A study has been made of the morphogenetic properties of anterior and posterior skin from the lower forelimb of the axolotl. The basic experiment consisted of a graft of a half cuff of skin from a donor to a host limb followed by a 2-week healing period, amputation through the graft, and a study of the resulting regenerate. Limbs with double posterior skin formed double posterior regenerates and, in contrast, limbs with double anterior skin formed normal or slightly hypomorphic regenerates. Posterior skin from post-metamorphic animals had a similar but weaker effect to that from ordinary axolotls.

Immunological rejection of allografts could be completely avoided if the donor limb was transplanted to the flank of the host when both were at the stage of tail-bud embryos, and the skin graft was later carried out between the supernumerary limb and one of the host limbs. This technique was used to show that immunological rejection does not affect the formation of duplicates from the limbs with double posterior skin, and to facilitate the studies of the cellular provenance of the regenerate.

The cellular composition of duplicate regenerates was studied by using both triploid donors and triploid hosts. It was shown that the posterior side of the duplications consisted wholly of host tissue and the anterior side consisted of mixed donor and host tissue. Formation of the duplicated regenerate therefore seems to involve positional reprogramming of both donor and host tissues together with metaplasia of the donor tissue.

It was not possible to inhibit the duplication-inducing property of posterior skin by treatment with a variety of enzymes.

A model based on the serial threshold theory of regeneration is advanced to explain the results. This model successfully accounts for the observed non-equivalence of anterior and posterior skin, and also explains the different regeneration behaviour of anterior and posterior half limbs, the limited regeneration of double anterior limbs, and the pattern expansion and contraction shown by regenerates from double posterior limbs.

The axolotl is an animal which can regenerate its limbs after amputation and in which the spatial arrangement of structures in the regenerate is restored with very high fidelity. This formation of a complex spatial pattern distinguishes true regeneration from other phenomena such as the hypertrophy of the mammalian liver after a part has been removed, or the regrowth of nerve axons down a pre-existing tract. It poses a specific biological problem : how do the cells of the regeneration blastema ‘know’ which structures to turn into and in what relative order these should be arranged ?

Certain theorists of regeneration have postulated that the cells in each region of tissue in a differentiated limb, or any other organ capable of regeneration, are labelled with ‘positional values’ which vary in a continuous way across the organ (Wolpert, 1971; Bryant & Iten, 1976; Maden, 1977; Lheureux, 1977). According to these authors, when cells near the amputation surface dedifferentiate and divide to form the blastema, their positional values are erased and are recomputed in such a way that a complete set is reformed which is continuous with the positional values represented in the stump. The pathway of cytodifferentiation to be followed by each group of blastemal cells is then selected in accordance with their new positional value, irrespective of their cytological type in the previous limb.

In a theoretical paper (Slack, 1980a) I have argued that these positional values are made up of combinations of ‘on’ and ‘off’ states of a set of biochemical switches, and that the arrangement of these combinations, or ‘codings’ is such that the structure of the missing parts can be computed from the codings represented at the amputation surface without any long range interactions with the remaining part of the organ. If this view is accepted then the problem of pattern formation can be rephrased as: ‘What is the relation between the anatomical position and the coding and what are the rules for altering codings during regeneration?’ One method of attacking this problem experimentally is to alter the arrangement of tissues in the organ in order to provoke the regeneration of an abnormal pattern. If a normal limb is amputated then the pattern of the regenerate is the same as the original, but this is not generally true of abnormal limbs generated by embryonic manipulation or by surgery on adults (Swett, 1924; Newth, 1958). If enough reliable data can be collected on the relationship between starting patterns and final patterns we might be able to deduce the number and arrangement of codings and the rules for their interconversion, and once the rules are known it may become possible to make informed guesses about the biochemical nature of the codings.

For some years it has been known that grafts of skin from one part of the limb to another can derange the pattern of a regenerate which is formed after amputation through the grafts (Droin, 1959; Rahmani, 1960; Lheureux, 1972) and the active component is known to be the dermis rather than the epidermis (Carlson, 1975). In the present paper a systematic comparison is made between anterior and posterior skin with respect to their morphogenetic properties. These two surfaces of the limb are indistinguishable histologically but it is concluded that their codings differ and that the posterior edge has more switches on than the anterior edge. This type of difference between tissues of the same histological type but different position in the body has been called ‘non-equivalence’ by Lewis & Wolpert (1976).

