/. Embryol. exp. Morph. Vol. 26, 1, pp. 135-156,1971
135
Printed in Great Britain
The analysis of
spatial distributions in mixed cell populations: a
statistical method for detecting sorting out
R. A. ELTON 1 AND C. A. TICKLE 2
From the Institute of Virology and the
Department of Cell Biology, University of Glasgow
SUMMARY
1. This work presents a quantitative measure, a, of the degree of segregation of two cell
types in sections of aggregates, and some results obtained with the measure relating to
'sorting out'. The method is designed particularly for the case where labelling of one type
of cell is incomplete, and the importance of this effect is assessed. Possible problems in
formulating such a model are discussed. The measure a is compared with methods used in
investigations of segregation in plant communities.
2. Segregation of chick heart and limb-bud cells in mixed aggregates has been analysed
using a. In control aggregates of mixtures of labelled and unlabelled cells of one type, a is
near to its random value of 1, and we suggest that the departure from random can be adequately accounted for by cell division. In mixed aggregates, significant segregation is consistently found, even in aggregates formed after 2 and 4 h. Both disaggregation procedures
(EDTA, trypsin or trypsin + EDTA) and reaggregation methods (reciprocating or gyratory
shaker) are found to have an effect on the degree of segregation. Possible reasons for these
findings are discussed.
3. Positioning of the cells relative to the outside of aggregates is also investigated for some
of the aggregates.
INTRODUCTION
A statistical test is reported here which describes the spatial arrangement of
cells in mixed close-packed populations in two dimensions. The possible distributions of cells can be divided into three main classes. The cell types can be
arranged randomly, form a regular, alternating array or be segregated.
In the experiments reported below, suspensions of chick heart and limb-bud
cells are mixed and allowed to reaggregate under various conditions; the segregation measure is applied to sections from the resulting aggregates. In such aggregates 'sorting out' has been reported to occur by many workers (for example,
Townes & Holtfreter, 1955; Moscona, 1962; Steinberg, 1964, 1970; Zwilling,
1968). This phenomenon is the grouping of cells according to type and the
1
Author's address: Medical Research Council Virology Unit, Church Street, Glasgow,
W.I, U.K.
2
Author's address: Department of Biology, Yale University, New Haven 06250, Conneticut, U.S.A.
136
R.A.ELTON AND C. A. TICKLE
positioning of these groups within the aggregate relative to the inside and outside. Theoretically, segregation of cell types could occur without 'positioning'
of the groups of like cells, although if 'positioning' occurs the cells will be
segregating. No previous quantitative tests have been made to measure the
segregation of cells in aggregates, although Adler (1970) has measured the
positioning.
Such quantitative measures require accurate identification of cell types. In
this work and other recent work on 'sorting out' (Adler, 1970; Burdick &
Steinberg, 1969) cell types have been recognized in aggregates by the radioactive
labelling of one cell type. This allows the fate of individual cells to be traced
and incidentally excludes the possibility that '^differentiation' of cells occurs
according to their position within the aggregate.
The occurrence of 'sorting out' has previously been judged subjectively. This
may not matter in clear cases, such as those figured by Steinberg (1964, 1970),
but other work (Trinkaus & Lentz, 1964) suggests that 'sorting out' may not
be an 'all or nothing' event. It can be seen that subjective criteria may be misleading, especially if the two cell types are present in the aggregate in widely
differing proportions. In this case the majority cell type may appear to be
segregated whereas in fact the cells are randomly arranged. The need for quantitative measures is greatest when examining changes in cell distributions under
varying conditions. In the present experiments the arrangement of cells in
aggregates formed after varying times of reaggregation has been investigated
quantitatively.
METHODS
The statistical model
The problem of measuring spatial segregation in mixed populations of cells
can be formulated by considering the probabilities of finding the different types
of cells in adjacent positions. This is essentially the approach used by Pielou
(1962) in a study of mixed plant communities. The study involved data in the
form of transects through a mixture of two tree types, and the analysis was
made under the assumption that the sequence of plant types along the transect
formed a Markov chain realization; the segregation measure was based on the
mean run lengths of the different species. In a further paper, Pielou (1963)
extended the analysis to a case involving three types of tree; the situation was
somewhat analogous to that of the present experiment, in which a small proportion of the cell type which was labelled failed to take up the label. However,
the model described below has been developed especially to take account of
labelling bias, and also possible differences in cell-counting efficiency in different
parts of the experiment. In the Discussion, the results are compared briefly with
those obtained using Pielou's technique.
We assume a population of two types of cell, denoted by A and B, and present
in the proportions 6 and 1-6 respectively. The A cells are unlabelled, and the
Sorting out in mixed cell populations
137
labelling of the B cells is incomplete, a proportion p (assumed known) remaining
unlabelled; labelled cells are denoted by L, and unlabelled ones by U. The
observational procedure consists of selecting a number of target cells at random
points in the aggregate and observing the proportion of labelled or unlabelled
surrounding cells in 'adjacent positions' (a term left undefined for the present
but to be discussed later) to each target cell. The segregation measure a is
defined by letting the probability P{A\B) of a surrounding cell being A, given
that the target cell is B, be ad. Thus in a randomly mixed population, where the
occurrence of A cells is not influenced by adjacent cells, this probability is 0 (i.e.
the proportion of A cells in the mixture) and a = 1; in a segregated population,
however, P(AjB) is depressed below the value 6, and a < 1 (a theoretical possibility is a regular, alternating type of cell distribution for which a > 1). This
measure has the advantage of treating the two types of cell symmetrically, since
P{B\A) = a(l —6); it is, however, somewhat arbitrary, and possible alternatives
are discussed below.
Because of the incomplete labelling, we are unable to observe P(A/B) and
P{BjA) directly. Instead, the parameters of direct experimental interest are
y = P(UjL) and z = P(LjU) (the proportions of unlabelled round labelled and
labelled round unlabelled cells respectively) ;(y + z) gives the equivalent measure
of segregation of L and U that a gives for the cell types A and B. Since all
L cells are B, it is straightforward to derive an expression for y:
y = a6+p(l-ocd).
