Prediction and experimental evidence of differentgrowth phases of the Podospora anserina hyphalnetwork

The growth of the network of a filamentous fungus is monotonous, showing an ever increasing complexity with time. The components of network growth are very simple and based on two mechanisms, the elongation of each hyphae and their multiplication by successive branching. These two mechanisms are sufficient to produce a complex network, and could only be localized at the tips of the hyphae. However, branching can be of two types, apical or lateral, depending on its location on the hyphae, imposing the redistribution of the necessary material in the whole network. From an evolutionary point of view, maintaining different branching processes, with its associated cost, is intriguing. We propose in this work to discuss the advantages of each of the two branching types using a new observable for the network growth allowing to compare growth configurations. For this purpose, we build on experimental observations of the Podospora anserina thallus growth, allowing us to feed and constrain a lattice-free modeling of this network based on a binary tree. First, we report the set of statistics related to the branches of P. anserina that we have implemented in the model. Then, we build the density observable, allowing us to discuss the growth phases. We predict that the evolution of the density is not monotonic but presents a marked stationary phase, clearly separating two other phases of growth. The location of this stable region appears to be driven solely by the growth rate. Finally, we show that the density is a good observable for stress differentiation.