/. Embryol. exp. Morph. Vol. 40, pp. 143-157, 1977
Printed in Great Britain © Company of Biologists Limited 1977
143
Changes in the properties of the
developing trophoblast of preimplantation mouse
embryos as revealed by aggregation studies
By PAUL S. BURGOYNE 1 A N D T H O M A S DUCIBELLA 2
From the Laboratory of Human Reproduction and Reproductive
Biology, Harvard Medical School, U.S.A.
With an Appendix by JOHN D. BIGGERS
SUMMARY
Mouse embryos (8-cell to early blastocyst) were denuded with pronase, and apposed in
pairs which represented a wide range of stage combinations. These pairs either formed aggregates which differentiated into double-sized blastocysts, or they failed to aggregate. The 8-1.6cell stages would not envelop late morulae/early blastocysts to form layered aggregates. This
must mean that as the embryo differentiates into a blastocyst, the outer surface of the trophoblast loses its capacity for supporting cell spreading. The aggregation data also demonstrate
that embryos almost completely lose their potential for aggregation at a very discrete stage in
development - namely, between 8 and 9 h before blastocoel formation. It is argued that this
is the stage at which the zonular tight junctional seal is completed, and that it is this physical
barrier which prevents aggregation.
It has been argued previously that the zonular tight junctional seal allows the creation of
the special microenvironment which is necessary for the determination of the inner cells as
inner ce'l mass. The completion of this seal 8-9 h before it is required for the formation of a
blastocoel would provide a suitable time period for this cell determination to occur.
The results obtained also relate to the technique of chimera production. Since the aim of
this technique is to generate mice with mixed cell populations, it is important that the blastocyst formed following aggregation should have both cell lines present in the inner cell mass.
This can best be assured by using relatively late morula stages (75 h post-HCG injection)
since these will have already segregated their inner cells, but the incomplete seal will still
allow aggregation to take place.
INTRODUCTION
Ultrastructural studies of the preimplantation mouse embryo have indicated
that the outer cells begin to differentiate into an epithelium - the trophoblast or
trophectoderm - well in advance of the blastocyst stage. At the 8-cell stage,
the blastomeres change shape and their lateral borders come into close apposition
(Ducibella & Anderson, 1975). Morulae develop zonular tight junctions between
1
Author's address: Department of Obstetrics and Gynaecology, University of Edinburgh,
23 Chalmers Street, Edinburgh, EH3 9EW, U.K.
2
Author's address: Laboratory of Human Reproduction and Reproductive Biology,
Harvard Medical School, 45 Shattuck Street, Boston, Massachusetts 02115, U.S.A.
144
P. S. BURGOYNE AND T. DUCIBELLA
the outer cells and microvilli become localized apically (Ducibella, Albertini,
Anderson & Biggers, 1975; Ducibella, Ukena, Anderson & Karnovsky, 1977). The
resulting epithelium has two functions: the isolation of the inner cells from the
external environment (Hillman, Sherman & Graham, 1972) as required by the
'inside/outside' theory of cell determination (Tarkowski & Wroblewska, 1967),
and the active transport of ions (Borland, Biggers & Lechene, 1977). The accumulation of blastocoel fluid is almost certainly coupled to this active transport
of ions, as has been demonstrated in the rabbit (Borland et al. 1976).
The changes associated with the development of this epithelium have been
investigated by the technique of embryo-embryo aggregation (Tarkowski,
1961; Mintz, 1962a). The completed zonular tight junctional seal would be
expected to act as a barrier preventing aggregation, while adhesive changes
which are typical of developing epithelia should be reflected in alterations in the
aggregation process. The results show that embryos lose their ability to aggregate more than 8 h before cavity formation. It can thus be argued that the
epithelial barrier, and therefore the microenvironment for the inner cells, is
established well in advance of the onset of blastocoel fluid accumulation. The
results also show that as the embryo differentiates into a blastocyst, the outer
surface of the trophoblast loses its capacity for supporting cell spreading.
MATERIALS AND METHODS
Embryos at various stages (8-cell to early blastocyst) were obtained from
gonadotropin-primed mice. C3H/Bi females were used as embryo donors in
expt. 1, and Fl hybrid females (C3HBi/C57BL10 and C57BL6/SJL) in expts. 2
and 3. For experiment 3 the females were maintained on a reversed light schedule
(lights on at 4 p.m., off at 6 a.m.). All females were mated to random-bred
Swiss albino males.
