/ . Embryol. exp. Morph. Vol. 63,pp. 161-180, 1981
Printed in Great Britain © Company of Biologists Limited 1981
The control of growth and the development
of pattern across the anteroposterior axis
of the chick limb bud
By DENNIS SUMMERBELL 1
From The National Institute for Medical Research, London
SUMMARY
Two grafts of zone of polarizing activity (ZPA) were made to host limb buds. The grafts
define the width of the shared responding field lying between them. They cause a change in
the growth pattern of the bud so that there is an increase in the width of the tissue between the
grafts. Concurrently they redefine (respecify) cell states in the responding tissue so as to cause
formation of a mirror-image reduplicate hand between them. The number and type of digits
formed depends on the initial distance between the grafts.
The results suggest that the initial presumptive hand field is very small (~ 300 /im), that it is
not a classical morphallactic system, and that it is able to regulate its growth pattern. A pointsource diffusion model is presented.
INTRODUCTION
During the last decade, the dominant conceptual framework of pattern
formation in development, has been the theory of positional information
(Wolpert, 1969, 1971). Principally this theory aided the resurgence of interest
(Lawrence, 1966; Locke, 1967; Webster, 1966 a, b; Stumpf, 1966, 1968) in
classical field gradients (extensively reviewed by Child, 1941; Huxley & de Beer,
1934). Among systems that seem particularly amenable to this type of explanation is the developing chick limb bud, and there now exists good evidence
for a gradient across the anteroposterior (craniocaudal) axis (Wolpert, Lewis &
Summerbell, 1975; Tickle, Summerbell & Wolpert, 1975; MacCabe & Parker,
1976; Summerbell & Tickle, 1977; J. A. MacCabe, Lyle & Lence, 1979;
Summerbell, 1979).
A favourite set of mechanisms for producing a gradient can be described by
the generic term of source-sink diffusion models (e.g. Crick, 1970; Lawrence,
Crick & Munro, 1972; Wolpert, Hornbruch & Clarke, 1974). Apart from the
wide application in the literature the general idea has strong virtues: it has a
clear-cut and plausible mechanism which is readily understood, it would work,
and, it is easy to simulate quantitatively; most important, it constitutes an
1
Author's address: The National Institute for Medical Research, The Ridgeway, Mill Hill,
London NW7 1AA, U.K.
162
D. SUMMERBELL
excellent paradigm for many other averaging models that set up positional
information. This paper was stimulated by problems experienced in adapting the
source-sink diffusion paradigm to the limb-bud system. While a model based on
these principles satisfies the general requirements of the experimental data
(Wolpert et al. 1975) there are serious difficulties in demonstrating that it works
quantitatively. Specifically, it is necessary to propose that the field organizer
must control growth as well as pattern (Tickle et al 1975; Summerbell & Tickle,
1977).
When tissue from the caudal lateral edge of the developing chick limb bud
is grafted to the anterior margin it causes the formation of supernumerary limb
parts with double posterior mirror-image symmetry (Saunders & Gasseling,
1968; A. B. MacCabe, Gasseling & Saunders, 1973; MacCabe & Abbott, 1974;
Summerbell, 1974a, b; Fallon & Crosby, 1975a, b\ Crosby & Fallon, 1975;
Tickle et al. 1975; Fallon & Crosby, 1977; Summerbell & Tickle, 1977; Smith,
Tickle & Wolpert 1978; Smith, 1979, 1980).
While it is clear that the grafted tissue, the so-called zone of polarizing activity
(ZPA) is provoking the reduplication, its role in normal development is uncertain and recently discussion has been enlivened by Saunders (1977), Fallon &
Crosby (1977), J. A. MacCabe, Calandra & Parker (1977), Smith (1979, 1980),
Summerbell (1979), Iten & Murphy (1980), Javois & Iten (1980). Prior to this it
was generally assumed that both host and graft ZPA were active and that the
limb bud between them constituted a single field with two symmetrical signalling
regions (Wolpert, 1969; Saunders, 1972; Wolpert et al. 1975).
