrovilli. KB cells are similar to FL cells (Fig. 9), but spot desmosomes are quitefew. Space between the cells is wide and there are interdigitating micro villibetween them (Fig. 9A). Cell affinity seems to be weaker because even the mostcareful sample preparation of critical-point-drying technique for SEM makeslarge artificial spaces between cells (Fig. 9B). KB cells also do not have anycontinuous junction between neighbouring cells (Fig. 9C,D).

Continuous junction between neighbouring cells such as tight junctions, beltdesmosomes and septate desmosomes are considered to reduce the numericalvalue of cell motility. It is worthy to note that dispersed spot desmosomes do notinterfere cell fluctuation.

Transition of a tissue between tensile and non-tensile states have been foundin the early development of the starfish embryo (from a non-tensile state to atensile one: Honda, Dan-Sohkawa & Watanabe, 1983), and the wound injuringand healing process in the corneal endothelium (from a tensile state to a non-tensile one, and then to a tensile one: Honda et al. 1982). Transition betweenstates of high and low motility in situ is found to take place during morphogenesisof the corneal endothelium where fibroblasts migrate on the surface of thestroma, attain confluence, and form a stable monolayered sheet with junctionalcomplex (Nelson & Revel, 1975; Bard & Hay, 1975; Kodama, unpublished).

Cell movement in a monolayer might be also influenced by the nature of thecontact 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, butonly 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 contactsbetween neighbouring cells than between the basal surface of the cell and theunderlying substratum.

Cell behaviour in a cell monolayer 327We 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 YumikoUeura for drawing.

REFERENCES

ABERCROMBIE, M. & HEAYSMAN, J. E. M. (1953). Observations on the social behaviour of cellsin tissue culture I. Speed of movement of chick heart fibroblasts in relation to their mutualcontacts. Expl Cell Res. 5, 111-131.

ABERCROMBIE, M. & HEAYSMAN, J. E. M. (1954). Observations on the social behaviour of cellsin tissue culture II. "Monolayering" of fibroblasts. Expl Cell Res. 6, 293-306.

BARD, J. B. & HAY, E. D. (1975). The behavior of fibroblasts from the developing aviancornea. Morphology and movement in situ and in vitro. /. Cell Biol. 67, 400-418.

CRAWFORD , B. (1979). Cloned pigmented retinal epithelium. The role of microfilaments in thedifferentiation of cell shape. /. Cell Biol. 81, 301-315.

CRAWFORD, B., CLONEY, R. A. & CAHN, R. D. (1972). Cloned pigmented retinal cells; theaffects of cytochalasin B on ultrastructure and behavior. Z. Zellforsch. mikrosk. Anat. 130,135-151.

DAN-SOHKAWA, M. & FUJISAWA, H. (1980). Cell dynamics of the blastulation process in thestarfish, Asterina pectinifera. Devi Biol. 77, 328-339.

DIPASQUALE, A. & BELL, JR., P. B. (1974). The upper cell surface: its inability to supportactive cell movement in culture. /. Cell Biol. 62, 198-214.

EGUCHI, G. (1977). Cell shape changes and establishment of tissue structure. Saiensu(Japanese edition of Scientific American) 7 (No. 5), 66-77.

EGUCHI, G. & OKADA, T. S. (1971). Ultrastructure of the differentiated cell colony derivedfrom a singly isolated chondrocyte in in vitro culture. Devi. Growth Diff. 12, 297-312.

EGUCHI, G. & OKADA, T. S. (1973). Differentiation of lens tissue from the progeny of chickretinal pigment cells cultured in vitro: A demonstration of a switch of cell types in clonal cellculture. Proc. natn. Acad. Sci., U.S.A. 70, 1495-1499.

GARROD, D. R. & STEINBERG, M. S. (1975). Cell locomotion within a contact-inhibitedmonolayer of chick embryonic liver parenchyma cells. /. Cell Sci. 18, 405-425.

HONDA, H. (1983). Geometrical models for cells in tissues. Int. Rev. Cytol. 81,191-248.HONDA , H. & EGUCHI , G. (1980). How much does the cell boundary contract in a monolayered

cell sheet? /. theor. Biol. 84, 575-588.HONDA, H., OGITA, Y., HIGUCHI, S. & KANI, K. (1982). Cell movements in a living mam-

malian tissue: long-term observation of individual cells in wounded corneal endothelia ofcats. /. Morph. 174, 25-39.

HONDA, H., DAN-SOHKAWA, M. & WATANABE, K. (1983). Geometrical analysis of cellsbecoming organized into a tensile sheet, the blastular wall, in the starfish. Differentiation25, 16-22.

KODAMA, R., HONDA, H. & EGUCHI, G. (1981). How is the regular hexagonal pattern ofepithelial tissues form? Devi. Growth Diff. 23, 456 (Abstract).

KODAMA, R. & EGUCHI, G. (1982). Dissociated limb bud cells of chick embryos can expresslens specificity when reaggregated and cultured in vitro. Devi Biol. 91, 221-226.

MIDDLETON, C. A. & PEGRUM, S. M. (1976). Contacts between pigmented retia epithelial cellsin culture. J. Cell Sci. 22, 371-383.

NELSON, G. A. & REVEL, J.-P. (1975). Scanning electron microscopic study of cell movementsin the corneal endothelium of the avian embryo. Devi Biol. 42, 315-333.

TIMPE, L., MARTZ, E. & STEINBERG, M. S. (1978). Cell movements in a confluent monolayerare not caused by gaps: evidence for direct contact inhibition of overlapping. J. Cell Sci. 30,293-304.

Documents

Cell behaviour in a polygonal cell sheet* · The BS procedure is briefly as follows: we consider a polygonal cellular pat-tern, which is a surface view of a cell monolayer. Two arbitrary