/. Embryol. exp. Morph. 76, 147-155 (1983)
Printed in Great Britain © The Company of Biologists Limited 1983
A test of the predictions of the boundary model
regarding supernumerary limb structure
By M. MADEN 1
From the National Institute for Medical Research, Mill Hill, London, U.K.
SUMMARY
The model proposed in the preceding paper (Meinhardt, 1983) makes specific predictions
about the handedness of supernumerary limbs generated after 180° rotation of blastemas.
These predictions are tested here by re-examining, in detail, the structure of 100 of these
supernumeraries. Of the four predictions, only one was found not to hold. The other three are
remarkably precise in their predictions and fit perfectly with the data. A possible reason for
the failure of this one prediction is suggested.
INTRODUCTION
In the last few years many models have been presented which attempt to
explain some or all aspects of pattern formation in amphibian limb regeneration
(review Tank & Holder, 1981). There are three areas of pattern formation which
comprehensive models must be capable of encompassing. The first concerns
experimental data on the proximodistal axis. It includes observations such as the
sequential regeneration of cartilage elements and that intercalation occurs when
distal blastemas are grafted to proximal levels but not vice versa.
The second aspect concerns experimental data on the transverse axes (anteroposterior - AP and dorsoventral - D V), involving procedures such as cutting half
the limb away, irradiating half the limb or making double- half limbs.
The third concerns the generation of supernumerary limbs which are produced
after either contralateral or ipsilateral grafting of regeneration blastemas. As a
result of detailed studies of the structure of supernumerary limbs (Maden, 1980,
1982; Maden & Mustafa, 1982) the following facts emerged. Supernumeraries
generated by contralateral grafting of blastemas to invert the anteroposterior
(AP) axis arise at the anterior and/or posterior poles and they have the handedness of the stump. After contralateral grafts to invert the dorsoventral (DV) axis
supernumeraries arise at the dorsal and/or ventral poles and have the handedness of the stump. But following inversion of both transverse axes (APDV) one,
two or three supernumeraries can appear at various locations. In regenerating
axolotl limbs there are four types of structure of which APDV supernumeraries
1
Author's address: Division of Developmental Biology, National Institute for Medical
Research, The Ridgeway, Mill Hill, London NW7 1AA, U.K.
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M. MADEN
are composed. These are normal, mirror imaged in the DV axis (double dorsal
or double ventral), part normal/part mirror imaged and part normal/part inverted. An example of each type is shown in Fig. 1 as well as a fifth type of supernumerary, the double posterior limb. This is an additional structure, only found
in significant numbers after ipsilateral inversion of Rana limb buds (Maden,
1981; Maden, Gribbin & Summerbell, 1983).
It is this latter aspect of pattern formation which severely tests most models
because they must be able to explain such variability of structure. This is the
subject of the work reported here - to see how the model proposed in the
accompanying paper (Meinhardt, 1983) copes with this data and to test its specific predictions about handedness of supernumeraries.
Class 1
Class 3
Class 2
D
D
Class 4
Class 5
Fig. 1
D
r
Supernumerary limb structure
149
RESULTS AND DISCUSSION
Predictions of the model regarding supernumerary limbs
As just described, there is an existing body of data on supernumerary limbs
which any valid model must be capable of explaining. Firstly DV and AP supernumeraries appear at the axial poles, their structure is normal, they have handedness of the stump and they are probably composed of both stump and graft
tissues. These facts are adequately encompassed by Meinhardt's model (fig. 6 of
Meinhardt, 1983). This is not by any means novel, as many other models do
likewise (French, Bryant & Bryant, 1976; Stocum, 1978; Slack, 1980).
Secondly, the model provides an explanation for the frequent observation of
'displaced' supernumeraries. When two supernumeraries are produced after a
blastemal rotation one of them (usually the posterior one) is displaced relative
to the other. Two examples of this are shown in Fig. 2 and can also be seen in fig.
2c of Wallace & Watson (1979) andfig.3b of Stocum (1982). However, it must
be said that this phenomenon does not always occur and not only after APDV
or AP inversions as expected, but also after DV inversions (see fig. 5 of Bryant
& Iten, 1976).
Thirdly, there is a great diversity of structure in supernumeraries generated by
inversion of both transverse axes (APDV supernumeraries). Meinhardt's model
predicts the existence of five types of structure - normal, mirror imaged, part
Fig. 1. Thefiveclasses of supernumerary structure which appear in APDV supernumeraries. Thefirstfour can only be revealed by serial sections to study their muscle
patterns because the anteroposterior axis (as revealed by cartilage staining) is normal. These four classes are exemplified by experiments on axolotl regeneration
blastemas. Thefifthclass does involve the anteroposterior axis and is exemplified by
a cartilage-stained limb from experiments on the developing limb buds of Rana.
