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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, SandM, of protein crystal structures.GandSinclude only non-membrane proteins with the latter having only monomers whileMhas only membrane proteins. The analyses show that SAS area per atomµ_sdecreases while probe area per atomµ_pincreases with the number of atoms in a moleculen. Most interestingly, the fitted power laws forµ_sintersect with those forµ_patn= 957 forG,n= 875 forSandn= 1, 061 forM. 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, SandM,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_pand toroidal µ_tpatches each follows a power law with n, the number of atoms in a structure or model. Specifically, µ_sdecreases while µ_pincreases with n. Most interestingly, the power laws for µ_sintersect with those for µ_pat n= 957forG,n= 875forSand n= 1, 061forM.They correspond respectively to60, 57and64residues. A SAS patch is convex while a probe one concave, thus a power law for µ_sintersects with that for µ_pwhen 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 forGandSare 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 <50residues, 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.