(1)
The expression for z is a more complicated exercise in conditional probability,
since some of the unlabelled target cells are really of type B, and we find
z = y(l-p)(l-O)l{p
+ d(l-p)}.
(2)
Expressions (1) and (2) can be solved explicitly for a and 0, to give
and
0 = {(1 -P) y-pz)l{(l -P) (y + z)}
oc = (y-p)l{0(l-p)}.
(3)
(4)
Problems and limitations of the model
It should be noted that the method is not dependent on an unbiased selection
of target cells, since it is only concerned with conditional probabilities, given
the target cell type. It may be of practical interest, however, to have a check on
the relative bias of target and surrounding cell selection, since labelled cells may
be more visible than unlabelled ones. This may be done by incorporating an
extra parameter into the model: the proportion q of cases in which unlabelled
cells are correctly identified as target cells. If x is the proportion of U target cells
observed, we have
x=ll(l+zlyq),
(5)
giving
q = xz/{y(l-x)}
(6)
as an estimate of the bias in target cell observation.
138
R. A. ELTON AND C. A. TICKLE
The possibility also arises that the identification of surrounding cells is biased,
introducing a fourth unknown parameter r, the corresponding parameter to q for
surrounding cells. The question of practical interest is the extent to which
variations in r affect the accuracy of the estimate a; in other words, given
observed values of y and z resulting in an estimate a, how far from the true
value (say, a') is this estimate if the true value of r is not really 1 ? The algebraic
expression for a' in terms of y, z and r is too complicated to be of any intuitive
guide here, but it appears in practical cases that doc/dr is small when r is close
to 1. Fig. 1 shows some typical plots of a' against r using real values of y and z,
showing that a does not greatly underestimate a' in the likely range of variation
ofr.
10
0-9 —
•
B
0-8 -
—
—
-
-
_
""""""
07 -
0-6
1
0-8
1
i
10
c
i
1-2
Fig. 1. Variation of a' with r for three typical values of y and z: (A) y = 0-40,
z = 0-54; (B) y = 0-68, z = 0-21; (C) y = 0-67, z = 008.
As an extra check on the usefulness of the model, it is important to carry out
control experiments in which labelled and unlabelled cells of the same type are
mixed. Assuming that labelling does not affect cell behaviour, it would be
expected that the labelled and unlabelled cells in these aggregates would be
randomly arranged, if also there is no gross exchange of label between cells.
A small divergence from a random pattern of cells in these aggregates was found
and the implication of this will be discussed (see Results).
A further problem referred to above is that of the arbitrariness of the measure
a. A priori, there is no reason other than mathematical convenience for choosing
a = P(AIB)IP(A)
as an index of segregation in preference to, for example, the cross ratio
{P(A/B) P(BlA)}j{P(A\A) P(B/B)}
or information or %2-type statistics. If we wish to evolve a measure which
genuinely reflects some intrinsic property of the segregating cells, we should
Sorting out in mixed cell populations
139
have to define the criteria of importance; we might, for example, select the
measure that remains constant under given experimental conditions as the value
of 0 is varied. No clear answer to this question emerges from the present study,
but further experiments could be designed to investigate it.
A general problem with this type of analysis is that the actual cell aggregates
are not regular, ordered arrays of uniformly sized spherical particles. Consequently, concepts like 'adjacent cells' or 'nearest neighbours' have to be
interpreted loosely during the experimental procedure itself. The criterion of
adjacency chosen for the present series of experiments was that of selecting as
surrounding cells what appeared to be the six nearest cells in the section to each
target cell. If the aggregate section were a regular close-packing lattice of cells
in two dimensions, this would be the logical thing to do, since each cell would
be in contact with six others, but inevitably in the practical situation the criterion
(like the segregation measure) is chosen somewhat arbitrarily. The development
of the model itself is not dependent on the nature of this criterion, but naturally
it would be expected that the value of a obtained would vary according to how
adjacency was defined. It is outside the scope of this study to investigate variations of a with different criteria; interest is confined to differences in segregation
under varying experimental conditions using the same criterion of adjacency.
It may be that differences in observational technique or experimental environment in two separate studies could introduce consistent bias in the results. What
is important is internal consistency within a complete series of experiments, so
that comparisons of the results under different experimental conditions are
meaningful.
Experimental methods
Five-day embryonic chick (De Kalb strain) hearts and limb buds were the
tissue types used. Embryos were labelled by pipetting 15 /tCi of tritiated thymidine (6-T(n) Thymidine, Radiochemical Centre, Amersham: specific activity
5-0 Ci/mM) on to the yolk sac of each egg, previously windowed (Zwilling, 1959),
and allowing incorporation for 24 h.
Cell suspensions of 'labelled' limb bud, 'unlabelled' limb bud, 'labelled'
heart and 'unlabelled' heart were prepared aseptically by one of the following
disaggregation techniques:
I. EDTA disaggregation (after Curtis & Greaves, 1965). The tissues were
washed three times in CMF (calcium and magnesium free saline, pH 7-8),
treated with 0001 M EDTA in CMF (pH 7-8) for 10min at 20 °C, and then
washed three times in CMF. The tissues were then mechanically disaggregated
in CMF by flushing several times through a fine-bore Pasteur pipette.
II. Trypsin and EDTA disaggregation (after Steinberg, 1963). The tissues were
washed twice in disaggregating medium, which was 3 % (w/v) trypsin (Difco
1:250, ca. 1000 BAEE units of tryptic activity per mg), 1 % (w/v) pancreatin
(Sigma) and 0-1 % (w/v) EDTA in CMF, pH 7-6. After a 20 min incubation at
140
R. A. ELTON AND C. A. TICKLE
37 °C in this medium the tissues were washed briefly with Hanks's solution
containing 50 % chick serum (Flow Laboratories) to stop tryptic activity. After
a further wash in Hanks's solution the tissues were mechanically disaggregated
(as in procedure I) in Hanks's solution/chick serum (50/50).
III. Trypsin disaggregation (after Roth & Weston, 1967). The tissues were
washed with Hanks's solution and CMF, prior to a 20 min incubation with
0-25 % trypsin (Difco 1:250, 1000 BAEE units of tryptic activity/mg) solution
at 20 °C. The tissues were then rinsed with Hanks's solution and chick serum
(50/50) and then with CMF. Disaggregation of tissues was then carried out as
in procedure II.
