The geometric properties of the molecular surfaces of protein crystal structures and AlphaFold predicted models

Abstract                 Previous analyses of protein structures have focused primarily on three-dimensional folds, their secondary structures, and binding or active sites while their molecular surfaces have received much less attention, due possibly to the lack of accurate and robust programs for their computation.                                    Using SESA we have analyzed the molecular surfaces of three mutually exclusive sets,                   G, S                   and                   M                   , of protein crystal structures.                   G                   and                   S                   include only non-membrane proteins with the latter having only monomers while                   M                   has only membrane proteins. The analyses show that SAS area per atom                   µ                                        s                                      decreases while probe area per atom                   µ                                        p                                      increases with the number of atoms in a molecule                   n                   . Most interestingly, the fitted power laws for                   µ                                        s                                      intersect with those for                   µ                                        p                                      at                   n                   = 957 for                   G                   ,                   n                   = 875 for                   S                   and                   n                   = 1, 061 for                   M                   . They correspond respectively to 60, 57 and 64 amino acid residues. The power laws and their intersections provide an explanation for protein structural integrity and stability in general and the transition in particular from peptides typically with random conformations in solution to proteins usually with a dominant conformation.                                  We have also analyzed the molecular surfaces of the AlphaFold models for twenty seven proteomes. The analyses show that the molecular surfaces for thirteen prokaryotic proteomes resemble those for the crystal structures while those for fourteen eukaryotic ones differ largely from both of them. The variation may have significant implication in theory in that there exist genuine differences between prokaryotic and eukaryotic proteomes, and in application in that the current AlphaFold models for eukaryotic proteomes are likely not adequate for structure-based drug design in particular.                                    Significance statement                                        A newly-developed analytic and robust program                     , SESA,                     has been applied to three mutually exclusive sets                     ,                     G, S                     and                     M                     ,                     of protein crystal structures and the AlphaFold models for twenty seven proteomes to compute their exterior solvent-excluded surface (SES) areas. The results show that for the crystal structures the areas per atom for SAS µ                                            s                                          ,                     probe µ                                            p                                          and toroidal µ                                            t                                          patches each follows a power law with n, the number of atoms in a structure or model. Specifically, µ                                            s                                          decreases while µ                                            p                                          increases with n. Most interestingly, the power laws for µ                                            s                                          intersect with those for µ                                            p                                          at n                     = 957                     for                     G                     ,                     n                     = 875                     for                     S                     and n                     = 1, 061                     for                     M                     .                     They correspond respectively to                     60, 57                     and                     64                     residues. A SAS patch is convex while a probe one concave, thus a power law for µ                                            s                                          intersects with that for µ                                            p                                          when the total area of the patches with a negative curvature equals that with a positive curvature if one ignores toroidal patches. The points of intersection for                     G                     and                     S                     are close to the number of residues required for a polypeptide to adopt a dominant conformation in solution, and thus provide an explanation for why a chain with &lt;                     50                     residues, that is, a peptide, has in general only random conformations in solution. In addition, the SESs of the AlphaFold models for thirteen prokaryotic proteomes resemble those for the crystal structures. However, in stark contrast with the crystal structures and the models for prokaryotic proteomes, the SESs for fourteen eukaryotic proteomes differ largely from both of them. The differences likely have significant implications for structural biology and the applications of AlphaFold models                     .