Math Biology Seminar: Tilmann Glimm

One of the best studied experimental models for selforganization in embryonic development is the formation of skeletal elements in tetrapod limbs, in particular in the chicken and the mouse. Here cells aggregate to form chondrogenic condensations, which later turn into cartilage, then bone. This behavior is also seen in vitro in so-called micromass experiments. Several models for the underlying pattern forming mechanism have been proposed, notably Turing-type reaction-diffusion mechanisms and positional information mechanisms based on spatiotemporal gradients of signaling molecules. However the exact regulatory mechanisms for this process are far from understood. We present a model based on the experimentally established dynamics of a multiscale regulatory network consisting of two glycan-binding proteins expressed early in chick limb development: CG (chicken galectin)-1A, CG-8 and their counterreceptors. The model consists of a system of partial differential equations containing a nonlocal term to represent cell-cell adhesion, adapted from the work of Armstrong, Painter and Sherratt. Due to the high dimensionality of the problem, published results have only been in one spatial dimension. We present new results in two spatial dimensions, which allow for exploration of the topology of two dimensional patterns that can be generated. The full model recapitulates qualitatively and quantitatively the experimental results of network perturbation and leads to new predictions. This talk is based on joint work with S. A. Newman (NY Medical College), R. Bhat (Indian Institute of Science, Bangalore) and J. Zhang (West. Wash Univ.) .