Zonae were removed with pronase (B grade, free of nucleases: Calbiochem
no. 537088) using a procedure which enabled the treatment of large numbers of
embryos while allowing good control of zona dissolution. The procedure
briefly was as follows: the embryos were transferred in a small volume of
medium to an embryological watch glass with a polished concavity (Columbia
culture dish, A. H. Thomas no. 9790-R10) containing 0-1 ml of dialyzed pronase
solution at 37 °C (Mintz, 19626).1 When the zonae began to swell (4-6 min)
the action of the pronase was 'braked' by quickly flooding the dish with 0-8 ml
of culture medium (the standard egg culture medium of Biggers, Whitten &
Whittingham (1971), with 0-3 % bovine serum albumin, gassed with 5 % CO2 in
air at 37 °C). The rush of fluid suspended the embryos, and they were returned
to the centre of the concavity by gently swirling the dish. Most of the fluid was
1
For studies of preimplantation development, calcium-free solutions should be avoided
because of the calcium dependency of cell adhesion and subsequent junction formation
(Ducibella & Anderson, 1975). In this respect, pronase in Hanks' balanced salt solution
(Mintz, 19626) should be used in preference to pronase in phosphate buffered saline.
Properties of the trophoblast of mouse embryos
145
then withdrawn using a drawn-out pipet (tip orifice — 180/tm in diameter)
attached to a vacuum line, and fresh medium was quickly added. The embryos
were then washed by repeating this last step three times.
The embryos were cultured under paraffin oil in carefully washed Terasaki
tissue culture plates (Falcon no. 3034), either as aggregating pairs (Tarkowski,
1961; Mintz, 1962) or singly to provide control data. An important characteristic
of these culture plates is that the wells damp out fluid movement during
handling. This minimizes the separation of embryos which have just been apposed. In expts. 2 and 3 the wells containing apposed pairs were vigorously
stirred with a fine glass rod 45 min after apposition. The few pairs which were
not stuck were reapposed in experiment 2; but in experiment 3 where the time
of apposition had to be well defined, pairs which were not stuck were excluded
(9 out of 106 pairs).
When all the embryos in a culture had reached the expanded blastocyst stage,
the pairs were scored as aggregants or non-aggregants. By this stage all pairs
that can aggregate have done so, and the non-aggregants have usually rolled
apart. (The outer surface of expanded blastocysts is non-adhesive.)
In all cases the number of hours since the injection of HCG (human chorionic
gonadotropin) into the donor females was used as an estimate of the stage of
the embryos at the time of apposition. However, this criterion for staging embryos is not perfect. At a given time post-HCG there are often clearcut stage
differences between the embryos from different females. In expt. 3 this
variation in staging was monitored by noting the time at which each embryo
formed a blastocoel during the culture period. This was done using a Zeiss
Standard UPL inverted microscope, assessments being made every hour.
RESULTS
Experiment 1
For this experiment the gonadotropin injection schedules had been arranged
so that two groups of embryos were available; the majority of one group
('early') being at the 8-cell stage and the other group ('late') consisting of late
morulae and early blastocysts. The embryos were apposed in pairs as early/
early, early /late or late/late combinations. At the time of apposition the 'early'
group was 71 h post-HCG and the 'late' group was 91 h post-HCG. The numbers of aggregant and non-aggregant pairs in each group is shown in Table 1.
Only the early/early pairs aggregated successfully. 'Early' embryos did not
spread over and envelop 'late' embryos. These preliminary results indicate that
there is an embryo surface change between the 8-cell and late morula/early
blastocyst stage which prevents aggregation; and that in asynchronous pairs it
is the nature of the surface of the older embryo which limits aggregation (Fig. 1).
146
P. S. BURGOYNE AND T. DUCIBELLA
Table 1. Aggregation within and between two groups of embryos
which are at different stages of development
Number of pairs
Combination
Aggregants
Non-aggregants
Early/early
Early/late
Late/late
10
0
0
At time of apposition: Early group = 71 h post-HCG (mostly 8-cell); Late group = 91 h
post-HCG (late morulae and early blastocysts).
