Background: A number of approaches to design stable and fast-folding sequences for model polypeptide chains have been based on the premise that optimization of the relative energy of the native conformation (or Z-score) is sufficient to yield stable and fast-folding sequences. Although this approach has been successful, for longer chains it often yielded sequences that failed to fold cooperatively, instead having multidomain folding behavior.
Results: We show that one of the factors determining single-domain or multidomain folding behavior is the dispersion of energies of native contacts. So, we study folding of sequences optimized to have the same native conformation as a global energy minimum but having different dispersion of native contact energies. Our results suggest that under conditions at which native conformation is stable, the best-folding proteins are those that have smaller heterogeneity of native contact energies. For them, the folding transition is all-or-none. On the other hand, proteins with greater heterogeneity of native contact energies have more gradual multidomain folding transition and fold into stable native conformation much slower than those proteins with small dispersion of native contact energies.