We have suggested that the available data argue that growth is regulated by a balance between the non-uniform growth factors, Wg and Dpp, and a non-uniform inhibitor of proliferation. We now consider this conclusion in more detail to assess its ability to accommodate known properties of Drosophila discs.
A simple model
Although the balancing act between growth factors and inhibitors might be complex, it seems best initially to consider a relatively simple model. It is known that Wg and Dpp are independently required for growth, and that they act synergistically. In a simple synergistic relationship, the growth potential (GP) is a function of the product of the concentrations of Wg (W) and Dpp (D): GP = W × D. Note that a variety of quantitative relationships can underlie synergy, and a mathematical relationship is presented as a conceptual aid rather than a proposal of the precise nature of the synergy. We are suggesting that growth potential is counterbalanced by an inhibitor which sets a threshold that must be exceeded for actual growth (AG), that is: AG = [W × D] − I. Accordingly, the enigmatic relationship between the distributions of Wg and Dpp and the uniform growth would be explained if the strength of inhibition (I) varied as some function of the product of the concentrations of Wg and Dpp ().
There are numerous possible relationships between the negative and positive growth factors, and little information to direct a more detailed model. Nonetheless, to avoid being vague, we have developed our model on the premise that the inhibitor is not diffusible and that, once established, its concentration is independent of subsequent changes in Wg and/or Dpp concentrations. Such a gradient of a non-diffusible inhibitor could be set up, for instance, by localized induction of the inhibitor near the boundaries between territories, in response to high levels of Wg and/or Dpp, and deposition of the inhibitor in the basement membrane: expansion of the basement membrane associated with growth would successively isolate regions of the basement from the local source of the inhibitor, and would then dilute the inhibitor within the basement membrane as growth progressed.
While we assume that normal disc growth requires at least a slight imbalance between the growth factors and the growth inhibitor, our model has not advanced a mechanism to explain the regulation of this imbalance. Nonetheless, the skeleton model we do present can explain a number of observations. According to the above model, if a high Dpp concentration is induced that saturates the Dpp signaling pathway, then the resulting growth should be determined by Wg concentration. This is consistent with the observed expansion of the wing disc along the dorsal–ventral boundary upon expression of high levels of Dpp. Similarly, other results summarized above are compatible with this model, but this is not surprising as it was these results that suggested the model in the first place. It is more relevant to ask if the model offers explanations for other phenomena.
A possible explanation for intercalary growth
Regeneration in numerous systems, including Drosophila discs, is associated with stimulation of proliferation, which, together with subsequent differentiation, erases discontinuities in the pattern by intercalating the missing elements. This has led to the proposal that juxtaposing cells from incongruous positions stimulates growth and differentiation. In other words, cells somehow sense which cells are their correct neighbors and respond to discordant neighbors by proliferating until they restore normal neighbors.
According to this view of intercalary growth, the induction of extensive proliferation around a clone of cells that expresses ectopic Dpp might be a secondary response — first Dpp would transform cell fates, and the presence of incongruous neighbors would then induce proliferation. However, clones expressing a constitutively active form of a Dpp receptor demonstrate that the growth response is an autonomous feature of Dpp signaling [46
]. Although cells within these clones over-proliferate in response to the activation of the Dpp signaling pathway, no proliferation — that is, no intercalary growth — is induced in the surrounding cells, despite the incongruous juxtapositioning of cell fates at the border of the clone. The unique feature of the transformed cells within these clones is that they have a fate normally associated with a high concentration of Dpp, but lack high Dpp levels. The failure to activate intercalary growth in this circumstance suggests that it is not the juxtapositioning of incongruous cell fates, but rather the juxtapositioning of cells with discordant levels of Dpp that induces this proliferation. Similar data argue that Wg also has a fairly direct role in stimulating intercalary growth [43
]. Thus, the discordance that induces intercalary growth appears to be a discontinuity in Dpp and/or Wg morphogen concentrations.
Our model provides a rationale for the stimulation of proliferation by a discontinuity in the concentration of Dpp and/or Wg. In the undisturbed disc, neighboring cells have a similar balance of growth factors and inhibitor (or near balance, if growth is ongoing). Cells at substantially different distances from the compartment boundaries have a different balance (). As the growth factors are diffusible, juxtaposing cells from different positions will change the balance of growth factors and inhibitor in cells bordering the junction (). When cells with high levels of diffusible growth factor and high levels of fixed inhibitor abut cells with low levels of growth factor and inhibitor, the growth factors will diffuse across the junction to stimulate the growth of the cells with low inhibitor levels (). A region that has high Dpp and low Wg levels might have the same growth potential as a region that has low Dpp and high Wg levels; nonetheless, when these two regions are juxtaposed, growth should be induced — as a result of diffusion of the two ligands, the juxtaposed cells will have intermediate levels of both regulators, which synergize to increase the growth potential ().
According to the above model, intercalary growth ought to result whenever cells with different levels of Wg and/or Dpp are juxtaposed. Within each quadrant of the wing disc, bordered by two compartment boundaries, we expect each cell to experience a unique combination of Wg and Dpp concentrations (), governed by its distances from the morphogen sources at the compartment boundaries. The excision of cells from within a quadrant should therefore always induce intercalation. While excisions between quadrants might juxtapose cells with similar combinations of Wg and Dpp levels, growth is still expected because the cells will belong to different compartments: interactions between the different compartments should establish a new compartment border and thus a new source of growth factor, Wg or Dpp. Thus, together with other aspects of morphogen regulation, the proposed balance of growth factors and inhibitor can explain some important features of proliferation during regeneration. Although these proposals fail to address several mysteries, such as the mechanisms that lead to de novo regeneration of a compartment after its complete excision, it seems that the roles of Wg and Dpp in intercalary growth are worth exploring.
Inhibitors of proliferation exist
The cutting of imaginal discs without excision leads to transient proliferation, suggesting that normal contacts inhibit proliferation. So while positive signals from incongruous neighbors are generally invoked to explain the proliferation seen during intercalary regeneration, it appears that general negative signals arise simply from contact. If the strength of contact inhibition of growth varies across the disc, contact inhibition could represent the negative signal for growth required by the above model. Recently, it has been found that nitric oxide acts as an inhibitor of proliferation in Drosophila
], and it is a candidate for being an inhibitor that functions in conjunction with the growth factors Wg and Dpp. Perhaps the details of the regulation of this newly defined inhibitor will give us insights into the basis for program of growth control in discs.
One of the most mysterious features of morphogenesis is that structures form themselves as they grow. In considering pattern formation the dominant thoughts are of gradients of morphogens across a preexisting field. But patterns are generally formed in conjunction with the growth that produces the field of cells that is patterned. How are the actions of morphogens coordinated with the process of growth? Studies of Drosophila development have demonstrated tight connections between the regulators of pattern and growth itself. While exposing the mysteries to molecular analyses, the results also issue a challenge: the connections between the concentrations of the growth promoting factors Wg and Dpp, and the growth they promote, is not direct, but it appears that if we could understand it we would have gained real insight into a mechanism that gives shape to biological structures.