0-5 h
Q
I
18 h
37 h
Fig. 1. The behavior of 'early/early' and 'early/late' pairs in expt. 1. The left-hand
sequence shows the successful aggregation of an 'early/early' pair. The right-hand
sequence illustrates the failure of an 'early' embryo to envelop a 'late' embryo.
Although not clear in the photograph the 'late' embryo had a clear blastocoel by
18 h. This has been outlined in thefigureby a dotted line.
Properties of the trophoblast of mouse embryos
147
100
20-
1
70
75
i
80 x
Hours post-HCG
i
i
85
90
Fig. 2. The relationship between the developmental age of embryos at the time they
are apposed, and their ability to aggregate. Developmental age is expressed as the
number of hours that had elapsed since administration of HCG to the embryo donors,
.v (81 1 h post-HCG) is the mean time at which morulae lose their potential for
aggregation, as estimated from the data for the closed circles (see appendix).
Experiment 2
For this experiment the embryos were apposed in pairs at times varying from
75-5-84 h after injection of the donor females with HCG. Different groups of
donor females were used for each time of apposition. Embryos were collected
from the females, and pronased, immediately before they were apposed in pairs.
The percentage of pairs which successfully aggregated in each group is plotted in
Fig. 2 (closed circles). Also included in this Figure are the results obtained in
expt. 1 for the 'early/early' and 'late/late' combinations (open circles). The
results confirm the preliminary conclusion from expt. 1 that mouse embryos
lose their potential for aggregation somewhere between the 8-cell and blastocyst
stages. More precisely the results shown in Fig. 2 can be used to estimate the
mean time and standard deviation, for the loss of the ability to aggregate (see
Appendix). The mean time is 81-1, S.D. 2-2, h after the administration of HCG.
The fiducial limits of error (P = 0-05) for the mean are 79-2-83-0 h.
Experiment 3
For this experiment the embryos had been apposed in pairs 79-5-81 h postHCG, and the developmental schedule of each embryo was monitored by
scoring at hourly intervals for the appearance of a blastocoel. Let the time of
apposition be denoted t0, and the times of cavity formation in the component
embryos of a pair by tx, t2 (tx ^ t2). The appositional stage of a pair can then
be denoted as (t± - to)/(t2 -1 0 ). For synchronous pairs (tx -10) and (t2 -10) will
be very similar, and for asynchronous pairs (?i-/ 0 ) a n d (t2-t0) will be dissimilar. The results are shown in Table 2. The staging of the pairs that aggre-
148
P. S. BURGOYNE AND T. DUCIBELLA
Fig. 3. Pair 47 from expt. 3, 11 h after apposition. The dotted line is the plane
which separates the two original embryos. The blastocoel began to form 4 h after
apposition {tt — t0 = 4). At 11 h after apposition it is clear that no cavity has formed
the embryo on the left (^ - t0 > 11).
gate is complicated by the fact that the component embryos are only transiently
distinguishable as separate entities. In the case of pair 51 there was no problem
because both members started to form blastocoels before aggregation had
started. In pair 47, one member formed a cavity 4 h after apposition, at which
time aggregation had not started (tx — t0 = 4). By 11 h post-apposition, although
aggregation was progressing, the limits of the two embryos were still definable;
and there was still no cavity in the second member of the pair (Fig. 3). Thus
(t2-to) is greater than 11 h, and the appositional stage of pair 47 is therefore
scored as 4/ > 11. In the remainder of the aggregant pairs cavitation did not
occur until after aggregation had begun, and in some cases not until aggregation
was complete. In no case did separate cavities form in the two members of a
pair during the period of time that they could still be distinguished. In Table 2
(A - ^o) is therefore recorded as the number of hours before cavity formation
in the composite, and (t2 —10) is assumed to be equal to or greater than
(fi-'o).
The data in Table 2 demonstrate two important points. First, embryos have
lost their potential for aggregation almost entirely, by 8 h prior to the formation
of a blastocoel. Thus in pairs 1-72 only two pairs (47 and 51) aggregated successfully. Unlike the other aggregants, these two pairs did not start to aggregate
until several hours after apposition. This suggests that they regained the ability
to aggregate, rather than possessing this capacity at the time of apposition.
