/. Embryo/, exp. Morph. Vol. 28, 2, pp. 449-462, 1972
Printed in Great Britain
449
The role of water-regulating
mechanisms in the development of the haploid
syndrome in Xenopus laevis
By LOUIE HAMILTON 1 AND P. H. TUFT 2
From the Department of Zoology, Edinburgh University
SUMMARY
The uptake of water by haploid and diploid sibling embryos of Xenopus laevis has been
investigated by measuring the density changes which occur during the development of intact
embryos from the blastula to the late tail-bud stage, and of explants from which most of the
presumptive endoderm has been removed.
The results show that up to the mid-gastrula stage there is no difference between the haploid
and diploid embryos; but from then on, whereas the diploid volume increases steadily, the
haploid gastrulae undergo a series of cyclical volume changes due to loss offluidthrough the
blastopore. It is concluded that this is the result of an excessive inflow of water through the
haploid ectoderm, because it was found that the volume of haploid ectodermal explants
increased much more rapidly than the volume of similar diploid explants. Excessflowthrough
the haploid ectoderm also accounts for other characteristics of the haploid syndromemicrocephaly and lordosis.
It is suggested that it is the doubling of the cell number in haploid embryos with the
consequent 25 % increase in aggregate cell membrane area which accounts for the difference
between the uptake of water by the two types of embryos. It is also suggested that changes in
the rate of water flow through the ectoderm and endoderm which are thought to account for
the accumulation of water in the blastocoel and archenteron in the normal diploid embryo
arise in a similar way.
INTRODUCTION
The majority of haploid embryos of Xenopus laevis develop into larvae which
show a characteristic syndrome - large accumulations of water occur under the
skin, the nerve cord is short, the brain is small, and there is considerable lordosis.
A study of the very few haploid embryos which do not show this syndrome led
Fox and Hamilton to conclude that the oedema is a result of an excessive inflow
of water through the ectoderm rather than renal failure, because they found that
in these embryos the kidneys were hypertrophied (Fox & Hamilton, 1964).
Accumulation of water in intercellular spaces, however, is a normal feature of
early development in the diploid embryo; water accumulates at an increasing
rate first in the blastocoel, a development of the cleavage cavity, and then in the
1
Author's address: Department of Biology as applied to Medicine, The Middlesex Hospital
Medical School, London, W.I, U.K.
2
Author's address: Department of Zoology, West Mains Road, Edinburgh, U.K.
450
L. HAMILTON AND P. H. TUFT
archenteron - a cavity formed by an invagination of the blastula surface and
lined by cells derived from the vegetal pole of the blastula. During the formation
of the archenteron the blastocoel decreases in volume and disappears.
It is therefore of some interest to know whether the factors which give rise to
the abnormal inflow of water through the haploid larval skin also affect the
uptake and distribution of water in the earlier stages of development. We have
accordingly carried out a series of experiments to determine the rate of water
uptake by decapsulated diploid and haploid siblings from the early blastula to
the late neurula stage, and also the water uptake of vesicles formed by blastula
explants from which most of the presumptive endoderm has been removed and in
which gastrulation does not occur. The results of these experiments indicate that
the rate of transcellular water flow in the presumptive ectoderm and endoderm
of the haploid embryo is abnormally high from the gastrula stage onwards
but only gives rise to abnormal volume changes in intact embryos during the
neurula stage.
MATERIALS AND METHODS
Embryos
The eggs were obtained from adult Xenopus laevis which were induced to
spawn by injection with chorionic gonadotrophin. The eggs were collected at
5 min intervals, and 10 min after laying half the eggs were irradiated with u.v.
light (2 x 10"4 J mm- 2 ) to produce androgenetic haploids (Gurdon, 1960). The
treated and control embryos were kept in crystallizing dishes in sterile tapwater at 25 °C in a thermostatic water bath. In what follows we shall assume
that irradiated embryos are haploid and we shall refer to them as such.
