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

Alexander M. Berezhkovskii, Mathieu Coppey, Stanislav Y. Shvartsman

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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 of 2-state reaction-diffusion systems. At each stage within such as a cascade, a diffusible particle is reversibly bound by immobile traps and can be annihilated in both mobile and immobile states. When trapped, these particles drive the next stage by converting mobile particles of a different type from a passive to active form. The cascade initiated by injection of mobile particles into the first stage. We derive analytical expressions for the steady-state concentration profiles of mobile and immobile particles and analyze how the output of a cascade is controlled by properties of the constituent stages.

Original languageEnglish (US)
Pages (from-to)1087-1092
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number4
StatePublished - Jan 27 2009

All Science Journal Classification (ASJC) codes

  • General


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