Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Modeling the galectin patterning network of the developing chick limb skeleton
Tilmann Glimm

Last modified: 2014-03-28


One of the best studied experimental models for self-organization in embryonic development  is the formation of skeletal elements in vertebrate limbs, in particular in the chicken. 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, serious questions remain
(for instance about the identities of the purported morphogens in a Turing-type mechanism) and the exact regulatory mechanisms for this process are far from understood.

We present a mathematical model for the morphogenesis and patterning of these mesenchymal condensations. One of the features of this model is that it is firmly based on the experimentally established dynamics of a multiscale regulatory network consisting of two glycan-binding proteins
expressed early in limb development: CG (chicken galectin)-1A, CG-8 and their counterreceptors. This network was shown to determine the formation, size, number and spacing of the "protocondensations''
that give rise to the condensations and ultimately serve as the templates of the bones. The model consists of a system of partial differential  equations containing a nonlocal term to represent cell-cell adhesion. We present numerical and analytical results to confirm that the system has pattern-forming capabilities and to explore the nature of the patterning instability. The full model recapitulates qualitatively and quantitatively the experimental results of network perturbation and leads to new predictions, which are verified by further experimentation.  The described mechanism represents an extension of the category of activator-inhibitor
processes capable of generating biological patterns with repetitive elements beyond the mechanisms of the Turing/Gierer-Meinhardt type.

This talk is based on joint work with S. A. Newman (NY Medical College) and R. Bhat (UC Berkeley) .


limb development, nonlocal PDEs, cell-cell adhesion, galectin network