Quantifying the Impact of Different Forms of Stress on Fungal Growth: an Inference Method Based on High-Resolution Pictures of the Mycelial Network.

In a previous work, a complete methodology for monitoring the growth of a filamentous fungus was introduced, allowing the automated extraction of its graph structure and of its key statistics. In parallel, a stochastic growth-fragmentation model for the dynamics of such mycelial networks was introduced and studied. This simple model depends on three parameters: the elongation speed v of a single filament, the branching rate b1 of a filament at its open end, and the per unit length rate b2 at which a budding event happens and creates a new filament branching off from an existing one. Leaving aside the spatial structure of the mycelium and describing its structure essentially through the empirical measure of the lengths of its filament segments, the three parameters of the growth dynamics encoded in the model summarise the local balance between mass creation and regulation through non-linear mechanisms such as anastomosis or density-dependent growth modulation. In this work, we develop a generic statistical inference method based on the large-time behaviour of the stochastic model, and on the high-resolution pictures of the mycelial network obtained using the methodology for fungal growth monitoring, to reconstruct the effective growth parameters v, b1 and b2 from a single panorama of the filament network pictured after several hours of development and an empirical measurement of the exponential rate of increase of the number of branch points and apexes. We use this method to analyse the growth dynamics of Podospora anserina mycelia observed under standard conditions and when several forms of stress are applied, in order to quantify the effect of these stresses on the different mechanisms of fungal growth. By comparing the reconstructed effective parameters with the hyphal elongation speed and branching rates estimated from the much more complex dynamical tracking of individual filaments, we find that the effective branching rates we infer are in close agreement with the individual branching rates estimated from the dynamical tracking procedure. This suggests that, in this application at least, the effects of non-linear local regulation mechanisms on branching are well encoded by an effective Markovian rate during the exponential growth phase of the mycelium. By contrast, the effective elongation speed reconstructed with our model-based approach is approximately twice as low as the hyphal elongation speed estimated from the dynamical tracking procedure, a bias that may be explained by a mismatch between the definitions of "elongation speed" used in the two approaches. Nevertheless, our results show that the three parameters of our growth-fragmentation model, combined with experimental data that are now readily available, enable us to quantify different components of the exponential growth dynamics of an expanding mycelial network.