Secondly, highly asynchronous pairs (e.g. 17-21 and 30-33) fail to aggregate,
thus confirming the observations with 'early/late' combinations in expt. 1.
Properties of the trophoblast of mouse embryos
149
Table 2. The relationship between the stage at which embryos are opposed in
pairs and their ability to aggregate {pooled data from three repeats)
Pair
Stage*
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
1/1
1/1
1/1
1/1
1/2
1/3
1/4
1/4
1/5
1/5
1/5
1/5
1/6
1/6
1/7
1/9
1/10
1/11
1/12
1/13
1/13
2/4
2/5
2/5
2/6
2/6
2/7
2/9
2/9
2/10
2/10
2/10
2/11
Aggregation
Pair
Stage*
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
3/4
3/6
3/7
Aggregation
3/11
4/4
4/4
4/4
4/5
4/6
4/6
4/8
4/9
77
4/11
4/>
5/5
5/6
5/6
5/6
5/7
5/7
5/7
5/9
5/10
5/10
5/11
5/11
5/11
5/11
5/15
6/6
6/7
6/9
6/9
+
Pair
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
Stage*
Aggregation
6/9
6/10
6/12
6/12
6/14
8/12
9/9
9/10
9/10
9/11
9/5*9
9/2*9
10/11
10/5*10
10/5*10
11/5*11
11/5*11
11/5*11
12/5*12
12/5*12
13/5*13
13/5*13
14/5*14
15/5*15
15/5*15
15/5*15
15/3=15
>15/>15
>15/>15
>15/> 15
* The appositional stage of a pair of embryos is given as ^ - / o | ? 2 - ^ , where t0 is the
time of apposition, and tx and t2 (tt ^ t2) are the times that the component embryos of the
pair cavitate.
After the process of aggregation begins the individual members of a pair
remain as distinct entities for varying periods of time. We refer to aggregate
pairs in this phase as 'dumb-bells' because of their appearance (Fig. 3). For pairs
of early morulae this phase only lasts an hour or so, but in aggregating later
stages it lasts for several hours. Many pairs pass through the dumb-bell phase
without forming blastocoels: these are probably pairs of relatively early embryos.
Others pass through the dumb-bell phase with a cavity forming in one half only:
these are presumably asynchronous pairs. However, throughout expts. 2 and 3,
150
P. S. BURGOYNE AND T. DUCIBELLA
dumb-bells with a cavity in both halves were rarely seen. In expt. 3, where cavity
formation was monitored systematically, the only pair with a cavity in each
embryo at the dumb-bell stage (pair 51) had formed these cavities prior to aggregation; there were no pairs in which a cavity formed in both embryos during
the dumb-bell phase.
For some reason, embryos do not form a randomly mixed pool in the dish
following the pronasing and washing procedures, but instead segregate to some
extent into early and late stages. As a result there is a non-randomness of pairing
on transferring the embryos to the culture plates. This is apparent in the data
presented in Table 2. When dispensing the pairs into the culture plates singles
were interspersed so that they, at least, would approximate to a random sample of
the population used for pairs. Of these singles 5 out of 35 cavitated more than
15 h after the time the pairs were apposed. Among the pairs a maximum of 24
out of 194 embryos cavitated more than 15 h after the time of apposition (Table
2). This argues against the possibility that aggregation itself delays cavity formation. In all other respects there was no evidence that the population of embryos
in the experimental pairs differed, with respect to cavity formation, from the
population of single embryos.
DISCUSSION
Since the pioneer work of Tarkowski (1961) and Mintz (1962), it has been
known that 8-16-cell mouse embryos have the potential for aggregation, and it
is generally accepted that this aggregation if accompanied by at least some
mixing (Garner & McLaren, 1974). However, the results from expt. 1 indicate
that this stage will not form any kind of aggregate (mixed or unmixed) with
late morula/early blastocyst stages. The zonular tight junctions between the
trophoblast cells of late morulae and early blastocysts (Ducibella, Albertini,
Anderson & Biggers, 1975) would be expected apriori to act as a physical barrier
preventing intermixing; but there must also be an embryo surface change which
is preventing the 8-16-cell stages from spreading over the late morulae and
early blastocysts to form layered aggregates. The general observation that
embryos apposed up to the early blastocyst stage will adhere but that late
blastocysts roll apart, may be reflection of this embryo surface change.
