Dissecting the mystery of embryonic scaling: The Scalers Hypothesis and its confirmation in sea urchin embryos

Embryonic scaling, the ability of embryos to regulate their spatial structure in proportion to size, remains a fascinating yet poorly studied problem in developmental biology. First described in sea urchin embryos by Hans Driesch, this phenomenon is now recognized as a striking example of how living organisms use non-equilibrium self-organization, based on reaction-diffusion (RD) systems, to generate pattern-determining morphogen concentration gradients that scale with size. Although specific molecular mechanisms for scaling such gradients have been described in some cases, a general approach for the targeted identification of such mechanisms had not been developed until recently. In search of a solution, we hypothesized the obligatory participation in scaling mechanisms of special genes, which we named "scalers." We supposed that these genes share two critical features: their expression is sensitive to embryo size, and their protein products determine the scale of morphogen concentration gradients. As proof of principle, we recently identified scalers by detecting differentially expressed genes in wild-type and half-size Xenopus laevis gastrula embryos. Furthermore, we described a mechanism by which one of the identified scalers, the gene encoding Metalloproteinase 3 (Mmp3), regulates the scaling of gradients of the morphogenic protein Bmp and its antagonists, Chordin and Noggin1/2. In the present work, we have made an important theoretical generalization of the Scalers Hypothesis by proving a statement regarding the obligatory presence of scalers in closed RD systems generating morphogen concentration gradients. Furthermore, through a systematic analysis of all known types of embryonic scaling models based on RD systems, we demonstrate that scalers are present in all known types of such models, either explicitly or implicitly. Finally, to test the universality of the Scalers Hypothesis, we applied our method to identify scalers that adjust Bmp/Chordin gradients to the size of the sea urchin embryo, Strongylocentrotus droebachiensis. Our results show that at least two members of the gene cluster encoding astacin metalloproteinases of the Span family, namely bp10 and Span, exhibit properties characteristic of scalers. Namely, their expression levels increase significantly in half-size embryos, and their protein products specifically degrade Chordin. Additionally, we found that the loss of function of bp10 and span leads to a narrowing of the dorsal domain of the Bmp signaling nuclear effector, pSmad1/5. These findings not only validate the Scalers Hypothesis but also uncover a novel mechanism by which Span proteinases fine-tune Chordin and Bmp morphogen concentration gradients in sea urchins. Thus, the Scalers Hypothesis and the approach to targeted search for such genes developed on its basis open up promising avenues for future research into scaling mechanisms in various biological systems.