The cell suspensions were then prepared as described by Curtis (19706). The
cells were passed through cell sieves (nickel electroformed grid of mesh, 22 /*m,
E.M.I. Ltd., Hayes, U.K.) before reaggregation, unless stated to the contrary.
The reaggregating medium was Hanks's solution 44-4 %, Medium 199 (Glaxo
Laboratories) 44-4 %, and chick serum 11-2 %. This medium was used for all
reaggregations except those in gyratory shakers, when the medium was Hanks's
solution 40 %, chick serum 40 % and embryo extract 20 % (Steinberg, 1963).
Reaggregation was carried out in one of the following ways:
(A) Flask shaker systems. Heart and liimVbud cells were mixed together in
various proportions, one tissue type being 'labelled', in a minimum concentration of 1 x 106 cells/ml in 2-3 ml of reaggregating medium in siliconed 10 ml
conical flasks. The cells were reaggregated for 1 or 2 days in flasks shaken on a
reciprocating shaker (Gallenkamp) at 92 strokes/min (excursion 4 cm) at 37 °C
(Curtis & Greaves, 1965). In one experiment the flasks were shaken in a gyratory
shaker (New Brunswick Scientific Co. Inc.) at 80 rev/min for 17 h, then the
rate of gyration was increased to 100 rev/min for a further culture period of 31 h
(Steinberg, 1962) at 37 °C to prevent further fusion of aggregates.
(B) Couette viscometer reaggregation (Curtis, 1969). The cells were mixed in
couette viscometers at a minimum concentration of 1 x 106 cells/ml in 15 ml of
medium. The cells were reaggregated at a shear rate of 8 see"1 at 37 °C. Under
these conditions of low shear fairly large aggregates are formed in a short time
period. Cells were reaggregated for 2 h or 4 h in this way.
Aggregates were fixed in Bouin's fluid, dehydrated and embedded in wax
(Pantin, 1964). Serial sections of thickness 5/*m were cut and coated with Ilford
nuclear emulsion gel L4 diluted 1:2 with water. The slides were exposed in lighttightboxes at 2 °C for approximately 40 days, then developed in D 19 b developer
for 5 min, fixed with 30 % sodium thiosulphate for 5 min and washed in running
tap water for 15 min (Rogers, 1967). The sections were stained through the
emulsion with Ehrlich's acid haematoxylin. Clearing was carried out as recommended by Le Blond, Kopriwa & Messier (1963) to prevent air bubbles.
The percentage labelling of labelled cell suspensions was determined by
counting the number of labelled and unlabelled cells in aggregates formed from
the labelled cell suspensions only, after 42 h reaggregation. The proportion/? of
Sorting out in mixed cell populations
141
unlabelled cells in 'labelled' aggregates was found to be 00673 for 'labelled'
limb-bud aggregates (n = 2612) and 00892 for 'labelled' heart aggregates
(n = 897), and p was assumed to be constant.
In each experiment aggregates were prepared from labelled heart and unlabelled limb bud cells and from the reciprocally labelled cell suspensions. This
provided a check on the exchange of label between cells. Control aggregates
were prepared from mixtures of labelled and unlabelled limb-bud cell suspensions. Aggregates were selected for counting in two ways. Either aggregate
sections were sampled throughout the aggregate length every third section, or
aggregates were sampled at random in every third section. Thus the measure of
segregation obtained refers to the 'whole' aggregate, and not to selected regions.
A field of the aggregate or group of aggregates was obtained at random. Target
cells were selected by means of a Chalkley grid eyepiece with 25 dots randomly
arranged (Curtis, 1960). The target cell was classified as labelled or unlabelled
and the six nearest cells were scored according to whether they were labelled
or unlabelled.
Table 1. Control aggregates: LB*LB(1) ('labelled' limb-bud cells mixed with
'unlabelled' limb-bud cells)
(LB*LB(1): cells disaggregated with trypsin, cells mixed together
without passage through cell sieves, aggregated for 42 h.)
Target cells
Aggregate f
A
no.
Total
L
U
y
z
q
205
338
311
306
0-70
0-66
0-69
0-68
0-57
0-67
0-68
0-69
0-30
0-23
0-23
0-20
1-21
0-67
0-76
0-91
I
II
in
IV
0-30
0-34
0-31
0-32
s2 = 00006. Mean y + z = 0-89.
e
0-63
0-73
0-73
0-76
Mean
a
0-85
0-89
0-91
0-89
0-88
RESULTS
Controls
In Table 1 complete data for the LB*LB(1) aggregates is shown; all other data
are condensed. The mean a value for the aggregates LB*LB (2) (cells disaggregated
with EDTA, cells sieved, aggregated for 24h) was 0-93 (s2 = 00025, mean
y + z = 0-94), and for aggregates LB*LB(3), 0-92 (s2 = 0-0009, mean y + z =
0-93).
If the cells are randomly arranged, a equals 1. In Table 2 the values of the
control aggregates are compared with a = 1, by means of a Mest.
The segregation of cells in aggregates LB*LB(1), in which the initial cell
suspensions were not sieved, could be explained by the presence of cell clumps
in the original cell suspension. The finding that this 'clumping' effect persists
in aggregates formed after 42 h can be predicted on the hypothesis of Steinberg
142
R.A.ELTON AND C. A. TICKLE
(1964) that 'sorting out' occurs by exchange of weak for stronger adhesions.
In these aggregates all the cells are of the same 'tissue type' and differ only in
that some are labelled. If labelling has no effect on cell behaviour it would be
expected that 'labelled' cell adhesions would be of the same strength as unlabelled adhesions of the same tissue type and thus no exchanges of adhesions
would be predicted. This argument assumes that the degree of segregation of
cells in LB*LB(1) is due only to clumps in the initial unsieved suspensions. That
Table 2. Mean a of control aggregates compared with a, = 1
Aggregate
type
t
D.F.
LB*LB (1)
LB*LB (2)
-9-618
-2-678
3
3
00025 > P > 0001
005 > P > 0025
LB*LB (3)
-4-505
3
0025 > P > 001
Segregation
Segregation at
5 % level
Segregation at
5 % level
LB*LB (1) cells disaggregated with trypsin, cells mixed together without passage through
cell sieves, reaggregated for 42 h.