The problem arises when trying to link this latter interpretation with a sourcesink diffusion model. When the two concentration profiles generated by the
organizing regions intersect, the resulting summed concentration in the centre is
too high to be consistent with the digits obtained between the organizers. The
obvious solution is to propose that the graft, simultaneous with changing the
pattern, changes the growth rate so as to increase the distance between the
organizers. The experiments in this paper were designed to test this prediction,
and to provide parameters for growth allowing one to finally construct a
quantitative simulation. The results show that there is indeed a strong connection between pattern specification and growth. Coincidentally they exclude the
simpler forms of intercalation'models and more'surprisingly they suggest that
the initial anteroposterior hand field may be much narrower than has generally
been assumed.
METHODS
Fertilised embryos from a local flock (Needle Farm) were incubated at 38 °C
and windowed on the third day of development. The windows were sealed with
Sellotape and returned to the incubator. Embryos at stages 18-20 (Hamburger &
Hamilton, 1951) were selected as hosts. A piece of tissue including the ectoderm,
mesoderm and AER was removed from the right wing bud opposite somite 16 or
Growth and pattern in chick limb bud
Oh
163
14 h
ZPA graft (G)
575
300/nm
S20]
ZPA graft (G)
800 urn
l200jum
325 /tern
24 h
40 h
Fig. 1 Camera-lucida drawings of embryo /640: 0 h, appearance of limb bud immediately after grafting, w0 measured between cut surfaces; 14 h, the positions of the
grafts (G) are marked by indentations, the pins, and by the appearance of the
tissue (opaque white, indicating extensive cell death); 24 h, the major outgrowth
between the grafts has widened considerably Wt/W0 = 1-33, lower than average);
40 h, major outgrowth continues to widen Wt/ WQ = 2-4, about average), minor
outgrowth (between host and graft ZPA) is regressing. Note the very marked apical
ectodermal ridge with very sharp boundaries near the graft, this appearance was
typical and greatly facilitated measuring the width.
somite 17 as shown in Fig. 1. The excised fragment measured about 200/tin
squared on the dorsal surface, and as far as I could judge kept the same profile
through to the ventral side. A second similar fragment was then removed from a
more caudal position. The distance between the two graft sites was then measured
using an eyepiece graticule calibrated in units of 25 /im. A stage-21 embryo was
used as the donor and two equivalent pieces of tissue (200 x 200 /im x depth of
D-V axis) were removed from the posterior lateral edge of left and right wing
buds. The two pieces of graft tissue were transferred to the host egg and fastened
into the prepared graft sites with platinum pins (25 [im diameter). The three bare
mesenchymal surfaces of the graft contacted the three bare mesenchymal
surfaces of the host but no attempt was made to otherwise preserve particular
164
D. SUMMERBELL
orientation of grafts or order of grafting. Sham controls were performed in the
same way as the main series except that equivalent anterior limb margin was used
in place of ZPA tissue.
Camera-lucida drawings were made of the completed operation, and at
varying intervals for two days. Not all experimental animals were treated in this
way because the handling of the embryos necessary to obtain good cameralucida drawings markedly lowers the survival rate. Measurement of subsequent
changes in the width of the limb bud between the grafts were all taken from
camera-lucida drawings. The majority of the animals for which no cameralucida drawings were made was still examined either one or two days after
operating. This was to determine the general shape of the limb bud (see Results).
All surviving embryos were fixed in 5 % aqueous trichloracetic acid on day 9 or
10 for 3 h. The staining schedule was as follows: (1) rinse distilled water; (2)
wash 70% alcohol, 10 min; (3) wash 70% acid alcohol (ethyl alcohol 70 ml,
distilled water 30 ml, hydrochloric acid 1 ml), 10 min; (4) stain in 0-1 % Alcian
green 2Gx (Gurr) in acid alcohol, 3 h; (5) differentiate 70 % acid alcohol,
overnight; (6) wash 70% alcohol, 10 min; (7) dehydrate in two changes absolute alcohol, 30 min each; (8) mount between glass coverslips in methacrylate
(Phillpotts, Data Sheet 11, Taab Laboratories, 52 Kidmore End Rd, Reading,
U.K.).
In a few cases quail embryos of stage 21 by chick criteria were used as donors.
