Modeling the Drosophila segment polarity network
Continuous and Boolean models for the Drosophila segment polarity network have shown that the system is able to maintain the wild-type pattern when subjected to sustained changes in the interaction parameters and initial conditions. Embryo development is likely to occur under fluctuating environmental conditions, and to our knowledge, except in one instance where the study is restricted to delay in establishing of the initial condition, the effect of transient perturbations (distinct from sustained stochasticity) on the ability of the system to recover the wild-type pattern has not been investigated.
Kartik Subramanian used a well-established Boolean model (Albert and Othmer, JTB, 2003) to explore the ability of the segment polarity network to resist transient changes. This led to several interesting results that have the possibility of broader interpretations than just the effect in this particular patterning regulatory circuit. For instance, the system appears to be more sensitive to changes that involve activation of normally inactive nodes. Also, a localized transient perturbation (restricted to one parasegment) is more deleterious than a global perturbation affecting all parasegments. A pre-publication version of a paper with details of these results that appeared in IET Systems Biology is available here.
Other projects
Previous work (with Hans Othmer and Bob Dillon) had involved incorporating the Sonic hedgehog and fibroblast growth factor (Fgf4, 10, etc) signaling pathways into the Dillon-Othmer framework for modeling chick limb development in order to explain certain non-intuitive experimental results. The paper reporting these results is available here.
There is no ongoing project in this area, but investigating the robustness of the pattern formation process, as well as modeling the signaling involved in embryo growth and patterning is a long-term interest.