LB*LB (2) cells disaggregated with EDTA, cells 'sieved', reaggregated for 24 h.
LB*LB (3) cells disaggregated with EDTA, cells 'sieved', reaggregated for 42 h.
this may only be partially true is suggested by the fact that the degree of segregation of cells in LB*LB(2) and (3) aggregates is not significantly different from
that in LB*LB(1) aggregates even though these aggregates were prepared from
'sieved' cell suspensions.
In control aggregates prepared with cell sieved suspensions, the cells show a
small but significantly different arrangement from random. Groups of like cells
could be produced in these aggregates by cell division, or by labelled material
diffusing into adjacent unlabelled cells; the phenomenon of metabolic cooperation between cells in contact demonstrated by Subak-Sharpe, Burk &
Pitts (1969) could explain the latter possibility. Mitotic figures have been observed in aggregates formed after 42 h reaggregation of mixed heart and limbbud cells, so it seems likely that cell division could adequately account for this
small departure from a random arrangement of cells in LB*LB (2) and LB*LB (3).
It would be expected, if this were the case, that this segregation effect would be
more marked in aggregates formed after 42 h in which more cell divisions have
taken place than in those reaggregated for 24 h. The degree of segregation,
although numerically higher (and therefore nearer random) in aggregates formed
after 24 h, is not significantly different from that in aggregates formed after 42 h.
Even so, it can be reasonably assumed that 'labelling' of a cell suspension does
not alter the behaviour of cells in aggregates more than slightly if at all.
This small degree of segregation, probably due to cell division, will also occur
in mixed aggregates of different cell types in addition to any segregation of cells
Sorting out in mixed cell populations
143
according to type. It is the latter segregation we are interested in. When testing
whether the mixed aggregates show any significant segregation according to cell
type, the a values of the control LB*LB(3) aggregates are used as the expected
values for a 'random' arrangement of cells, thus including the correction for
any pseudo-segregation due to cell division. In this way we can test whether there
is any additional segregation due to the mixing of the two different cell types.
Mixtures of cell types
Experiments were performed using 'labelled' heart and 'unlabelled' limb-bud
cells and the reciprocally labelled cell suspensions. In no cases were the a values
obtained in these reciprocal experiments statistically different. In other words,
the a value was not affected by which cell type was labelled. The mean a values
obtained under a given set of conditions in reciprocal experiments (and, where
indicated, also duplicate experiments) are shown in Table 3. In some reciprocal
experiments the proportions of the two cell types were markedly different and
this was found not to grossly affect the a values.
Table 3. Mean values ofoc in aggregates of mixed cell types
Cells reaggregated
for (h)
No. of samples
examined
2
4
42 (reciprocating
shaker)
48 (gyratory
shaker)
6
5
7
2
4
42
2
4
42
6
Total no. of
target cells scored
I. EDTAL disaggregation
2162
22J5
2059
1980
11. EDTA + Trypsin disaggregation
3348
10
3437
8
2509
8
(including
duplicate
experiment)
III. Trypsin disaggregation
1871
4
1662
6
3961
9
(including
duplicate
experiment)
Mean
y+z
Mean
a
.s2
0-68
0-70
0-90
0-62
0-64
0-88
0003
0002
0002
0-73
0-65
0004
0-69
0-76
0-82
0-65
0-70
0-76
0003
0004
0005
0-81
0-83
0-85
0-74
0-73
0-83
0001
0003
0002
To test whether the cells in the mixed aggregates showed significant segregation of cell types, the degree of segregation (a) of aggregates prepared by each
procedure at each time interval was compared with the value of the control
LB*LB(3) aggregates (aggregated for 42 h and cell sieved) by a two-sample
144
R. A. ELTON AND C. A. TICKLE
/-test, (see Table 4). All groups of aggregates, except those prepared by EDTA
and aggregated for 42 h in a reciprocating shaker, have a values which are
significantly lower than the a values of the control LB*LB (3) aggregates and
therefore the cells are segregated according to type.
Table 4. Comparison of mean cc value of mixed aggregates with mean a
value of aggregates LB*LB(3), which equals 0-92, s2 = 00009
Type of aggregates
Disaggregated
with
EDTA
EDTA
EDTA (recip.)
EDTA (gyrat.)
EDTA + Trypsin
EDTA + Trypsin
EDTA + Trypsin
Trypsin
Trypsin
Trypsin
Reaggregated
for (h)
Total
mean a
s
t
D.F.
2
4
42
48
2
4
42
2
4
42
0-62
0-64
0-88
0-65
0-65
0-70
0-76
0-74
0-73
0-83
0044
0036
0044
0053
0052
0059
0059
0030
0050
0037
10-51
11-80
1 59
7-86
8-76
6-91
4-65
8-93
5-84
4-24
8
7
9
8
12
10
10
6
8
11
P
P < 0001
P < 0001
0-2 >P> 01
P < 0001
P < 0001
P < 0001
P < 0001
P < 0001
P < 0001
0002 >
P > 0001
The main conclusions relating to 'sorting out' which can be drawn from these
segregation measures are that the cells in aggregates formed after 2 and 4 h
reaggregation in couette viscometers are consistently more segregated irrespective of the disaggregation procedure used than those in aggregates formed
after 42 h reaggregation in reciprocating shakers. In aggregates formed after
48 h reaggregation in gyratory shakers the cells are as highly segregated as in
those formed after 2 and 4 h. The disaggregation procedure was found to affect
the arrangement of cells in aggregates formed after 2, 4 and 42 h reaggregation.
These results will be discussed in relation to previous work o n ' sorting out' later.
Statistical considerations
(a) Comparison of y + z and a
As was pointed out in the development of the model, the parameter y + z
measures the segregation of labelled and unlabelled cells in the same way as
a measures that of the two cell types; the difference between these two parameters is an indication of the extent to which incomplete labelling affects the
apparent segregation, since, as can be seen from (3), they are the same if/? = 0.