Density gradients
Linear density gradients of colloidal thorium oxide stabilized with dextrin
were made by upward displacement in parallel-sided glass tubes using a simple
gradient machine; the gradient tubes were then transferred to a glass-fronted
thermostatic bath at 25 °C (±0-001 °C). Details of the gradients are given in
Table 1.
The gradients were calibrated by measuring the position of glass density
standards that had previously been calibrated against droplets of KC1 solutions
in a brom-benzene/kerosene (Solve Esso 15) gradient set-up in a similar way
and saturated with water as described by Linderstrom-Lang & Lanz (1938).
Using this technique it is possible to make gradients 20 cm high with a density
range from top to bottom of 0-045gcm~3givingasensitivityof0-0002gcm~3mm~1
and linearity such that changes in density can be measured to ± 0-0001 g cm"3.
In experiments in which the embryos remained in the gradient throughout their
development, the oxygen tension was maintained by circulating oxygen or air
through loops of thin-walled polyethylene catheter immersed in the gradients.
The haploid syndrome in Xenopus
451
Table 1. Details of typical density gradient
1. Gradient tube: length 30 cm, diameter 2-5 cm.
2. Density medium:
Disperse phase - colloidal thorium oxide (5 nm) stabilized with dextrin ('Troka'
163 Henkel International)
Continuous phase - sterile tap-water
Conductivity - 5 x 10~5 Cr 1 cm"1 (^=0-2 mM electrolyte)
3. Method of formation - upward displacement
4. Height of gradient - 25 cm
5. Calibration: glass standards calibrated against KC1 solution in brom-benzene
kerosene gradient.
Position (cm)
Density
Bottom of gradient ...
80
1084
Density standard
9-3
10838±00002 gem- 3
(1)
1-0730
14-1
(2)
10606
19-8
(3)
10515
24-0
(4)
10438
27-8
(5)
10400
Top of gradient
33-0
6. Height of linear portion
18-7 cm
Sensitivity (density change per mm)
00002 gcm- 3
7. Temperature of water bath:: 25 ± 0-001 °C
Density measurements
In order to obtain the density data required to calculate the change in volume
of the haploid and diploid embryos three series of experiments were carried out.
In the first, successive batches of control and irradiated sibling embryos of
known age were decapsulated surgically in l/10th Holtfreter solution and their
density measured 10 min after they had been introduced into the density gradient.
In the second series, four or five haploid and diploid blastulae were placed
in identical gradients set up side by side in the thermostat bath. The gradients
were photographed at intervals of 15 min with an automatic 'Robot' camera.
The density of the embryos was determined by projecting the negative image of
the gradients on to a linear density scale using the calibration beads as reference
points.
In a third series of experiments the same technique was used to monitor the
density change of ectodermal explants from irradiated and unirradiated embryos.
In these experiments, the bottom third of stage 8 (Nieuwkoop & Faber, 1963)
sibling blastulae was removed with fine forceps. The remaining upper two thirds
were allowed to round up inl/lOth Holtfreter solution before being introduced
into the gradients. These explants formed stable vesicles whereas similar explants
from a stage 9 blastula containing more ectoderm tended to burst.
452
L. HAMILTON AND P. H. TUFT
The determination of changes in volume and water content
It can be shown that the volume changes which occur during Xenopus
development up to the early tail-bud stage are entirely due to changes in the
water content of the embryo as follows: the weight of the embryo in water, its
reduced weight (RWe) is a function of the mass of the embryo (We), its volume
(Ve) and the density of water at the same temperature (/?„.)•
RWe=We-VePw.
(1)
The density of the embryo (pe) is in turn a function of its mass and volume:
W
Pe = jr-
(2)
From (1) and (2) the reduced weight can be expressed in terms of its mass and
density,
A,
(3)
Pel
or as the sum of the reduced weights of its constituents ( S J R ^ ) and their
weights (Wi) and densities (pt) (Lovtrop, 1953):
RWe = ZRJVi = £ wJl-^\.
(4)
Since the reduced weight remains unchanged from cleavage to the early tailbud stage (Tuft, 1962) it follows from (4) that any change in density must be due
to the uptake or loss of matter with the same density as water.