Class 1 - normal. A section through the metacarpal level showing a normal muscle
pattern with crescent-shaped extensores digitorum breves (edb) on the dorsal surface
of the limb (arrows) and a large mass of muscle, composed of 16 separate muscles,
on the ventral side. A = anterior, P = posterior, D = dorsal, V = ventral.
Haematoxylin and eosin staining. Mag. x50. Class 2 - mirror imaged. The upper
section is a double dorsal limb with edb on both dorsal and ventral surfaces. Mag.
x45. The lower section is a double ventral limb with no edb and large amounts of
muscle dorsally and ventrally which fuses to completely surround the digits in muscle. Mag. x48. Class 3 - part normal/part mirror imaged. The upper section shows
a limb in which the two left hand digits are normal with edb on the dorsal surface
(arrows) and the two right hand digits are double dorsal with edb above and below
(compare with Class 2). This is part normal/part double dorsal. Mag. x45. Lower
section shows the two left hand digits are normal and the two right hand digits are
completely surrounded in muscle (compare with Class 2). This limb is part normal/
part double ventral. Mag. X50. Class 4 - part normal/part inverted. The two right
hand digits are in the normal orientation with edb (arrows) on the dorsal surface and
ventral muscles below. The two left hand digits are upside down with edb below
(arrows) and normal ventral muscle on the upper surface. Mag. x 50. Class 5 - double
posterior. Victoria-blue-stained Rana limb showing the rotated limb (upper limb)
and a double posterior supernumerary with the digital formula of 5 4 4 5. Mag. x30.
Supernumerary limb structure
149
RESULTS AND DISCUSSION
Predictions of the model regarding supernumerary limbs
As just described, there is an existing body of data on supernumerary limbs
which any valid model must be capable of explaining. Firstly DV and AP supernumeraries appear at the axial poles, their structure is normal, they have handedness of the stump and they are probably composed of both stump and graft
tissues. These facts are adequately encompassed by Meinhardt's model (fig. 6 of
Meinhardt, 1983). This is not by any means novel, as many other models do
likewise (French, Bryant & Bryant, 1976; Stocum, 1978; Slack, 1980).
Secondly, the model provides an explanation for the frequent observation of
'displaced' supernumeraries. When two supernumeraries are produced after a
blastemal rotation one of them (usually the posterior one) is displaced relative
to the other. Two examples of this are shown in Fig. 2 and can also be seen in fig.
2c of Wallace & Watson (1979) andfig.3b of Stocum (1982). However, it must
be said that this phenomenon does not always occur and not only after APDV
or AP inversions as expected, but also after DV inversions (see fig. 5 of Bryant
&Iten, 1976).
Thirdly, there is a great diversity of structure in supernumeraries generated by
inversion of both transverse axes (APDV supernumeraries). Meinhardt's model
predicts the existence of five types of structure - normal, mirror imaged, part
Fig. 1. Thefiveclasses of supernumerary structure which appear in APDV supernumeraries. Thefirstfour can only be revealed by serial sections to study their muscle
patterns because the anteroposterior axis (as revealed by cartilage staining) is normal. These four classes are exemplified by experiments on axolotl regeneration
blastemas. Thefifthclass does involve the anteroposterior axis and is exemplified by
a cartilage-stained limb from experiments on the developing limb buds of Rana.
Class 1 - normal. A section through the metacarpal level showing a normal muscle
pattern with crescent-shaped extensores digitorum breves (edb) on the dorsal surface
of the limb (arrows) and a large mass of muscle, composed of 16 separate muscles,
on the ventral side. A = anterior, P = posterior, D = dorsal, V = ventral.
Haematoxylin and eosin staining. Mag. x50. Class 2 - mirror imaged. The upper
section is a double dorsal limb with edb on both dorsal and ventral surfaces. Mag.
x45. The lower section is a double ventral limb with no edb and large amounts of
muscle dorsally and ventrally which fuses to completely surround the digits in muscle. Mag. x48. Class 3 - part normal/part mirror imaged. The upper section shows
a limb in which the two left hand digits are normal with edb on the dorsal surface
(arrows) and the two right hand digits are double dorsal with edb above and below
(compare with Class 2). This is part normal/part double dorsal. Mag. x45. Lower
section shows the two left hand digits are normal and the two right hand digits are
completely surrounded in muscle (compare with Class 2). This limb is part normal/
part double ventral. Mag. x50. Class 4 - part normal/part inverted. The two right
hand digits are in the normal orientation with edb (arrows) on the dorsal surface and
ventral muscles below. The two left hand digits are upside down with edb below
(arrows) and normal ventral muscle on the upper surface. Mag. x50. Class5-double
posterior. Victoria-blue-stained Rana limb showing the rotated limb (upper limb)
and a double posterior supernumerary with the digital formula of 5 4 4 5. Mag. x30.
