The Polar Coordinate Model of Positional Information in the Developing and Regenerating Limb
Supernumerary limb elements
Research on developing and regenerating limb buds has also shown another level of pattern formation. When anterior and posterior cells from regeneration blastema or limb buds are juxtaposed, the results are dramatic and strange: the resulting limb contains supernumerary structures, often with two or three sets of digits (Figure 1; Bryant and Iten, 1976; Javois and Iten, 1986).
Moreover, this patterning mechanism appears to be the same for both regenerating and normally developing limbs. When axolotl limb buds were transferred to regenerating axolotl blastema stumps, in a way that maintained the original polarity with respect to the stump, normal limbs developed. However, when the polarity of the anterior-posterior axis was reversed with respect to the stump, mirror-image supernumerary digits emerged (Figure 2; Muneoka and Bryant, 1982). These results strongly suggest that the patterning rules are the same for developing and regenerating limbs.
Polar coordinate model
By comparing such results in regenerating vertebrate limbs, insect limbs, and insect imaginal discs, French and his colleagues (1976; Bryant et al., 1981) have proposed a series of empirical rules that predict the outcome of a wide variety of experimental perturbations with regenerating appendages. Starting from Wolpertis (1969) premise that pattern arises from a cellis recognition of its relative positions in a developing population, they speculate that a cell assesses its physical location in a system of polar (clocklike) coordinates (Figure 3). In this system, each cell has a circumferential value (from 0 to 12) as well as a radial value (from A to E). In regenerating limbs, the outer circle represents the proximal (shoulder) boundary of the limb field; the innermost circle represents the most distal regions.
As we have seen, when normally nonadjacent tissues of a field are juxtaposed, duplications often arise. Yet other transplanted tissue (not of the field) will not cause these duplications. The polar coordinate model has been extremely useful in predicting the extent of these duplicated structures. The Shortes Intercalation Rule states that when two normally nonadjacent cells are juxtaposed, growth occurs at the junction until the cells between these two points have all the positional values between the original points (Figure 4). The circular sequence, like a clock, is continuous, 0 being equal to 12 and having no intrinsic value. Being circular, however, means that there are two paths by which intercalation can occur between any two points. For example, when cells having the values 4 and 7 are placed next to each other, there are two possible routes between them: 4, 5, 6, 7 and 4, 3,2, 1, 12,11, 10, 9, 8, 7. According to this model, the shortest route is taken. The exception, of course, is when the cells have values that fall exactly opposite each other in the coordinate system, so that there is no one shortest route. In this case, all values are formed between the two opposites.
The second rule is the Complete Circle Rule for Distal Transformation. Once the complete circle of positional values has been established on the wound surface, the cells proliferate and produce the more distal structures. The mechanism by which this is thought to occur is outlined in Figure 4 and, again, involves intercalation of structures between cells having different positional information (Bryant et al., 1981). The predictive value of these rules can be seen when a transplant is made between regeneration blastemas, a transplant in which the anterior and posterior axes are reversed (Figure 5). The result is a limb with three distal portions (Iten and Bryant, 1975). This outcome can be explained by viewing the anterior-posterior axis on the grid as having two opposite numbers say—3 and 9. In juxtaposing the values of 3 and 9, one generates a complete circle of values at each of the extreme sites and a smaller intercalating series at all other sites. The result is three complete circles, which, by the law of distal transformation, will generate three complete limbs from that point on.
The polar coordinate model also predicts the effects of regulation when a portion of the tissue is lost. The newly formed cells would have positional values intermediate between those of the remaining cells and would reconstruct the appropriate part of the tissue. Because the basis of regeneration appears to be the recognition of differences between adjacent tissues, it is probable that epimorphic pattern formation during regeneration and normal pattern formation during embryonic limb development are the result of the proximate interactions between adjacent cells rather than the result of long-range gradients (Bryant et al., 1981).
Retinoic acid and the intercalation
Crawford and Stocum (1988) showed that retinoic acid is able to change the positional values of the regeneration blastema cells in a proximal direction. Normal wrist blastema cells will sort out with other wrist cells in vitro and will migrate to the wrist region when transplanted to an amputated limb (Chapter 15). Wrist blastema cells soaked in retinoic acid sorted out in vitro and in vivo to the forearm region. Not only did the retinoic acid wrist cells sort out to the forearm level, but when retinoic acid-treated wrist blastema were apposed to forearm stumps, no intercalary regeneration was stimulated. Therefore, the cellular mechanism that recognizes the disparities between non-neighboring cells along the proximal-distal axis and initiates intercalary regeneration is proximalized along with the positional imemory.i
It is possible that retinoic acid acts as a morphogen to establish the positional values on the cell surfaces of the developing limb and the limb blastema cells. This may have important consequences for the interpretation of the retinoic acid as ZPA morphogen. Wanek and colleagues (S. Bryant, personal communication) have found that anterior chick limb bud cells adjacent to a retinoic acid-soaked bead acquire ZPA-like properties. If the RA-exposed cells are grafted to the anterior margin of a host limb, they act as a ZPA and cause the formation of supernumerary digits. When this experiment is done between retinoic acid-exposed chick cells and host quail embryos, the supernumerary digits are almost exclusively from the quail. Thus, retinoic acid treatment changes cells next to the bead into extreme posterior (ZPA) cells. Since one of the proposed properties of the ZPA is to make retinoic acid, the cells originally exposed to the retinoic acid-soaked bead are now able to produce more of this retinoic acid. This causes a problem with the gradient model, because if retinoic acid causes adjacent cells to become posterior ZPA-like cells, one should find the entire limb bud becoming progressively more ZPA-like and the levels of retinoic acid growing increasingly high, eliminating the gradient.
Bryant and her colleagues interpret these experiments to show that retinoic acid does not provide a gradient of positional information. Rather, retinoic acid is seen as being capable of transforming anterior limb bud tissue into posterior limb bud tissue. The host limbs would now contain iposteriori tissue (the graft of retinoic acid-treated anterior cells) next to anterior tissue (the host limb bud). The result would be intercalary regeneration to restore the positions between the two normally nonapposed tissues. In this interpretation, retinoic acid is an agent that can modify positional values within the limb field.
Bryant, S. V. and Iten, L. E. 1976. Supernumerary limbs in amphibians: Experimental production in Notophthalamus viridescens and a new interpretation of their formation. Dev. Biol. 50: 212-234.
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Crawford, K. and Stocum, D. L. 1988. Retinoic acid proximalizes level-specific properties responsible for intercalary regeneration in axolotl limbs. Development 104: 703-712.
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