Some highly designable protein structures have dented on the surface of their native structures, and are not full compactly folded. According to hydrophobic-polar (HP) model the most de-signable structures are full compactly folded. To investigate the designability of the dented structures, we introduce the hydrogen bond energy in the secondary structures by using the secon-dary-structure-favored HP model proposed by Ou-yang etc. The result shows that the average designability increases with the strength of the hydrogen bond. The designabilities of the structures with same dented shape increase exponentially with the number of secondary structure sites. The dented structures can have the highest designabilities for a certain value of hydrogen bond energy density.
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