/. Embryol. exp. Morph. Vol. 30, 2, pp. 499-509, 1973
Printed in Great Britain
499
Measurements of cell adhesion
I. Quantitative studies of adhesion of embryonic chick cells
By JANET E. HORNBY 1
From the Department of Zoology, University of Reading
SUMMARY
Cell suspensions were prepared from the kidney, liver and heart of chick embryos of
5 or 8 days of incubation, and from the limb-buds of chick embryos of 5, 6, 7, 8 or 9 days of
incubation. When these suspensions were aggregated under laminar shear in a Couette viscometer or random motion in a reciprocating shaker they obeyed the theoretical relationships
derived for flocculating lyophobic sols. The values of the collision efficiency found for the
different cell types under given conditions were used to calculate the force of interaction
between cells of each type. The force of interaction ranged between 9 x 10~u N (8-day heart)
and 3 x 10~9 N (8-day liver). The forces of interaction between cells appear to be responsible
for aligning the membranes of adjacent cells with a 10-20 nm gap. It is possible to arrange
the cell types in a hierarchy based on the forces of interaction between them. The possible
role of these forces in cell specificity is considered.
INTRODUCTION
The similarities between dissociated vertebrate embryonic cells and hydrophobic colloids have been reviewed by Curtis (1962, 1967). Aggregating suspensions of embryonic cells follow the relationship derived for the flocculation of
hydrophobic colloids (Curtis & Greaves, 1965) and the force of interaction
between different cell types may therefore be calculated (Curtis, 1969) using the
theoretical relationships between the forces of repulsion and attraction and the
time course of flocculation derived for hydrophobic colloids (Derjaguin &
Landau, 1941; Verwey & Overbeek, 1948; Curtis & Hocking, 1970). The force
of interaction may be equivalent to the force of adhesion. Differences in the
force of adhesion between different cell types may explain cell specificity but
the two phenomena may not be controlled by the same forces. The forces of
interaction between the cells of several tissue types at different ages of incubation
were calculated from their experimental collision efficiencies.
1
Author's address: Department of Zoology, University of Reading, Whiteknights, Reading
RG6 2AJ, U.K.
500
J. E. HORNBY
METHODS OF STUDYING THE FLOCCULATION OF
CELL SUSPENSIONS
1. Theory
(a) Laminar shear
The Smoluchowski relationship for the flocculation of a sol in a laminar shear
system may be applied to a heterogeneous hydrosol flocculating under laminar
shear, provided thafthe 'self-preserving hypothesis' holds (Swift &Friedlander,
1964). It is also an advantage to use large particles (> 1/«n in diameter)
in a laminar shear situation because then no account need be taken of flocculation due to Brownian motion (Mason & Bartok, 1959).
The Smoluchowski relationship:
n In N^
n In Nx0
y }
'
(where JV^ and Nmt are the total number of particles at time 0 and t sec, 0 is the
volume fraction of the particles, G is the shear rate in reciprocal seconds and
a is the collision efficiency) should be directly applicable to cell suspensions
aggregating under laminar shear because of their large size. The relationship
should give a straight line if the cell suspensions are following flocculation
kinetics, and the gradient of the line will give the value for the stability ratio
for the cells at a given rate of shear.
(b) Random movement
Mechanical energy may be supplied to the cell suspensions by shaking the
suspensions in closed 10 ml flasks in a reciprocating shaker. The motion of the
shaker produces turbulent movement of the fluid in the flask. The fluid molecules will transmit this mechanical energy to the cells. This energy may be
considered as independent of time and random in direction, therefore in general
form it will mimic the energy causing the flocculation of sols under Brownian
motion.
The modified (Swift & Friedlander, 1964) Smoluchowski relationship for
slow flocculation under Brownian motion, considering the fall in numbers of
single particles against time, may be written as:
where NKQ is the total number of (single) particles at time t = 0,v1 is the total
number of single particles at time t sec, a is the collision efficiency and X is the
new rate constant.
The relationship between the loss of single particles and time in the shaker
system should fit equation (2) if the rate constant, Y, for random motion is
substituted for the Brownian motion rate constant, X, 7 may be found by cali-
Measurements of cell adhesion. I
501
brating the shaker against the Couette viscometer. Since collisions due to
Brownian motion, in a sol with particles > 1 /im subjected to a shear rate of
1 sec \ may be disregarded (Overbeek, 1952; Curtis, 1969) the data for flocculation due to random motion should give a straight line if the cells are following
flocculation kinetics.
