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- W2068801740 abstract "Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally." @default.
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- W2068801740 date "2012-01-01" @default.
- W2068801740 modified "2023-10-12" @default.
- W2068801740 title "Fractional calculus and morphogen gradient formation" @default.
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- W2068801740 doi "https://doi.org/10.1063/1.4772174" @default.
- W2068801740 hasPublicationYear "2012" @default.
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