/ . Embryol. exp. Morph. Vol. 29, 2, pp. 311-330, 1973
Printed in Great Britain
Evidence of morphogenetically
significant diffusion gradients in Hydra viridis
lengthened by grafting
By STANLEY SHOSTAK 1
From The Department of Biology, University of Pittsburgh
SUMMARY
Morphogenetic inhibitory gradients were produced in Hydra viridis having 2-5 gastric
regions or 2-5 peduncles grafted in tandem. The frequency of head regeneration at graft
borders changed as a function of distance from the terminal head, and the frequency of foot
regeneration changed as a function of distance from the terminal foot. The object of the study
was to characterize and compare these morphogenetic inhibitory gradients in light of Crick's
(1970) model of diffusion gradients.
Heads regenerate more easily on gastric regions and feet on peduncles. This is shown in
several ways: (1) on gastric regions more heads and fewer isolated tentacles and 'spikes'
(isolated hypostomes) form, while the opposite is true on peduncles; (2) more heads are
regenerated at graft borders between gastric regions than at those between peduncles at
comparable distances from the terminal head, while more feet are regenerated at graft borders
between peduncles than at those between gastric regions at comparable distances from the
terminal foot; (3) the Y intercepts for gradients of the frequencies of head and of foot regeneration as functions of distance (which are the theoretical frequencies of regeneration at the ends
of the animal) are higher for head regeneration on gastric regions than on peduncles, and for
foot regeneration on peduncles than on gastric regions. This is explained in terms of relative
differences in either competence to regenerate or sensitivity to inhibitors.
The slopes of the frequencies of head and of foot regeneration as functions of distance
from the respective ends change inversely with the numbers of gastric regions and peduncles
grafted. This is explained in terms of changes in the distance between the sources of diffusible
inhibitors and the sinks which use them up. The results are taken to support Crick's model
in which a linear gradient of a diffusible substance is produced between its source and sink.
INTRODUCTION
Crick's (1970) model which was 'to make the idea of diffusion gradients
respectable to embryologists' is particularly welcome because features of it can
be tested. The problem Crick confronts is that theoretically a steady-state
distribution of a diffusible material in a fixed space is not gradated, but is uniform.
His model connects diffusion to gradients by providing a source of the diffusible
material separated by some distance from a sink where the material is used up
1
Author's address: Department of Biology, University of Pittsburgh, Pittsburgh, Pa. 15213,
U.S.A.
312
S. SHOSTAK
or degraded. Diffusion of the material then produces a linear gradient in the
concentration of the material between the source and the sink.
Two consequences of the model are crucial for the proposed test, namely (1)
the slopes of gradients in the steady state must be inversely proportional to
distance between the source and the sink; (2) each source and sink must have a
basis in structure. If the model is correct, and were it possible to change the
distance between a source and a sink experimentally, then the slopes of the
gradients produced at the different distances would change in an inverse ratio to
distance.
The difficulty in testing Crick's model arises in translating these physical terms
to biological ones. Above all, there is the problem of relating gradients of
diffusible substances to gradients of biological activities.
The freshwater coelenterate Hydra has many features which recommend it as
a test system for Crick's model. First, not only does the animal regenerate its
head (ring of tentacles and hypostome) and foot (basal adhesive disc) at its
terminal ends, as is well known, but it can also regenerate similar structures
subterminally (secondary structures) under particular conditions. Secondly, the
corresponding parts of different animals can be readily grafted together to form a
single composite animal with essentially normal morphology at first except for
increased length (multiple-grafted animal). It is at the borders between these
grafted parts (graft borders) that secondary heads and feet can form (King,
1901; Tardent, 1954, 1960). Moreover, the frequencies with which secondary
heads and feet form at graft borders in multiple-grafted animals are directly
proportional to the distance from the ends of the animals bearing the corresponding terminal structures (Shostak, 1972).
Although statistics are generally not employed, the preponderance of experimental evidence supports the existence of diffusible inhibitors, particularly of a
head inhibitor produced in the vicinity of the hypostome (Burnett, 1961, 1966;
Webster, 1966, 1971; Wilby & Webster, 1970; Wolpert, Clarke & Hornbruch,
1972). Where statistics are employed it has been shown that foot regeneration at
graft borders in the peduncle is significantly inhibited by the presence of the
animal's terminal foot (MacWilliams & Kafatos, 1968; MacWilliams, Kafatos
& Bossert, 1970; but also see Shostak, 1972), and head regeneration at graft
borders between gastric regions in animals lengthened by the addition of a
gastric region is significantly inhibited by the presence of the animal's terminal
head (Shostak, 1972).
Anti-parallel morphogenetic inhibitory gradients of head and of foot formation have long and continuously been hypothesized to exist in Hydra (Hyman,
1928; Goetsch, 1929; Burt, 1934; Child, 1941; Mookerjee, 1963; Sinha, 1966;
Wolpert, 1971; Shostak, 1972). In light of Crick's model, one would theorize
that two sources - an apical one in the vicinity of the terminal head and a basal
one in the vicinity of the terminal foot - produce a head inhibitor and a foot
inhibitor, respectively. These would prevent the morphogenesis or regeneration
Diffusion gradients in hydra
313
of secondary heads and feet elsewhere on the animal. The sinks for the diffusible
inhibitors would then be located near the opposite ends of the animals, and the
head inhibitory gradient and the foot inhibitory gradient would stretch between
the sources and the sinks.
The link between the experimental evidence for diffusible inhibitors and hypothetical morphogenetic inhibitory gradients has remained open, however,
because few actual quantitative gradients have been available for study. The
present report rectifies this deficiency.