(c) The calculation of the Hamaker coefficient of attraction and the energy and
force of adhesion.
The Hamaker coefficient of attraction, A{1), may be calculated from the Curtis
& Hocking (1970) relationship between a and A(l) for electrically neutral particles
in a shear system, assuming that multiple collision is negligible:
(3)
where H = 10 1178v ' a - 10 86, /.i is the viscosity in poise, a is the particle radius in
cm, G is the shear rate in sec"1.
The potential energy of attraction and the force of attraction may be calculated using the Hamaker (1937) solution for the interaction between two parallel
flat plates (Brooks, Millar, Seaman & Vassar, 1967; Curtis, 1969):
vA = Al/4&7rd\
(4)
FA = Alltond*,
(5)
where VA = potential energy of attraction, FA = force of attraction and Id is
the distance between the plates at equilibrium.
2. Experimental methods
(a) The preparation of single cell suspensions for adhesion studies
The organs from which cell suspensions were to be prepared were removed
from the chick embryo (White Leghorn) of appropriate age and transferred to
Hanks' saline solution. The organs were washed three times in Ca- and Mg-free
Hanks' saline (CMF) and then treated with CMF containing 0-001 M ethylene
diamine tetra acetic acid (EDTA-CMF) at pH 8 and at room temperature. The
duration of the EDTA-CMF treatment depended on the particular organ being
studied, embryonic liver was incubated in EDTA-CMF for 2 min, kidney for
3 min, heart and limb-bud for 7 min. The EDTA-CMF was removed by three
washes of CMF saline. The disintegration of the organs was then aided by
mechanical agitation - that is, by drawing the organs in and out of narrow-bore
pipettes until a dense cell suspension was obtained. The suspension was then
centrifuged at approximately 20 g for 1 min in order to sediment any remaining
large particles. The supernatant was then removed and centrifuged at approximately 100 g for 3 min to bring down the cells and leave the debris from the
damaged cells in suspension. The supernatant was removed and the cells resuspended in CMF to a population density of approximately 8-4 x 106 cells/cm3.
502
J. E. HORNBY
The population density of the cell suspension was found using a FuchsRosenthal haemocytometer.
At the beginning of the experiment the cell suspension was added to the test
solution in a 10 cm3 siliconed conical flask (1 cm3 suspension^ cm3 of solution) to give an approximate density of 1-4 x 106 cells/cm3. The cell density was
then determined using a haemocytometer.
(b) Aggregation under laminar shear
Apparatus. A rotational viscometer (described in Curtis, 1969) was used in
a constant temperature room maintained at 37 °C.
Method. Twenty ml of a suspension of a known concentration of cells from a
given tissue were introduced into the gap between the bob and the cylinder of
the rotational viscometer. Samples were removed from the gap at regular
intervals using a Pasteur pipette and placed in a haemocytometer so that the
density of the different size classes of particles could be estimated and the
total number of particles at any time t could be found.
(c) Aggregation due to random movement
Apparatus. The conditions mimicking the form of Brownian motion were
produced by shaking the test suspension in 10 ml siliconed conical flasks,
stoppered with silicone bungs, in a Gallenkamp shaking reaction incubator
1-H-35O maintained at 37 °C. The rate constant for the random motion occurring in the flasks is 4-17 x 10~4 ± 0-60 x 10~4 sec"1.
Method. Flasks containing a suspension of single cells of a known concentration from a given tissue were shaken backwards and forwards, at a fixed rate,
in a shaking reaction incubator. Samples were taken from the flasks at regular
intervals using wide-bore Pasteur pipettes, and the single cell density was
counted in a haemocytometer.
(d) Quantitative comparisons of the aggregation of different tissues, and the same
tissues at different ages
The collision efficiencies at known rates of shear were found for chick embryonic cells of certain types, sheared in a medium composed of 50 % Hanks'
saline and 50 % 199 (Glaxo Laboratories Ltd.). The Hamaker coefficients and
the energy and force of attraction between the cells were then calculated. Comparisons were made between different tissues, and the same tissues at different
ages:
(i) by laminar shear; 5-, 6-, 7- and 9-day embryonic chick limb-bud
(ii) by random motion: 5- and 8-day embryonic chick limb-bud, liver, heart
and kidney.
