Shh has been shown to oligomerize, and it has been proposed that the higher-order multimers mediate long range signalling (Feng et al., 2004, Zeng et al., 2001, Chen et al., 2004). The relative signaling potencies of the different forms have been debated, but it seems reasonable that there should be a dynamic equilibrium between them (even if no interconversion was observed in vitro by Chen et al., 2004), and that signaling could be mediated by the monomeric form, while multimeric forms diffuse without interacting with the receptors. The available biochemical data is not sufficient to propose one specific Shh multimerization scheme; different oligomerization extents have been reported, from 6-mers to about 30-mers. Therefore, in order to assess the possibility for such multimerization to provide a suitable gradient of receptor-bound monomer, an arbitrary, generic scheme was adopted, in which any two oligomers can combine to create one of higher size, provided that the size of the product is smaller than the maximum being considered. The reactions are reversible, and any oligomer can split into two smaller products. Equations are detailed in section A.5.