We have proposed that positional information along the anteroposterior axis is specified by a signal from the polarizing region and that position may be specified by the concentration of a diffusible morphogen. While this model can account for a variety of results it is now clear that a model based on intercalation by growth of positional values can do the same. The distinction between the two models lies in whether a grafted polarizing region can alter existing positional values and in the distance over which it exerts its influence. The two models make different predictions as to the effect of grafting two polarizing regions. The intercalation model predicts that this effect will be the sum of two single grafts, whereas the morphogen model predicts different results depending on how close together the two polarizing regions are placed. The pattern of digits following grafts of two polarizing regions show that it is sensitive to the distance between the grafts and consistent with a model based on long-range interaction, such as a diffusible morphogen.

The pattern of cellular differentiation in the chick limb has been considered in terms of positional information (Wolpert, Lewis & Summerbell, 1975). For the anteroposterior axis we suggested that position is specified with respect to a region at the posterior margin of the limb, the zone of polarizing activity, originally discovered by Saunders & Gasseling (1968) (reviewed, Tickle, 1980). Our model proposed that a signal from this region set up a gradient of positional information along the anteroposterior axis. More specifically, we suggested a mechanism based upon diffusion of a morphogen from the polarizing region (Tickle, Summerbell & Wolpert, 1975). It was assumed that the morphogen was broken down at a rate proportional to its concentration, and thus an exponential concentration gradient with its highpoint at the posterior margin was set up. If the signal from the polarizing region was a diffusible morphogen, it could be expected to diffuse across a substantial portion of the limb bud.

Following a graft of an additional polarizing region, the new distribution of the morphogen was assumed to assign to the cells new positional values. Using the digits as markers for different positions along the anteroposterior axis, it was shown that this model could reasonably account for the pattern obtained when an additional polarizing region was placed at different positions along the anteroposterior axis. An important proviso was that the limb bud widened prior to digit specification (Tickle et al. 1975; Summerbell & Tickle, 1977). Recently, Summerbell (1979) has provided further evidence for such a gradient in the early limb bud. He inserted barriers at different positions along the anteroposterior axis and found that the defects obtained were consistent with position being specified by a diffusible morphogen. Further evidence has also been provided by MacCabe & Parker (1976) and Smith, Tickle & Wolpert (1978). However, following discussion with Drs Susan Bryant and Laurie Iten, it has become apparent that many of the results obtained by grafting on additional polarizing regions to the developing wing bud could be accounted for on a rather different model, intercalary regeneration, similar to that observed in insect imaginai discs and cockroach legs (French, Bryant & Bryant, 1976). The essential mechanism is that when tissues are grafted such that non-contiguous positional values are opposed, growth occurs at the junction and new positional values are generated until the discordance is no longer present (see Iten & Murphy, 1980).

The difference between the two models can be illustrated by how they account for the pattern of digits when a polarizing region is grafted at the anterior margin, or if it is placed near the tip of the limb. When it is placed at the anterior margin opposite somite 16, the pattern of digits is 4 3 2 2 3 4, and when at the centre of the limb the pattern is typically 2344 or 234434 depending on its precise position.

For the intercalary model in Fig. 1, it is assumed that there is an even distribution of positional values along the anteroposterior axis of the limb bud. The three digits, 2, 3 and 4 are considered to form opposite somites 18 and 19 and they are thus assigned positional values 5, 6/7 and 8 respectively, which is more or less in line with Summerbell (1979). When a polarizing region is grafted to different positions along the anteroposterior axis such that non-contiguous positional values are adjacent to one another, intercalary growth occurs so as to generate the missing values. Thus, when the polarizing region, which has a positional value of 10 is placed at the anterior margin, there is intercalation between the graft positional value 10 and the adjacent host value of 3. Thus, a complete new set of digits is formed (Fig. 1,b). When the graft is opposite somite 18, the predicted result is 2 3 4 4 4 (Fig. 1 c) though experiments show that one of the 4’s is usually absent. The model can thus reasonably account for grafts of the polarizing region to different positions along the anteroposterior axis.