Morphogenetic inhibitory gradients, defined operationally as the changing
frequencies of head and of foot regeneration along the lengths of elongated
animals, were obtained in animals having equivalent body regions grafted in
tandem. Animals with multiple grafts of 2-5 gastric regions or peduncles were
employed. Comparison of these gradients answered the questions of whether
lengthening animals to different extents changes the slopes of the gradients
inversely with the number of grafted pieces, and, by implication, whether the
distances between sources and sinks of the diffusible inhibitors also change.
The results show that the slopes of the morphogenetic inhibitory gradients
do, indeed, change inversely with the number of grafted pieces, thereby supporting the concept of diffusion gradients with morphogenetic inhibitory activity
operating in Hydra. Furthermore, the source of and sink for the head inhibitor
are tentatively identified as the gastric and budding regions adjacent to the
terminal head, and the peduncle adjacent to the terminal foot, respectively. The
source of and sink for foot inhibitor, however, eluded efforts to narrow them
down consistently to particular structures or levels of the animals.
In practice, this project was complicated by what is interpreted as differential
competence to regenerate heads and feet, and differential sensitivities to inhibition on the gastric regions and peduncles. Nevertheless, these results support
Crick's model on animals with multiple gastric region grafts and on those with
multiple peduncle grafts.
MATERIALS AND METHODS
Animals were cultured and grafts were made with the procedures previously
described (Shostak & Kankel, 1967). In each case, animals used in grafting had
at least two buds. The types of grafts made are described in Figs. 1 and 2.
Extreme care was taken to retain the polarity of each piece during the grafting
process. Grafts between gastric regions remained on the grafting hairs for at least
3 h and as long as 6 h to ensure healing. Grafts between peduncles remained on
the grafting hairs for one hour which was sufficient in these cases.
Data were only taken from animals whose graft borders were intact one day
after grafting. Any border which had ruptured at that time disqualified the
entire animal from consideration.
The first-order regression equations were calculated by the method of least
squares and the probabilities of fit by the t test.
314
S. SHOSTAK
Host
Graft
Donors
Fig. 1. Illustrates the grafting procedures and nomenclature for the results summarized in Table 1. Each row shows another combination of multiple gastric region
grafts, the names of which are given above the arrows connecting the host and donor
animals (left) with the graft (right). The presence of normal and untraumatized
parts of the animals are not mentioned in the names, only what distinguishes the
graft from normal. The dashed lines passing through the host and donor animals
and extending on both sides indicate where they were cut to provide the parts for
each type of graft. The ' graft' column indicates how the parts were assembled. The
animals and their parts are drawn proportionally to the lengths of these as
described by Shostak (1968) with a scale of 16:1. The head is represented by two
symbolic tentacles lying at right angles from the pointed apical end (hypostome).
The budding region is represented by a triangle protruding to the left of each animal.
The gastric region is the part of the animals between the head and budding region.
The feet of the hydras are symbolized by the bold lines at their lower ends. The
peduncle is the part of the animals between the budding region and foot. For
identifying the parts of a graft the letter 'g' is used for gastric region. The host is considered the part containing an original budding region and its gastric region is number
one (1). The adjacent gastric regions are numbered consecutively. These designations
correspond to those used in Table 1.
RESULTS
A. Regeneration of secondary structures and scoring
When Hydra viridis is lengthened by the addition of gastric regions or
peduncles in tandem (Figs. 1,2), heads, feet, and budding regions may regenerate
in the vicinities of the different graft borders. These regenerates are referred
to as secondary structures. The frequencies with which they appear on any of
the grafted pieces comprising a composite animal are listed in Tables 1 and 2.
Diffusion gradients in hydra
Host
315
Donors
FIGURE 2
Illustrates the grafting procedures and nomenclature for the results summarized in
Table 2. Each row shows another combination of multiple peduncle grafts, the
names of which are given above the arrows connecting the host and donor animals
(left) with the graft (right). (See the caption for Fig. 1 for explanation of graphic
representations and terms.) For identifying the parts of a graft the letter ' p ' is used
for peduncle. The host is considered the part containing an original budding region
and its peduncle is number one (1). The adjacent peduncles are numbered consecutively. These designations correspond to those used in Table 2.
Frequencies refer to the number of grafted pieces scored as having the secondary
structure in question divided by the total number of grafted animals of the
particular type. The identification of the graft pieces in Figs. 1 and 2 correspond
to the nomenclature used in Tables 1 and 2, respectively. What follows is a
description of the secondary structures and how they are scored.
The regenerated secondary head (h in Figs. 3 and 4) does not emerge around
the entire circumference of the graft border. Rather the head appears at a point
on the border. The axis of the head is perpendicular to the main axis of the
animal. Occasionally two secondary heads appear at the same graft border, but
these are scored here as only one.
In some cases only secondary tentacles form, or what appear to be elongated
hypostomes which may possess one to two tentacles. These are referred to as
spikes (Fig. 4). The frequencies with which spikes and secondary tentacles
appear are listed in the tables, and the sums of frequencies of secondary heads,
316
S. SHOSTAK
FIGURE 3
Diffusion gradients in hydra
317
tentacles and spikes are listed in the rows entitled 'total'. The object in taking
this sum was to acquire an index of total head-forming activity, in a sense giving
credit for effort even when only a part of a head (hypostome or tentacle) was
produced.
A single graft piece occasionally has more than one of these types of secondary
structures appearing on it. Thus the 'total' of the frequencies can exceed 1-0
(i.e. 100% of the animals). The 'total' should not be understood to mean that
some secondary structure necessarily occurred on that fraction of the grafted
pieces, since more than one type of head structure might have formed on a piece
on one animal and none on this same piece on another animal.
The type of secondary foot formed differs as a function of the graft border
involved, but feet were not scored by types (comparable to secondary heads,
tentacles and spikes). In all cases secondary feet appear by the day after grafting.