The hosts were fixed in half-strength Karnovsky's fixative after 24 h and embedded in methyl methacrylate. Samples of 2 /im transverse sections (containing dorsoventral and anteroposterior axes of limb) were taken at intervals of
50/*m, stained by the Feulgen technique and mounted. Three good sections
from each level were photographed using a Zeiss photomicroscope with a
x 10 objective and at a final print magnification of x 50. The sections were then
re-examined under the microscope using a x 40 planapochromat objective and
the position of quail cells marked on the appropriate photographs. A computer
generated three-dimensional reconstruction of the limb bud with the distribution of quail and chick cells was made using the techniques developed by
Perkins, Barrett, Green & Reynolds (1979).
RESULTS
A normal wing bud has three digits in the sequence 2 3 4 ( Z ) (anterior to
posterior). In principle, given complete interaction, one might expect a single graft
of caudal tissue to interact with the host to produce a maximum digit sequence
2 3 4 G 4 3 2 2 3 4 (Z) and a double graft to produce 2 3 4 G 4 3 2 2 3 4 G 4 3 22 3 4 (Z) (cranial to caudal) where G represents graft and (Z) the putative host
ZPA
I originally performed double ZPA grafts on 125 host embryos of which 99
(80%) survived to day 10. Two of these survivors had reduced hands and I was
Growth and pattern in chick limb bud
165
Table 1. Digits formed between the two grafts. Somite number
indicates the position of the anterior graft
Total
G234G G2234G G3(223)4GG4(3223)4G
Somite 16
70
34
Somite 17
Total
27
97
1
4
0
4
8
55
6
14
20
75
(Digits enclosed by brackets were not always present.)
unable to identify which digits were present; the results are therefore based on
the remaining sample of 97 embryos. The limbs never possessed the maximum
possible complement of digits, the most that I obtained was seven (see Table 1),
the same number as that reported inTickleef al. (1973). I obtained a digit anterior
to a somite-16 graft only once (4 G 4 3 2 3 G(Z)) but somite-17 grafts normally
had anterior digits; 4 G..., 18 cases; 2 3 G..., 3 cases; G...,6 cases.These anterior
digits were always of the same handedness as the host, as they did not lie between two graft regions I have not considered them further.
The digits between the grafts were usually arranged in mirror image symmetry
about the mid-line, with a digit 4 adjacent to each graft, though in 22 cases out of
97 the symmetry was incomplete, most frequently because one of the digits 4 was
missing (see Table 1). There was no obvious systematic reason for these 'incomplete' reduplications and they occur at about the same frequency in other
experiments involving ZPA grafts. Summerbell & Tickle (1977) suggest that it is
indicative of the effective 'strength of activity' of the ZPA graft and more
recently Honig, Smith, Hornbruch & Wolpert (1980) have proposed a more
discriminating method of assessing this effective strength. The digit nearest the
graft is scored on an integer scale from 3 to 0 with 'digit 4' high ( = 3 ) and 'no
digits' low ( = 0). The 'strength' is calculated as the percentage of the possible
maximum score for the sample. Using this method the average score was 94 %
with no significant variation for anterior or posterior graft or for the position of
the anterior graft (somite 16 or 17).
Graft cells do not participate in outgrowth
Serial reconstructions of double quail ZPA grafts to chick hosts were used to
determine the contributions of quail cells to the reduplicated bud between the
grafts. Though I cannot exclude the presence of occasional isolated quail cells, it
appeared that essentially no graft cells were incorporated into the distal part of
the outgrowth and that there was only a very small contribution to the proximal
part. I estimate the largest quail component in any of the eight cases reconstructed as less than 10 % of the total volume of the outgrowth. A typical case is
shown in Fig. 2.
166
D. SUMMERBELL
Anterior
quail
graft
Posterior
quail
graft
200 pm
Fig. 2. Three-dimensional reconstruction of serial sections of limb bud 24 h after
grafting. The stippling indicates the maximum extent of quail cells (summated after
each section had been superimposed). Neither graft extends into the tip of the
outgrowth. Volumes were estimated using a base line drawn arbitrarily to maximise the proportions of the grafts: anterior outgrowth (between grafts) 58 units, posterior outgrowth 54 units, anterior graft 7 units, posterior graft 6-5 units (50 units ~
0-14 mm3).
Because of this observation I have not included any allowance for graft tissue
in my estimate of the initial width of the field across which the two grafts act.
This parameter was measured as the width of host tissue, as described in the
methods.
