Mathematical modelling of morphogenesis in fungi: a key role for curvaturecompensation ('autotropism') in the local curvature distribution model

The assumption that the mushroom stem has the ability to undergo autonomic straightening enables a mathematical model to be written that accurately mi mics the gravitropic reaction of the stems of Coprinus cinereus. The straig htening mechanism is called curvature compensation here, but is equivalent to the 'autotropism' that often accompanies the gravitropic reactions of ax ial organs in plants. In the consequently revised local curvature distribut ion model, local bending rate is determined by the difference between the ' bending signal' (generated by gravitropic signal perception systems) and th e 'straightening signal' (proportional to the local curvature at the given point). The model describes gravitropic stem bending in the standard assay with great accuracy but has the virtue of operating well outside the experi mental data set used in its derivation. It is shown, for example, that the mathematical model can be fitted to the gravitropic reactions of stems trea ted with metabolic inhibitors by a change of parameters that parallel the i ndependently derived physiological interpretation of inhibitor action. The revised local curvature distribution model promises to be a predictive tool in the further analysis of gravitropism in mushrooms.