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M. MADEN
s,
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s2 j ?
2A
^
B
Fig. 2. Two examples of 'displaced' supernumeraries. Victoria blue staining to show
the cartilage patterns. (A) A pair of APDV supernumeraries (Si and S2) generated
by 180° ipsilateral rotation of a blastema (G). Si appeared on the posterior side of
the stump (anterior side of the grafted blastema) and is displaced distally relative to
S2 which appeared on the anterior side of the stump (posterior side of the grafted
blastema). (B) A pair of AP supernumeraries (Si and S2) generated by contralateral
grafting of a blastema (G) to invert the anteroposterior axis. Si appeared on the
posterior side of the stump (anterior side of the graft) and is displaced slightly distal
to the anterior supernumerary (S2). Mag. (A) xl5, (B) xl3.
normal/part mirror imaged, part normal/part inverted and double posterior.
All five types are found after inversion of Rana limb buds (Maden etal. 1983) and
only four types after inversion of axolotl regeneration blastemas (Maden &
Mustafa, 1982). The difference between these two species is explained by variation in parameters such as the circumference of the leg cylinder.
Fourthly, the model explains the production of supernumerary limbs at angles
of rotation of less (or more than) 180°. Ipsilateral rotation of blastemas through
angles of 45 °-315 ° provokes the generation of supernumerary limbs (Wallace,
1978; Maden & Turner, 1978; Wallace & Watson, 1980; Turner, 1981; Stock,
Krasner, Holder & Bryant, 1980).
These latter two aspects represent a considerable advance in theoretical
analysis because previous models have not been capable of explaining such
diverse behaviour. But in addition, Meinhardt's model makes further specific
predictions about the handedness of normal and complex APDV supernumeraries which is related to their position of origin. These are:-
Supernumerary limb structure
151
(1) A supernumerary which grows out at the posterior host side has the opposite handedness of the host.
(2) A supernumerary which grows out at the anterior host side has host handedness.
(3) In supernumeraries with changing DV polarity the anterior part has the
expected handedness as listed under (1) and (2). In the posterior part it is the
reverse.
(4) Partially symmetrical limbs can occur in the anterior or posterior part of
a supernumerary limb. If the posterior part is symmetrical, the anterior part
should have the handedness listed under (1) and (2). If the anterior part is
symmetrical, the posterior part should have the opposite handedness to that
listed in (1) and (2).
These predictions are clearly very stringent and can be tested on an existing
body of data already presented (Maden & Mustafa, 1982), but which has not
been analysed in such detail. This was a study of 100 supernumerary limbs
generated by ipsilateral inversion of both axes and so provides a large enough
sample for analysis.
Do the predictions fit the data?
Prediction 1: This applies to supernumeraries of normal structure which were
located in the posterior half of the host limb. Eight cases were of this type and
of these, two were of opposite handedness to the host and six of the same
handedness. These data do not conform with the prediction.
Prediction 2: This again applies to supernumeraries of normal structure, but
those located in the anterior half of the host limb. Seven cases were of this type,
all of which were of the same handedness as the host. This therefore fully supports the prediction.
The reason for the contradiction of prediction one, but correspondence with
prediction 2, is that as pointed out in Maden & Mustafa (1982), all single supernumeraries of normal structure are of host handedness. Opposite handedness
supernumeraries only appear when they are one of a pair (Table 2 of Maden &
Mustafa, 1982). Therefore this phenomenon is not position dependent, as Meinhardt's predictions state. Examples of supernumeraries which do and do not fit
predictions 1 and 2 are shown in Fig. 3.
