The revised local curvature distribution model, which provides accurate computer simulations of the gravitropic response of mushroom stems, was found to produce accurate simulations of the gravitropic reaction of wheat (Triticum aestivum) coleoptiles. The key feature of the mathematical model that enables it to approach universality of application is the assumption that the stem has an autonomic straightening reaction (curvature compensation or 'autotropism'). In the model, the local bending rate for any segment of the organ is determined by the difference between the 'bending signal' (generated by the gravitropic signal perception system) and a 'straightening signal' (which is proportional to the local curvature of the segment). The model reveals three major differences between the gravitropic reactions of wheat coleoptiles and Coprinus mushroom stems. First, in Coprinus, the capacity for autonomic straightening is much more concentrated in the apical region of the stem. Second, local perception of the gravitropic signal, which is necessary for exact simulation in Coprinus, is not needed in wheat coleoptiles (the corresponding constant in the model can be set to zero). Third, the transmission rate of the gravitropic signal is about seven times faster in wheat coleoptiles than in the mushroom stem. Thus, we demonstrate that a single model, depending on the values given to its parameters, is able to simulate the spatial organization of the gravitropic reaction of wheat coleoptiles and Coprinus mushroom stems. The model promises to be a valuable predictive tool in guiding future research into the gravitropic reaction of axial organs of all types.