The dry mass of the embryo would tend to decrease during development as
the result of a loss of solutes and the oxidation of respiratory substrates. The
former is so small that it cannot be detected (unpublished data) and the latter,
which is also small, can be estimated from the oxygen consumption of the
embryo. The rate of oxygen consumption rises gradually during development of
the Xenopus embryo, reaching 4-8 x 10~4ml h" 1 per embryo during the late
neurula stage (Tuft, 1953). If we assume that 1 g of respiratory substrate
(p = 1-000) involves the uptake of 1-0 x 103 ml O2 then weight will be lost at the
rate of 4-8 x 10~4 mg h" 1 ; thus for an embryo with a density of 1 -050 g cm"3 and
reduced weight of 0-0879 mg, the density will increase at a rate of 1-4 x 10~5g
cm"3 h"1. This is below the limit of resolution of the density measuring technique
we have used.
The relative change in volume of the embryo or its water content (VtIVQ) can
then be calculated from the density of the embryo at t = 0 (p0) and t (pt) and the
density of water (pw) as follows.
The haploid syndrome in Xenopus
From equations (1) and (2):
v
o=——,
453
(5)
Pt — Pw
Y_t _ Po ~Pw
v
0
Pt
/n\
Pw
RESULTS
Morphological differences
Examples of the morphological differences between haploid and diploid
embryos from the blastula stage to late gastrula are illustrated in Fig. 1. As will
be seen, there is very little difference between the anatomical appearance of the
two kinds of embryo except that onset of gastrulation is delayed in the haploids
and, by the time it does begin, the haploid blastocoel is very much larger than
that in the corresponding diploid embryo. The preparations also show that the
dorsal lip of the blastopore is less tightly applied to the yolk plug and that the
archenteron contains less fluid in haploids.
Density changes
Intact embryos
The results of the first series of experiments, in which the densities of embryos
in a series of different age-groups were measured, showed that up to the late
blastula stage there was no significant difference between the irradiated and
control groups, but during the late gastrula and neurula stages the two groups
differed considerably. The densities of the irradiated group were more variable
than the control group and had a significantly higher mean density. However,
after the control embryos had collapsed and the archenteron had emptied, the
difference between the mean densities was again insignificant.
In the second series of experiments the embryos were allowed to remain in the
gradient throughout their development and the density was monitored at 15 min
intervals. The results of one such experiment are is shown in Fig. 2, where the
density changes which took place in each embryo are shown. It will be seen that,
as before, the density of both haploid and diploid embryos decreased uniformly
until the late gastrula stage. The diploid densities then continued to decrease
steadily until the archenteron collapsed at 22 h, except for a brief transient increase at stage 13 when the yolk plug is withdrawn. The density of the haploid
embryos on the other hand went through a series of cyclical changes of varying
amplitude which lasted from the mid-gastrula to the late neurula stage.
Results from all experiments in the second series have been pooled and the
mean density of all embryos of the same age has been calculated. The samples
454
L. HAMILTON AND P. H. TUFT
Diploid
Be
Haploid
Fig. 1. Drawings of half embryos arranged to illustrate the difference between the
rate of morphological development in haploid and diploid embryos of Xenopus
laevis. Each haploid embryo in the left-hand column was the same age as the
corresponding diploid embryo in the right. Aa = Archenteron, Be = blastocoel.
were tested for homogeneity, and where the F value at the 5 % level was not
significant the difference between the mean values of treated (androgenetic
haploids) and control groups (diploids) was tested using a two tailed t test.
When the variances of the samples were not homogeneous, a non-parametric
test was used.
The results of this analysis given in Table 2 confirm the results of the earlier
The haploid syndrome in Xenopus
455
107
o
Q
'
Q
.o
. 0 Q/ > a x>.goo< )
'0"0 i A * '
106
105
104
10
12
14
16
18
20
Age (h)
Fig. 2. The density of four haploid and four diploid embryos developing in a density
gradient at 25 °C, measured at 15 min intervals, plotted against age.
experiments; they also show that from 24 h to 48 h the mean density of haploid
and diploid embryos does not differ significantly. The relative volume changes
(Vt/V0) calculated from the mean density values in Table 2 are shown in Fig. 3.
