Global Optimization of Protein–peptide Docking by a Filling Function Method

Molecular docking programs play a crucial role in drug design and development. In recent years, much attention has been devoted to the protein–peptide docking problem in which docking of a flexible peptide with a given protein is sought. In this work, we present a docking algorithm which is based on the use of a filling function method for continuous global optimization. In particular, the protein–peptide docking position is found by minimizing the conformational potential free energy function based on a new approximate mathematical model. The resulting global optimization problem presents some difficulties, since it is a large-scale one and the objective function is non-convex, so that it has many local minima. To solve the problem, we adopt a global optimization method based on the use of a filling function to escape from local solutions. Moreover, in order to obtain more accurate results, we search the correct docking position by performing a two-phase optimization process. In particular, in a first step, only the carbon $$\mathrm{C}_\alpha $$ C α atoms of the protein and peptide are considered, thus obtaining an approximate docking solution. Then, the energy function is completed by considering all the peptide and protein atoms so that, starting from the solution of the first phase, the new minimization process gives a more accurate result. We present numerical results on a set of benchmark docking pairs and their comparison with those obtained by the known software package PacthDock for molecular docking.