The provenance of the different cells in the compound regenerates has been investigated using both triploid donors and triploid hosts, and a new method of ensuring immunological compatibility between cytologically-labelled grafts and hosts has been introduced by growing an embryonic limb rudiment of one ploidy on the flank of an embryo of the other ploidy.

In the Discussion a set of rules is proposed based on the serial threshold theory which can explain both the new results presented here, and also some previous experimental results published by myself and by other authors.

The basic graft which was used in these experiments was the transplantation of a half cuff of skin from one surface (anterior or posterior) of the lower forelimb to the other. The animals were axolotls of length 10–15 cm which were obtained either by natural or by artificial matings (the artificial mating procedure is given in Slack & Forman, 1980). They were allowed to develop in individual plastic containers to avoid cannibalism with its associated risk of the displacement of limb tissues. Up to 4–5 cm in length they were kept in 20 % Steinberg solution made up with glass-distilled water and fed daily on brine shrimps. Above this size they were transferred to tap water and fed three times per week, first on Tubifex and later on minced lambs’ hearts with supplementary vitamins and minerals. The aquarium temperature was 20 °C giving a water temperature of 18 °C.

The animals were anaesthetised in 1 /2000 MS222 (Sandoz) in tap water. The skin on one side (anterior or posterior) of the lower forelimb was removed with iridectomy scissors and fine forceps. It was transferred to a dish containing ‘normal amphibian medium’ (Slack & Forman, 1980) and examined to ensure that no muscle was adhering. A similar-sized piece of skin was removed from the host limb and discarded, and the graft was attached with its proximodistal and dorsoventral axes the same as the host and secured with four sutures, one at each corner (tied with ‘Ethilon’, W2814 Ethicon Ltd.). The host animals were returned to tap water and were allowed to recover in the dark at 10 °C for two days before being returned to the aquarium. Two weeks after the graft, both forelimbs were amputated through the mid-zeugopodium; in the case of the experimental limb this was approximately through the centre of the graft. Regeneration was complete after another 6–8 weeks, and both limbs were amputated through the upper arm and prepared for examination.

In some cases the donors or hosts were not just ordinary axolotls but had received some special treatment. Triploid animals were made as follows (see Namenwirth, 1974). Thirty minutes after artificial fertilization eggs were heated to 36 °C for 10 min which drives the second polar body back into the eggs. The larvae were allowed to hatch and screened for triploidy by examination of squashes of small pieces of tail tip by Nomarski interference microscopy (Fig. 1). According to Fankhauser & Humphrey (1943), the number of nucleoli per cell in the axolotl corresponds to the ploidy, so that normal larvae have two nucleoli per nucleus and triploids have three. This method yielded about 50 % triploids among the surviving larvae and also about 0 · 5 % uni-nucleolate cases which were presumed to be haploids. There was a small amount of mortality among the triploid larvae but those which survived and grew appeared to be identical to diploids, although a few which were grown to sexual maturity proved to have abnormal gonads; the females had rudimentary ovaries and the males had apparently normal testes but were sterile.

Fig. 1.

Axolotl larval tail-tip cells viewed by Nomarski differential interference microscopy, (a) Diploid, (b) triploid. Scale bars indicate 20 μm.

Fig. 1.

Axolotl larval tail-tip cells viewed by Nomarski differential interference microscopy, (a) Diploid, (b) triploid. Scale bars indicate 20 μm.

Animals bearing supernumerary limbs were prepared by grafting an extra limb rudiment from one stage-34 embryo to the flank of another (Slack, 1977, for updated grafting procedures see Slack, 1980b). These animals were reared in the same way as the normal ones and the skin grafts were later carried out between the supernumerary limb and one of the host limbs. The reason for this is that a supernumerary limb grown from a limb rudiment transplanted to the flank of a host embryo is later tolerated by the immune system of the host and it is therefore possible to prepare animals in which the supernumerary is triploid and the host diploid. So the fate of donor cells in the combination can be followed at any subsequent time without the complication of immunological rejection (Fig. 2).

Fig. 2.

Protocol for the experiments involving immunologically tolerant hosts.

Fig. 2.