The results from expt. 2 demonstrate that 95-5 % of mouse embryos lose their
potential for aggregation between 76-7 and 85-5 h after the injection of the
donor females with HCG, the mean time for this loss being 81-1 h. This mean
time can be related to various developmental events by using the relationship
between hours post-HCG and mean cell number as determined by Barlow,
Owen & Graham (1972). These authors used embryos from random-bred
Swiss mice, which we find are comparable in developmental rate to those from
the hybrid mice used here. The relationship is expressed as follows:
x = 32-23 log y + 39, where x is hours post-HCG and y is mean cell number.
Properties of the trophoblast of mouse embryos
151
-65 -
Compaction
- 8 -
-70-
First
inside cell
-75-16-80-
Permeability
seal
Morulae lose
their potential
for aggregation
-85 -
-32-
Cavitation
^90-
Mean Hours
cell
postnumber HCG
Fig. 4. The relationship between the time that mouse embryos lose their potential
for aggregation, and their state of differentiation.
Compaction is an important event in the development of the mouse embryo
which occurs in vivo at the 8-cell stage (Ducibella & Anderson, 1975). On average,
embryos have 8 cells at 68-1 h post-HCG. One of the products of division of
these 8 cells (i.e. during the 9-16-cell phase) becomes the first 'inside cell' of the
compacted embryo (Barlow et al. 1972). Embryos have an average of 16 cells,
and therefore at least one inside cell, by 77-8 h post-HCG. Beginning at the
8-cell stage focal tight junctions begin to develop between the cells at the level
of the embryo surface (Ducibella & Anderson, 1975). Subsequently these tight
junctions become zonular, and by using the extracellular tracer lanthanum
Ducibella et al. (1975) were able to show that the junctions become effective as
a seal somewhere between the 16- and 32-cell stages (77-8-87-5 h post-HCG).
Unless disassembly of junctions occurred, this seal would be expected to act as
a physical barrier preventing intermixing of apposed embryos. Significantly,
embryos lose their potential for aggregation at 81-1 h post-HCG (a mean of
20-4 cells) which correlates well with the estimated stage (16-32 cells) for the
completion of the seal. From expt. 3 it can be argued (see below) that at 81-1 h
the embryos are between 8 and 9 h before cavitation. This temporal correlation
between the completion of the seal and the loss of the ability to aggregate is
shown in Fig. 4. On the strength of this correlation, the following hypothesis can
be suggested to explain the inability of later stages to aggregate. First, the com-.
152
P. S. BURGOYNE AND T. DUCIBELLA
pletion of the tight junctional seal forms a physical barrier which cannot be
penetrated by the cells of other embryos. Secondly, an embryo surface change
occurs which prevents the cells of earlier stages from spreading over and enveloping the embryo.
As observed earlier it takes a period of nearly 9 h (76-7 - 85-5 h post-HCG)
for 95-5 % of the embryos to lose their ability to aggregate. The results from
expt. 3 clearly indicate that most of this time span represents the time taken for
the embryos to pass a critical stage of development. As a general rule, pairs of
embryos aggregated successfully when both members were nine or more hours
before cavitation, but they failed to aggregate when at least one member was
8 h or less before cavitation. Out of the 97 pairs in expt. 3 there were only
seven exceptions to this rule. These fall into two groups. First, there are those
pairs (73-76 and 79 in Table 2) where aggregation is predicted, but did not occur.
The members of these pairs were remarkably synchronous (appositional stages:
9/9, 9/10, 9/10, 9/11, 10/11) and were apposed when they were close to the
postulated 8-9 h transition period. This suggests the possibility that pairs of
embryos which have their tight junctional seals almost complete are unable to
deform sufficiently to spread on each other. This group of synchronous pairs
which failed to aggregate, would also account for the absence of dumb-bells with
two cavities (see p. 150).
The second class of exceptions is represented by pairs 47 and 51. These
aggregated despite the fact that at least one member of each pair was closer
than 8 h to cavitation at the time of apposition. It was noted, that in contrast to
the other aggregant pairs, these did not begin to aggregate until several hours
after apposition. Possibly these two exceptions are cases where there has been
invasion through temporary breaks in the seal which may be produced when
trophoblast cells divide.