The foot regenerated at the base of the host peduncles (p-1, see Fig. 2) is
frequently formed around the entire graft border, having the appearance thus of
a swollen sticky annulus (Fig. 4, /basal to arrow no. 1). At other graft borders,
secondary feet are more often perpendicular protrusions (/in Figs. 3 and 4) from
the basal end of the apical grafted piece. When these protrusions begin small,
particularly on gastric regions (Fig. 3), they can be reduced to only a sticky
patch on the surface of the grafted pieces after one or two days.
Budding regions also regenerate (Fig. 3). The problem of distinguishing
between a secondary head and a bud forming in a budding region is resolved by
making observations on each of the three consecutive days following grafting.
A secondary head appears as a small outpocketing with rudimentary tentacles
on the first day, and a well-formed head capable of ingesting prey on the second
FIGURES 3 AND 4
These are examples of grafted animals with either five gastric regions (5 g) or five
peduncles (5 p), respectively. The terminal head is identified by H, the host budding
region (Fig. 4) by BR, and the terminal foot by F. Regenerated secondary structures
are identified by lower case letters, h for head, b for budding region, and/for foot.
Arrows with numbers point to the different grafted pieces and identify them
according to the numbering scheme used in Figs. 1 and 2 and Tables 1 and 2. The
animals were photographed on the second day after grafting. About x ] 5.
Fig. 3. This 5 g animal has a typical distribution of secondary structures. An early
bud on the original budding region on the host piece is turned away in the view seen
and is not identified in the Fig. It appeared, however, at about the level of the first
arrow. This host piece bears a secondary head (/?)• The next gastric region (g-2,
arrow no. 2) has a budding region (b) basally and secondary head (h) apically. The
third gastric region (g-3, arrow no. 3) has a secondary foot (/), a secondary budding
region (b), but no head. The fourth gastric region (g-4, arrow no. 4), likewise, has a
secondary foot (/), and a secondary budding region (b), and no head. The last
gastric region (g-5, arrow no. 5) has only a secondary foot (/). The differences in the
apparent lengths of these grafted gastric regions is in large part due to the different
states of stretching vs. contraction that the pieces were in at the time the animal was
photographed.
21
E M B 29
318
S. SHOSTAK
FIGURE 4
This 5 p animal illustrates the types of secondary structures formed, but does not
have all of them in typical distributions. The host peduncle (p-1, arrow no. 1), as
typical, has a secondary foot (/) as does the next peduncle (p-2, arrow no. 2) (/). The
third peduncle (p-3, arrow no. 3), atypically, has a secondary head (h), and a
secondary foot (/). Peduncle four (p-4, arrow no. 4) has produced a partial head
which is called a spike (s) in the text, but no foot. The most basal peduncle (p-5,
arrow no. 5) has, as is typical, regenerated a secondary head.
319
Diffusion gradients in hydra
Table 1. Multiple gastric region grafts
Designation (see Fig. 1)
Symbol in Fig. 5
No. of animals
5g
Circle
49
Level and type of secondary structure
g-5
Secondary
g-4
Secondary
Spike
Secondary
(Total)
Secondary
g-3
Secondary
Spike
Secondary
(Total)
Secondary
g-2
Secondary
Spike
Secondary
(Total)
Secondary
4g
Square
76
3g
Triangle
73
2g
Diamond
123
Frequencies
foot
0-94
—
—
tentacle
0
0
004
(004)
0-67
—
—
—
—
0-86
—
—
—•
—
—
0
004
018
(0-22)
0-24
0
001
004
(005)
017
—
—
—
0-62
0
004
0-27
(0-31)
006
001
004
0-21
(0-26)
005
0
0
008
(008)
007
0-28
002
006
0-72
(0-80)
0
0
0-61
(0-61)
0
001
0-45
(0-46)
0
0
0-23
(0-23)
head
foot
tentacle
head
foot
tentacle
head
foot
8-1
Secondary tentacle
Spike
Secondary head
(Total)
•
—
—
—
•
—
—
•
—
—
—
—
• — •
—
—
—
-
-
• — •
—
•
day. The secondary head does not form its own peduncle nor does a constriction
form between it and the parent to which it is attached. Buds, on the other hand,
form translucent peduncles on the day following their appearance, at the same
time that tentacles appear, and a constriction precedes the ultimate separation
of the bud from the parent. These developments are almost always indicated on
buds by the second day. Whenever there was any ambiguity observations were
made on the third, fourth and even fifth days to be certain that what had been
scored a secondary head remained attached and what had been scored a bud
detached.
A large discrepancy appears in the results for multiple gastric region grafts
(Table 1) compared to those for multiple peduncle grafts (Table 2): more
secondary tentacles and spikes formed on peduncles compared to gastric regions,
while fewer secondary heads formed on peduncles compared to gastric regions.
If the secondary tentacles and spikes are interpreted as abortive heads, it would
appear that it is easier for a head as such to regenerate on a gastric region than
on a peduncle.
320
S. SHOSTAK
Table 2. Multiple peduncle grafts
Designation (see Fig. 2)
Symbol in Fig. 6
No. of animals
5p
4p
3p
2p
Circle
Square
Triangle
Diamond
50
58
57
122
0-70
Level and type of secondary structure
Frequencies
P-1
Secondary foot
0-96
100
0-88
0
004
004
002
007
004
0
002
0
(008)
0-76
(013)
0-57
(002)
008
009
007
005
010
0-48
(0-64)
0-28
0-42
(057)
002
0-12
—
0-24
0-40
(0-66)
0-36
019
• — •
—
—
—
p-2
Secondary tentacle
Spike
Secondary head
(Total)
Secondary foot
0
0
0
(0)
017
p-3
Secondary tentacle
Spike
Secondary head
(Total)
Secondary foot
0-20
0-24
(052)
0-70
—
•—•
. .