In a segregating system, y + z is always greater than a, and this is true of the
experimental values shown in Table 3. Fig. 2 plots mean y + z against mean a for
each of the experimental conditions investigated. It should be noted that the two
values tend to equality as they both tend to unity: when the two cell types are
Sorting out in mixed cell populations
145
randomly mixed, so are the unlabelled and labelled cells. The extent and consistency of the deviations from equality provide some justification for the use of
the more complicated model involving the labelling correction.
Fig. 2. Mean values of y + z and a for each set of aggregates. Open circles
represent control values.
(b) PieloiCs method
If we consider two cell types mixed together in an aggregate, we can obtain
a distribution of run lengths for each cell type by taking line transects across the
aggregate and recording the type of each cell in succession. We have the following observations, after Pielou (1962), but introducing our notation: mL = mean
run length of labelled cells, mv = mean run length of unlabelled cells.
If the probability of encountering a labelled cell is / and that of encountering
an unlabelled cell is u, then the maximum likelihood estimators of / and u are
and u = 1 jmL respectively. We also have
„
1 mL-\
and
as sample variances of these estimators. Then, if labelled and unlabelled cells
are unsegregated, it follows with a 95 % probability that
= 1±
since the run lengths are independent of each other.
EM B 2 6
146
R . A . E L T O N AND C. A. T I C K L E
The results of this test for segregation are shown for a few aggregates in
Table 5. In control aggregates the labelled and unlabelled cells are not segregated. In the aggregates formed after 2 h from cells disaggregated with EDTA,
the labelled and unlabelled cells are segregated. We can compare the value of
l + u directly with y + z; as both represent measures of the degree of segregation
of labelled and unlabelled cells in the aggregates (see Table 6). The results show
that there is little difference in the degree of segregation of labelled and unlabelled cells obtained by the two methods.
Table 5. Tests for segregation by Pielou's method
Cell types
in aggregates
\\mv
LB*\
LB j
LB*»
H J
H*»
LB J
\jmL
l+u
\l(sl + s?)
1 ± 1-96 VC*« + s?)
0-28
0-69
0-97
005
1+0114
0-40
0-23
0-63
008
1 ±0-156
0-30
0-37
0-67
005
1 ±0 105
LB*LB aggregates: disaggregated with EDTA, cells sieved and reaggregated for 42 h.
LB*H and H*LB aggregates: formed from cells disaggregated with EDTA, reaggregated
for 2 h.
Table 6. Comparison of l + u and y + z
Aggregate
type
Control
LB*LB
LB*H
H*LB
l+u
Mean
y+z
t
0-97
0-93
-303
3
01 > P > 005
0-62
0-67
0-70
0-65
3-25
-0-73
3
1
005 > P > 002
0-8 > P > 0-5
D.F.
P
Control aggregates LB*LB: disaggregated with EDTA, cells' sieved', reaggregated for 42 h.
LB*H and H*LB aggregates: cells disaggregated with EDTA, reaggregated for 2 h.
(c) Positioning of cells in aggregates
Segregation of cells according to type may lead to 'positioning' which has
been defined relative to the inside and outside of an aggregate and has been
considered to be characteristic of a given combination of tissue types; for
example, limb-bud precartilage segregates internally when mixed with heart
(Steinberg, 1963).
The positioning of cell types has been measured in a few groups of aggregates
in which the cells have been shown to be segregated. A square grid was fitted
across aggregates of cells disaggregated with EDTA and reaggregated for 48 h
in a gyratory shaker. The number of labelled cells per square, across an approxi-
Sorting out in mixed cell populations
147
mate diameter of each section was counted under x 400 magnification, and the
results were grouped according to the number of grid squares across the diameter. Counts across small diameters will come either from small aggregates
1
.£
2
3
2
3
1
2
3
4
5
6
7
8
9
10
8
9 10
B
-° 5
'o 4
JO
3
1
3
4
5
6
7
5 •
4 3 2 -
|
1
.
1 1 2 3
1 2 3 4 5 6 7 8 9
10
Aggregate size expressed as number of grid squares across aggregate diameter
Fig. 3. Mean number of labelled cells/square across aggregate sections of small
and large diameters (5-15 samples/aggregate size class). (A) LB*H aggregates: cells
disaggregated with EDTA, reaggregated for 2 days in gyratory shaker. (B) H*LB
aggregates: cells disaggregated with EDTA, reaggregated for 2 days in gyratory
shaker. (C) LB*LB aggregates: cells disaggregated with EDTA, reaggregated for
42 h in reciprocating shaker.
148
R. A. ELTON AND C. A. TICKLE
or from sections near to either end of larger aggregates. In the latter case, when
'sorting out' is occurring, it would be expected that the smaller aggregate
widths would show a more uniform distribution of labelled cells than the larger
ones, since internally positioned cells will not occur in the centre of their
diameters. Fig. 3 A and B shows the distribution of labelled cells across aggregates formed in reciprocal experiments. Heart cells are positioned externally.
100 90 -
80 70 60 _
50 40 -
30 20 10 1 2
3
4
5
6
1 2
3
4
5
6
7
5
6
7
8
/o
60
-
50
40
30
-
20
r
10 1
2
3
4
5
6
1
2
3
4
8
Aggregate size expressed as number of grid squares across aggregate diameter
Fig. 4. Mean percentage of labelled cells/square across aggregate sections of representative diameters (6-15 samples/aggregate size class). (A) LB*H aggregates: cells
disaggregated with EDTA, reaggregated for 2 h in couette viscometers. (B) H*LB
aggregates: cells disaggregated with EDTA, reaggregated for 2h in couette
viscometers.
The labelled cells can be shown by a x2 test to be distributed non-randomly.
Histograms of the mean number of labelled cells/square across control aggregates LB*LB(3) (see Fig. 3C) show an even distribution of labelled cells across
aggregates, and this has also been shown statistically by means of a x2 test.