Which digit belongs to which field?
During the second day after operating it is possible to determine by observation how the bud has responded to the three organizers (two grafts and one
host). The new bud fields are distinctive outgrowths, separated from each other
by indentations seen over the ZPA tissue (see Figs 1 and 2). The graft itself is
whiter and more opaque than the host tissue, and usually the platinum pin is
still visible. This, aided by the morphology of the hand at day 10, enables one to
assign a position to each graft relative to the digits present. In many cases this
preliminary observation was crucial in determining which digits were present
between the grafts. I have where necessary used the notations 2,3,4 and G (for
graft) to identify the graft sites amongst digits.
Growth and pattern in chick limb bud
167
432234(
e
o
e
e
o
4 3 2~2 3 4 [
4 3234 [
e§o
43 234[
o
S
4334[
©
g
4334[
D^o
JD
•I
5
:
434[
434
o
o
OB
oe
e
o
ggo
oo
ooo
«
o
o
o
B
°DC °B°a OOD
I
44[
4^4 (
D
41
O°PODO
4l
e
- [
*0*
DO oo OD o n
DD OO DD
100
200
300
4^0
500
Wo: initial distance between grafts (jum)
600
700
Fig. 3. Relationship between the initial width of the shared field and the digits
obtained between the grafts. 3A3 indicates digits 3 fused together across the midline,
3 indicates a reduced digit 3 on the midline. Circles indicate anterior graft opposite
somite 16, squares indicate anterior graft opposite somite 17, half filled indicates cases
with at least one reduced digit 4.
Wide fields make many digits
Figure 3 shows the relationship between the initial distance between the
grafted ZPA's (± 25 ju>m) and the digits obtained between the grafts. The digit
score was based on the number and type of digits present, a pair of digits fused
across the mid-line (e.g. 4 3A3 4) or an unpaired reduced digit on the mid-line
(e.g. 4 3 2 3 4) were each scored as a half a digit as shown in the figure. Apart from
this digits 4 were frequently reduced, often lacking the phalange. Nevertheless if
the metacarpal was recognizable as belonging to digit 4 then it was scored as a
full digit, unless it fell within the fusion across mid-line scoring convention.
Figure 4 shows cleared and stained 10-day limbs. The purpose of this figure is to
indicate how particular limbs were scored (see legend) and the examples
chosen concentrate on the type of marginal decision described above.
Only limbs from the last column of the table (digit 4 adjacent to both grafts)
have been included in Figs 3 and 5-7. Results from anterior graft opposite
somites 16 and 17 are included in Fig. 3, the two groups seem to behave very
168
D. SUMMERBELL
4
3
#
*/T
id)
Growth and pattern in chick limb bud
169
432234(
4 3 2~2 3 4 [
43234(
•<
5
43234[
4334[
o
4 3~3 4 [
o
oggooo%
4 3 4[
o
434[
o
op
o
o
oe
o
o o
44[
4[
4[
o o oo
XX oo
« oo
*? o o o o o
OO
0 0
0
100
200
300
400
500
Wo: initial distance between grafts
600
?00
Fig. 5. Relationship between the initial width of the shared field between the grafts
and the digits obtained between the posterior graft and the host ZPA. Conventions
as Fig. 3.
similarly and I could detect no difference in these results other than those caused
by the restrictions imposed on the possible initial field widths. Circles indicate
somite 16 results, squares indicate somite 17 results, half solid characters
indicate cases in which digit 4 was reduced.
There appears to be a linear relationship between the distance between
grafts and the digits obtained save perhaps for distances below about 200 jum
when the slope perhaps increases.
For completeness the digits obtained between the posterior graft and host
ZPA are shown in Fig. 5. The distance is again the graft-graft distance and not
an estimate of the posterior graft-host ZPA distance. The graph therefore
Fig. 4. Stained and cleared 10-day limbs, score represents digits between grafts in
Fig. 3, bar ~ 1 mm. (a) Wo = 450 /«n, good mirror image G 4 3 3 4 G, scores 4. (b)
Wo = 400 iim, digits fused across midline, G43 A 34, scores 3£. (c) Wo = 550 /im,
unfused reduced digit in midline, G 4 3 2 3 4 G 4 , scores ty. (d) Wo = 550/*m, digits 4
reduced, 4 3 2 3 4, scores 5. (e) Wo = 575 /tm, missing digit 4, ? G 4 3 2 3 G, not
counted in Fig. 3. (/) WQ = 625 /zm, missing digits 3 and 4 G 2 2 3 4 G, not counted
in Fig. 3. (g) Wo = 150/*m, ant = si6, an unusual result, 4 G 4 G 4 (post 4 may be
4A4), scores 1. (h) normal control limb.