The previous literature relating to embryo aggregation seems to be contradictory. Mulnard (1971) states that embryos with more than 16 cells rarely aggregate. In contrast, Mintz (1965) and Stern & Wilson (1972) state that aggregation
occurs up to the early blastocyst stage. Clearly, in the light of the results presented here, both statements are correct. However, both Mintz (1965) and Stern
& Wilson (1972) seem to infer a much higher success rate with early blastocyst
stages than we have observed. It is possible that a harsher pronasing treatment
than that used here might disrupt junctions and allow more aggregation at later
stages. Stern (1972), for example, has successfully aggregated late blastocysts
following partial disruption of the junctions. Mintz, in the discussion of
Mulnard's (1971) paper, emphasizes that she is careful to maximize the appositional surface between the embryos. This would increase the likelihood of there
being cell division in the apposed areas of trophoblast, which may allow aggregation at these late stages. A possible criticism of Stern & Wilson's (1972)
work is that they pool the data for late morulae and early blastocysts. Many
embryos visually classified as late morulae will be more than 8 h before cavitation;
Properties of the trophoblast of mouse embryos
153
and, as demonstrated here, these morulae behave very differently from early
blastocysts.
The results obtained here also relate to certain technical and theoretical problems. First, the production of chimeric (allophenic, tetraparental) mice, by whatever means, requires that the inner cell mass of the resulting blastocyst should
contain both cellular genotypes. Combination of 8-cell embryos can result in the
chance exclusion of one genotype from the subsequent population of inner cells.
On the other hand, ensuring a mixture by injecting cells into the blastocoele
(Gardner, 1968) is technically difficult. However, aggregation of morulae a few
hours before the tight junctional seal is complete should ensure a contribution
from both genotypes, because at this time the inner cells have already been
segregated. From our observations, approximately 75 h after injection of the
donor females with HCG would seem to be the optimum time for apposition,
but it must be remembered that developmental schedules do differ between
strains.
Second, Hillman et al. (1972) have argued that blastomeres from early morulae
need to be on the inside of an artificially created composite for at least 8 h in
order to suppress their potential for differentiating into trophoblast. The sealing
of the trophoblast between 8 and 9 h before cavitation, as evidenced here, thus
allows 8 h for the determination of the inner cells to occur during normal development. This function for the tight junctional seal has been postulated by
Ducibelia et al. (1975).
Third, these results support the idea that the outer cells of the mouse embryo
begin to differentiate into an epithelium long before the blastocyst stage
(Ducibelia, 1977). The development of zonular tight junctions and the failure of
the outer cell surface to support cell spreading, are characteristics of epithelial
cells (Middleton, 1973; Vasiliev et al. 1975; DiPasquale & Bell, 1975; Elsdale
& Bard, 1975). It is likely that the new cell surface properties that prohibit cell
spreading are related to those which prevent premature attachment of the
embryo to the uterus following hatching from the zona pellucida (especially in
the case of delayed implantation). Later the embryo surface must change
again in preparation for attachment to the uterine lining (Holmes & Dickson,
1973; Mayer, Nilsson & Renius, 1967).
The preimplantation mouse embryo provides a unique system for studying
cellular aggregation. This system has the advantages (1) of using a completely
defined medium (2) of avoiding commonly used harsh enzymatic procedures
which alter cell-cell relationships and adhesion, and, (3) of being able to return
the aggregated tissue to its normal environment in vivo to demonstrate that the
cells are still viable and capable of normal differentiation to produce pups.
We would especially like to thank Dr Everett Anderson and Dr John Biggers for encouragement throughout this study, and for their critical reading of the manuscript. We acknowledge
support from: National Institute of Child Health and Development (NICHD) Center Grant
HD 06645; NICHD Grant 1F22 HD 03103-02 (TD); Ford Foundation Training Grant
720-0369 (PSB).
154
P. S. BURGOYNE AND T. DUCIBELLA
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Properties of the trophoblast of mouse embryos
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APPENDIX
Maximum likelihood estimate of the time when morulae lose
their potential to aggregate
JOHN D. BIGGERS
Laboratory of Human Reproduction and Reproductive Biology,
Harvard Medical School, 45 Shattuck Street, Boston,
Massachusetts 02115, U.S.A.