Protocol for the experiments involving immunologically tolerant hosts.

Metamorphosed animals, here called ‘efts were prepared by giving repeated injections of L-thyroxine dissolved in ‘normal amphibian medium’ into the dorsal musculature of 10 cm axolotls. Injections were given three times a week, the dose being varied between 2 and 5 μg depending on the visible pace of metamorphosis. The gills and tail fin were usually resorbed after about 3 weeks after which the injections were stopped. Metamorphosis was judged to be complete when the skin pattern of white spots on a black background was fully developed. This was 6 to 8 weeks after commencement of the injections.

Limbs were prepared for examination either as whole mounts or as histological sections, the latter being necessary to locate the triploid tissue in triploid-diploid combinations. For whole mounts the limbs were fixed in 4 % formaldehyde, 1 % CaCl2, 50 mM-Tris pH 7·0 overnight. They were bleached, where necessary, by exposure to Mayer’s bleach overnight, followed by H2O2 (100 vol.)/distilled water/alcohol 20:10:70 until white. They were equilibrated in 1 % HC1 in 70 % alcohol and stained for 1 h in 1 % Victoria Blue 4R (Lambs) in the same solution. They were dehydrated and cleared in Oil of Wintergreen. Limbs were classified into one of the following groups :

Normal

Hands bear four digits, digital formula I, II, III, IV. The first, second and fourth have two and the third digit has three phalanges. The usual complement of carpals is eight (three proximal, two central, three distal) but limbs are still classified as normal if adjacent carpals are fused. Most control regenerates have the radiale fused to the radius.

Hypermorphic

These contain all the normal structures plus some additional ones. e.g. I, II, III, IV, IV.

Hypomorphic

These contain only some of the normal structures, e.g. I-II-III.

Duplicate

Hands have variable numbers of elements but these comprise two sets of posterior structures arranged around a longitudinal axis of mirror symmetry. In this work most have five or six digits with their associated carpals, e.g. IV’, III’, IT, II, III, IV.

Partial duplicates

These are similar to duplicates but lack one posterior extremum, e.g. III’, II’, II, III, IV.

Duplicate with serial repetition

Similar to duplicates but with one or more elements repeated away from the axis of symmetry, e.g. IV’, IV’, III’, III’, II’, II, III, IV.

Representative examples of each type are shown in Fig. 3.

Fig. 3.

Types of regenerate formed in these experiments, (a) normal, (b) hypomorphic, (d) duplicate, (e) partial duplicate, (f) duplicate with serial repetition. Scale bars represent 2 mm.

Fig. 3.

Types of regenerate formed in these experiments, (a) normal, (b) hypomorphic, (d) duplicate, (e) partial duplicate, (f) duplicate with serial repetition. Scale bars represent 2 mm.

For histology the limbs were fixed in 4% glutaraldehyde 0·1M sodium phosphate pH 7·4 overnight at 4 °C, washed in buffer, and decalcified in 5%EDTA in 0·1 M sodium phosphate pH 7·4 for several days. They were dehydrated, embedded via xylene in 58 °C wax, and sectioned at 15 μm. The sections were brought to water and incubated for 1 h at 37 °C in 0·2 mg/ml DNAase in 30 mM-MgSO4, 10 mM Hepes pH 7·4. This removes most of the nuclear DNA from muscle and cartilage cells and allows the nucleoli to be visualised more easily (Namenwirth, 1974). They were stained in Unna-Pappen-heim stain with double pyronin (0·2 % methyl green, 0·125 % pyronin in 0·1 M sodium acetate pH 4·8), dehydrated in graded acetones and mounted in DPX.

Although most cells in a triploid animal have three nucleoli, all three may not be seen in a particular section if part of the nucleus is in the adjacent section. So the proportion of trinucleolate cells seen is always an underestimate of the proportion of triploid cells in the tissue. In order to make quantitative comparisons it is necessary to examine the same tissue type, since larger nuclei are less likely to lie entirely within a section, and to control the orientation of the organ relative to the section since for non-spherical nuclei orientation also affects the chances of finding the whole nucleus in a section.

Structure of compound regenerates

In Table 1 are shown the structures of regenerates which were formed following a skin graft, a two week healing period, and amputation through the graft. The limbs with double anterior skin regenerated normal or hypomorphic limbs, the latter lacking the posterior parts. In contrast, limbs with double posterior skin regenerated duplicates with double posterior symmetry.