170
D. SUMMERBELL
30
2-5
2-0
1-5
10
0-5
Standard deviation
repeat measurements
16
24
'
32
Time after operating (h)
40
48
Fig. 6. Change in width between grafts as a function of time (velocity curve). The
change is shown as the ratio to the initial width (Wt/W^. O, initial width > 200/im;
# , initial width *$ 200 /«n; x , sham control. The bar shows a typical standard deviation for repeated measurements of the same specimen. Some of these points were
the result of 3 successive measurements taken from the same embryo and the heavy
lines show two cases with the overall fastest and slowest change of widths.
suggests the reverse slope. Results from anterior grafts opposite somite 17 are not
included in this figure as the majority did not develop digits between posterior
graft and host ZPA. In four cases where the distance between the grafts was
150 /im or less this responding field produced a digit 4 (e.g. Fig. 4g).
ZPA grafts increase the growth rate
Figure 6 shows the change in the distance between the two grafts (width of
field) with time (Aw/0- Because of variation in the original width I have shown
this change as the ratio of the width at time t to the original width. Initially the
host tissue contracted slightly, presumably a response to operative trauma
(Summerbell, 1977). Within 7-10 h the buds had recovered sufficiently for the
ratio to have returned to the starting value. The region then developed into a
Growth and pattern in chick limb bud
171
&•
•
• •
00412
16
20
24
Time after operating (h)
32
36
Fig. 7. Intrinsic rate of change of width with time (acceleration curve). The change
is shown as the rate of change of length per unit length per unit time. The dotted
line shows the approximate equivalent rate for the change of length of the proximodistal axis.
distinct outgrowth, leaving the two graft areas proximally (see Figs 1 and 2).
The outgrowth normally had more or less parallel sides and a distinct distal edge
with a well developed apical ridge. The measurements of width were taken from
camera-lucida drawings. It is difficult to be consistent in making this estimate but
repeat measurements indicate that it is probably reproducible to + 50 fim so that
my base unit of 25 /im gives a false impression of the accuracy. Measurements
were made up to 48 h, after which changes in the outline of the limb made it
difficult to know where to measure the width.
The open circles indicate results from fields with an initial width of 200 /om or
more. Within this group I was unable to detect any relationship between the
initial width and the ratio at later times, but all limbs showed a rapid increase in
the width between the grafts.
The closed circles represent results from fields with an initial width of less than
200 /-cm. Though this width too increased it did so markedly less than in the
preceding group.
The crosses indicate results of the sham controls with anterior margin grafts
instead of ZPA (the accuracy of these measurements at 48 h is rather low). These
showed very small increases in the width. Both grafts were left proximally on a
single normal developing outgrowth.
172
D. SUMMERBELL
Figure 7 shows the intrinsic growth rate for the anteroposterior axis, that is the
rate of change of width per unit width per time (A W/ W. Af) against time (/). The
figure includes only those results with a starting width of 200 /tm or more. The
initial conti action, the rapid increase in intrinsic growth rate followed by a slow
fall towards zero are all obvious. The dotted line shows the intrinsic growth rate
for the proximodistal axis during the same period.
DISCUSSION
Changes in the width are caused by changes in the cell-cycle time
During early normal development the bud elongates proximodistally but
maintains roughly constant dimensions across its other two axis. All of the cells
at the tip are apparently in the division cycle (Summerbell & Lewis, 1975) and
the cell cycle time has been estimated at between 6 h (Cairns, 1977) to 13 h
(Janners & Searles, 1970). Following the juxtaposition of anterior mesenchyme
with mesenchyme from the posterior lateral edge, Camosso & Roncali (1968)
found that limbs examined after 13 h already showed an enhanced mitotic index.