Fig. 1

Diagrams to illustrate the pattern of digits to be expected in terms of a model based on intercalation. It is assumed that, as in (a), there is a set of positional values along the anteroposterior axis and that the digits develop at particular positional values. For example, digit 2 forms at positional value 5. When grafts are made of polarizing region, whose positional value is 10, to different positions along the anteroposterior axis, intercalation occurs, and the pattern of digits will be determined by the resulting positional values. When the polarizing region is grafted opposite somite 16 as in (b) intercalation occurs to give 4 3 2 2 3 4. When grafted opposite somite 18 (c) the pattern after intercalation is 23 4 4 4. In (d) polarizing regions are grafted opposite somites 16 and 18, and the resulting pattern of digits is 4 3 2-23444.

Fig. 1

Diagrams to illustrate the pattern of digits to be expected in terms of a model based on intercalation. It is assumed that, as in (a), there is a set of positional values along the anteroposterior axis and that the digits develop at particular positional values. For example, digit 2 forms at positional value 5. When grafts are made of polarizing region, whose positional value is 10, to different positions along the anteroposterior axis, intercalation occurs, and the pattern of digits will be determined by the resulting positional values. When the polarizing region is grafted opposite somite 16 as in (b) intercalation occurs to give 4 3 2 2 3 4. When grafted opposite somite 18 (c) the pattern after intercalation is 23 4 4 4. In (d) polarizing regions are grafted opposite somites 16 and 18, and the resulting pattern of digits is 4 3 2-23444.

The model for a diffusible morphogen providing the positional signal assumes that the polarizing region is a source which keeps the concentration of the morphogen at a constant value of 100 (Fig. 2). The substance is assumed to be broken down at a rate proportional to its concentration, thus giving an exponential gradient. It is important to note that once the position of the digits is fixed, only one parameter can be varied. This is the relation between the diffusion constant and the rate of breakdown of the morphogen and it determines the steepness of the morphogen gradient. We have chosen a gradient such that the thresholds for digits 2, 3 and 4, are morphogen concentrations 4, 15 and 45 respectively. Following grafting of a polarizing region, the limb widens 50% at 36 h after the graft (Tickle et al. 1975; Smith & Wolpert, 1980). This is the time at which the digits begin to be laid down (Summerbell, 1974). Thus, in calculating the new distribution of the morphogen following a polarizing region graft, we have assumed that the distance between the polarizing regions has increased by 50%. As can be seen, this model gives similar predictions for the standard grafts, but it should be regarded as no more than semi-quantitative since numerous assumptions such as diffusion in a single dimension and point sources, are made. A more biochemically realistic gradient without point sources could be generated using the mechanism proposed by Meinhardt & Gierer (1974).

Fig. 2
(a) The concentration of a postulated morphogen, produced by the polarizing region, along the anteroposterior axis. Digits are specified at different concentrations of the morphogen. In (b) a polarizing region has been grafted opposite somite 16 and the resulting pattern of digits is 4 3 2 2 3 4. In (c) the polarizing region has been grafted opposite somite 18 and the pattern of digits is 23 444. Note the similarity of pattern of digits in (b) and (c) with those predicted by the intercalation model in Fig. 1 (b) and(c).In(d)polarizingregions have been grafted opposite somites 16 and 18 and the pattern of digits is 43 3 44 4 and is different from that predicted by intercalation in Fig. 1 (d). In (e) polarizing regions are grafted opposite somites 16 and 17 and the pattern of digits is 4 4 3 3 4. The expression for the concentration of the morphogen for two sources distance d apart is
formula
C source has been taken as 100, and P which reflects morphogen breakdown and diffusion constant, as 70.
Fig. 2
(a) The concentration of a postulated morphogen, produced by the polarizing region, along the anteroposterior axis. Digits are specified at different concentrations of the morphogen. In (b) a polarizing region has been grafted opposite somite 16 and the resulting pattern of digits is 4 3 2 2 3 4. In (c) the polarizing region has been grafted opposite somite 18 and the pattern of digits is 23 444. Note the similarity of pattern of digits in (b) and (c) with those predicted by the intercalation model in Fig. 1 (b) and(c).In(d)polarizingregions have been grafted opposite somites 16 and 18 and the pattern of digits is 43 3 44 4 and is different from that predicted by intercalation in Fig. 1 (d). In (e) polarizing regions are grafted opposite somites 16 and 17 and the pattern of digits is 4 4 3 3 4. The expression for the concentration of the morphogen for two sources distance d apart is
formula
C source has been taken as 100, and P which reflects morphogen breakdown and diffusion constant, as 70.
Fig. 3

Normal wing at 10 days of incubation. The pattern of digits is 2 3 4.