Measurements of cell adhesion. I
20
40
60
t (min)
80
503
100
Fig. 1. An example of the relationship between (n In A^ro()/24OG0 and t when
5-day chick limb-bud cells were aggregated under laminar shear conditions.
3. Computation
(a) Laminar shear
The data for the 5-day chick limb-bud cells were used in order to check
linearity (Draper & Smith, 1966). The best line was fitted between
and t using the counts from the individual haemocytometer squares at each
sampling time as the repeat observations.
Least-squares lines were fitted between (n In Nm^j2^G(j) and t for the data
for 5-, 6-, 7-, 8- and 9-day chick limb-bud cells at given rates of shear using the
means of the cell counts from the individual haemocytometer squares (standard
procedure) using a computer program for comparison of regressions. The
gradients of these lines gave the value of the collision efficiency for the cells.
Log A (/) was calculated from these values for the given rates of shear, the
Hamaker coefficient for the tissue was found from the mean of log A (I).
(b) Random motion
Least-squares lines were fitted between 1/^(NKQ VX) and t for each set of experimental data, as was the best parallel line for groups of data found for each
tissue type. The experimental values of l/VC^o vx) at t = 0 were not used in the
computation. The gradients of the individual lines gave estimates of oc Y. Since
the values of a Y do not show any dependence on shear rate over the range of
shaker rates used, the parallel lines gave weighted means of a Y which were used
with the mean shear rate to calculate a, log A (I), with its 95 % confidence limits
and hence the net Hamaker coefficient for each tissue.
504
J. E. HORNBY
20
0
50
t (min)
100
150
Fig. 2. An example of the relationship between \js]{Nxo vx) and t when
5-day chick limb-bud cells were aggregated by random motion
Age of limb-bud
cells and method:
5 day (L.S.)
6 day (L.S.)
7 day (L.S.)
8 day (R.M.)
9 day (L.S.)
-250
-240
-230
Log A (0
-220
Fig. 3. Log A (/), with 95 % confidence limits, of 5-, 6-, 7-, 8- and 9-day embryonic
chick limb-bud, found by random motion (R.M.) or laminar shear (L.S.).
RESULTS
(a) Laminar shear
(n In Nmt)f240G(f> plotted against t gave a good straight-line relationship,
as illustrated in Fig. 1, in all cases. In the formal test for linearity for the data
for 5-day chick limb-bud the variance ratios were compared using the F test.
As might be expected most of the ratios were slightly greater than 1 but only
two out of eight would have been significant at the 0-1 % level. The F test is not
strictly applicable due to the non-normality of the data.
The values of log A (/) for 5-, 6-, 7- and 9-day chick limb-bud cells are shown
with their 95 % confidence limits in Figs. 3 and 4. The values of the net Hamaker
coefficient of attraction are given in Table 1.
Measurements of cell adhesion. I
505
Tissue and method
5 day:
Limb-bud (L.S.)
Kidney (R.M.)
Liver (R.M.)
Heart (R.M.)
8 day:
Limb-bud (R.M.)
Kidney (R.M.)
Liver (R.M.)
Heart (R.M.)
-250
-240
-230
-220
Log A (0
-210
Fig. 4. Log A (/), with 95 % confidence limits, of 5- and 8-day embryonic chick
limb-bud, kidney, liver and heart, found by laminar shear (L.S.) or random motion
(R.M.).
(b) Random motion
1/VWoO vi) Pitted against / gave a good straight-line relationship in all cases
(Fig. 2).
The values of log A (/) for 5-day heart, kidney and liver and 8-day heart,
kidney, liver and limb-bud are shown in Figs. 3 and 4 with their 95 % confidence
limit. The values for the net Hamaker coefficient of attraction are given in
Table 2.