In small aggregates of cells disaggregated with EDTA and reaggregated for
Sorting out in mixed cell populations
Fig. 5. (A) Part of a control aggregate, LB*LB (cells disaggregated with trypsin,
mixed together without passage through cell sieves, reaggregated for 42 h) under
dark-field illumination, showing an almost random arrangement of labelled and
unlabelled cells. (B) An aggregate, LB*H (cells disaggregated with EDTA, reaggregated for 2 h), showing segregation of labelled and unlabelled cells; note also
that the labelled cell type, limb bud, is positioned externally. (C) Part of an aggregate, LB*H (cells disaggregated with EDTA, reaggregated for 42 h in a reciprocating shaker) showing an almost random arrangement of cells. (D) An 'end' of
an aggregate, LB*H (cells disaggregated with EDTA, reaggregated for 48 h in gyratory shaker) under dark-field illumination (the cells are segregated and note the
eccentric but internal positioning of the labelled cell type, heart).
149
150
R.A.ELTON AND C. A. TICKLE
2 h the total number of labelled and unlabelled cells/square was counted in
square grids across the aggregate under x 900 magnification. The percentage
of labelled cells across aggregates reciprocally labelled is shown in Fig. 4. The
distribution of cell types across these aggregates was tested by a x2 test. In
LB*H aggregates there is evidence that the cell types are not distributed
randomly across the aggregates but a similar conclusion cannot be drawn from
the data in H*LB aggregates. As mentioned before, segregation of cells need
not necessarily lead to 'positioning'. The irregularity of these early aggregates,
however, could obscure any 'positioning' measured by these methods. The
problem of dealing with irregular aggregates has been mentioned by Adler
(1970). Tentatively, limb-bud cells may be positioned externally (see also Fig. 5).
This suggests that the 'positioning' of cell types in early aggregates may be the
reverse of that found in aggregates formed after 2 days in gyratory shakers.
Table 7. Distribution of labelled cells surrounding labelled targets in a sample of
aggregates LB*H disaggregated with EDTA, reaggregated for 2 h (value of
a = 0-67)
No. of surrounding cells
Observed frequency of
labelled cells
0
1
1
1
2
10
3
4
5
6
34
67
81
52
(d) Distributions of surrounding cells and transect runs
In addition to considering the mean proportions y and z for a number of
target cells in a given aggregate, it is also possible to compile distributions of
frequencies of surrounding cells of each type. This is done by recording for
each target cell the number of cells among the six nearest neighbours that are
labelled and unlabelled. A typical distribution of this kind is shown in Table 7.
In unsegregated mixtures, the distribution would be expected to be binomial,
since each set of six surrounding cells would be the equivalent of a random
sample from the population of cells. In the segregated mixtures, however, the
distribution might be expected to depend in a complex way on the nature of the
segregating forces and on the extent of the positioning effect discussed in the
previous section.
Pielou (1962) considered an analogous problem for line transects by looking
at the distribution of lengths of runs of each type. The question of the nature of
these distributions when segregation is taking place may be answered more
easily in the one-dimensional case; in particular, if the sequence of cell types
forms a Markov chain, the run length distributions are geometric.
Data on both types of distribution were collected for some of the aggregates,
and it was found that there were no significant deviations from binomial or
Sorting out in mixed cell populations
151
geometric distributions. This was the case even where positioning had been
shown to be operating. It may be that the deviations expected from these
distributions when positioning occurs are too small to be detected by the sample
sizes used here; in any case, a satisfactory interpretation of these results must
await a more detailed stochastic model of cell segregation.
(e) Homogeneity of data
We can test the homogeneity of the observed proportions y and z in aggregates prepared under the same conditions. As an illustration, aggregatesLB*LB(1) (disaggregated with trypsin, not cell 'sieved', reaggregated for 42 h)
have been examined. Table 8 (a) shows that the proportions of labelled and
unlabelled target cells in the four aggregates are not statistically different.
In Table 8(6) the distributions of cells surrounding labelled targets are
shown; although they are significantly heterogeneous, the x2 value is not high
enough to indicate an important departure from the model.
Table 8. Distribution of cells in LB*LB(1) aggregates
(a) The proportions of labelled and unlabelled targets
L
U
Aggregate I
62
Aggregate II
114
Aggregate III
97
Aggregate IV
97
X2 = 0-86, D.F. 3, 0-9 > P > 0-8.
143
224
214
209
(b) Labelled cells surrounding labelled targets
No. of surrounding cells labelled
Agg. I
Agg. II
Agg. III
Agg. IV
0
1
2
3
4
5
6
4
18
11
13
14
25
24
26
8
31
34
34
19
25
21
15
12
12
6
7
5
2
1
1
0
1
0
1
Treated as
one class
X* = 30-32, D.F. ]15, 005 > P > 001.
DISCUSSION
The preliminary results relating to 'sorting out' using the measure of segregation described above illustrate the usefulness of quantitative measures of this
phenomenon. It has been found that in aggregates formed after short periods
of reaggregation (2 and 4h) in couette viscometers the cells are markedly
segregated according to type.
152
R. A. ELTON AND C. A. TICKLE
The possibility that this result is due to the presence of undisaggregated
clumps of cells in the original cell suspensions has been eliminated by the use of
cell sieves.
Previously it has been thought that 'sorting out' could be divided into two
phases (Townes & Holtfreter, 1955; Moscona, 1962,1965). At first the cell types
adhere in a random manner, later segregation occurs; although sponge cells
may not 'coalesce' at all with cells of different species in still culture systems
(Galtsoff, 1925). The experimental evidence for the existence of these two phases
arises mainly from aggregation in still culture systems. By extrapolation from
these results it has been assumed that in aggregates formed in shaker systems
the cells adhere at first randomly. Adler (1970) is the only worker who has
attempted to assess an aspect of 'sorting out' quantitatively. He found that the
'positioning' of embryonic chick neural tube cells in aggregates formed after
1^ h was statistically random. As segregation of cell types could occur without
'positioning' this is not at variance with the present results on the grouping of
cells in early aggregates.
The finding here that the cells in early aggregates are segregated suggests that
'sorting out' may occur during aggregate formation in shaker systems; a possibility mentioned by Curtis (1967). How can this marked degree of segregation
be interpreted? Moscona (1962, 1965) has suggested that 'sorting out' can be
explained on the theory that there are specific mechanisms by which cells of
different types adhere (Specific Adhesion Theory). This theory, although attractive as an explanation of segregation, cannot account for the defined
'positioning' of cell types in aggregates, as was pointed out by Curtis (1962a)
(see Steinberg (1970) for recent catalogue of 'positioning'), and if it were taken
to its logical conclusion, separate aggregates of each cell type and species type
should always result. However, it can be postulated that adhesions between like
cells are stronger than adhesions between unlike cells (Steinberg, 1958; Roth,
1968). Thus the segregation of cell types after short periods of reaggregation
could be interpreted as showing that specific adhesion does occur during the
first 2 h after disaggregation.
