Physical origins of protein superfamilies
  In this work, we discovered a fundamental connection between selection for protein stability and emergence of preferred structures of proteins. Using standard exact 3-dimensional lattice model we evolve sequences starting from random ones and determining exact native structure after each mutation. Acceptance of mutations is biased to select for stable proteins. We found that certain structures, wonderfold, are independently discovered numerous times as native states of stable proteins in many unrelated runs of selection. Diversity of sequences that fold into wonderfold structures gives rise to superfamilies, i.e. sets of dissimilar sequences that fold into the same or very similar structures. Wonderfolds appear to be the most designable structures out of complete set of compact lattice proteins. Furthermore, proteins having wondefolds as their native structure tend to be most thermostable among all evolved proteins. This effect is purely due to the favorable geometric properties of wonderfolds and, thus, dominates any dependence on sequences. The present work establishes a model of prebiotic structure selection, which identifies dominant structural patterns emerging upon optimization of proteins for survival in hot environment. Convergently discovered prebiotic initial superfamilies with wonderfold structures could have served as a seed for subsequent biological evolution involving gene duplications and divergence. 
Konstantin B. Zeldovich, Igor N. Berezovsky, Eugene I. Sha