  Protein design is the inverse approach of the three-dimensional (3D)
structure prediction for elucidating the relationship between the 3D structures
and amino acid sequences. In general, the computation of the protein design
involves a double loop: a loop for amino acid sequence changes and a loop for
an exhaustive conformational search for each amino acid sequence. Herein, we
propose a novel statistical mechanical design method using Bayesian learning,
which can design lattice proteins without the exhaustive conformational search.
We consider a thermodynamic hypothesis of the evolution of proteins and apply
it to the prior distribution of amino acid sequences. Furthermore, we take the
water effect into account in view of the grand canonical picture. As a result,
on applying the 2D lattice hydrophobic-polar (HP) model, our design method
successfully finds an amino acid sequence for which the target conformation has
a unique ground state. However, the performance was not as good for the 3D
lattice HP models compared to the 2D models. The performance of the 3D model
improves on using a 20-letter lattice proteins. Furthermore, we find a strong
linearity between the chemical potential of water and the number of surface
residues, thereby revealing the relationship between protein structure and the
effect of water molecules. The advantage of our method is that it greatly
reduces computation time, because it does not require long calculations for the
partition function corresponding to an exhaustive conformational search. As our
method uses a general form of Bayesian learning and statistical mechanics and
is not limited to lattice proteins, the results presented here elucidate some
heuristics used successfully in previous protein design methods.
