Structure optimization by heuristic algorithm in a coarse-grained off-lattice model

A heuristic algorithm is presented for a three-dimensional off-lattice AB model consisting of hydrophobic (A) and hydrophilic (B) residues in Fibonacci sequences. By incorporating extra energy contributions into the original potential function, we convert the constrained optimization problem of AB model into an unconstrained optimization problem which can be solved by the gradient method. After the gradient minimization leads to the basins of the local energy minima, the heuristic off-trap strategy and subsequent neighborhood search mechanism are then proposed to get out of local minima and search for the lower-energy configurations. Furthermore, in order to improve the efficiency of the proposed algorithm, we apply the improved version called the new PERM with importance sampling (nPERMis) of the chain-growth algorithm, pruned-enriched-Rosenbluth method (PERM), to face-centered-cubic (FCC)-lattice to produce the initial configurations. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we found the ground state energies are lower than the best values reported in the present literature.