• — •
—
p-4
Secondary tentacle
Spike
Secondary head
(Total)
Secondary foot
0-76
(107)
—
•
• — •
—
—
—
—
P-5
Secondary tentacle
Spike
Secondary head
(Total)
014
014
0-78
(106)
—
—
—
—
—
—
• — .
—
—
—
•
.
.
—
• — •
B. Inhibitory gradients
If the terminal structures give rise to gradients of substances which specifically
inhibit the regeneration of similar structures at graft borders elsewhere on the
animal, then the degree of regeneration of a structure would increase over some
distance from the respective terminal structure until 100% regeneration was
reached. This is to say, the degree of inhibition would decrease over this distance
to0%.
Since data were accumulated in terms of regeneration, the results are summarized in Tables 1 and 2 and graphically illustrated in Figs. 5 and 6 in terms of
regeneration. The frequency with which a structure regenerates on a grafted
piece is computed from the number of times the structure appeared, expressed
as a function of the number of animals having the particular type of graft. The
percentages plotted in the figures for 'head' regeneration actually are the sums
of frequencies of secondary heads, spikes and secondary tentacles (i.e. see
'total' rows in Tables 1 and 2). With the objective of viewing the figures in
321
Diffusion gradients in hydra
0
JO
20
-i 30
5
- «vvv
40
f 50
Head
Foot
\\\\ \\
\» \\
D
\
« 70
SO
90 100 H
ram
1
1
1
Jxg
2xg
3xg
1 2
3
Distance from head
1
4 x g 4xg+ 3xg+ 2xg+ lxg+
4 5
4
3
2
Distance from foot
BR
1
FIGURE 5
Figs. 5 and 6. The data presented in Tables 1 and 2 are plotted in these figures. Both
figures are divided into a left-hand portion in which the distance from the head is
indicated along the abscissa, and a right-hand portion in which the distance from the
foot is indicated. These distances are given in mm according to standard dimensions
of Hydra viridis reported by Shostak (1968). The distances are also given in repeats of
body units, g for gastric regions and p for peduncles corresponding to the grafting
procedures. For example, 3 x g represents a distance of three grafted gastric regions.
For gastric region grafts (Fig. 5) the distances from the foot (right hand side) involves
the addition of the length of the host budding region (BR) and peduncle (p) to
lengths of the grafted gastric regions. This addition is symbolized by the plus sign (+).
Likewise, for peduncle grafts (Fig. 6) the distance from the head (left side) involves
the addition of the length of the host gastric region (g) and budding region (BR)
which is also indicated by the plus sign. The ordinate shows percentage regeneration
of the particular structure involved. The percentages increase in a downward
direction giving the curves the overall impression of decreasing as a function of
distance from the terminal structures. Open symbols in Fig. 5 indicate results
on gastric regions, while closed symbols in Fig. 6 indicate results on peduncles.
Diamonds indicate the results when a region is doubled, triangles when a region is
tripled, squares when it is quadrupled, and circles when it is quintupled. Solid lines
connect circles, short dashes connect the squares, long dashes the triangles, and the
diamonds stand alone. Shaded areas are intended to draw attention to points whose
relationships are emphasized in the text. The frequencies of head regeneration at
different distances from the head are shown on the left, and of foot regeneration at
different distances from the foot on the right of these figures. Head regeneration
includes secondary tentacles and spikes (see 'total' in Tables).
Fig. 5. On the left-hand side the shaded area covers points which represent results
on host (g-l) gastric regions. These points seem to be below the other points where
they might have been expected to be, were distance from the head alone influencing
the result. Foi example, the triangle at 2 mm from the head is below the square and
circle. On the right-hand side the shaded area covers points which represent results
on the most apical gastric regions bearing the terminal head (g-5 on 5 g, g-4 on 4 g,
g-3 on 3 g, g-2 on 2 g animals). These points also seem to be below the other points
where they might have been expected to be were distance from the head alone
influencing the results. Proximity to the terminal head, therefore, might influence
foot regeneration as well as distance from the foot.
322
S. SHOSTAK
.
0
Head
Foot
10
20
vy
30
40
50
60
70
80
90
100
:
H
i
g
BR+lxp
i
\ \1
f
+ 3xp
+2xp
+4xp
20 2-7 3-4 4-1
Distance from head
4xp 3xp 2xp 1 xp
2-8 21
1-4
Distance from foot
0-7
Fig. 6. On the left-hand side the slopes of the curves between 20 and 2-7 mm from
the terminal head appear nearly constant. However, the curve for 4 p animals
(squares) is below the curve for the 5 p animals (circles) at 3-4 mm from the terminal
head. On the right-hand side the slopes of the curves are not nearly as constant as on
the left. The shaded area covers points which represent results on host (p-1)
peduncles. These points seem to be below the other points where they might have
been expected to be.
terms of inhibition the ordinates have been inverted from the usual orientation. The degree of inhibition thus may be viewed as increasing along the Y
axis.
The overall shapes of the curves in Figs. 5 and 6 are consistent with, indeed
paradigmatic of, inhibitory gradients. The frequencies with which secondary
structures regenerate decrease as functions of increasing distance from the end
of the animal bearing the similar terminal structure. The correlation coefficients
for the curves approach - 1 in each case (where there are three or more points).
There are, in addition, several other interesting points about the curves and
comparisons between them.
The curves for secondary head regeneration in gastric regions (Fig. 5) do not
reach 100% regeneration even at a distance of 4 mm from the terminal head,
while the curve for 4 p animals (Fig. 6, squares) reaches this point at less than
4 mm, and for 5 p animals at about 4 mm from the head. Similarly, the curves
for secondary foot regeneration in gastric regions (Fig. 5) approach 100%
regeneration at about 5 mm from the foot, but reach this point at only about
2 mm in peduncle tissue (Fig. 6). The shorter distances from terminal structures
over which peduncle tissue seems to be inhibited for both secondary head and
foot formation suggest that the peduncle is less sensitive to inhibition than is the
gastric region.