Open embryos
Density measurements on embryos which have been operated on in such a way
that the blastocoel and archenteron are open to the environment ('opened
embryos') show that at the early and mid-gastrula stage the mean density of the
haploid cell mass is significantly less than that of the corresponding diploid cell
mass. The difference, however, is small and represents an increase in volume of
about 4 % (Table 3). Measurements made at later stages suggest that this difference does not persist.
Animal pole explants
Attempts to compare the volume changes of vesicles made from the roof of
the late blastulae failed because, although they formed vesicles, they were unstable, going through a series of cyclical density changes and finally disintegrating.
However, when stage 8 embryos were used and only the vegetal third of the
blastula was removed - that is to say, most of the presumptive endoderm - the
vesicles were more stable and behaved very much like normal embryos except
that they did not gastrulate.
The relative volume changes VtIVQ of explants of the latter type calculated
456
L. HAMILTON AND P. H. TUFT
Table 2. The difference between the density of diploid and haploid embryos at
different ages
Diploid
Difference
between
Haploid
ivitauj
Mean p
No.
S.D.
Mean p
No.
S.D.
10663
1-0642
10603
10587
10542
10544
10506
10481
10486
10444
10527
1-0579
10577
10517
10415
1-0448
50, 50± 10410
53
10413
70, 701 1-0329
20
26
33
36
37
36
32
36
30
33
28
33
13
5
13
24
20
00018
00029
00040
00034
00059
00052
00053
00043
00055
00049
00080
00050
00046
00033
00039
00030
00031
00017
00039
10657
1-0643
10608
10595
10602
10600
10581
10576
10586
1-0585
10597
10598
1-0571
10534
10450
10461
1-0449
10400
1 0297
16
22
35
34
32
30
31
30
30
29
28
29
00015
00033
00033
00068
00061
00058
00065
00052
00067
00058
00052
00055
00070
00016
00033
00045
00023
00025
00058
Age
10
12
14
16
17
18
19
20
21
22
23
24
27
36
46
48
14
21
12
5
12
17
12
12
15
Odip-Phap)
t
+ 00006
0-85
-00001
0-37
-00008
0-58
-00008
0-59
400
-00059
409
-00056
-00075
4-93
800
-00095
-00100
6-44
-00141
10-25
-0-0070
3-81
-00019
1-46
+ 0-0060 (d = 0-25)
102
-0-0017
-00035
2-43
116
-00013
3-73
-00039
+ 0-0013
1-49
203
+ 00032
D.F.
P
cance
34
44
66
68
67
64
61
64
58
60
54
60
23
8
23
39
30
0-4
0-8
0-6
0-5
NS
NS
NS
NS
S
< 0-001
< 0-001
< 0001
< 0001
< 0001
< 0001
< 0001
0-1-0-2
24
0-001
0-1-0-2
34
01
NS
0025
0-3
11 -
14
16
18 20
Age (h)
22
s
s
s
s
s
NS
NS*
NS
NS
NS
S
NS
0-3
NS = not significant.
S = Significant.
* Non-parametric test.
12
s
24 26
Fig. 3. The relative volume change (Vt/V10) of haploid and diploid embryos from the
age of 10 to 27 h at 25 °C calculated from the mean densities in Table 2.
The haploid syndrome in Xenopus
457
Table 3
Mean density
of open embryos
Difference,
<
Stage
Haploid
Diploid
Pdip ~~ Phap
D.F.
