  Protein sequences are believed to have been selected to provide the stability
of, and reliable renaturation to, an encoded unique spatial fold. In recently
proposed theoretical schemes, this selection is modeled as ``minimal
frustration,'' or ``optimal energy'' of the desirable target conformation over
all possible sequences, such that the ``design'' of the sequence is governed by
the interactions between monomers. With replica mean field theory, we examine
the possibility to reconstruct the renaturation, or freezing transition, of the
``designed'' heteropolymer given the inevitable errors in the determination of
interaction energies, that is, the difference between sets (matrices) of
interactions governing chain design and conformations, respectively. We find
that the possibility of folding to the designed conformation is controlled by
the correlations of the elements of the design and renaturation interaction
matrices; unlike random heteropolymers, the ground state of designed
heteropolymers is sufficiently stable, such that even a substantial error in
the interaction energy should still yield correct renaturation.
