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P.312 box 1 left column top paragraph: "Morphogen gradients in a developmental biology context often rely on local protein production, followed by diffusion and eventual degradation. The symmetry breaking necessary for gradient formation therefore relies on a localized source, which can be provided by previous localization of morphogen mRNA. Provided each morphogen protein is degraded independently at a constant rate, a simple mathematical analysis reveals a concentration profile that decays exponentially with distance from the (planar) source. The decay length of the gradient (the distance over which it decays to 1/e of its highest value) has also been measured in several cases (and is approximately 100µm for Bicoid and 20µm for Dpp). Modulating the decay process can produce qualitatively different gradient shapes, for example, if a dimerization reaction is required for decay (an example of self-enhanced degradation), a power law decay results at large distances. In this case, at large distances from a planar source, the concentration decays with distance as 1/(distance)^α, where α is equal to two for the dimerization reaction." |