Table 1.

Classification of structures of regenerated limbs

Classification of structures of regenerated limbs
Classification of structures of regenerated limbs

Some control experiments were carried out in which anterior skin was grafted anteriorly and posterior skin grafted posteriorly. These all gave normal regenerates after amputation through the graft. Normal regenerates were also formed when the posterior half cuff was removed and not replaced, the wound simply being allowed to heal for two weeks before amputation.

Since one of the objects of these experiments was to follow the fate of cells in marked grafts, operations had to be carried out between different animals rather than between right and left limbs of the same animal. So it was of some importance to determine whether immunological rejection of the graft had any bearing on the morphogenetic phenomena. Rejection of skin grafts in urodeles has been investigated by Cohen (1971), who describes it as a slow process which lasts many weeks and depends on several weak histocompatibility loci. Rejection in the present series was detectable in the dissecting microscope by the destruction of graft melanophores, and in histological sections by infiltration of the grafts by small mononuclear cells (Fig. 4,b). No rejection was apparent in sections at the time of amputation, which was 2 weeks after the graft, or at the stage of dedifferentiation one week later. After 6–8 weeks of regeneration the degree of rejection varied in individual cases from very slight to very extensive. In the series of grafts in which double posterior skin was assembled, eleven cases were carried out between different individuals, and eleven cases using donor limbs which had been originally grafted to the flank of the host at the stage of the tailbud embryo following the protocol of Fig. 2. The former group of regenerates showed various degrees of rejection of the donor tissue while the latter group showed no rejection at all, judged either by gross inspection or by histology. Since the structures of the regenerates obtained in the two series were not significantly different it can be concluded that in these experiments immunological rejection neither potentiates nor inhibits the formation of duplications. However, it is to be expected that the effect of the graft would be inhibited if a long enough healing period were allowed between the graft and the amputation, because eventually the grafted skin would be completely destroyed.

Fig. 4.

Histology of skin, (a) Normal axolotl skin. Epi, epidermis; L, Leydig cell; BM, basement membrane; Der, dermis; M, melanophore; Muse, muscle, (b) axolotl skin allograft infiltrated by small mononuclear cells, (c) eft skin. Epi, epidermis; Der, dermis; Muse, muscle; Gl, mucus gland. Scale bars indicate 50μm Sections are 6μm thick and stained with haematoxylin and Biebrich scarlet.

Fig. 4.

Histology of skin, (a) Normal axolotl skin. Epi, epidermis; L, Leydig cell; BM, basement membrane; Der, dermis; M, melanophore; Muse, muscle, (b) axolotl skin allograft infiltrated by small mononuclear cells, (c) eft skin. Epi, epidermis; Der, dermis; Muse, muscle; Gl, mucus gland. Scale bars indicate 50μm Sections are 6μm thick and stained with haematoxylin and Biebrich scarlet.

It was thought to be of some interest to examine some metamorphosed axolotls (efts), since in other amphibia regenerative ability often falls off at metamorphosis (Scadding, 1977) and the eft has skin with a quite different histological structure, notably a thick dermis containing huge mucous glands (Fig. 4a, c). A number of grafts were carried out in which posterior forearm skin from the eft was grafted to the anterior forearm of an axolotl and the usual protocol followed thereafter. The regenerates showed a range of structures intermediate between those obtained from the double anterior and double posterior skins, with a few duplications and some minor abnormalities (Table 1). In this group it did seem as though the cases which did not form duplicates were those showing the most graft rejection. The eft donors had their legs amputated at the proximal limit of the graft and these regenerated normally, although both healing and regeneration were about three times slower than for a similar size axolotl. This small series is perhaps not conclusive, but it could indicate that the codings are still present after metamorphosis but that interactions between eft and axolotl skin occur less readily than between axolotls.

Provenance of cell in duplicates

In order to interpret the morphology of compound regenerates in terms of their formation it is important to know the cellular composition of the different parts. If it can be shown that formerly anterior host tissue has contributed to posterior structures, then this means that the tissue in question has been reprogrammed in terms of its positional coding. If it can be shown that graft-derived cells contribute to tissue types not present in the graft then this means that metaplasia has occurred.

