  We explore the possibility for the native state of a protein being inherently
a multi-conformation state in an ab initio coarse-grained model. Based on the
Wang-Landau algorithm, the complete free energy landscape for the designed
sequence 2D4X: INYWLAHAKAGYIVHWTA is constructed. It is shown that 2DX4
possesses two nearly degenerate native states: one has a helix structure, while
the other has a hairpin structure and their energy difference is less than 2%
of that of local minimums. Two degenerate native states are stabilized by an
energy barrier of the order 10kcal/mol. Furthermore, the hydrogen-bond and
dipole-dipole interactions are found to be two major competing interactions in
transforming one conformation into the other. Our results indicate that
degenerate native states are stabilized by subtle balance between different
interactions in proteins; furthermore, for small proteins, degeneracy only
happens for proteins of sizes being around 18 amino acids or 40 amino acids.
These results provide important clues to the study of native structures of
proteins.