Prediction 3: There were 24 supernumeraries with changing DV polarity (part
normal/part inverted - Table 1 of Maden & Mustafa, 1982). 21 of these could
be analysed in enough detail to test prediction 3.19 of these 21 fitted the prediction perfectly, two examples of which are shown in the drawings of Fig. 4. The
two supernumeraries that did not conform were the only ones in this sample
where the blastema had derotated. Clearly, derotation would totally disrupt the
axial organization of the supernumerary and therefore these two abnormal cases
can justifiably be excluded, thereby giving a 100 % fit to the predictions. Thus in
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M. MADEN
V
Fig. 3. Two examples of normal supernumeraries generated by 180° inversion of
blastemas on left limbs (see Fig. 1, Class 1). The outer circle represents the stump,
the central elipse represents the inverted blastema and the smaller elipse represents
the supernumerary. (A) Here a left-handed supernumerary appeared at the anterior
side of the stump. Being of the same handedness as the stump, this supernumerary
conformed with prediction 2 of the model. (B) Here a left-handed supernumerary
appeared at the posterior side of the stump. Being of the same handedness as the
stump, this supernumerary contradicted prediction 1 of the model.
Fig. 4. Two examples of part normal/part inverted supernumeraries after 180°
inversion of blastemas on left limbs - (see Fig. 1, Class 4). Same representations as
in Fig. 3. (A) The supernumerary (small elipse) appeared on the anterior side of the
stump. The anterior part of the supernumerary had left handedness and the posterior
part right handedness. This conforms with prediction 3 of the model. (B) A supernumerary (small elipse) which appeared at the posterior side of the stump. Each part
of the supernumerary has the opposite handedness to (A) and therefore conforms to
prediction 3 of the model.
Supernumerary limb structure
153
Fig. 5. Two examples of part normal/part mirror-imaged supernumeraries after
180 ° inversion of blastemas on left limbs, showing that the mirror imaging can occur
either in the anterior or the posterior part of the supernumerary (see Fig. 1, Class 3).
Same representations as in Fig. 3. (A) Posterior part of the supernumerary mirror
imaged (double dorsal), anterior part of left handedness. This conforms to prediction
4 of the model since it appeared on the anterior side of the stump. (B) Anterior part
of the supernumerary mirror imaged (double ventral), posterior part of left handedness. This conforms to prediction 4 of the model since it appeared on the posterior
side of the stump.
contrast to the normal supernumeraries just discussed the precise structure of
part normal/part inverted supernumeraries is position dependent.
Prediction 4: 21 cases of part normal/part mirror-imaged limbs were analysed
in detail to test prediction 4. The mirror-imaged part of the supernumerary was
in the posterior half in 8 cases and in the anterior half in 13 cases. There seems
to be no preference for which half is mirror imaged therefore. The half that is
normal, however, should follow the rules of predictions 1 and 2, i.e. be position
dependent. Of the 21 cases, 19 fitted the predictions perfectly, 2 did not. These
latter two were, as in the previous example, both limbs where the blastema had
derotated and should not really be included. Two examples of supernumeraries
of this type are shown in Fig. 5. Thus prediction 4 fitted the data 100 %.
CONCLUSIONS
The model presented in the preceding paper (Meinhardt, 1983) encompasses
many aspects of limb development and regeneration from the positioning of the
limb primordium in the early embryo to the developmental and regenerative
behaviour following a variety of surgical manipulations. It is proposed that the
condition required for a limb to develop or regenerate is the presence of a DV
border in anterior tissue flanked on one side by polarizing (posterior) cells. As
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M. MADEN
such it is capable of explaining experimental data on the polarizing zone of
amphibians and the zone of polarizing activity of chicks. With regard to
regeneration experiments it provides an explanation for the many observations
which have revealed a difference between the anterior and posterior sides of the
limb (see Tank & Holder, 1981) and the generation of supernumerary limbs.
There have been other models which have described one or some of these
aspects of pattern formation in limbs, but not one of them has been so all
encompassing. What particularly distinguishes Meinhardt's model from these
others is that the complex array of supernumerary limb structures generated by
180 ° rotation of blastemas can also be explained. Two types of structure, the part
normal /part inverted limbs and the part normal/part mirror-imaged limbs, are
totally contrary to other models based on local intercalation and continuity rules
such as the polar coordinate model (French et al. 1976). What is more, these
structures regenerate themselves after amputation (Maden, 1982) which again
is contrary to continuity rules.
In addition, Meinhardt's model makes specific predictions about the handedness of parts of the supernumeraries which depend upon their position of origin.
These predictions have been tested here and with one exception found to be
wholly consistent with the experimental data. The exception concerns single,
normal supernumeraries whose structure should have been position dependent
like the other types, but was not. It is possible that these single, normal supernumeraries are the exception because they represent regeneration from the
stump in the absence of any interaction between stump and host. This is currently
being tested with the use of the triploid marker which will not only provide an
answer to this specific question, but further test the validity of contemporary
models.
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{Accepted 13 April 1983)