Scaling in dynamical Turing pattern formation: density of defects frozen into permanent patterns

Abstract

We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern together with its defects. A defect-free pattern can be obtained by spatially inhomogeneous activation of the genes.

7 pages, 5 figures