323
Diffusion gradients in hydra
Table 3. Average Y intercepts and slopes of the regeneration curves
Head regeneration
Type of graft
(fl)
Y intercept
(b)
Slope: frequency
of heads regenerated
per mm from
terminal head
3g
4g
5g
3p
4p
5p
-0-30
-0-25
-026
-1-55
-1-20
-0-74
0-38
0-28
0-24
0-77
0-67
0-44
Foot regeneration
(fl)
Y intercept
(b)
Slope: frequency
of feet regenerated
per mm from
terminal foot
-106
-0-84
-0-54
-0-48
-011
0-23
0-56
0-40
0-29
100
0-52
0-27
The other ends of the curves approach zero frequencies or regeneration. The
curves for foot regeneration in peduncle tissues (Fig. 6), however, do not get as
close to zero as do the corresponding curves for gastric region tissues (Fig. 5),
and this despite the fact that observations on peduncles were made at levels
nearly three times closer to the foot than on gastric regions. It seems that the
lesser sensitivity of the peduncle to inhibition may be combined here with a
greater competence for foot regeneration to give higher degrees of regeneration
closer to the foot than those found for the gastric region.
On the other hand, these relative differences in sensitivity and competence are
inadequate to explain all the observations. Head regeneration on peduncles
(Fig. 6) is seen to approach zero percentage regeneration 2-0 mm from the head
while at this distance in gastric regions (Fig. 5) the frequencies of head regenerations are between 20 and 50%. Possibly the greater ease with which heads
regenerate in gastric regions explains this result, or perhaps the budding regions
which are contiguous with the peduncle pieces in question add to the level of
head inhibitor influencing these peduncles. In any event, this result is incompatible with the simple statement that the peduncle is less sensitive to inhibitors
than the gastric region and invites additional hypotheses.
Host pieces in general may have unique properties for regeneration which are
not influenced by distance from the terminal structures in the same way that
most grafted pieces are influenced. At given distances from the terminal structures
the frequencies with which heads are regenerated on the host gastric region (g-1),
and with which feet are regenerated on the host peduncle (p-1), are greater than
the frequencies for other grafted parts. This is shown in Figs. 5 and 6 where the
shaded area on the left of Fig. 5 and on the right of Fig. 6 cover points representing the results on the host pieces.
It is not results on the host pieces alone, however, which are exceptional. The
shaded area on the right of Fig. 5 covers points representing results on the most
324
S. SHOSTAK
apical gastric regions, namely the ones bearing the terminal heads of animals
with different numbers of gastric regions. It would seem, therefore, that some of
the grafted pieces comprising multiple-grafted animals may not be equivalent,
and that the apical end pieces and host pieces may have special properties in
which regeneration is either promoted or inhibition is less effective compared to
other pieces.
Discrepancies appear among the slopes calculated for the best fit of the points
representing the different types of grafts. These slopes are listed in Table 3.
Their examination reveals that the values decrease as the number of grafted
pieces increase. For example, the slopes for head regeneration decrease from
0-38 to 0-24 frequency of heads regenerated per mm from the terminal head.
This suggests a systematic difference in the grafted pieces at a given distance
from a terminal structure in the grafted animals consisting of different numbers
of grafted pieces.
The Y intercepts for the straight lines fitting the points in Figs. 5 and 6 are
also listed in Table 3. In general, the ^intercepts for the head regeneration curves
are larger for gastric region grafts than for peduncle grafts, while for foot
regeneration the values for peduncle grafts are larger than for gastric region
grafts. That is, there is theoretically more head regeneration on gastric regions
at the level of the terminal head than there would be were there a comparable
level in peduncles, and there is theoretically more foot regeneration on peduncles
at the level of the terminal foot than there would be were there a comparable
level in gastric regions. Terminal heads, of course, are not normally found on
peduncles nor are terminal feet normally found on gastric regions. The point
made by the differences in the Yintercepts for head and for foot regeneration in
gastric regions and peduncles is that heads seem to regenerate more easily on
gastric regions than on peduncles, and feet seem to regenerate more easily on
peduncles than on gastric regions. This difference in ability or ease of regeneration
is referred to as competence. The gastric region, therefore, appears to be more
competent for head regeneration than the peduncle, and the peduncle more
competent for foot regeneration than the gastric region.
DISCUSSION
The present study provides the link between the experimental work on
diffusible inhibitors (Burnett, 1961, 1966; MacWilliams & Kafatos, 1968;
MacWilliams et al. 1970; Shostak, 1972; Webster, 1966, 1971; Wilby &
Webster, 1970; Wolpert et al. 1972) and hypothetical inhibitory gradients
(Crick, 1970, 1971; Wolpert, 1969, 1971). Much of this experimental work deals
with the time and distance over which inhibition operates rather than with
gradients as such. The question remained whether inhibitors were present in
gradients only transiently as they moved toward a uniform distribution in the
steady state, or whether gradients were present in the steady state too. Shostak
Diffusion gradients in hydra
325
(1972) confirmed the latter possibility by examining the temporal changes in
inhibitory gradients in doubly grafted animals. The object of the present study
was to produce additional gradients in multiple-grafted animals so that the
parameters of these steady state gradients could be determined and compared
to predictions based on Crick's model of diffusion gradients.
