Feedback, ratios and robustness in Hedgehog signaling
by
David Irons
University of Sheffield, UK
Coauthors: Nick Monk (University of Nottingham, UK)

The secreted protein Hedgehog (Hh) acts a morphogen, forming a concentration gradient and controlling cell fate decisions in various developmental stages in many animals. Here we consider Hh gradient formation in one such developmental context, the Drosophila wing disc.

One evolutionarily conserved component of this pathway, of particular interest, is a feedback loop where Hedgehog signalling up-regulates its own receptor, Patched (Ptc). It has been suggested that this feedback loop could enhance the robustness of the steady-state Hh gradient against variability in Hh production levels. However, previous models have failed to take into account two important issues in the biological system. Firstly, interpretation of the gradient by responsive cells (and hence Ptc production) is dependent on the 'ratio' of unbound Ptc to bound Hh-Ptc in the cell. Here, the Hh-Ptc complex 'dilutes' the inhibitive effect that Ptc has on its production, altering the very nature of the feedback loop. Secondly, total Hh levels and the expression range of downstream target genes, such as Decapentaplegic (Dpp), are growing over time, implying that both the formation and interpretation of the gradient are dynamic throughout wing development.

In order to re-examine the formation and interpretation of the Hh gradient, we present a new multi-cellular differential equation model that represents the core logic of the feedback loop. The model is centred on the three primary factors, Hh, Ptc and Hh-Ptc complex; other components of the signaling pathway (such as Smo, Ci and Cos2) are grouped together into a single 'pathway activity' variable. We use this model to investigate the two biological issues discussed above. In particular, we show that making Hh gradient interpretation dependent on Hh-Ptc levels (as well as on Ptc levels) results in a number of beneficial changes, including:

1. A refinement in signal interpretation, so that cells receiving Hh levels just above / below a threshold are more likely to respond in the appropriate way,

2. A boost in Ptc production in response to high levels of Hh, strengthening the effect of the feedback loop,

3. Enhanced robustness of the expression ranges of downstream target genes, in response to variable Hh levels.

We also use the model to examine how the expression ranges of downstream target genes (e.g. Dpp) expand as the wing disc grows. We show that making interpretation dependent on Hh-Ptc levels (as well as on Ptc levels) has a limiting effect on this expansion, indicating that the 'dilution' of Ptc function by Hh-Ptc also plays a role in size regulation.

PDF

Date received: April 23, 2008