The use of mathematical modelling to formulate and test theories is still quite rare in biology. It has now been applied to show how a robust, sharp peak of signalling molecules can be formed in developing fruitfly embryos.
It was proposed many years ago that, during animal development, graded concentration profiles of signalling molecules could provide information telling cells where they are in the embryo and what they should do. Since then, many examples of such molecules — known generically as morphogens — have been found1,2. Concentration gradients can be generated through the production of morphogens at a particular source, followed by their diffusion and degradation in appropriate regions. Often, sharp peaks occur in the distribution of morphogens, which might suggest that they require a sharply localized source. But in fact nature has circumvented this requirement, as can be seen from the development of the dorsal–ventral (back-to-belly) body axis in insects and vertebrates, where the source is plateau-like. The question of how this leads to a sharp concentration peak is difficult to tackle by traditional experimental means, as the system contains many variables. On page 304 of this issue, Eldar and colleagues3 describe how they used mathematical modelling to address the problem, and carried out experiments to back up their predictions.
The authors3 were looking at the development of the dorsal–ventral pattern of fruitfly embryos. The embryo first becomes polarized by a gradient of the Dorsal protein, with highest levels at the ventral side, defining the ventral midline of the embryo. (The name of the protein, Dorsal, refers to what happens if it is mutated — the embryo has no ventral pole and forms only dorsal structures.) The subdivision of the embryo into dorsal and ventral regions then occurs through the activation or repression of target genes, in a manner that depends on the concentration of Dorsal.
Some of these target genes are needed to create another gradient — in this case, of activated morphogens from the bone morphogenetic protein (BMP) family. Highest levels of active BMPs will be at the dorsal side, defining the embryo's dorsal midline. One of the target genes encodes the BMP called Decapentaplegic (Dpp), which is expressed in a large dorsal domain. A second BMP — Screw (Scw), which cooperates with Dpp — is expressed uniformly. A further target of Dorsal is the BMP inhibitor called Short gastrulation (Sog), which is expressed in ventral–lateral regions.
A first look at this system suggests that some sort of conventional source–sink mechanism is at work: overall, the BMPs are mainly produced in the dorsal region (the source), and are antagonized by Sog spreading from the ventral site (the sink), leading to graded BMP activity4. But matters aren't quite so simple. First, Sog has not only a short-range inhibitory effect on BMP activity, but also a long-range enhancing effect5,6. And second, the BMPs and Sog are all produced in broad rather than sharply focused regions, so one would expect the BMP gradient also to have a plateau-like distribution. Yet in fact the levels of active BMPs peak sharply in a stripe along the dorsal midline. Eldar et al.3 now offer an explanation for this phenomenon: they propose that Sog coordinates BMP transport with BMP release, and show by modelling that this produces a robust, sharp peak of active BMPs.
The authors began with computer simulations, based on a set of equations, in which they varied both the components and the parameters (protein concentrations and rate constants). To test their findings, they carried out experiments using Dpp. In essence, Eldar et al. show that BMPs by themselves probably have a very low diffusion rate. Only when bound to Sog do they become mobile, enabling them to be moved around the embryo. The enzyme Tolloid cleaves Sog, and Eldar and colleagues' models suggest that this happens preferentially when Sog is bound to BMPs, as proposed previously7. This releases the BMP molecules, which can act on cells in areas where the concentration of inhibitory Sog is low. That mainly happens at some distance from the ventral source of Sog. In this way, a sharp focus of active BMPs can be built up at a distance from the source of Sog and on a plateau-like source of BMPs (Fig. 1).
Significantly, the authors show that this molecular network is robust to changes in the dosage of the genes involved. They first modelled a simplified system consisting only of Sog, Tolloid and one BMP. In this case, with certain parameters the system was insensitive to the gene dosage of all its components. If both Dpp and Scw were included, the system became unstable. Moderate stability was achieved if molecularly distinct complexes transported the two BMPs, with Sog alone transporting Scw, and both Sog and Twisted gastrulation (Tsg) transporting Dpp. This fits with experimental data6,8,9. However, even in the presence of Tsg the system remained sensitive to the Dpp gene dosage, again in agreement with experiments. Whether dealing with the simple or the more complex system, the most remarkable outcome of the simulations is that robustness to variations in system components is always linked to production of a sharp dorsal peak of BMP activity.
A similar mechanism is probably at work in vertebrates, where the same molecular players are involved10 — although in opposite regions11. For instance, the Dpp homologues BMP2 and BMP4 are morphogens; they are produced in a broad ventral region, and are antagonized by the Sog homologue Chordin, localized dorsally in the so-called Spemann organizer. Homologues of Tolloid and Tsg8,9 are also found in vertebrates.
The puzzle that remains is why such a sophisticated mechanism is needed. At large distances from a localized source or sink, a gradient may be shallow and thus inappropriate for reliable subdivision. In many cases this problem is circumvented by using two gradients with opposite slopes, generated from independent sources at each end of the axis. An example is the fruitfly head-to-tail (anterior–posterior) axis, which is set up by anterior and posterior morphogen gradients that form largely independently of each other12. Why isn't dorsal–ventral patterning achieved in a similar way?
The answer may lie in a peculiarity of the dorsal–ventral pattern: the initial peak of Dorsal protein must have the geometry of a long, narrow stripe rather than a small patch. The generation of such a pattern requires a complex set of interactions; otherwise, the stripe would be crooked, or decay into separated patches, or bifurcate. Correct patterning is achieved in vertebrates and insects in different ways — in vertebrates by a sequential elongation of the midline by the organizer, in insects by a repulsive effect from the dorsal side, which orients the Dorsal gradient and localizes the ventral midline13. Maybe the effort involved in generating one such midline was so great that the Sog–Tsg–BMP system was developed to use the information contained in that midline to create another at the opposite pole.
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Development Genes and Evolution (2011)
FEBS Journal (2009)