Fig. 3

Normal wing at 10 days of incubation. The pattern of digits is 2 3 4.

Fig. 4

Mirror image reduplication following a polarizing region grafted opposite somite 16. The pattern of digits is 4 3 2 2 3 4.

Fig. 4

Mirror image reduplication following a polarizing region grafted opposite somite 16. The pattern of digits is 4 3 2 2 3 4.

The essential difference between the two models is that between morphallaxis and epimorphosis (Wolpert, 1971). In morphallaxis, positional values are changed and interaction and signalling may occur over most of the field, whereas with epimorphic regulation, all existing positional values are retained and new ones generated by growth (Wolpert, 1971; Cooke, 1979). In terms of the particular case under consideration, the distinction lies in two important processes: (1) The change in positional values adjacent to the polarizing region. If there is signalling as in morphallaxis, then one would expect the polarizing region to alter the positional values of the cells adjacent to it. With an epimorphic process, all the existing positional values should be retained and the new ones generated by growth. No positional values should be lost (see Fig. 1). (2) The distance over which the polarizing region exerts its influence. In the case of morphallaxis it would signal over about 400 μm altering the positional value of adjacent cells (Fig. 2). In epimorphosis, in principle at least, the signal from the polarizing region need not extend more than one cell diameter.

In drawing the distinction between morphallaxis and epimorphosis, it is the processes involved that are important and not any absolute distinction. As Cooke (1979) has pointed out, both may be involved in a particular system. Moreover, even in epimorphosis, the distance over which the interactions occur may be quite extensive. Thus, the important questions are whether the polarizing region alters existing positional values and over what distance it exerts its influence.

We have approached these problems by grafting two additional polarizing regions to different positions in the limb bud. As pointed out above, a single polarizing region grafted to the anterior margin - opposite somite 16-gives 4 3 2 2 3 4, whereas if it is grafted opposite somite 18, it typically gives 2344. Both results are explicable in terms of the two models. What will happen if the two grafts are made in the same limb? What structures will develop between the two grafted polarizing regions? According to an intercalation model the results sould be additive, giving 4 3 2 2 3 4 4 since no positional values would be lost (Fig. 1 d). Most important, when one polarizing region is opposite somite 16 then wherever the other polarizing region is placed, digits 4 3 2 2 3 4 should always form between the two grafts. However, on a signalling model the prediction would be that 4 3 3 4 form between the grafts since the two polarizing regions would be so close to each other that the concentration of the morphogen would be too high to allow a digit 2 to form between them (Fig. 2d).

We have thus explored the effect of grafting one polarizing region opposite somite 16 and a second polarizing region at different positions along the anteroposterior axis.

The model we have analysed in Fig. 1 is based on linear intercalation, and is thus similar to that proposed by Bohn (1970) for the proximodistal axis of the cockroach leg. Since Iten & Murphy (1980) have suggested that the polar coordinate model may be more appropriate, it is necessary for us to explain why we have not used it. Our linear intercalation model largely accounts for the standard results, whereas, as yet, no polar coordinate model has been put forward to account for the results of the polarizing region grafts. The diagnostic features of the polar coordinate model in other systems are regeneration, duplication, and incomplete distal transformation when a complete circle of circumferential values is not present (French et al. 1976.) None of these have been demonstrated in the chick limb bud. For example, removal of posterior tissue often leads to the loss of digit 4 (Tickle et al. 1975: Fallon & Crosby, 1975). In a polar coordinate system regeneration, or duplication, should result. As has been pointed out by Fallon & Crosby (1975) the supernumerary structures that form when the tip is rotated 180 0 are dependent on the polarizing region. By contrast dorsoventral inversion of the tip does not lead to the formation of supernumerary structures (Saunders, Gasseling & Gfeller, 1958) as required by the polar coordinate model.

