Schedule   Participants   1998-1999 Mathematics in Biology 

Pattern formation and morphogenesis in developmental biology involves the spatio-temporal coordination of growth, cell-cell signaling, tissue movement, gene expression and cell determination. The spatial pattern of signals to which cells respond may be set up by diffusion, or it may consist of local modifications to the extracellular matrix that cells detect and respond to. The cellular response to these signals can involve oriented cell movement (chemotaxis), signal relay, and gene activation, while cellular movement can in turn alter the mechanical stresses in a tissue, thereby enhancing or retarding movement. This workshop will focus on the fundamental aspects of chemotaxis, cell and tissue movement, and chemical and mechanical mechanisms for pattern formation. Applications of these basic processes in the context of specific developmental systems will be the focus of the second workshop.

This workshop will bring together leading theoreticians from the mathematical and biological communities. The mathematical problems to be discussed include pattern formation in reaction-diffusion systems (how are patterns generated reliably in the face of biological variation), the long-term behavior of chemotaxis equations (are there stable, bounded non-constant solutions or do solutions blow up in finite time), and issues of effective homogenization (how does one incorporate information about the microscopic behavior of individual cells into a macroscopic continuum description). Computational aspects that arise include effective methods for computing solutions of systems of reaction diffusion (RD) equations or coupled RD/fluid problems in three space dimensions, and the numerical bifurcation analysis of systems of partial differential equations.