In addition to gradients, qualitative and perhaps other quantitative differences can also exist along the lengths of animals. It has been shown in the Results
that competence to regenerate a structure in the gastric region is different from
that in the peduncle, as is sensitivity to inhibition. It is well established that body
regions close to terminal structures regenerate them more easily than do body
regions from the opposite ends of animals (Peebles, 1897; Burt, 1934; Brien &
Reniers-Decoen, 1950; Kass-Simon, 1969). The developmental history of a
tissue seems to operate directly on the cells in delineating differential morphogenetic potentials since these survive disaggregation and reaggregation (Gierer
et al. 1972). Diffusion, therefore, would not account for polarized differences
in competence and sensitivity between gastric regions and peduncles.
Possibilities of these sorts inevitably hamper efforts to study gradients on
normal animals where confusion can exist between properties inherent in body
regions as opposed to gradients of inhibition. The multiple-grafted animals
employed here avoid this pitfall by providing repeated units of the same body
region - that is, either gastric regions or peduncles. Comparisons can then be
made between results on theoretically equivalent body regions.
Testing Crick's (1970) model, as outlined in the Introduction, depended on
the formation of morphogenetic gradients in animals lengthened by multiple
grafts of gastric regions or peduncles. Regenerations of heads and of feet in the
vicinities of the graft borders were observed and the frequencies of these so-called
secondary structures did, indeed, exhibit patterns characteristic of specific
inhibitory gradients. Thus, the frequency of secondary heads increased as a
function of increasing distance from the terminal head, and decreasing distance
from the terminal foot, and the frequency of secondary feet increased as a
function of increasing distance from the terminal foot and decreasing distance
from the terminal head.
Gradients, sources and sinks require redefinition at this point in order to
translate the language of diffusion gradients into the language of morphological
observations. Quotation marks will be used for the words when used in the
context of morphology, while they will continue to be used without quotation
marks when they are intended to refer to diffusion gradients as such.
The 'gradients' are defined as the lengths of grafted animals over which the
frequencies of secondary structures go from 0% to 100% regeneration. The
distance from a terminal structure over which there is 0% regeneration is
defined as a 'source', and the distance from the terminal structures over which
there is 100% regeneration is defined as a 'sink'.
These definitions differ from those used by Crick and set forth in the Intro-
326
S. SHOSTAK
duction. Were the 'sources' as defined here to correspond to those defined by
Crick it would mean that all and only the completely inhibited levels of multiplegrafted animals were producing inhibitors. Likewise, were the 'sinks' as
defined here to correspond to those defined by Crick, all and only the completely
uninhibited levels would be using up the inhibitors. Drawing identities between
'sources' and sources, and between 'sinks' and sinks is only done here as a
tentative assumption and basis for speculation.
The definitions of'sources' and 'sinks' encounter some additional difficulties
if taken too literally. While 'sources' should be completely inhibited for
regeneration, presumably by the inhibitor, their location near the terminal
structures would indicate that they are regions capable of regenerating these
structures most easily. Likewise, 'sinks' should be completely uninhibited for
regeneration, but were this the case, a hydra would have feet growing at the head
end and heads growing at the foot end. Obviously, no definitions of sources and
sinks can be considered complete in the light of the evidence without including
competence and sensitivity in their formulation, and without describing the
trigger as well as the mechanism of regeneration. This is, of course, not yet
possible. While the present definitions are incomplete in these ways, they can,
nevertheless, be useful if not forced beyond their limits.
The lengths of 'sources' are computed by solving for X in the equation
Y = a + bX'm which a, the F intercept, and b, the slope, are taken from Table 3,
and Y, the frequency of regeneration for any secondary structure on a grafted
piece, is set equal to 0. The lengths of the ' sinks' are computed by also solving
for X using the same equation and the same values of a and b, but setting Y
equal to 10, and then subtracting Xfrom the total length of the grafted animal
less its head and foot. (The total lengths of animals less heads and feet are
based on 1 mm for each gastric region, 0-3 mm for the budding region, and
0-7 mm for each peduncle; Shostak, 1968.) The lengths of the 'gradients',
therefore, are equal to the differences between the total lengths of the animals
less heads and feet, and the sums of the lengths of the 'sources' and 'sinks'. The
slopes of these 'gradients' are reciprocals of their lengths. (These definitions of
'source', 'sink' and 'gradient' are intended to supplant those given earlier by
Shostak, 1972.)
The computed lengths of the 'sources', 'sinks' and 'gradients' are listed in
Table 4. (Actually, the length of the 'source' of foot inhibitor in 5 p animals
was computed to be -0-85 mm. Since this means either that the 'source' is not
part of the animal, or that an insufficient amount of foot inhibitor was produced by the source to completely inhibit secondary foot formation, a value of
0-0 mm was assigned to the length of this 'source'.)
The values listed indicate that lengthening the animals has no great effect on
the lengths of the ' sources' or ' sinks' among animals in the different groupings.
That is, the results for animals with multiple gastric region grafts or those with
multiple peduncle grafts are fairly consistent and, with one exception, not
327
Diffusion gradients in hydra
Table 4. Lengths {mm) of1 sources', 'sinks'1 and 'gradients'
Head inhibitor
Type
grafts
Lengths
animals
less heads
and feet
(mm)
from
head
(' source ')
from
foot
('sink')
3g
4g
5g
3p
4p
5p
40
50
60
3-4
41
4-8
0-8
0-9
1-1
20
1-8
1-2
0-6
0-5
0-7
01
0-8
0-8
Foot inhibitor
A.
mm
mm
mm
mm
of
'gradients'
2-6
3-6
4-2
1-3
1-5
2-3
mm
mm
of
from
foot
('source')
from
head
('sink')
'gradients'
20
2-1
1-9
0-5
0-2
00
0-3
0-4
0-7
J-9
20
2-1
1-7
2-5
3-4
1-0
1-9
2-9
statistically significantly different. The exception is the 'source' of foot inhibitor
in animals with grafted peduncles which while increasing statistically significantly as tested by x2 (0-05>P>0-025) did not increase beyond the length of
a single peduncle. On the other hand, longer animals had increased distances
between their' sources' and ' sinks' as shown in the columns headed ' gradients'.
