Background: A number of approaches to design stable and fast-folding s
equences for model polypeptide chains have been based on the premise t
hat optimization of the relative energy of the native conformation (or
Z-score) is sufficient to yield stable and fast-folding sequences. Al
though this approach has been successful, for longer chains it often y
ielded sequences that failed to fold cooperatively, instead having mul
tidomain folding behavior. Results: We show that one of the factors de
termining single-domain or multidomain folding behavior is the dispers
ion of energies of native contacts. So, we study folding of sequences
optimized to have the same native conformation as a global energy mini
mum but having different dispersion of native contact energies, Our re
sults suggest that under conditions at which native conformation is st
able, the best-folding proteins are those that have smaller heterogene
ity of native contact energies. For them, the folding transition is al
l-or-none. On the other hand, proteins with greeter heterogeneity of n
ative contact energies have more gradual multidomain folding transitio
n and fold into stable native conformation much slower thin those prot
eins with small dispersion of native contact energies. Conclusions: Th
ese results give further guidance for the design of stable, fast-foldi
ng and cooperatively folding sequences.