The results of Iten & Murphy (1980) do not demand a polar coordinate model for their interpretation and, in fact, on the whole, are consistent with the long-range signal model. Their approach has been to graft anterior margin tissue as a wedge to the polarizing region. They found that this results in supernumerary limb structures being formed. They recognise that this can be understood in terms of a signal to the graft from the host polarizing region, but point out that anterior margin tissue gives more structures than tissue taken from a slightly more posterior position, and this is not predicted with such a model. The difference is quite small and is essentially that tissue from opposite somite 16/17 results in an additional 4 3 whereas tissues from opposite 17/18 gives only 3. We have no explanation for this difference but do not regard it as evidence for a polar coordinate model. In fact, no explanation is offered by Iten & Murphy in terms of their model.

Both a linear intercalation model and a polar coordinate model would be expected to give similar results when anterior tissue is confronted with posterior margin, whether the anterior margin is grafted to a posterior position or whether posterior margin is grafted anteriorly. This is not the case since the former invariably results in an extra digit 2, whereas the latter rarely does according to Iten & Murphy (1980). This is to be expected in terms of our model since the graft will be too close to the polarizing region to allow a digit 2 to form.

Finally it is very difficult to understand attenuation in terms of a polar coordinate model. Attentuation of the signal from the polarizing region has been demonstrated in several ways. Smith, Tickle & Wolpert (1978) showed that when the polarizing region was subjected to increasing doses of y-irradiation, the ‘highest’ new digit specified changed from 4 to 3 to 2. Tickle (1981) has shown the same phenomenon both by diluting the polarizing region grafted with non-polarizing region cells, and by grafting small numbers of cells in a monolayer.

Fertilized White Leghorn eggs from a local breeder were incubated at 38 ± 1°C and windowed on the fourth day of incubation. The embryos were staged according to Hamburger & Hamilton (1951). Embryos at stages 19 and 20 were chosen as hosts and polarizing regions were taken from donors at stage 21. The polarizing region was excised from opposite somite 20 and measured not more than 150 by 150 μm. The site for the graft was prepared by removing a cube of tissue the same size as the graft from along the anterior margin of the host limb bud. The graft was kept in place with a platinum wire pin. As controls, anterior margin tissue from opposite somite 16 was used for grafting in the same manner. For some grafts of polarizing region, no material was removed, but following Iten & Murphy (1980) a slit was made in the host and a wedge-shaped piece of tissue from the polarizing region inserted.

Six days after the operation the limbs were fixed in 5% trichloracetic acid, stained with Alcian green (Summerbell & Wolpert, 1973), cleared in methyl salicylate and examined.

The results of grafting two polarizing regions are shown in Table 1, and Table 2 has been constructed from Table 1 by determining the pattern of the digits formed between the grafted polarizing regions. The results in Table 2 show the distribution of the ‘lowest’ digits found, digit 2 being ‘lower’ than digit 3. In constructing Table 2 from Table 1 it was necessary to infer where the polarizing regions had been placed. In some cases this is quite easy where digit 4 provides the boundaries. In other cases it is less obvious. However, we can make use of Summerbells’ (1980) results which are substantially similar and which are based on observation of the limbs following grafting.

Table 1

Pattern of digits following grafts of two polarizing regions

Pattern of digits following grafts of two polarizing regions
Pattern of digits following grafts of two polarizing regions
Table 2

Digits that develop between two grafted polarizing regions

Digits that develop between two grafted polarizing regions
Digits that develop between two grafted polarizing regions

From Tables 1 and 2 it can be seen that as the second polarizing region is placed in successively more anterior positions, the probability of a digit 2 forming between them falls. When it is placed opposite somite 19, the pattern of digits is unchanged and is usually 4 3 2 2 3 4, as when only polarizing region is grafted to the anterior margin opposite somite 16. At least one digit 2 forms between the polarizing regions in every case, and two digit 2s form in most cases. However, when the second polarizing region is placed opposite somite 18/19, two digit 2s form in only 40% of the cases, and a digit 2 only develops 80% of the time. When the second polarizing region is opposite somite 18 two digit 2s only form in 12% of the cases, and no digit 2 at all forms in 56% of the limbs. When the polarizing regions were grafted opposite somites 16 and 17, no digit 2 formed at all (Fig. 5).

