Abstract
Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its capabilities of development, survival, and self-organization. During aggregation it produces and relays a chemical signal (cAMP) which shows spirals and target centers. Nevertheless, the natural emergence of these structures is still not well understood. We present a mechanism for creation of centers and target waves of cAMP in D.d. by adding cell inhomogeneity to a well known reaction-diffusion model of cAMP waves and we characterize its properties. We show how stable activity centers appear spontaneously in areas of higher cell density with the oscillation frequency of these centers depending on their density. The cAMP waves have the characteristic dispersion relation of trigger waves and a velocity which increases with cell density. Chemotactically competent cells react to these waves and create aggregation streams even with very simple movement rules. Finally we argue in favor of the existence of bounded phosphodiesterase to maintain the wave properties once small cell clusters appear.
Highlights
Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its capabilities of development, survival, and self-organization
We show through numerical simulations that cell inhomogeneity produces naturally stable target patterns which are centered in areas of higher cell density and relayed in the areas of lower density
The receptors’ state changes between an active and an inactive state depending on the cAMP concentration at which they are exposed through the functions f1 and f2
Summary
Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its capabilities of development, survival, and self-organization During aggregation it produces and relays a chemical signal (cAMP) which shows spirals and target centers. The chemical signaling part of the process presents spirals and target centers, these structures are characteristic of both oscillatory and excitable systems, and are present in many systems in nature such as the cardiac muscle[2], calcium waves in oocytes[3], NADH waves in glycolysis[4], among others. A distributed oscillatory system would produce bulk oscillations if it is well stirred, that is, the whole system oscillates synchronously If it is not stirred and presents some inhomogeneities, such as scratches on the container surface or dust particles, concentric circular waves will appear[7,8]. We show that a form of degradation which scales with local cell density is needed to have streaming at higher local densities, this degradation can exist in the form of phosphodiesterase bounded to the cell membrane
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