a, The stickiness of an amino acid is defined by the log-ratio of its frequency at protein interfaces relative to protein surfaces. Thus, sticky residues are those enriched at protein interfaces relative to protein surfaces. Stickiness shows strong similarity to hydrophobicity, but also notable differences22. In this analysis, we use stickiness as a measure of ‘interaction propensity’ of surface patches. b, The structure of the dipeptidase (PDB 1POK) is coloured according to nDp calculated with respect to the four-fold axis of symmetry. Structural analyses presented in Fig. 4 consider residues associated with symmetry axes along which fibres can grow, meaning that their nDp values are lowest with respect to those axes. This notion is illustrated with the lower structures, where nDp values of red-coloured residues are smaller with respect to the four-fold axis, while nDp values of residues coloured in grey are smaller with respect to two-fold axes. This strategy enables measuring of negative design along three-, four-, or five-fold axes, while eliminating potential confounding effects due to the two-fold axes. c, Among cyclic complexes, only heterotypic interactions can trigger the formation of infinite fibres71, but such interactions are less likely to form by mutation than by homotypic interactions1,3,4,72. d, We observed that mutations at the ‘tip’ of dihedral complexes are more likely to trigger the formation of supramolecular assemblies than mutations situated farther from the tip, where nDp is larger. Accordingly, we found that stickiness is tuned according to that distance, with regions at greater risk (orange bins, x axis) being associated with lower stickiness (y axis). Lines show the median stickiness of surface patches in any given nDp window and dark-red-coloured error bars correspond to two standard errors. The green dashed line is based on an alternative measure where all residues are counted, irrespective of their distance to two-fold symmetry axes (see Methods). Both measures show that stickiness is tuned as a function of nDp in dihedral homomers. Interestingly, however, we do not observe such tuning in cyclic homomers.