In the present work triploidy has been used as the marker and a number of cases have been examined histologically in which either the donor or the host was triploid. All these experiments involved grafts of posterior skin to the anterior. Altogether, seven cases of diploid grafts to triploid hosts were examined histologically, and sixteen cases of triploid grafts to diploid hosts. Of the latter, seven cases were performed with tolerant hosts following the protocol of Fig. 2.

Where the host was triploid and the donor skin diploid the results were as follows. On the posterior side of the duplication, which was the side away from the grafts, all tissues contained abundant trinucleolar cells with frequencies similar to those in triploid control limbs. On the anterior side, there were many trinucleolar cells in the epidermis and connective tissue but their frequency in the cartilages fell off from the mirror plane to the anterior digit IV (see Table 2 and Fig. 5 f).

Table 2.

Percentage of trinucleolar cells found in the metacarpals of double posterior duplications

Percentage of trinucleolar cells found in the metacarpals of double posterior duplications
Percentage of trinucleolar cells found in the metacarpals of double posterior duplications
Fig. 5.

(a) Cartilage cells in a triploid limb, (b) muscle cells in a triploid limb, (c) a trinucleolar cell in the mesenchymal part of the early blastema resulting from a triploid skin graft on a diploid host, (d) a trinucleolar cartilage cell in the anterior part of the duplicate regenerate formed from a triploid skin graft on a diploid host, (e) a trinucleolar muscle cell in the anterior part of a similar regenerate. (f) a trinucleolar cartilage cell anterior to the midline in a duplication formed from a diploid graft to a triploid host. Nucleoli are indicated by arrows, scale bars represent 10 μm.

Fig. 5.

(a) Cartilage cells in a triploid limb, (b) muscle cells in a triploid limb, (c) a trinucleolar cell in the mesenchymal part of the early blastema resulting from a triploid skin graft on a diploid host, (d) a trinucleolar cartilage cell in the anterior part of the duplicate regenerate formed from a triploid skin graft on a diploid host, (e) a trinucleolar muscle cell in the anterior part of a similar regenerate. (f) a trinucleolar cartilage cell anterior to the midline in a duplication formed from a diploid graft to a triploid host. Nucleoli are indicated by arrows, scale bars represent 10 μm.

Where the host was diploid and the donor skin triploid nine grafts were made to non-tolerant hosts. In four of these the regenerates were examined eleven days after the amputation which is the stage of dedifferentiation. They showed no immunological rejection and had abundant trinucleolar cells on the anterior side of the apical ectodermal cap. A few trinucleolar cells were also found among the dedifferentiated mesenchymal cells on the anterior side (Fig. 5 c). In the other five cases the regenerates were examined after 6–8 weeks. All of these showed extensive graft rejection and only a few trinucleolar cells could be recognised because of the extensive degradation of the tissues. Those that were found were present in the epidermis, muscle and cartilage on the anterior side of the duplication. In the seven cases in which the hosts were tolerant there was no rejection and in most but not all cases many more trinucleolar cells were visible. They were abundant on the anterior side of the mirror plane, particularly in digits III’ and IV’. Particularly large numbers were found in the cartilages, but they were also found in muscle cells, connective tissue and epidermis (Fig. 5d, e and Table 2).

It seems therefore that the posterior side of the duplication is composed wholly of host tissue and the anterior side of a mixture of donor and host tissue. With respect to metaplasia, the present results confirm those of Dunis & Namenwirth (1967) which showed that descendent cells from a skin graft could become incorporated into the muscle and cartilage of the regenerate.

It therefore seems as though formation of the duplication involves extensive positional reprogramming of host tissue and some reprogramming together with metaplasia of donor tissue.

Enzyme treatment of posterior grafts

The reprogramming ability of posterior but not anterior skin implies that the former contains something which the latter lacks. It was thought that if the substances which embody the codings were present in the extracellular matrix as suggested by Tank & Holder (1979), then perhaps they could be destroyed by enzymic treatment without destroying the cells. Accordingly posterior halfskin cuffs were soaked in various concentrations of nine enzymes for 1 h at room temperature before being grafted to the anterior side of host limbs. The grafts were allowed to heal for 2 weeks and the limb amputated through the graft. In this experiment, a positive result would consist of normal limbs growing after high dose treatment and duplications growing after low-dose treatment, a negative result would consist of duplications growing after any dose. The results are shown in Table 3. There is perhaps a slight tendency for high concentrations of the proteases to inhibit the formation of duplications, but the really remarkable thing is that the treatments have so little effect. There are so many possible reasons for this failure that the experiment cannot be regarded as informative and it is mentioned here solely to record a negative result.