'Gradients' increase with an average of 1-0 mm per grafted gastric region, and
0-6 mm per grafted peduncle. Since these values compare well with the published
values for the lengths of the gastric region (1-0 mm) and peduncle (0-7 mm) of
normal animals (Shostak, 1968), the increases in the lengths of the gradients
appear to be entirely due to the addition of the grafted pieces. Furthermore, since
the lengths of the ' gradients' are the reciprocals of the slopes, the increasing
lengths of the' gradients' mean decreasing slopes. It is concluded, therefore, that
the slopes of the 'gradients' decrease entirely as functions of the number of
grafted pieces.
Crick's model thus passes its test for Hydra viridis lengthened by grafting: the
distance between 'sources' and 'sinks' change; the slopes of the 'gradients' are
not constant; the slopes of the 'gradients' change inversely with the changing
distance between the 'sources' and the 'sinks'. Diffusion gradients are therefore
plausible explanations for the morphogenetic inhibitory gradients observed here.
An important consequence follows from the estimate of the maximum length
of the 'gradient' made here. Crick predicted that 1 mm (1970) or 2 mm (1971)
was maximum, but lengths of as much as 4 mm were found. Since the diffusion
constant (D) of a diffusible substance is proportional to the square of distance, if
Crick's estimate of length is wrong by as much as a factor of 4, his estimate of D
could be wrong by as much as 16. Instead of a value of 0-08 x 10~5 cm2 sec"1
used by Crick, values in the order of 1-2 x 10~5 cm2 sec"1 are appropriate. Instead
of materials the size of organic molecules such as cyclic AMP or steroids as
Crick suggests, the diffusible inhibitors could be strong electrolytes such as
CaCl2 or small organic molecules such as glycolamide. This is consistent with
328
S. SHOSTAK
the views of Macklin & Burnett (1966) who suggested that inorganic ions play a
controlling role in differentiation in Hydra, and of Lenhoff (1968) who implicated low-molecular-weight materials in the development, physiology and
behavior of these animals.
The next question is, what are the structural bases of the sources and sinks
in the animal? However tentative, answers can be sought by equating 'sources'
to sources and 'sinks' to sinks, and consulting Table 4. All the 'sources' for
head inhibitor (column 3) are between 0-8 mm and 2-0 mm from the head
(average 1-3 mm) and the means for the two groupings (i.e. for the animals with
multiple grafts of gastric regions and the animals with multiple grafts of
peduncles) do not differ statistically significantly as tested by the F statistic
(0-10>P>0-05). Since the gastric region and budding region of a normal
animal together measure 1-3 mm (Shostak, 1968), these regions could be the
source in the sense of the producer of head inhibitor. In this same way, the sink
for the head inhibitor is identifiable as the basal peduncle. All the' sinks' for the
head inhibitor (column 4) are essentially located in the basal peduncle, which
covers 0-7 mm from the foot of a normal animal. This is reminiscent of Burnett's
(1961) conclusion that head inhibitor does not pass through the peduncle and
foot.
In both cases of the ' source' and ' sink' the structural bases are not seen to
correspond to single levels of the animal or particular structures but to regions.
It would be more appropriate to speak of regional sources and sinks therefore
than point sources and sinks as is usually done. This would be in keeping with
the suggestion made earlier (Shostak, 1972) on the basis of ablation and addition
experiments.
Proceeding with the assumed identities of the morphological ' source' with
the diffusion source, and of the morphological 'sink' with the diffusion sink, it
appears that only the apical gastric region bearing the terminal head produces
head inhibitor and only the basal peduncle bearing the terminal foot uses up or
degrades head inhibitor. Gastric regions in general do not act as the source, nor
do peduncles in general act as the sink, but only the gastric region adjacent to
the terminal head acts as a source, and only the peduncle adjacent to the
terminal foot acts as a sink. This raises the possibility that the terminal head
induces the adjacent gastric and budding regions or tissue as far as the nearest
graft border (which ever comes first) to be the source of head inhibitor, and the
terminal foot induces the adjacent peduncle as far as the nearest graft border to
be the corresponding sink.
The locations of the source and sink for foot inhibitor are not ascertainable
from the available data. The estimates of the lengths of' sources' and ' sinks' of
foot inhibitor differ in the two groupings by factors of 10 and 4, respectively,
and no easy way is available for making these different estimates compatible.
The ' source' for foot inhibitor on animals with multiple gastric region grafts
(Table 4, column 6, upper 3 rows) corresponds to the length of the host piece
Diffusion gradients in hydra
329
including the gastric region, budding region, and peduncle (a total of 2 mm),
but on animals with multiple peduncle grafts (lower 3 rows) corresponds to
something less than the length of the basal peduncle (0-7 mm). The ' sink' for the
foot inhibitor on animals with multiple gastric-region grafts (column 7, upper
3 rows) corresponds to the upper part of the apical gastric region, but on
animals with multiple peduncle grafts (lower 3 rows) corresponds to the entire
length of the host piece.
Perhaps an explanation based on differential competence to regenerate feet,
and differential sensitivity to inhibition may ultimately explain these inconsistencies, but this is beyond the scope of this report. It is of interest, nevertheless,
that the source of and sink for foot inhibitor, like their counterparts for head
inhibitor, would be present exclusively on pieces bearing terminal structures.
Possibly the same type of inductive activity hypothesized to occur in the case of
the source of and the sink for head inhibitor takes place in the case of the source
of and sink for foot inhibitor.
