Physical principles of morphogenesis in mushrooms

Mushroom species display distinctive morphogenetic features. For example, Amanita muscaria and Mycena chlorophos grow in a similar manner, their caps expanding outward quickly and then turning upward. However, only the latter finally develops a central depression in the cap. Here we use a mathematical approach unraveling the interplay between physics and biology driving the emergence of these two different morphologies. The proposed growth elastic model is solved analytically, mapping their shape evolution over time. Even if biological processes in both species make their caps grow turning upward, different physical factors result in different shapes. In fact, we show how for the relatively tall and big A. muscaria a central depression may be incompatible with the physical need to maintain stability against the wind. In contrast, the relatively short and small M. chlorophos is elastically stable with respect to environmental perturbations; thus, it may physically select a central depression to maximize the cap volume and the spore exposure. This work gives fully explicit analytic solutions highlighting the effect of the growth parameters on the morphological evolution, providing useful insights for novel bio-inspired material design.