The Turing instability was proposed more than six decades ago as a mechanism leading to spatial patterning, but it has yet to be exploited in a synthetic biology setting. Here we characterize the Turing instability in a specific gene circuit that can be implemented in vitro or in populations of clonal cells producing short-range activator N-Acyl homoserine lactone (AHL) and long-range inhibitor...

We observe traveling waves emitted from Turing spots in the chlorine dioxide-iodine-malonic acid reaction. The newborn waves are continuous, but they break into segments as they propagate, and the propagation of these segments ultimately gives rise to spatiotemporal chaos. We model the wave-breaking process and the motion of the chaotic segments. We find stable segmented spirals as well. We att...

The formation of localized structures in the chlorine dioxide-idodine-malonic acid ~CDIMA! reactiondiffusion system is investigated numerically using a realistic model of this system. We analyze the onedimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations ~Turing instability! in the plane transverse to thes...

The reaction diffusion Gray-Scott model with time delay is put forward the assumption of Neumann boundary condition satisfied. Based on Turing bifurcation condition, curves two parameter plane are discussed without delay. normal form computed via applying Lyapunov-Schmidt reduction method in system PDE, and bifurcating direction pitchfork underlying codimension-1 singularity point computed. con...

1. Growing modes in a reaction-diffusion system In this section we summarize the classical linear Turing instability criterion for a reaction-diffusion system. Consider a reaction-diffusion system of 2-species as ∂U ∂t = ∇ · (D1 (U,V )∇U) + f (U,V ) , (1.1) ∂V ∂t = ∇ · (D2 (U,V )∇V ) + g (U,V ) , where U (x,t) ,V (x,t) are concentration for species, D1, D2 diffusion coefficients, f, g reaction ...

Cross diffusion is a phenomena in which a gradient in the concentration of one species induces a flux of another chemical species which was generally been neglected in the study of reaction-diffusion systems. We study the Turing bifurcation of two species reaction transport systems, where particle dispersal is governed by diffusion and cross diffusion. we performed linear stability analysis to ...

The Turing instability has now been established as a canonical mechanism of stationary pattern formation both theoretically as well as experimentally. In this brief article the basic theory of this instability will be sketched, with special emphasis on the characteristics it has in common with symmetry breaking in equilibrium systems. A very brief introduction to some experimental and numerical...

Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other model parameters to be unequal, we find th...