More specifically (Cooke & Summerbell, 1980), we have found that a ZPA graft
to anterior tissue increases the labelling index in the host following incubation in
[3H]thymidine for 1 h. There was a significant enhancement at 5, 9 and 17 h
after grafting. The mitotic index was marginally higher at 9 h after operating and
almost doubled after 17 h. (The relatively low number of mitotic figures in the
limb means that there have to be large relative changes before differences become significant.) As all cells are dividing it seems therefore that the presence
of the graft shortens the mean cell cycle time of cells in the adjacent mesenchyme
by raising the rate of entry into ' S ' phase within a few hours of the operation.
The full effect, in terms of cell division itself is not apparent at 9 h but is great at
17.
This correlates well with the results presented in this paper. One cannot
compare the growth rate directly with the cell cycle time since the latter is
equivalent to the intrinsic rate of growth (or widening: A Wj W. A/), as shown in
Fig. 7. Following the double ZPA grafts at 0 h there is an initial contraction of
host tissue between the grafts. This is probably the result of trauma: a similar
reaction occurs following the removal of the apical ectodermal ridge
(Summerbell, 1977). Within 4-6 h the intrinsic growth rate measured across the
anterioposterior axis begins to increase (passes 0). It reaches a maximum at
12-16 h. This fits well with the cell cycle data where the change in the cell cycle
time is small at 9 h and great at 17 h. It may appear from this that the change in
intrinsic growth rate is rather low compared with the change in cell cycle time,
but one must remember there is also expansion of the proximodistal axis, and
changes in cell-packing density. In fact one can make a rough estimate of the
change in cell cycle time necessary to produce the observed growth rate taking
into account these parameters. I have used values for the mitotic index taken
Growth and pattern in chick limb bud
173
from Hornbruch & Wolpert (1970), the cell packing density taken from
Summerbell & Wolpert (1972), the growth rate for the proximodistal axis taken
from Summerbell (1976); and the calculation was performed as described in
Summerbell (1977). The mean cell cycle time required for the period between
12 and 26h post grafting would be 13-3 h for the control limb and 7-7h for the
operated limb giving an enhancement of the mitotic index of 1-7. Because the
parameters come from various sources and the limb is heterogeneous one
should treat these estimates with caution. Nevertheless it is useful to know that
they compare well with the enhancement of mitotic index reported in Cooke &
Summerbell (1980) (1-6-2-2 depending on position) and fall within the range of
cell cycle times suggested by Cairns (1977) and Janner & Searles (1980). The
spatial correlation is not so good, but this will be discussed elsewhere.
How to control the rate of growth
In previous papers (Tickle et al. 1975; Summerbell & Tickle, 1977), we presented a model in which the position of digits across the anteroposterior axis
was specified with respect to the zone of polarizing activity. The problem with
the model was that it did not fit the data without a major ad hoc assumption:
that the grafted region modified the growth of the host bud so as to increase the
width of the anteroposterior axis. The results in this paper provide decisive
justification of this assumption.
It raises in turn the problem of how to control this change in size. The
mechanism that I will now discuss is based on an idea for size control suggested
by Lawrence (1972). He suggested that the length of the field could be controlled
by allowing cell division to continue until the gradient of positional value across
the field reached the correct slope. The field then having reached the correct
length, cell division would stop. My modification again measures the slope but
uses it to control the growth rate rather than the absolute size.
I start with the source-sink diffusion paradigm for interactive models described in the appendix to Summerbell (1979), a model satisfying the requirements outlined in Lewis, Slack & Wolpert (1977). The ZPA acts as the source of
a morphogen, the local concentration of which is held relatively constant. The
morphogen is free to diffuse into adjacent mesenchyme cells where it is broken
down. This gives a concentration profile with an exponential form with the high
point at the posterior edge. The position of a cell relative to the ZPA is specified
by the local concentration of the morphogen, and the cell uses this information
to program its differentiation. There are two additional assumptions:
(a) cells are able to measure the slope (m) of the concentration profile, either
by monitoring the flux or by comparing the concentration (c) in nearest neighbours :
_
"
where x is the distance between cells;
1 l
2x
174
D. SUMMERBELL
(a)
Equilibrium concentration profile
100
8h
16 h
24 h
800
32 h 40 h 48 h
1000
1200
Distance between grafts
Fig. 8. (a) The equilibrium concentration profile and its slope for the parameters used
in the simulation for a normal ZPA. The simulation was performed as described in
Summerbell (1979). I previously omitted to specify the degradation term, the simulation is relatively insensitive to variation in this parameter and a value of c' = 0-96 c
(where c is the concentration) gives a fair fit to the data, the fit is slightly improved
by using any function giving a relatively higher rate of degradation at higher concentrations. (/>) The concentration profiles between two ZPA grafts at successive
times. The anterior graft is opposite somite 16, and the initial width of the shared
field is 500 /tm. The grafts were made at stage 18/19 and the 48 h curve would be
equivalent to about stage 27/28. The predictions made by the curve for points on Figs
6 and 7 are within the limit of variation of the observed results.
