  Protein structure prediction is considered as one of the most challenging and
computationally intractable combinatorial problem. Thus, the efficient modeling
of convoluted search space, the clever use of energy functions, and more
importantly, the use of effective sampling algorithms become crucial to address
this problem. For protein structure modeling, an off-lattice model provides
limited scopes to exercise and evaluate the algorithmic developments due to its
astronomically large set of data-points. In contrast, an on-lattice model
widens the scopes and permits studying the relatively larger proteins because
of its finite set of data-points. In this work, we took the full advantage of
an on-lattice model by using a face-centered-cube lattice that has the highest
packing density with the maximum degree of freedom. We proposed a graded
energy-strategically mixes the Miyazawa-Jernigan (MJ) energy with the
hydrophobic-polar (HP) energy-based genetic algorithm (GA) for conformational
search. In our application, we introduced a 2x2 HP energy guided macro-mutation
operator within the GA to explore the best possible local changes exhaustively.
Conversely, the 20x20 MJ energy model-the ultimate objective function of our GA
that needs to be minimized-considers the impacts amongst the 20 different amino
acids and allow searching the globally acceptable conformations. On a set of
benchmark proteins, our proposed approach outperformed state-of-the-art
approaches in terms of the free energy levels and the root-mean-square
deviations.
