Why do protein architectures have Boltzmann-like statistics?

A theoretical study has shown that the occurrence of various structural elements in stable folds of random copolymers is exponentially dependent on the own energy of the element. A similar occurrence-on-energy dependence is observed in globular proteins from the level of amino acid conformations to the level of overall architectures. Thus, the structural features stabilized by many random sequences are typical of globular proteins while the features rarely observed in proteins are those which are stabilized by only a minor part of the random sequences.