Croissance et forme de l'hyphe modelées par une instabilité
Résumé
We propose a theory of growth and form of hyphae in analogy with dendritic growth, the basic ingredients for the organization of the hyphal tip being the vesicles used for the growth and the proton pumps at the origin of membrane potential. The uniform growth may be unstable, favoring the formation of vesicle clusters separated with a characteristic distance essentially determined by the dependance of the proton current with the internal pH and the membrane potential, the ionic current entering the more depolarized sites of the membrane where the aggregates form. This model is well adapted to the hyphoïd curve model [9], since it allows to propose an organization of the hyphal tip coupling proton currents and vesicle motions. One can determine the aggregation rate of a Spitzenkörper N as a function of the symport current and thus the external concentration of the co-transported substance, as well as a length scale $\lambda \approx d \sqrt{\tau} / \chi^{1/4}$ which can be associated to the current loop size. These first results are in good agreement with experimental results, suggesting that the coupling between vesicles and ionic channels is an essential mechanism of the morphogenesis of these organisms.