DISCUSSION
It has been shown that aggregating suspensions of chick embryonic cells obey
the theoretical relationships derived for flocculating lyophobic sols. The values
found for the Hamaker coefficient of the different cell types, between 10~23 and
10~25 J, are small compared with the theoretical predictions, between 10~19 and
20 20 j (Hamaker, 1937), and values found for various colloid sols, between 10~19
and 10~22 J (Albers & Overbeek, 1960; Schenkel & Kitchener, 1960; Ottewill &
Wilkins, 1962; Watillon & Joseph-Petit, 1966). This might be expected since the
relationship between the collision efficiency and the Hamaker coefficient (Curtis
& Hocking, 1970) was derived for electrically neutral particles aggregating under
laminar shear conditions and does not take account of the interaction of the
repulsive electrical forces with the attractive Van der Waals forces. There are
two cases where the Curtis & Hocking relationship will still be useful if the
particles concerned do have a surface charge: when the sum of the potential
energy of attraction and repulsion (VA+ VE) results in a net attraction in the
506
J. E. HORNBY
Table 1. Energies and forces of interaction found by laminar shear
for limb-bud cells at different ages
Tissue type
5-day limb bud
6-day limb bud
7-day limb bud
9-day limb bud
n
10
6
6
3
A (in J)
24
2-4 xlO"
3-6xlO~24
l-5xlO- 23
3-2 xlO- 25
VA (J/m2)
VA (in J)
FA (N/m2)
FA (in N)
8
19
1
6xlO- 10
lOxlO 1 0
4x10-°
8xlQ-u
1-6 xlO"
2-4 xlO"8
1-OxlO"7
21 x 10"9
6xlOlOxlO"19
4xlO" 18
8xlO- 20
1-6X10
2-4 xlO 1
1-OxlO2
2-1x10°
Table 2. Energies and forces of interaction found by random motion
for various tissues at different ages
Tissue type
n
5-day kidney
5-day liver
10
10
5-day heart
19
8-day
8-day
8-day
8-day
12
10
4
13
limb bud
kidney
liver
heart
A (in J)
24
8-7 xlO1-9 xlO" 2 3
3-2 xlO- 2 4
3-9 x 10- 25
6 1 x lO"25
1 -4 x lO"23
3-5 x lO"25
VA (J/m2)
8
5-7 x lO"
1-3 xlO- 7
2 1 x lO" 8
2-6 xlO" 9
4 0 x 10- 9
7-5 x 10- 8
2-3 x 10- 9
VA
2x
5x
8x
lx
2x
3x
9x
OnJ)
FA (N/m2)
10-is
1
1 O -18
io- 1 9
10-19
10-19
10-18
10-20
5-7 xlO
1-3 xlO2
21 x IO1
2-6x10°
40x10°
7-5 xlO 1
2-3 x 10°
FA
2x
5x
8x
lx
2x
3x
9x
(inN)
10 9
l O -9
l O -io
10 io
lO-io
io-911
io-
primary minimum and no repulsive peak, or when VA + VR results in a high
repulsive peak and fairly strong attraction in the secondary minimum. In these
cases a net Hamaker coefficient (which will include a function of surface charge)
will be calculated from equation (3). The value calculated from the net Hamaker
coefficient and equation (4) will be an approximation of the energy VA + VR
(VT of Brooks et al. (1967)) which may be equivalent to the adhesive energy
between the cells. The interaction between the attractive and repulsive forces on
cells will probably result in adhesion in the secondary minimum, giving a gap
between the cells comparable to that observed in the electron microscope (Curtis,
1967). There is some dispute as to whether this gap exists in life (Lilien, 1969).
Overton (1969) has shown that there is a lanthanum staining layer beyond the
unit membrane, but in intact tissues this lies close to the cell surface lining the
gap. Brightman's (1965) work on ependymal cells is particularly interesting.
These epithelial cells are unusual in that they lack a zonnula occludens at the
junction between the epithelial cells and the brain ventricle. Ferritin molecules
(approximately 10 nm in diameter) injected into the ventricle of the brain before
fixation penetrated the intercellular spaces. Ferritin molecules injected after
fixation did not penetrate the intercellular spaces, suggesting that the gap does
exist in life but may become filled at fixation. Adhesion in the secondary minimum for large particles has been predicted theoretically (Verwey & Overbeek,
1948) and found experimentally (Schenkel & Kitchener, 1960; Watillon &
Joseph-Petit, 1966). In this case the effective outer boundary of the cell may be
Measurements of cell adhesion. I
507
taken as the outer boundary of the repulsive peak where VR+VA = 0, and the
gap between the outer limits of the two apposed repulsive peaks, 2 nm, was used
to calculate the potential energy and force of attraction from the Hamaker
coefficient. Accurate measurements of the area of contact between the different
cell types were not made, but Curtis (1967) gives an approximate area of contact
for embryonic cells of 4 x 10~7 cm2 and this value was used to give an estimate
of the actual energies and forces of attraction between the particular cell types
(Tables 1 and 2).
