Effects of external interactions on protein sequence-structure relations of beta-trefoil fold

Proteins with symmetric structures are ideal models to investigate the sequence-structure relations. We investigate proteins with beta-trefoil fold and find they have different degrees of sequence symmetries although they show similar symmetric structures. To understand this, we calculate the strength of interactions of the beta-trefoil folds with surrounding environments and find the low degrees of sequence symmetries are often correlated with large external interactions. Our results give an additional confirmation of Anfinsen's thermodynamic hypothesis that protein structures are not only determined by their sequences but also by their surrounding environments. We suggest the external interactions should be considered additionally in protein structure prediction through ab initio folding.