Theoretical model
At a particular time after the injection of HCG the mouse morula loses the
ability to aggregate with another morula. The time varies from one morula to
another. If these times are normally distributed, the probability at time t of a
morula drawn at random being potentially able to aggregate with another is
given by:
^
\\"
{-(/-/0 2 /2^} dt,
(1)
where ft is the mean time that embryos lose their potential to aggregate and <r
is the standard deviation. (An alternative assumption is that the times are
lognormally distributed; in this case t in (1) is replaced by In t).
The ability of a morula to aggregate, however, can only be determined by
observing it aggregate with another morula that also possesses the potential to
aggregate. Thus the probability of a pair aggregating at time t is P2. At time t
let n pairs of morulae be drawn at random and placed in apposition, and let r of
the pairs aggregate. Then the probability of r pairs aggregating follows the
distribution:
(2)
Prob(r/n) = nll{r\(n-r)\}P2r(l -Pjn-r\
Let groups of embryos be tested at k different times, denoted by tt (i = 1,2...,
k), and let r,- pairs out of nt aggregate at each of these times. Then the maximum
likelihood estimates of [i and a are those which maximize
V = S
This function is different from that maximized in standard probit analysis
(Finney, 1971) because the parameter of (2) is P2 rather than P.
156
P. S. BURGOYNE AND T. DUCIBELLA
Table 1. Number of pairs ofmorulae of different
ages that aggregate in vitro
Time after
HCGfo) (h)
75-5
77-25
79-25
81-25
82
84
No. pairs
tested (tu)
No. pairs
aggregated (r{)
Proportion
aggregated (/?<)
15
11
12
11
19
19
15
8
4
6
3
2
100
0-73
0-33
0-55
016
011
Table 2. Estimates of the mean (ja), standard deviation (<r) and fiducial
limits of error (P = 0.05) of the mean assuming the times the morulae
lose the ability to aggregate are normally distributed
Time after HCG
(h)
Mean O)
Standard deviation
Fiducial limits of error of the mean (P = 005)
81 1
216
79-2-83-0
Computational method
Expression (1) can be rewritten as
Y = a —fit,
where 7 is the probit of P (Finney, 1971). The parameters a and /? are related to
li and a, by
* =w 1
(3)
It is advantageous to determine estimates of a and /?. The maximum value of L'
was determined using a lattice search procedure (Lee, unpublished) that involves
the repeated calculation of L' for several combinations of values assigned to a
and p. Initial estimates were obtained by fitting a linear regression between the
probit of the square root of the observed proportions of pairs that aggregated
and time after HCG administration. At the completion of the search the variance-covariance matrix of a and ft was^calculated as follows:
I SI//da
dLlda, d/Sl _
I-PL'I dad/3
-82L'ldp
\
Estimates of JLO and a were then computed using equation (3), and the fiducial
limits of error of JLI calculated using the formula derived by Fieller (1944).
Properties of the trophoblast of mouse embryos
157
RESULTS
The mean time that embryos lose the ability to aggregate and the standard
deviation have been estimated from the data of Table 1, assuming both the
normal and lognormal distributions. There were no large differences between
the estimates obtained by the two models and therefore only the results assuming the normal distribution are presented (Table 2). Unfortunately, satisfactory
goodness of fit tests could not be done because the expected number of pairs
aggregating or not aggregating in the groups are too small for the valid application of the x2 test (Finney, 1971). The estimated values of/t and a were then
inserted in equation (1) to calculate P, and hence P 2 , as a function of time. The
estimated curve is shown in Fig. 2 in the main text. Note that although P is a
symmetrical function of t, P2 is an asymmetrical function of t.
I am indebted to Dr Eddington Y. Lee for assistance in writing the program used in the
analysis of the data.
REFERENCES
E. C. (1944). A fundamental formula in the statistics of biological assay, and some
applications. Q. Jl Pharm, Pharmac. 17, 117-123.
FINNEY, D. J. (1971). Probit Analysis, 3rd edn. Cambridge University Press.
FIELLER,
EMB 40