Saturday, October 13, 2012: 12:00 PM
Hall 4E/F (WSCC)
Many animals have patterns on their coats and the way that these patterns are formed has perplexed
scientists for decades. A specific example studied by Kondo is the zebra fish whose stripes have a
certain spacing in between them. In order to keep that spacing consistent as the fish grows, more stripes
must be inserted. The blueprint for the pattern formation is encoded in the animal's genes to produce
certain molecules which propagate or diffuse to create patterns. By classifying the molecules as
activators and inhibitors in pattern formation, Turing (1952) suggested that animal pattern formation
could be modeled using the reaction-diffusion (RD) equation. Molecular biologists identify the network
of molecules and qualitatively describe the chemical phenomena that drives the pattern formations.
With the identification of activators and inhibitors, numerical simulations allow us to translate the
information to a quantitative description by fitting the relevant data. Once we have established the
basic infrastructure of the finite element code using a one dimensional model, we can work our way up to a two
dimensional plane, and possibly a three dimensional curved surface. The correlation between the
results of the RD equation and the actual zebra fish will show that there is, indeed, an autonomous
molecular mechanism driving the pattern formation, as suggested by Turing.
scientists for decades. A specific example studied by Kondo is the zebra fish whose stripes have a
certain spacing in between them. In order to keep that spacing consistent as the fish grows, more stripes
must be inserted. The blueprint for the pattern formation is encoded in the animal's genes to produce
certain molecules which propagate or diffuse to create patterns. By classifying the molecules as
activators and inhibitors in pattern formation, Turing (1952) suggested that animal pattern formation
could be modeled using the reaction-diffusion (RD) equation. Molecular biologists identify the network
of molecules and qualitatively describe the chemical phenomena that drives the pattern formations.
With the identification of activators and inhibitors, numerical simulations allow us to translate the
information to a quantitative description by fitting the relevant data. Once we have established the
basic infrastructure of the finite element code using a one dimensional model, we can work our way up to a two
dimensional plane, and possibly a three dimensional curved surface. The correlation between the
results of the RD equation and the actual zebra fish will show that there is, indeed, an autonomous
molecular mechanism driving the pattern formation, as suggested by Turing.