A crucial point in aiding interpretation is whether the cell types are 'positioned' in early aggregates. As the evidence presented here is tentative in nature
the possibility that specific adhesion takes place cannot be excluded. It should
be noted that the tentative evidence for 'positioning' of the cell types used in
these experiments after 2 h reaggregation is not in agreement with the results
of Adler (1970). If the cells are 'positioned' as well as segregated after short
times of reaggregation it seems likely that the results can be interpreted on the
'differential adhesion' (Steinberg, 1964,1970) or the 'timing' hypothesis (Curtis,
1961, 1962/7).
Steinberg's differential adhesion hypothesis (1964, 1970) predicts that as soon
as there is a choice of adhesions the cells will 'sort out', although he has not
made this point in regard to the time course of' sorting out'. It would seem there-
Sorting out in mixed cell populations
153
fore that the finding of segregation of cells according to type in aggregates
formed after short periods could fit this hypothesis. The internally segregating
cell type is said to be the most adhesive (Steinberg, 1964) and from the results
can be tentatively identified as heart cells after 2 h disaggregation with EDTA
on this model.
The timing hypothesis of Curtis (1961, 19626) provides an alternative interpretation of the results. Heart cells, tentatively found to be internally positioned,
would aggregate first on this model, because they become adhesive before the
limb bud cells. Later limb-bud cells become adhesive and reaggregate on to preformed clusters of heart cells. This would lead to segregation of the cells and
positioning. The timing hypothesis is attractive because it is possible to interpret
the marked degree of segregation of cells in aggregates formed after a few hours
without postulating that the cells are motile. However, segregation in early
aggregates on Steinberg's hypothesis could be brought about not by gross
movement but rather by small displacements of cells and small clusters which
have been observed in pelleted aggregates (Trinkaus & Lentz, 1964).
Any attempt to trace the time course of segregation from the results reported
here is hampered for lack of data on how cells are arranged in aggregates
formed during intermediate times of reaggregation between 4 and 42 h. The
interpretation of the results is further complicated by the fact that the aggregates have been prepared from cells reaggregated in three different rotationmediated aggregation systems. There is evidence that arrangement of cells
in aggregates prepared in reciprocating shakers or by gyratory shaker techniques for equivalent time periods is markedly different. It should be stressed
therefore that results from one system cannot be extrapolated to another and
that the segregation of cell types which occurs in early aggregates produced in
couette viscometers may not arise when aggregates are built up in different
shaking systems.
Cells in aggregates formed after 42 h in reciprocating shakers are more
randomly arranged than those in early aggregates; in aggregates of comparable
age formed by the gyratory shaker technique the cells are markedly segregated
and 'positioned'. It should be pointed out that the segregation and'positioning'
in these aggregates is not absolute (see the histograms in Fig. 3 A, B); however,
this may be due to the heterogeneity of cell types used and to the fact that individual cells can be recognized. The differences in the arrangement of cells in
resultant aggregates of the two systems could be due to the manner of aggregate
build-up in each system, or to the fact that embryo extract was present in the
medium in gyratory-produced aggregates.
There is some evidence that in reciprocating shakers and gyratory shakers
aggregates may be built up in different ways. Roth & Weston (1967) showed
that the number of single cells collected by an aggregate varied directly with
aggregate diameter in reciprocating shakers but inversely in gyratory shakers.
This further suggested that in flasks on gyratory shakers a velocity gradient will
154
R.A.ELTON AND C. A. TICKLE
be set up across the flask and that aggregates of large mass tend to move towards the outside of the flask. Curtis (1970a) has suggested that another type
of zoning occurs and that the aggregates tend to move toward the centre of the
flask where the flow rate is decreased. This effect could remove aggregates, as
they form, from the regions in which the single cells zone. It should also be
noted that in the gyratory technique (Steinberg, 1963) the rate of gyration is
increased after 17 h to prevent 'further fusion' of aggregates; thus the aggregates are cultured separately for the rest of the culture time.
However, it has been shown here, using the same reaggregation procedure as
Steinberg (1964, 1970), that 'sorting out' occurs in aggregates and that heart
cells are positioned externally, which is in agreement with Steinberg's results
(1964, 1970). It is interesting, however, that this 'positioning' is the reverse of
that which may exist in aggregates formed after 2 h reaggregation in couette
viscometers. Here the cells were disaggregated with EDTA; but Curtis (19706)
has shown that the adhesiveness of chick embryonic liver and neural retina cells
do reverse in the first 5 h after disaggregation with trypsin. This result of
Curtis's incidentally provides evidence that temporal changes in adhesiveness
do occur after disaggregation, which lends support to his timing hypothesis.
Another finding of this work is that the disaggregation procedure used to
prepare the initial cell suspensions does affect the arrangement of cells in
aggregates produced after all the three time periods of reaggregation used. How
these results can be interpreted is not clear; for example, it could be argued that
cells are more altered by disaggregation with EDTA than by any of the other
disaggregation procedures, if initial segregation is considered an artifact of the
disaggregation procedure; the reverse argument, that EDTA-disaggregated cells
are least altered by the disaggregation procedure, could also be put forward.
The finding that, in aggregates formed after 42 h in reciprocating shakers,
the disaggregation procedure affects the degree of segregation of cells is surprising and suggests that the treatment of cells during disaggregation may have
long-term effects. An alternative attractive explanation is that different disaggregation procedures release different proportions of cell types from limb
buds or hearts. However, a similar proportion of 'labelled' cells were released
from labelled limb buds by each disaggregation procedure, which is a slight
indication that this sort of selection may not be occurring in limb-bud suspensions. The proportions of the tissue types in aggregates formed after 42 h
reaggregation with the EDTA or with the Trypsin procedure were similar to
the proportions of cells initially mixed together. However, in similar aggregates
formed from cells disaggregated with the Trypsin + EDTA procedure there was
a smaller proportion of heart cells than expected from the initial proportions.