Fig. 5

Limbs that developed following the grafting of polarizing regions opposite somites 16 and 17. In (a) the pattern of digits is 4344334 and in (b) it is 4 3 3 4, note that there are two ulnae.

Fig. 5

Limbs that developed following the grafting of polarizing regions opposite somites 16 and 17. In (a) the pattern of digits is 4344334 and in (b) it is 4 3 3 4, note that there are two ulnae.

In all the above grafts, host material was removed when the polarizing region was grafted. This might affect the results, and so following a suggestion of L. Iten, polarizing regions were also grafted as wedges, no host material being removed. When these were grafted opposite somites 16/17 and 17/18, no digit 2 formed between them (Fig. 6). A further control involved grafting a polarizing region opposite somite 16 and a piece of anterior margin (from opposite somite 16) to opposite somite 18. As can be seen from Table 3, a digit 2 is formed in all cases though the number of double digit 2s is reduced by half.

Table 3

Pattern of digits following grafts of combinations of polarizing region and anterior margin

Pattern of digits following grafts of combinations of polarizing region and anterior margin
Pattern of digits following grafts of combinations of polarizing region and anterior margin
Fig. 6

Limb that developed following graft of two polarizing regions as wedges opposite somites 16/17 and 17/18. The pattern of digits is 4 3 4 3 3 4. Note that the distal humerus is reduplicated and the bud seems to be split into two.

Fig. 6

Limb that developed following graft of two polarizing regions as wedges opposite somites 16/17 and 17/18. The pattern of digits is 4 3 4 3 3 4. Note that the distal humerus is reduplicated and the bud seems to be split into two.

Some grafts of a single polarizing region and anterior margin were also carried out as controls (Table 4). A polarizing region opposite somite 18 usually gave 2 3 4, or 2 3 4 4 (Fig. 7). When it was grafted opposite somite 17, a central digit 2 formed in 40% of the cases, and when it did not, an anterior digit 3 usually developed. When a polarizing region was grafted as a wedge into a slit opposite somite 17/18, there was only one case of a digit 2 centrally, whereas an anterior digit 2 formed in every case. (Table 5) (Fig. 8).

Table 4

Pattern of digits following single polarizing region grafts

Pattern of digits following single polarizing region grafts
Pattern of digits following single polarizing region grafts
Table 5

Pattern of digits following wedge-shaped grafts without removal of host tissue

Pattern of digits following wedge-shaped grafts without removal of host tissue
Pattern of digits following wedge-shaped grafts without removal of host tissue
Fig. 7

Limb that developed following a graft of a polarizing region opposite somite 18.

Fig. 7

Limb that developed following a graft of a polarizing region opposite somite 18.

Fig. 8

Limbs that developed following a graft of a polarizing region as a wedge opposite somite 17/18. In (a) the pattern of digits is 23 43 3 4 and there is a radius with two ulnae. In (b) the pattern of digits is 2344334 and there is one radius and three ulnae. It appears in this case that the bud has been split into two.

Fig. 8

Limbs that developed following a graft of a polarizing region as a wedge opposite somite 17/18. In (a) the pattern of digits is 23 43 3 4 and there is a radius with two ulnae. In (b) the pattern of digits is 2344334 and there is one radius and three ulnae. It appears in this case that the bud has been split into two.

