Stochastic gene expression: Density of defects frozen into permanent Turing patterns - art. no. 011909

We estimate density of defects frozen into a biological Turing pattern whic h was turned on at a finite rate. Self-locking of gene expression in indivi dual cells, which makes the Turing transition discontinuous, stabilizes the pattern together with its defects. Defects frozen into the pattern are a p ermanent record of the transition-they give an animal its own characteristi c lifelong "fingerprints" or, as for vital organ formation, they can be fat al. Density of defects scales like the fourth root of the transition rate. This dependence is so weal; that there is not enough time during morphogene sis to get rid of defects simply by slowing down the rate. A defect-free pa ttern can be obtained by spatially inhomogeneous activation of the genes. I f the supercritical density of activator spreads slower than certain thresh old velocity, then the Turing pattern is expressed without any defects.