Growth and pattern in chick limb bud
175
(b) at equilibrium the slope at any point will be a function of the concentration, and all cells have programmed within them the equilibrium slope for all
positions along the concentration profile. During development cells compare
their observed slope with the expected equilibrium slope. Discrepancies cause a
modification of the cell cycle time (Tc):
Tca(m-
meq).
If the slope is too steep, the field is not long enough, so the cells divide faster. If
the slope is too shallow the field is too long, so the cells stop dividing. A simulation of the model for double ZPA grafts with anterior graft opposite somite 16
is shown in Fig. 8.
Epillaxis or morphamorphosis
From the outset the theory of positional information has been afflicted by the
awkward dichotomy of epimorphosis (the regulation of pattern by the sequential addition of 'new' cells with progressively different positional values at a
boundary), and morphallaxis (the regulation of pattern by the reassignment of
positional values to existing cells between two boundaries). This was unintentional as Wolpert (1971) initially pointed out that in many cases pattern
formation would involve both. Nevertheless it has led to the situation (Wolpert
et ah 1975) in which one could refer to the proximodistal axis of the limbs as
being of the epimorphic type while the anteroposterior axis was morphallactic.
The results reported here demonstrate that at least in the latter case the
mechanism is not quite so straightforward. The process of specifying new
positional values in the reduplicated hands cannot proceed to completion
without cell division, but simultaneously there are changes in positional value
taking place across a significant width of tissue indicating long-range signalling.
The system shows characteristics of both types of pattern regulation and it seems
that in this case at least these twin concepts are misleading and unhelpful.
Other models also have their problems
The idea of using twin ZPA grafts to define a shared responding field was
suggested to me by Lewis Wolpert and Amata Hornbruch. They were using the
technique to compare the predictions of the source-sink diffusion and an intercalation model based on the type of cell interaction used in the polar coordinate
model of French, Bryant & Bryant (1976) as applied to the chick wing bud. Iten
has recently argued in favour of the latter interpretation (Iten & Murphy, 1980a,
b; Javois & Iten, 1980) and the experiment was designed as a test of her working
hypothesis.
The principle is that the tissues across the limb carry positional values in a
graded series. When tissues with disparate values are placed next to each other,
cell division is stimulated at the junction and 'new' cells adopt values intermediate to nearest neighbours (i.e. intercalate) until the difference between
176
D. SUMMERBELL
neighbours falls to a minimum step size equivalent to the equilibrium or normal
state. The posterior margin is therefore not an area of particular significance, but
is only dissimilar to tissue at the anterior margin. The intercalation hypothesis
predicts that following double grafts of posterior margin to the anterior margin,
the digits formed by the responding tissue should be a function of the position of
the responding tissue along the anteroposterior axis, and not of the width of the
responding tissue between the grafts.
A comparison of the results when the anterior graft was opposite somite 16 or
somite 17 (Fig. 3) shows that the digits formed between the grafts depended on
the distance between the grafts and not the position of the anterior graft.
Wolpert & Hornbruch (1980) have performed a much more thorough study of
this aspect with a wider range of anterior graft positions and I confirm their
conclusions. They thoroughly analyse and discuss their data and it seems unnecessary for me to do likewise.
Iten & Murphy (1980) and Javois & Iten (1980) have also performed similar
experiments using two ZPA grafts. However, the position of their anterior
graft was always kept constant so that they effectively varied only the distance
between grafts. They obtained results"compatible with Wolpert & Hornbruch
(1981) and with mine.