Table 3.

Structure of regenerates formed after enzyme treatment of posterior skin cuff

Structure of regenerates formed after enzyme treatment of posterior skin cuff
Structure of regenerates formed after enzyme treatment of posterior skin cuff

The results presented in this paper show that anterior and posterior skin are nonequivalent. A graft of posterior skin to the anterior followed by amputation results in the formation of double posterior duplications in which there is some reprogramming of host tissue and some metaplasia and reprogramming of donor tissues. The converse graft results in the formation of normal or hypomorphic regenerates.

These and other results will now be discussed in terms of the serial threshold theory of regeneration (Slack, 1980). According to this theory pattern formation in regeneration can be accounted for by assuming that the differentiated organ is partitioned into territories which consist of groups of cells plus their associated extracellular matrix. These territories are coded in such a way that all of a set of biochemical switches are on at one end and successive territories across the organ each have one more switch off. It is assumed that the ‘on’ state of a switch corresponds to the presence of a particular substance, the switch product, and that the ‘off’ state corresponds to its absence. So each territory contains the information for making all the territories further down in the sequence in much the same way that each of a stack of Russian dolls contains all of the smaller dolls in the set. In the case of the anteroposterior axis of the amphibian limb, the results suggest that the posterior edge should be identified as the region in which all the switches are on.

In order to explain the mechanism of regeneration one has to do more than identify the arrangement of the codings: it is necessary also to explain how a blastemal territory can become respecified by its surroundings, and this can be done by postulating two simple relationships between the states of the switches in neighbouring blastemal territories. The first, which is necessary for the spread of pattern information through the tissue, is the dominance of higher over lower switches such that the product of a particular switch turns on all the lower switches in the sequence but has no effect on the higher ones. The second is a spatial averaging property which causes each switch in each territory to tend to adopt the same state as in the majority of neighbouring territories. This sort of diffusion process necessarily accompanies situations of intercellular communication.

It is assumed that there is an early stage immediately following dedifferentiation during which the cells of the blastema have all their switches off. The pattern of the regenerate is then controlled by the codings of the most distal layer of territories in the stump because the switch products present in this region can influence the codings adopted by the neighbouring blastemal territories. These can then in turn influence their neighbours and so the blastema as a whole will pass through a sequence of unstable states until a final stable arrangement of codings has been set up. This stable arrangement corresponds to a ‘determined’ blastema, although since it would still be possible to change the codings at this stage by surgical rearrangement the determination is not irreversible.

The process will be illustrated by a series of diagrams which represent the blastema viewed from the dorsal aspect as shown in Fig. 6. Each territory will be shown as a hexagon and its coding by a group of binary digits. The ‘on’ state of each switch is shown as ‘1’ and the ‘off’ state as ‘O’. An empty hexagon represents the coding 00000, which means that all the switches are off. In the diagrams the lowest row of hexagons belong to the most distal layer of stump tissues next to the blastema and since these are differentiated tissues their codings cannot be changed. The remainder of the hexagons represent the mesenchymal part of the blastema. In reality the blastema would be growing at the same time as these territories are being specified but in order to keep the presentation simple the process is depicted as though the blastema has a fixed size and the specification proceeds stepwise from the proximal edge.

Fig. 6.

Diagram of a regenerating left limb viewed from the dorsal side. The following figures depict the region enclosed by the dashed line.

Fig. 6.

Diagram of a regenerating left limb viewed from the dorsal side. The following figures depict the region enclosed by the dashed line.

In order that the predicted sequence of events be unambiguous it is necessary to put the principles of serial dominance and spatial averaging into a precise form, and this can be done as follows with (1) and (2) expressing the former and with (3) expressing the latter.

  1. The ith switch is turned on in a territory (hexagon) with no time delay if the i +1 th switch is on in that territory. This ensures that the sequence of switches which is on in a territory is uninterrupted.

