Finding the minimum energy conformation of protein-like heteropolymers by Greedy Neighborhood Search

The prediction of a protein's tertiary structure, given its amino acid sequence, is one of the intriguing problems in biophysics and computational biology. Anfinsen's thermodynamic hypothesis indicates that the tertiary structure of a protein is the minimum free-energy conformation 1. Based on Anfinsen's hypothesis, the protein structure predict-tion problem can be treated as a global optimization problem of its given energy function. Unfortunately, there is no analytical solution for this problem because of the complexity of the energy function. Many global optimization methods such as Simulated Annealing (SA) 2 , Genetic Algorithm (GA) 3 , and Conformational Space Annealing (CSA) 4 have been proposed to deal with such hard optimization problems and successfully applied to various fields of science and engineering problems. A greedy algorithm is any algorithm that always takes the locally optimal solution while finding the global minimum of a function. Compared with above mentioned methods, it often fails to find the global minimum being trapped in a deep local minimum. A newly proposed global optimization method called Greedy Neighborhood Search (GNS) is belonged to the greedy algorithm class. GNS randomly generates the new solution adjacent to the current solution and then replaces the current one with the new one if the new one is better. Also GNS locates all the solutions on the minimum where the first derivative is zero and the second derivative is greater than zero by means of a local minimization algorithm. Because GNS randomly picks candidates on a minimum at each stage, it could escape from a deep local minimum unlike conventional greedy algorithms. In this paper, the GNS method with a novel conformational sampling method using a spherical distribution called von Mises-Fisher distribution 12 is applied to find the minimum energy conformation of a protein-like heteropolymer model called AB model 5. The AB model consists of only two types of monomers, Hydrophobic (A) and Hydrophilic (B) monomers analogous to the real proteins. Despite its simplicity, finding the minimum energy conform-ation of the AB model is very difficult and NP-complete problem. Unlike the traditional Hydropho-bic (H), Polar (P) lattice model 6 , only a few works were devoted to search the minimum energy con-formations of the AB model polymers 7-11. Because there is no rigorous proof to discriminate the true global minimum from many metastable local minima, the question is still open. The AB model The AB model polymers are modeled as an …