Paint-by-numbers: pattern formation in two-dimensional sheets of cells

Paint-by-numbers: pattern formation in two-dimensional sheets of cells

-
Stanislav Shvartsman, Princeton University
Fine Hall 314

One of the basic mechanisms responsible for the formation of three-dimensional organs relies on the regulated folding of epithelia (two-dimensional sheets of cells). This process is driven by the spatially nonuniform and dynamic distribution of multiple chemical components (products of gene expression) across the epithelia that prepare for folding. Some of the key questions in this class of biological problems are related to the total number of involved genes, the diversity and dynamics of their expression patterns, and the mechanisms of pattern formation. I will present the results of our experimental and computational work that explores these questions during the formation of an elaborate three-dimensional structure (the fruit fly eggshell). I will also try to discuss the mathematical problems associated with the combinatorial construction of complex two-dimensional patterns from a small number of building blocks and dynamics of piecewise linear models of epithelial patter ning.