New way for cell differentiation: Reaction, diffusion and chaotic waves

In this paper, we consider reaction-diffusion systems, which describe the propagation of waves with chaotic and time periodic fronts. Using this property, we show that there exist reaction-diffusion models with a few of reagents, which, by a variation of initial data, is capable to generate all possible one-dimensional cell patterns. We describe algorithms, which allow to obtain any prescribed target cell patterns by chaotic waves. Our model can be considered as a reaction-diffusion analogue of universal Turing machine. So, we propose a new robust mechanism of positional information transfer, which, in contrast to Wolpert' gradients, can work at long distances. Universality of our model helps to explain why genes, responsible for morphogenesis, are highly conservative within long evolution periods.