Universal law for diffusive mass transport through mycelial networks

Filamentous fungal cell factories play a pivotal role in biotechnology and circular economy. Hyphal growth and macroscopic morphology are critical for product titers; however, these are difficult to control and predict. Usually pellets, which are dense networks of branched hyphae, are formed during industrial cultivations. They are nutrient- and oxygen-depleted in their core due to limited diffusive mass transport, which compromises productivity of bioprocesses. Here, we demonstrate that a generalized law for diffusive mass transport exists for filamentous fungal pellets. Diffusion computations were conducted based on three-dimensional X-ray microtomography measurements of 66 pellets originating from four industrially exploited filamentous fungi and based on 3125 Monte Carlo simulated pellets. Our data show that the diffusion hindrance factor follows a scaling law with respect to the solid hyphal fraction. This law can be harnessed to predict diffusion of nutrients, oxygen, and secreted metabolites in any filamentous pellets and will thus advance the rational design of pellet morphologies on genetic and process levels.