Far East Journal of Dynamical Systems
Volume 10, Issue 1, Pages 1 - 21
(February 2008)
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ON THE DYNAMICS OF MORPHOGEN CONCENTRATIONS IN THE DEVELOPING EYE OF A XENOPUS LAEVIS FROG
Crystal Cooper (USA) and Kevin Conway (USA)
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Abstract: We have used a computer program to model the dynamics of morphogen concentrations in the developing eye of a Xenopus laevis frog. The dynamics are modeled because it is believed that the behavior of the morphogen concentrations determine how the developing eye maps to the brain. The eye in the Xenopus grows as a series of rings, and thus this is the model used. The basis for the simulation is experiments done by Sullivan et al. [11]. Following Sullivan et al. [11], an eye ring is “split” in half, inverted, and then “pasted” onto a donor half. The purpose of the program is to replicate and analyze the results that are found experimentally: a graft made on a north to south axis (dorsal to ventral) produces a change in vision along the east to west axis (anterior to posterior). Four modified Gierer-Meinhardt reaction-diffusion equations are used to simulate the operation. |
Keywords and phrases: morphogenesis, reaction-diffusion, pattern formation, retina, Xenopus laevis. |
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