These results show that when two polarizing regions are grafted to the early limb bud, such that one is at the anterior margin, then the pattern of digits formed between them depends on the distance between the two grafts (Table 2). When the two polarizing regions are far apart, two digit 2s usually form between them. However when one is opposite somite 16 and the other opposite somite 18, two digit 3s is the typical result. When polarizing regions are opposite somites 16 and 17, no digit 2 forms at all. This is not due to the removal of material to make place for the grafted polarizing regions since a similar result is obtained when polarizing regions are grafted, without removing host material opposite somites 16/17 and 17/18.

These results strongly indicate that an intercalary model of the type outlined in the introduction is not valid, since it predicts the presence of two digit 2s between the two polarizing regions in all cases. By contrast, the model based on a diffusible morphogen accounts for the results reasonably well considering how idealized it is. The concentration of the diffusible morphogen and thus the pattern of digits formed is very sensitive to the distance between polarizing regions. When the initial distance is about 600 μm or less the concentration everywhere is too high for digit 2 to be specified.

It is important to remember that all the diffusion curves have been based on a 50% increase in the distance between the grafted polarizing regions when the digits are specified. Following a polarizing region graft, widening starts within about 10 h and the width has increased by 50% within 36 h (Smith & Wolpert, 1980). If this increase in width is prevented by a low dose of X-irradiation following a polarizing region graft then the pattern of digits will be altered because the host and grafted polarizing regions will remain closer together. This should result in the absence of digit 2 and this is in fact what happens (Smith & Wolpert, 1980).

The effect of polarizing region on growth has been studied by Cooke & Summerbell (1980) who found a significant increase in labelling with [3HJ-thymidine within a few hours after grafting. Summerbell (1981) has specifically studied the effect on growth along the anteroposterior margin using double polarizing region grafts.

It is of interest to consider the pattern of digits formed when the polarizing regions are close together as when they are at somite 16 and 17, or in slits opposite somites 16/17 and 17/18. In several cases, as many as 7 digits were obtained and this is the maximum so observed. A typical pattern has 4 3 4 4 3 3 4 which can be understood in terms of the anterior 4 3 4 lying between the two grafted polarizing regions (Figs 5 and 6). This is clearly illustrated by first considering a polarizing region graft in a slit opposite somites 17/18 where a typical pattern was 2 3 4 4 3 3 4. When an additional polarizing region is placed at 16/17, the anterior 2 is transformed to a 4. It also means that three digits 4 3 4 can form from about one somite’s width of material. One can exclude significant contribution from the polarizing region (Summerbell, 1981). This is consistent with the presumptive digit pattern of Summerbell (1979) where the three digits in the normal limb occupy just over a somite’s length of limb-bud mesoderm. When polarizing regions are grafted opposite somites 16 and 17 only digit 4 should be expected to form between them (Fig. 2e). However, as pointed out in several cases, a 4 3 4 developed. This may reflect a delay in the diffusion of the morphogen. It should be noted that in the model presented here it is assumed that equilibrium has been achieved by the time the digits are specified.

An examination of the curves with respect to the idea of thresholds for digits shows that in some cases much thicker digits, or fused digits, might be expected. This is not normally the case and digits, particularly the phalanges, are remarkably discrete. However, sometimes the metacarpal of, for example, digit 3 is very thick, and distally there are two sets of phalanges, Fig. 8(a). More proximally, it is quite common to find fusion between ulna and radius. It thus seems that there may be some additional mechanism for keeping digits discrete.

In one case where a polarizing region was grafted opposite somite 16 and a piece of anterior margin grafted opposite somite 18 a 3 2 4 pattern resulted. This is the first time we have observed a 2 adjacent to a 4 in over a thousand grafts. It can be understood in terms of the anterior margin graft causing damage to the apical ridge and thus loss of the host digit 3.

In conclusion, the results presented here are consistent with the signal from the polarizing region being a diffusible morphogen which acts over a distance of several hundred microns. Further direct evidence for such long-range signalling has been obtained by Honig (1981). He interposed leg tissue between the grafted polarizing region and the responding wing-bud tissue and showed that the polarizing region could affect tissue more than 200 /an away from it.

This work is supported by the Medical Research Council.

We wish to thank Dr C. Tickle for her comments and advice, D. Wolpert for a computer programme, and Miss M. Maloney for preparing the paper.

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