It seems possible that the Trypsin and EDTA procedure may select a population
of heart cells; however, the proportions of heart cells in aggregates formed after
48 h reaggregation in gyratory shakers by cells disaggregated with EDTA are
also lower than expected from the initial proportions of the tissue types. This
Sorting out in mixed cell populations
155
may be due to the way aggregates are built up, which has already been discussed,
or to a burst of mitotic activity in limb-bud cells at 2 days in culture.
It can be seen that these preliminary results using quantitative measures for
cell arrangements raise a number of questions about cell behaviour in aggregates. While they substantiate quantitatively the results of Steinberg (1964,1970)
under the same conditions, it is clear that the degree of 'sorting out' can be
influenced not only by the disaggregation procedure but also by the reaggregation methods.
We are grateful to Professor A. S. G. Curtis for his advice on all aspects of the work. One
of us (C. A.T.) was supported by an S.R.C. studentship during the course of this research.
REFERENCES
R. (1970). Changes in reaggregation pattern during neural tube differentiation.
Devi Biol. 21, 403-423.
BURDICK, M. L. & STEINBERG, M. S. (1969). Embryonic cell adhesiveness: do species differences exist among warm-blooded vertebratesIProc. natn. Acad. Sci. U.S.A. 63,1169-1175.
CURTIS, A. S. G. (1960). Area and volume measurements by random sampling methods.
MecL biol. Must. 10, 261-266.
CURTIS, A. S. G. (1961). Timing mechanisms in the specific adhesion of cells. Expl Cell Res.,
Suppl. no. 8, 107-122.
CURTIS, A. S. G. (1962a). Pattern and mechanism in the reaggregation of sponges. Nature,
Loud. 196, 245-248.
CURTIS, A. S. G. (19626). Cell contact and adhesion. Biol. Rev. 37, 82-129.
CURTIS, A. S. G. (1967). The Cell Surface. London: Logos Academic Press.
CURTJS, A. S. G. (1969). The measurement of cell adhesiveness by an absolute method.
/. Embryo!, exp. Morph. 22, 305-325.
CURTIS, A. S. G. (1970a). Problems and some solutions in the study of cellular aggregation.
Symp. zool. Soc. Lond. 25, 335-352.
CURTIS, A. S. G. (19706). On the occurrence of specific adhesion between cells. /. Embryo!.
exp. Morph. 23, 253-272.
CURTIS, A. S. G. & GREAVES, M. F. (1965). The inhibition of cell aggregation by a pure
serum protein. /. Embryol. exp. Morph. 13, 309-326.
GALTSOFF, P. S. (1925). Regeneration after dissociation. (An experimental study on sponges.)
I. Behaviour of dissociated cells of Microciona prolifera under normal and altered conditions. /. exp. Zool. 42, 183-222.
LE BLOND, C. P., KOPRIWA, B. M. & MESSIER, B. (1963). Radioautography as a histochemical tool. In Histochemistry and Cytochemistry (ed. R. Wegmann), pp. 1-33. London:
Pergamon.
MOSCONA, A. A. (1962). Analysis of cell recombinations in experimental synthesis of tissues
in vitro. /. cell. comp. Physiol. 60 (Suppl. I), 65-80.
MOSCONA, A. A. (1965). Recombination of dissociated cells and the development of cell
aggregates. In Cells and Tissues in Culture, vol. I (ed. E. N. Willmer), pp. 489-531. London:
Academic Press.
PANTJN, C. F. A. (1964). Notes on Microscopical Technique for Zoologists, p. 77. Cambridge
University Press.
PIELOU, E. C. (1962). Runs of one species with respect to another in transects through plant
populations. Biometrics 18, 579-593.
PIELOU, E. C. (1963). Runs of healthy and diseased trees in transects through an infected
forest. Biometrics 19, 603-614.
ROGERS, A. W. (1967). Techniques of Autoradiography, p. 338. Amsterdam: Elsevier.
ROTH, S. A. (1968). Studies on intercellular adhesive selectivity. Devi Biol. 18, 602-631.
ADLER,
156
R . A . E L T O N AND C. A. T I C K L E
S. A. & WESTON, J. A. (1967). The measurement of intercellular adhesion. Proc. natn.
Acad. Sci. U.S.A. 58, 974-980.
STEINBERG, M. S. (1958). On the chemical bonds between animal cells: a mechanism for
type-specific association. Am. Nat. 92, 65-82.
STEINBERG, M. S. (1962). On the mechanism of tissue reconstruction by dissociated cells.
I. Population kinetics, differential adhesiveness, and the absence of directed migration.
Proc. natn. Acad. Sci. U.S.A. 48, 1577-1582.
STEINBERG, M. S. (1963). 'E.C.M.'; its nature, origin, and function in cell aggregation. Expl
Cell Res. 30, 257-279.
STEINBERG, M. S. (1964). The problem of adhesive selectivity in cellular interactions. In
Cellular Membranes in Development (ed. M. Locke), pp. 321-366. New York: Academic
Press.
STEINBERG, M. S. (1970). Does differential adhesion govern self-assembly processes inhistogenesis? Equilibrium configurations and the emergence of a hierarchy among populations
of embryonic cells. /. exp. Zool. 173, 395-434.
SUBAK-SHARPE, H., BURK, R. R. & PITTS, J. D. (1969). Metabolic cooperation between
biochemically marked mammalian cells in tissue culture. /. Cell Sci. 4, 353-367.
TOWNES, P. L. & HOLTFRETER, J. (1955). Directed movements and selective adhesion of
embryonic amphibian cells. J. exp. Zool. 128, 53-120.
TRINKAUS, J. P. & LENTZ, J. P. (1964). Direct observation of type-specific segregation in
mixed cell aggregates. Devi Biol. 9, 115-136.
ZWILLING, E. (1959). A modified chorioallantoic grafting procedure. Transplantn Bull. 6,
115-116.
ZWILLING, E. (1968). Morphogenetic phases in development. In The Emergence of Order in
Developing Systems, 27th Symposium for the Society for Developmental Biology, ed.
M. Locke, pp. 184-207.
ROTH,
{Manuscript received 20 January 1971)