Hi
1-0723
10698
10683
10752
10719
10686
+ 00029
+ 00021
+ 00003
23
7
11
24-25
t
P
Mean haploid volume
Mean diploid volume
3-815 < 0001
0025
2-884
0-272
0-8
1039
1029
100
1-9
1-8
1-7
1-6
Diploid
vesicles
Haploid
vesicles
'- 5
1-4
1-3
1-2
11
10
1
2
3
4
5
6
7
8
9
10
II
12
13
14
15
Hours
Fig. 4. Changes in the relative volume (Vt/V0) of vesicles formed by blastula explants
from which most of the vegetal pole material has been removed. Calculated from the
density of each vesicle measured at 15 min intervals after it was placed in the density
gradient.
from equation (7) are plotted against time in Fig. 4. This shows that the relative
volume of haploid explants increases more rapidly and they reach their maximum
sooner than the diploids.
DISCUSSION
The first thing to note about the results obtained in the present experiments is
that the density/time curves for the diploid embryos differ from those previously
published (Tuft, 1962, 1964). They do not show a decrease in rate of density
change during gastrula stages and the collapse of the late neurula occurs 22 h
rather than 18 h after fertilization. These differences are the result of the way in
which the data for the density/time curves were obtained in the two series of
experiments.
458
L. HAMILTON AND P. H. TUFT
In the earlier experiments embryos were decapsulated surgically immediately
before their density was measured and the curves constructed from the mean
densities of the different age-groups. In the present experiments, on the other
hand, the curves are based on successive measurements of the density of individual embryos after decapsulation at the late blastula stage.
Deformation of the embryo during removal of the capsule at the gastrula
stage is responsible for the apparent decrease in the rate of density change in the
earlier experiments because it tends to cause a loss of fluid from the newly
formed archenteron before the blastopore is tightly closed. This tends to increase
the mean density of embryos at this stage. At later stages when the blastopore is
tightly closed loss of fluid is less likely to occur.
In encapsulated embryos the elasticity of the capsule opposes the elongation
of the notochord and long axis of the embryo at the late neurula stage. As
a result, when the embryo loses its lateral stability it jackknifes, causing a sudden
and complete emptying of the archenteron cavity. In decapsulated embryos, on
the other hand, there are no external forces acting on the embryo, and under these
circumstances the only forces tending to raise the pressure inside the archenteron
are elastic forces developed in the body wall itself as the embryo elongates. These
forces take longer to develop sufficient pressure to collapse the archenteron.
Nevertheless, monitoring the density of naked embryos after decapsulation at
the blastula stage reveal important differences in the uptake of water by haploid
and diploid embryos. The density/time curves of the kind illustrated in Fig. 2?
for example, show that from the blastula until the mid-gastrula stage, density
changes in the two types of embryo do not differ significantly, and this is confirmed by the combined results in Table 2. The net accumulation of water must
therefore be the same in both types of embryo (see above). This does not
necessarily mean, however, that its distribution within the embryo is the same.
From Table 3 it will be seen that the density of the cell mass in haploid embryos
tends to be slightly less than in the diploid - that is, its volume is greater and the
volume of the large intercellular spaces smaller. The morphological data, on the
other hand, suggest that when gastrulation begins in the haploid (Fig. 1) the
blastocoel is in fact enlarged. These two observations are not incompatible,
because when haploids reach this stage the archenteron in the diploids has already begun to form, and it is not possible to distinguish between density changes
due to water accumulating in the blastocoel and in the archenteron from the
density of the intact embryo alone.
From the mid-gastrula stage onwards, however, the two types of embryo
behave very differently (Table 2). Whereas the mean density of the haploid
embryos remains more or less constant, the diploid density decreases continuously from 14 to 23 h. The density/time curves of individual embryos (Fig. 2)
show that the difference between the two types of embryo is even more striking;
the haploid neurulae, unlike the diploid neurulae, undergo a series of cyclical
density changes which are the result of successive filling and emptying of their
The haploid syndrome in Xenopus
459
archenterons. After 23 h, however, there is again no significant difference between mean density of the haploid and diploid embryos; that is to say, there is
no difference between their volumes. This also appears to be true for subsequent
stages in spite of the fact that haploid embryos look very abnormal, with large
water-filled cavities under the skin. However, the procedures used at these stages
to immobilize the embryos may alter their water content. For this reason we will
only consider the differences between haploid and diploid embryos in the precollapse stages.