  2. The i th switch is turned on at time t if the i +1 th switch was on at time t-1 in one or more of the neighbouring territories. This ensures that positional information spreads through the blastema and that a series of decreasing codings is set up along the axis in question. A special rule is necessary for the top switch in the sequence (the nth) because it has no higher product which can turn it on. It seems reasonable to suppose that it can be turned on by its own product in territories adjacent to a lateral edge. Therefore : the nth switch is turned on in edge territories at time t if it was on in one or more neighbouring territories at t-1.

  3. In the absence of influences from higher switches, the state of the i th switch at time t is adjusted to be the same as that in the majority of the neighbouring territories at t-1. This means that the boundaries between regions tend to be straightened and to lie perpendicular to the axis. Since hexagons pack with a coordination number of six, ‘majority′ here means four or more out of six, or in the case of edge territories, three out of five, three out of four or two out of three.

The operation of the model is depicted in Fig. 7 for normal regeneration. At t = 0 only the row of stump territories have codings and the blastemal territories have all their switches off. By t = 1 the first row of blastemal territories has become specified, although not necessarily with their final codings. A later intermediate stage is shown at t = 3, and by t = 5 a configuration of codings is reached which is stable in the sense that it does not spontaneously change thereafter. This is of course the normal pattern in which all switches are on at the posterior edge and each territory towards the anterior has one more switch off.

Fig. 7.

Time course of specification of the blastema during normal regeneration.

Fig. 7.

Time course of specification of the blastema during normal regeneration.

In this model the normal pattern is not the only stable pattern and it is to be expected that a rearrangement of the stump territories may lead to the regeneration of a stable but abnormal pattern. If an extra posterior territory is added to the anterior edge, as shown in Fig. 8, then the same set of rules generate a double posterior duplication. This is the result obtained in the experimental section of this paper when a posterior half cuff of skin is grafted to the anterior side and the combination later amputated through the graft. Furthermore, if only the right hand column of blastemal territories is regarded as being composed of cells derived from the graft then the cellular composition indicated by the model is also roughly similar to that found in reality with a large contribution of donor tissue at the anterior edge but with much of the duplicate being formed from host tissue. The widespread metaplasia of donor tissues found experimentally indicates that the clonal origin of cells is not relevant to the new codings which they acquire in the blastema, and so this factor is not included in the model.

Fig. 8.

Predicted regenerate following a graft of posterior skin to the anterior.

Fig. 8.

Predicted regenerate following a graft of posterior skin to the anterior.

The converse experiment of grafting anterior skin to the posterior and later amputating through the graft is simulated in Figs 9 and 10. In Fig. 9 an extra anterior territory is added to the posterior edge of the stump. This has little effect on the regenerate which develops a normal pattern slightly twisted towards the operated side. In Fig. 10 the graft replaces the most posterior territory of the stump, and this gives rise to a hypomorphic regenerate lacking the most posterior structures. Reference to Table 1 will show that the normal limb and the hypomorph are the two most common outcomes of this experiment. In Table 1 it is also shown that the simple removal of the posterior skin leads to normal regeneration. This result is consistent with the model if it is assumed that during the healing period the gap is filled by posterior tissue from the proximal and distal edges of the wound.

Fig. 9.

Predicted regenerate following a graft of anterior skin to the posterior.

Fig. 9.

Predicted regenerate following a graft of anterior skin to the posterior.

Fig. 10.

Predicted regenerate following a graft of anterior skin to the posterior with removal of the most posterior host territory.

Fig. 10.

Predicted regenerate following a graft of anterior skin to the posterior with removal of the most posterior host territory.

The application of the serial threshold theory to the amphibian limb in the form of the present model also allows the explanation of a number of related experiments by myself and others which have not been satisfactorily explained in the past :

Half limb regeneration

The morphogenetic potency of anterior and posterior half limbs has been studied by Goss (1957) and Maden (1979). The posterior half from the upper arm will frequently regenerate an entire hand whereas the anterior half forms a regenerate consisting only of a few anterior structures. This situation is represented in Fig. 11 by a full size blastema with only a partial set of stump territories, and it may be seen that the posterior half contains information which initiates a course of events close to the normal while the anterior half does not. If the posterior blastema were only of half size in terms of territory number then it should form a posterior half regenerate, as found by these authors for half lower arms.

