Mathematical Modeling of Molecular Response to Surgical Intervention During Early Vertebrate Limb Development

Chetan Gadgil

Limb development in chicken is considered to be a model system for vertebrate limb development. We have developed a geometrically and biochemically realistic model for tissue growth that incorporates the dynamics of protein interactions. Surgical interventions in the form of implantation of beads containing key molecules such as sonic hedgehog or members of the FGF family lead to interesting responses that help elucidate molecular interactions during the limb development process.

The protein Sonic hedgehog (Shh) is expressed in the Zone of Polarizing Activity (ZPA) located in the posterior region of the developing bud. Experiments on the effect of implants that lead to ectopic Shh presence in the anterior region on the expression of its receptor Patched (Ptc), which is also a Shh signaling target, have let to some non-intuitive results. When a bead containing high-diffusivity Shh is implanted at the anterior end, the expression of Ptc at the diametrically opposite (posterior) end of the implant site increases before Ptc expression is detected near the site of implant. When cultured tissue derived from the ZPA is implanted, it induces a cyclic localized Ptc expression profile.

We have developed a mechanistic model for the Shh hedgehog signal transduction pathway. I will demonstrate that, through a simulation of Shh signal transduction in the growing limb, we successfully explain the puzzling experimental results and gain insight into the mechanism of Shh action during vertebrate limb development. This work demonstrates the utility of mathematical models that incorporates details of the molecular mechanism in the analysis of complex signal transduction pathways.