Stochastic gene expression: density of defects frozen into permanent Turing patterns.
We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. Self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern together with its defects. Defects frozen into the pattern are a permanent record of the transition-they give an animal its own characteristic lifelong "fingerprints" or, as for vital organ formation, they can be fatal. Density of defects scales like the fourth root of the transition rate. This dependence is so weak that there is not enough time during morphogenesis to get rid of defects simply by slowing down the rate. A defect-free pattern can be obtained by spatially inhomogeneous activation of the genes. If the supercritical density of activator spreads slower than certain threshold velocity, then the Turing pattern is expressed without any defects.
Dziarmaga
J
J
Theory Division T-6, MS-B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
D000818:Animals; D015870:Gene Expression; D006801:Humans; D008954:Models, Biological; D008957:Models, Genetic; D015233:Models, Statistical; D013269:Stochastic Processes; D013489:Suppression, Genetic