Fig. 11.

Predicted regenerates from anterior and posterior half limbs.

Fig. 11.

Predicted regenerates from anterior and posterior half limbs.

Pattern contraction of double anterior limbs

Double anterior limbs have been constructed surgically by Bryant & Baca (1978), Stocum (1978) and Tank (1978). They show little if any capacity for regeneration and the structures which are formed are of anterior character (Fig. 12).

Fig. 12.

Pattern contraction in the regenerate formed from a double anterior limb.

Fig. 12.

Pattern contraction in the regenerate formed from a double anterior limb.

Pattern contraction and expansion of double posterior limbs

Bryant (1976) showed that surgically constructed double posterior limbs would regenerate few if any structures. Slack & Savage (1978) described regeneration behaviour of embryonically produced double posterior limbs and found good regeneration with a slight tendency for pattern contraction and also a number of cases of expansion. Tank & Holder (1978) partly resolved this conflict of results by showing that contraction of regenerates from surgically constructed limbs became more acute the longer the healing time allowed between the graft and the amputation. The exact course of events during healing is not known, but it seems likely that cell death, cell division, revascularisation and changes in the extracellular matrix would all affect the diffusion of the active factors. If diffusion constants were reduced then the size of the territories would be reduced and more territories would be established in a blastema of given size. If diffusion constants were increased then less territories would be established. Such changes will thus be represented here by changes in territory number across the blastema.

In Fig. 13A-C are shown cases in which the blastema narrows, keeps the same width and widens. The first shows a severe contraction in which three types of territory are eliminated from the midline of the regenerate. The second shows a retention of all the types of territory present in the stump, and the third shows the addition of two extra types of territory in the midline. This is exactly the type of behaviour observed by Slack & Savage (1978). In this study we found that expansion and contraction always involved the addition or subtraction of elements at the centre of the pattern, and that the new elements were always neighbours of the ones already present. Furthermore branching of midline cartilages could occur and could be either proximally or distally directed. Both types of branching are shown by the group of territories coded 01111 in Fig. 13 C : these are separated in the stump, then coalesce in the proximal part of the blastema and diverge again more distally.

Fig. 13.

(a) Pattern contraction in the regenerate from a double posterior limb where the number of territories across the blastema is less than that in the stump. (b) Pattern stability in the regenerate from a double posterior limb in which the number of territories across the blastema is the same as that in the stump, (c) Pattern expansion in the regenerate from a double posterior limb in which the number of territories across the blastema is greater than that in the stump.

Fig. 13.

(a) Pattern contraction in the regenerate from a double posterior limb where the number of territories across the blastema is less than that in the stump. (b) Pattern stability in the regenerate from a double posterior limb in which the number of territories across the blastema is the same as that in the stump, (c) Pattern expansion in the regenerate from a double posterior limb in which the number of territories across the blastema is greater than that in the stump.

Reprogramming of blastemas

Iten & Bryant (1975) showed that very early blastemas could be reprogrammed in the anteroposterior axis if they were inverted on the contralateral stump, later blastemas were partially reprogrammed and produced hypermorphs and duplicates, and later blastemas still could produce complete supernumerary hands from the incongruent junctions. According to the present model, the very early blastema is completely bland, the intermediate blastema has some territories specified but is still labile, and the later blastema is fully determined. In the last case the formation of a supernumerary limb requires a ‘de-determination’ at the junction and the formation of an intercalary blastema with polarity depending on the codings of the adjacent territories.

The idea which lies at the heart of the serial threshold theory is that a region of tissue can regenerate structures with all the Tower’ codings but not those with the ‘higher’ ones. This property is shown not only in the anteroposterior axis of the amphibian limb but also in the distal regeneration of vertebrate and arthropod appendages and in the posterior regeneration of worms (see Slack, 1980a). The widespread occurrence of this type of phenomenon must suggest the possibility of a common biochemical basis for the incremental codings in all such cases. It is therefore unfortunate that to date most developmental biochemistry has concentrated on the differences between different tissues rather than on the differences between the same tissue in different places.

I should like to thank Shirley Williams for technical assistance, Bob Bloomfield for supervising the axolotls and John Cairns for his interest in serial thresholds.

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