The four tissue types studied have similar forces of interaction at five days of
incubation (5 x 10"9 to 6x lO"10 N), but with the exception of liver (3 x 10~9 N
at 8 days) the forces of interaction within a tissue appear to have decreased by
8 days of incubation (1 x 10~10 to 9 x 10"11 N). The limb-bud studies show that
there is a slight increase in the force between 5 and 7 days of incubation (6 x 10~10
to 4x 10~9N) followed by a sharp fall between 7 and 8 days, which is maintained on the ninth day. Brooks et al. (1967) using a directly comparable
method involving the separation of cells pretreated with EDTA, working on
neonatal and adult mouse liver, found a value for the force of adhesion of liver
cells to be of the order of 10~9 N; this agrees with the present measurements for
the force of adhesion between 5-day liver cells and between 8-day liver cells
(5xlO~ 9 Nand 3xlO- 9 N).
The forces of interaction have been calculated from the experimental values
found for the logarithm of the Hamaker coefficient (log A (/)). There is considerable overlap between the confidence limits of log A (I) for the different tissue types
so it is not possible to put too much weight on the individual values for the forces
of interaction. However, disregarding the confidence limits a hierarchy of cell
attractiveness may be built up on the basis of the energy or force of attraction
between cells: 5-day liver > 7-day limb-bud > 8-day liver > 5-day kidney
> 6-day limb-bud > 5-day heart > 5-day limb-bud > 8-day kidney > 8-day
limb-bud > 8-day heart > 9-day limb-bud. If the force of attraction between cells
is related to their strength of adhesion then these results agree with Moscona's
(1961) measurements of the index of aggregation when he found that liver is
a comparatively adhesive tissue. The work based on the way in which different
cell types sort out in mixed aggregates (Steinberg, 1962, 1970) has produced
a similar hierarchy on the assumption that the most adhesive cells move to the
centre of the aggregate: 4-day limb-bud > 5-day heart > 5-day liver. This
does not agree with the present hierarchy. Gershman's (1970) results suggest
that adhesiveness is not related to cell specificity since he was unable to show
any tendency for cells of different ages of heart to sort out although their
adhesiveness apparently decreases with age, nor did the cells of different ages
of liver or neural retina sort out. It is however difficult to compare the present
hierarchy with that of Steinberg. The present experimental work deals with the
initial stages of adhesion whereas Steinberg's results are obtained from the end
point or equilibrium condition. Curtis (1970) has shown that the strengths of
33
EMB
30
508
J. E. HORNBY
adhesion between cells can change with time. The forces of adhesion between
7-day liver cells decreased during the course of 5 h while the forces of adhesion
between 7-day neural retinal cells increased. Therefore the sorting out of cells
and the phenomenon of cell specificity could be due to time dependent changes
in the forces of adhesion between cells (Curtis, 1962). Alternatively the forces
of adhesion may only be responsible for aligning the cell membranes and once
the cells are positioned in the secondary minimum direct contact may be made
between the cells in the form of tight junctions, as observed in migrating embryonic tissues (Trelstad, Hay & Revel, 1967). Furshpan & Potter (1968)
consider tight junctions to be the most likely sites of cell communication in vertebrate cells and Loewenstein (1968) has shown that cell communication is rapidly
established between cells when they are brought into contact. Sorting out of
cell types may depend on the exchange of intercellular messages of some kind
rather than the recognition of surface patterns (Steinberg, 1958) or on the production of extracellular matrices (Moscona, 1962; Lilien & Moscona, 1967).
The latter may be concerned with cellular or membrane integrity rather than
cell specificity. Various workers have shown that cell adhesion is dependent on
cell metabolism in the long term (Ball, 1966; Moscona & Moscona, 1963;
Kemp, Jones, Cunningham & James, 1967) and Loewenstein (1968) has shown
that general cell metabolism is necessary for the maintenance of cell
communication.
I am most grateful to Professor A. S. G. Curtis for supervising this work which was
carried out during the tenure of an S.R.C. Research Studentship in the Department of Zoology, University College, London, and completed in the Department of Zoology, University
of Reading. I am grateful to Professor M. Abercrombie and Professor A. Graham for the
facilities provided. I should also like to thank Mr D. Arnold for technical assistance at
University College, London, and Mr R. Stern, Department of Applied Statistics, University
of Reading, for valuable assistance with the statistical analysis.
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{Received 14 July 1972, revised 14 May 1973)
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