For reasons that have been given in earlier papers (Tuft, 1962, 1964) it has
been suggested that water-regulating mechanisms in the cell membranes maintain the relatively constant cell volume observed during the early stages of
development, and are so arranged that they also give rise to a net transcellular
inflow of water through the animal pole and a net outflow through the vegetal
pole of the blastula. The difference between the magnitudes of these two flows
results in an accumulation of water in the blastocoel. But when, subsequently,
the derivatives of the vegetal pole cells come to line the archenteron cavity, as
a result of invagination, both flows are directed inwards and give rise to a very
rapid increase in the volume of the archenteron cavity (Tuft, 1962). This is
illustrated diagrammatically in Fig. 5.
If this hypothesis is correct then the difference between the behaviour of the
haploid and diploid embryos could be explained in one of two ways: either the
blastopore lips in the haploid neurulae are weakened in some way and are unable
to withstand the normal pressures developed within the archenteron by a normal
inflow of water, or alternatively the net inflow across the haploid ectoderm and
endoderm is abnormally high and the blastopore lips cannot withstand the
excess pressure developed.
The behaviour of animal pole explants enables us to distinguish between these
two alternative explanations. It will be recalled that in these experiments most
of the vegetal (that is, endodermal) surface of the blastula was removed and the
remaining portion, comprising mainly presumptive ectoderm, was allowed to
round up. It will be seen from the results illustrated in Fig. 4 that the volume of
vesicles formed by haploid explants increased very much more rapidly than the
volume of similar diploid vesicles, and after reaching a maximum also decrease
more rapidly, suggesting that both the inflow and outflow are increased.
The decrease in volume is not due to bursting of the vesicle, because the rate
of change is too small, but probably results from an increase in the net outflow
of water due to the growth of vegetal pole material left in the explants when they
were made. This is consistent with the observation that diploid vesicles take
about 6 h to empty whereas in intact diploid embryos, which have more vegetal
pole surface, the blastocoel empties in 3 h.
These experiments demonstrate that the flow through the haploid ectoderm is
greater than that through the diploid, and it follows from what has been said
earlier that the flow through the haploid endoderm is also greater. We can con30
EMB 28
460
L. HAMILTON AND P. H. TUFT
>'•
-V
Blastula
*
-V
Mid-blastula
Early gastula
Neuruki
Fig. 5. Diagram to illustrate the net water flows through presumptive ectoderm and
endoderm in the Xenopus embryo at different stages in its development after Tuft
(Tuft, 1962). Aa = Archenteron; Be = blastocoel.
elude therefore that the successive filling and emptying of the intact haploid
archenteron is at least in part the result of an increased inflow of water.
It is interesting to note that an increased inflow through the ectoderm could
also account for dorsal flexure and microcephaly - two other characteristics of
the haploid syndrome. The neural tube is formed by invagination of the neurectoderm, and in the normal diploid embryo it is flexed ventrally at first, but as
water is removed from its lumen it straightens out. An increase in this outflow
would therefore be expected to maintain a very much reduced neural volume.
The haploid neurulae differ from the diploid in one other important respect
- they have twice as many cells, and the cells are half the size of those in the
diploid. Although the aggregate cell volume is the same in both haploid and
diploid embryos, doubling the cell number gives rise to an increase of 25 % in
the aggregate cell surface area in the haploids. (See Appendix.)
If the hypothesis outlined earlier is correct, an increase in cell number will
therefore increase the number of water-regulating sites responsible for the net
transcellular water flows across the ectodermal and endodermal cells.
The explant experiments lend support to this view. It will be recalled that the
explants used in these experiments, which consisted of all the presumptive
ectoderm and a little of the endoderm, were made at the mid-blastula stage and
were allowed to heal before being introduced into the density gradient. That is
to say the measurements began when the intact embryo would normally be at
stage 9. At this stage the rate of cell multiplication in diploid embryos decreases
rapidly until it reaches the relatively low rate characteristic of later stages in
development. In haploid embryos on the other hand the high rate of division
characteristic of the earlier stages is maintained for about an hour until the cell
number has been doubled, after which the rate becomes the same as the diploid.
