research partners    
Ph.D. students    
consortium members    

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
phone: +48 22 5544551
fax: +48 22 5544700

Models of morphogen transport
Dariusz Wrzosek (MIM University of Warsaw) and Philippe Laurençot (CNRS, University of Toulouse)
The project is carried out by Marcin Małogrosz at University of Warsaw
The process of cell differentiation is still one of the fundamental problems of developmental biology. A basic commonly accepted [2], [4] mechanism which explains the cell differentiation and patterning of a tissue in an embryo is related to the concept of positional signaling. It links the expression of target gens with local concentration of morphogen molecules (ligands). Different concentrations of morphogens are able to activate transcription of distinct target genes and thus cell differentiation. According to recent laboratory and theoretical studies morphogens are secreted by a group of cells in some restricted region of a tissue and then transported in an adjacent tissue. Several kinds of proteins are known to act as morphogens. Different hypotheses about the nature of the morphogen transport have been investigated in the literature [2], [3], [4] e.g. by free or passive diffusion in an extracellular medium or by directed diffusion with a key influence of receptors at a cell surface (''bucket brigade'' model). Another mechanism called transcytosis includes several steps initiated by the formation of morphogen-receptor complexes followed by internalization and their subsequent externalization and final release of ligands at a different site of the cell surface. In [1] models for morphogen transport related to transcytosis and directed diffusion were proposed in simplified one dimensional geometry. Research goals for the Ph.D. include extension of these models to two or three dimensions, study of their well-posedness and building algorithms to solve them numerically. The collaboration with numerical analysts from the group of Prof. Dryja and with Philippe Laurencot is planned within this Ph.D. project.

[1] P. Krzyżanowski, Ph. Laurençot and D. Wrzosek, (2008) SIAM J. Math. Anal., 40: 1725-1749.
[2] M. Kerszberg and L. Wolpert, (1998) J. Theor. Biol., 191: 103-114.
[3] A.D. Lander, Q. Nie and F.Y.M. Wan, (2002) Dev. Cell, 2: 785-796.
[4] J.B. Gurdon and P.-Y. Bourillot, (2001) Nature, 3: 797--803.