There is an unfortunate mystique concerning the reaction-diffusion model
(Gierer & Meinhardt, 1972) perhaps encouraged by the formal method of
presentation. Basically the model creates a concentration profile across a field.
It is no better and no worse at this than, for example, the source-sink diffusion
model. Some idiosyncrasy of the model may on occasion provide a particularly
apt explanation for a particular observation, but then some other observation
will require a particularly clumsy extension to the model.
The major strength of the model, compared with any averaging model (e.g.
source-sink diffusion, Wolpert et al. 1974; intercalation, French et al. 1976; or
the particularly simple and elegant averaging model of Maden, 1977) is the way
in which the reaction-diffusion mechanism can be used to determine which genes
are turned on for a given position along the gradient. A similar mechanism can
also be used to control switching in the genome. This feature is quite independent
of the specification of positional information, and interpretation by reactiondiffusion sits as well on the shoulders of source-sink diffusion as it does on its near
relative.
To return to the chick limb bud, Meinhardt (1977, 1978a, b) has suggested
that the reaction diffusion model provides a good natural explanation of the
observations reported in Tickle et al. (1975), particularly the phenomenon of
'distal deepening'. The explanation depends on a peculiarity of the model: that
two sources in close proximity cause mutual inhibition and a consequent overall
reduction in the concentration profile. This allows central deepening of the
concentration profile without a change in width and hence a more normal
complement of digits. It is not intuitively obvious how the reaction-diffusion
Growth and pattern in chick limb bud
111
model will adapt to the changing data and further simulation will be necessary.
The main difficulty will probably not be the lateral inhibition, but rather the
cause and effect of growth. The model is particularly sensitive when applied to
growing systems, requiring continual adjustment to the source strength of the
organiser.
The limb field is very small
The most surprising outcome of this project concerns the initial size of the
limb field.
First it was unexpected to discover from the quail grafts illustrated in Fig. 2
that the graft does not contribute appreciably to the limb. This observation lends
limited support to the argument of Smith (1979) that continued activity of the
ZPA is not necessary to produce a hand.
Second it was unexpected that so little distance is required to specify a whole
hand. Working from Fig. 3, the width of tissue needed to make two full hands
can be estimated as 575-675 fim. This suggests that the initial width of the field
necessary to produce a half reduplication must be no more than about 300 /wn.
This tissue then expands under the influence of the ZPA so that it will measure
(from Fig. 6) 500 /.im at stage 24 and 650 ju,m at stage 25/26 - the time at which
the hand plate starts to differentiate. This compares well with estimates for
normal development of 550 //m at stage 24 taken from Figs 6 and 7 in Stark &
Searles (1973) and 700 /im at stage 26 taken from Fig. 1c in Summerbell (1976).
It suggests a slight inaccuracy in my simulation (Summerbell, 1979) when the
width of the presumptive hand plate was taken as 550 fim at stage 25/26. It also
makes a rather profound difference to some of the other parameters in this
simulation. One of the problems was reconciling the very fast propagation of the
signal necessary for it to spread across the whole limb bud during initial development, with the rather slow changes that follow perturbation of the field later in
development. This incompatibility was solved by adopting a very long time for
the initial concentration profile to develop. I allowed the ZPA to function as
early as stage 10/11, the time at which the craniocaudal axis of the limb becomes
autonomous (Chaube, 1959). However, the earliest stage at which there is any
direct evidence of ZPA activity is stage 15 (A. B. MacCabe et al. 1973), which is
some 16 h later. By extending the growth regulation model used in this paper to
the normal case, it is possible to establish a concentration profile similar to that
found in the original simulation at stage 20, assuming ZPA activity to commence at stage 15.
I suggest therefore that one can think of the normal limb as having a presumptive anteroposterior presumptive digit field of about 300/tm at stage 15.
The field gradually expands during development until it reaches something
approaching equilibrium, with a width of about 650 jam, at stage 25/26 just
prior to differentiation.
178
D. SUMMERBELL
My thanks for advice and help go to John Asante, Jonathan Cooke, Mike Gaze, Larry
Honig, Amata Hornbruch, Lauri Iten, Malcolm Maden, Jonathan Slack, Victoria Stirling,
Cheryl Tickle, David Willshaw and Lewis Wolpert.
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