The aggregate cell surface in the haploid explants will therefore tend to
increase very much more rapidly than it does in the diploid, and, if our hypothesis is correct, the explants should reach their maximum rate of volume change
sooner than the diploids, which, as we have seen, is exactly what the experimental
results show (Fig. 4).
The haploid syndrome in Xenopus
461
We may therefore conclude from these experiments that the abnormal development of the haploid embryo, like that of the tadpole described by Fox &
Hamilton (1964), is the result of an excessive inflow of water. Furthermore if, as
has been suggested, the uptake of water by the embryo involves water-regulating
sites in the cell membranes, the excess flow into the haploid archenteron can be
attributed to the increase in total cell membrane area which is a consequence of
doubling the number and halving the size of the cells at the late blastula stage.
Changes in the relative rate of water flow through the presumptive ectoderm
and endoderm which are thought to account for the accumulation of water in
the blastocoel and archenteron of the normal diploid embryo may arise in
a similar way. Thus during the formation of the blastocoel the rate of cell
division in the presumptive ectoderm is very much greater than it is in the
endoderm, whereas the reverse is true during gastrulation and formation of the
archenteron. If this is so the simple model put forward to account for the uptake
and distribution of water by the Xenopus embryo in earlier papers (Tuft, 1962,
1964) will have to be modified and detailed information obtained about the
ultrastructure and dimensions of the cells in the two layers.
APPENDIX I
Effect of cell number on total area of cell membrane
The aggregate cell surface area A in an embryo consisting of nx cells and
having a total cell volume V can be calculated as follows: let vl5 rx, ax be the
volume, radius, and area respectively of the individual cells. Then assuming the
cells are spherical,
vi = I = W ,
/ 1V \ -2-
1 - 4^)*.
(1)
(3)
Then the aggregate surface area
A x = n xa x
(4)
Ax = /ii(47r)4(3K)*.
(5)
and from (3) and (4)
Similarly, for an embryo with the same volume V but with «2 cells,
A% = 4(4ar)*(3F) f •
(6)
The ratio of the aggregate cell surface area in the two embryos from (5) and (6)
is then
A2
\n2)
(7)
462
L. HAMILTON AND P. H. TUFT
For diploid and haploid embryos where F h a p = F dip and « hap = 2« dlp ,
A
=2*.
(8)
•A,'dip
This work was carried out in the Department of Zoology, University of Edinburgh. We
would like to thank Professor Mitchison for the facilities provided, Mr Holmes who did the
illustrations, and Mrs Ann Muir for technical assistance. One of us, P. H. Tuft, also wishes
to thank the Distillers Company for the grant in aid.
REFERENCES
Fox, H. & HAMILTON, L. (1964). Pronephric system in haploid and diploid larvae of Xenopus
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LINDERSTROM-LANG, K. & LANZ, H. (1938). Studies on enzymatic histochemistry. XXIX.
Dilatometric micro-estimation of peptidase activity. C. r. Trav. Lab. Carlsberg, (Chim.) 21,
315-338.
L0VTROP, S. (1953). Energy sources of amphibian embryogenesis. C. r. Trav. Lab. Carlsberg
28, no. 14, 372-396.
NIEUWKOOP, P. D. & FABER, J. (ed.) (1956). Normal Table of Xenopus laevis (Daudiri).
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TUFT, P. H. (1953). Energy changes in development. Archs. neerl. Zool. 10, (Suppl 1), 59-75.
TUFT, P. H. (1962). The uptake and distribution of water in the embryo of Xenopus laevis.
J. exp. Biol. 39, 1-19.
TUFT, P. H. (1964). The uptake and distribution of water in the developing amphibian embryo.
Symp. Soc. exp. Biol. no. xix, pp. 385-402. Cambridge University Press.
{Manuscript received 20 March 1972)