Modeling the spread of Phytophthora

• Published in: Journal of mathematical biology Vol. 65; no. 6-7; pp. 1359 - 1385
• Main Authors: Henkel, A., Müller, J., Pötzsche, C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.12.2012; Springer Nature B.V
• Subjects: Applications of Mathematics; Computer Simulation; Glucose - metabolism; Hyphae - growth & development; Hyphae - metabolism; Mathematical and Computational Biology; Mathematics; Mathematics and Statistics; Models, Biological; Phytophthora; Phytophthora - growth & development; Phytophthora - metabolism; Stochastic Processes; 92B05; 35L02; 35Q92
• ISSN: 0303-6812; 1432-1416; 1432-1416
• DOI: 10.1007/s00285-011-0492-7

We consider a model for the morphology and growth of the fungus-like plant pathogen Phytophthora using the example of Phytophthora plurivora . Here, we are utilizing a correlated random walk describing the density of tips. This random walk incorporates a delay in branching behavior: newly split tips only start to grow after a short while. First, we question the effect of such a delay on the running fronts, for uniform- as well as non-uniform turning kernels. We find that this delay primarily influences the slope of the front and therewith the way of spatial appropriation, and not its velocity. Our theoretical predictions are confirmed by the growth of Phytophthora in concrete experiments performed in Petri dishes. The second question addressed in this paper, concerns the manner tips are interacting, especially the point why tips stop to grow “behind” the interface of the front, respectively in confrontation experiments at the interface between two colonies. The combination of experimental data about the spatially structured time course of the glucose concentration and simulations of a model taking into account both, tips and glucose, reveals that nutrient depletion is most likely the central mechanism of tip interaction and hyphal growth inhibition. We presume that this is the growing mechanism for our kind of Phytophthora in infected plant tissue. Thus, the pathogen will sap its hosts via energy depletion and tissue destruction in infected areas.