Signaling gradients in cascades of two-state reaction-diffusion systems

Signaling gradients in cascades of two-state reaction-diffusion systems.

Biological networks frequently use cascades, generally defined as chain-like arrangements of similar modules. Spatially lumped cascades can serve as noise filters, time-delay, or thresholding elements. The operation and functional capabilities of spatially distributed cascades are much less understood. Motivated by studies of pattern formation in the early Drosophila embryo, we analyze cascades...

Universality in Two Classes of Reaction–Diffusion Systems

We investigate the asymptotic properties of two reaction–diffusion systems. The first is an annihilation/scattering system with the reactions 2A → ∅, 2A → 2B, 2B → 2A, and 2B → ∅. The second one consists of competing annihilation and fission processes, 2A → ∅ and 2A → (n+2)A. We find that both these diffusion–limited reaction systems belong to the same universality class as the single species a...

A Diffusion-Reaction Model of Signal Transduction by MAPK Cascades

The mitogen-activated protein kinase (MAPK) cascade is a highly conserved signaling module comprised of three sequentially activated protein kinases, which are rapidly phosphorylated near the membrane and dephosphorylated in the cytosol. It regulates various important biological processes including differentiation, proliferation, and synaptic plasticity. In this paper, a diffusion-reaction mode...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Diffusion-Driven Instability in Reaction Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction diffusion systems are discussed and an example is given to show applications. 2001 Academic Press