  We analytically derive the lower bound of the total conformational energy of
a protein structure by assuming that the total conformational energy is well
approximated by the sum of sequence-dependent pairwise contact energies. The
condition for the native structure achieving the lower bound leads to the
contact energy matrix that is a scalar multiple of the native contact matrix,
i.e., the so-called Go potential. We also derive spectral relations between
contact matrix and energy matrix, and approximations related to one-dimensional
protein structures. Implications for protein structure prediction are
discussed.