In conclusion, the role for diffusion gradients in the control of morphogenesis
in Hydra is supported by the results of the present study. The slopes of gradients
in the frequencies of head and of foot regeneration at graft borders in multiplegrafted animals changes as predicted by the consequences of Crick's model as
outlined in the Introduction. In addition, the source of and sink for the head
inhibitor are tentatively identified as the terminal head bearing gastric and budding regions, and the terminal foot bearing peduncle, respectively. Webster (1966,
1971) and Wolpert (1969, 1971) have called attention to the need to speak of
more than one gradient in trying to describe Hydra as did Burnett (1961) before
them. The present study conjures up a picture of Hydra as a collage of control
systems with anti-parallel head and foot inhibitory diffusion gradients, prior
history of a tissue, and induction playing parts while competence and sensitivity
lie in the background. Diffusion gradients are not the whole picture, but they do
seem to be a part of it.
REFERENCES
BRIEN, P. & RENIERS-DECOEN, M. (1950). Etude d'Hydra v/nV//.s(Linneaus). (La blastogenese,
la spermatogenese, I'ovogenese.) Annls Soc. r. zool. Belg. 81, 33-110.
BURNETT, A. L. (1961). The growth process in Hydra. J. exp. Zool. 146, 21-84.
BURNETT, A. L. (1966). A model of growth and cell differentiation in Hydra. Am. Nat. 100,
165-190.
BURT, D. R. R. (1934). The capacity of different regions of Pelmatohydra oligactis Pall, to
form head or foot. / . exp. Zool. 68, 59-93.
CHILD, C. M. (1941). Patterns and Problems of Development. Chicago: Chicago University
Press.
CRICK, F. H. C. (1970). Diffusion in embryogenesis. Nature, Lond. 225, 420-422.
CRICK, F. H. C. (1971). The scale of pattern formation. Symp. Soc. exp. Biol. 25, 429-438.
GIERER, A., BERKING, S., BODE, H., DAVJD, C. N., FLICK, K., HANSMANN, G., SCHALLER, H.
& TRENKNER, E. (1972). Regeneration of Hydra from reaggregated cells. Nature, New Biol.
239, 98-101.
330
S. SHOSTAK
W. (1929). Das Regenerations-material und sein experimented Beeinflussung.
Versuch zur einheitlichen Beurteilung der regenerativen Ercheinung. Wilhelm Roux Arch.
EntwMech. Org. 117, 211-311.
HYMAN, L. (1928). Miscellaneous observations on Hydra, with special reference to reproduction. Biot. Bull. mar. biol. Lab., Woods Hole 54, 65-108.
KASS-SIMON, G. (1969). The regeneration gradients and the effects of budding, feeding
actinomycin and RNAse on reconstitution in Hydra attemtata Pall. Revue suisse Zool. 76,
565-599.
KING, H. D. (1901). Observations and experiments on regeneration in Hydra viridis. Wilhelm
Roux Arch. EntwMech. Org. 13, 135-178.
LENHOFF, H. M. (1968). Behavior, hormones, and Hydra. Science, N.Y. 161, 434-442.
MACKLIN, M. & BURNETT, A. L. (1966). Control of differentiation by calcium and sodium
ions in Hydra pseudoligactis. Expl Cell Res. 44, 665-668.
MACWILLIAMS, H. K. & KAFATOS, F. C. (1968). Inhibition by the basal disk of basal disk
differentiation in Hydra. Science, N.Y. 159, 1246-1247.
MACWILLIAMS, H. K., KAFATOS, F. C. & BOSSERT, W. H. (1970). The feedback inhibition of
basal disk regeneration in Hydra has a continuously variable intensity. Deri Biol. 23,
380-398.
MOOKERJEE, S. (1963). Determination of cell system in Hydra. Proc. XVlth Int. Congr. Zool,
Washington 2, 237.
PEEBLES, F. (1897). Experimental studies on Hydra. Wilhelm Roux Arch. EntwMech. Org. 5,
794-819.
SHOSTAK, S. (1968). Growth in Hydra viridis. J. exp. Zool. 169, 431-446.
SHOSTAK, S. (1972). Inhibitory gradients of head and foot regeneration in Hydra viridis.
Devi Biol. 28, 620-635.
SHOSTAK, S. & KANKEL, D. R. (1967). Morphogenetic movements during budding in Hydra.
Devi Biol. 15, 451-463.
SINHA, A. K. (1966). Experimental determination of polarity in Hydra. Wilhelm Roux Arch.
EntwMech. Org. 157, 101-116.
TARDENT, P. (1954). Axiale Verteilungs-Gradienten der interstitiellen Zellen bei Hydra and
Tubularia und ihre Bedeutung fur die Regeneration. Wilhelm Roux Arch. EntwMech. Org.
146, 593-649.
TARDENT, P. E. (1960). Principles governing the process of regeneration in hydroids. In
Developing Cell Systems and their Control, (ed. D. M. Rudnick), pp. 21-43. New York:
Ronald Press.
WEBSTER, G. (1966). Studies on pattern regulation in Hydra. III. /. Embryo!. exp. Morph. 16,
123-141.
WEBSTER, G. (1971). Morphogenesis and pattern formation in hydroids. Biol. Rev. 46, 1—46.
WILBY, O. K. & WEBSTER, L. (1970). Experimental studies on axial polarity in Hydra.
J. Embryol. exp. Morph. 24, 595-613.
WOLPERT, L. (1969). Positional information and the spatial pattern of cellular differentiation.
/. theor. Biol. 25, 1-47.
WOLPERT, L. (1971). Positional information and pattern formation. In Curr. Top. Devi Biol.
6, 183-224 (ed. A. A. Moscona & A. Monroy). New York: Academic Press.
WOLPERT, L., CLARKE, M. R. B. & HORNBRUCH, A. (1972). Positional signalling along Hydra.
Nature, New Biol. 239, 101-105.
GOETSCH,
{Received 19 June 1972, revised 1 November 1972)