Abstract: Accurately computing the free energy for biological processes like protein folding or protein−ligand association remains a challenging problem. Both describing the complex intermolecular forces involved and sampling the requisite configuration space make understanding these processes innately difficult. Herein, we address the sampling problem using a novel methodology we term “movable type” (MT). Conceptually it can be understood by analogy with the evolution of printing and, hence, the name movable type. For example, a common approach to the study of protein−ligand complexation involves taking a database of intact drug-like molecules and exhaustively docking them into a binding pocket. This is reminiscent of early woodblock printing where each page had to be laboriously created prior to printing a book. However, printing evolved to an approach where a database of symbols (letters, numerals, etc.) was created and then assembled using a MT system, which allowed for the creation of all possible combinations of symbols on a given page, thereby, revolutionizing the dissemination of knowledge. Our MT method involves identifying all of the atom pairs seen in protein−ligand complexes and then creating two databases: one with their associated pairwise distant dependent energies and another associated with the probability of how these pairs can combine in terms of bonds, angles, dihedrals, and nonbonded interactions. Combining these two databases coupled with the principles of statistical mechanics allows us to accurately estimate binding free energies as well as the pose of a ligand in a receptor. This method, by its mathematical construction, samples all of the configuration space of a selected region (the protein active site here) in one shot without resorting to brute force sampling schemes involving Monte Carlo, genetic algorithms, or molecular dynamics simulations making the methodology extremely efficient. Importantly, this method explores the free energy surface eliminating the need to estimate the enthalpy and entropy components individually. Finally, low free energy structures can be obtained via a free energy minimization procedure yielding all low free energy poses on a given free energy surface. Besides revolutionizing the protein−ligand docking and scoring problem, this approach can be utilized in a wide range of applications in computational biology which involve the computation of free energies for systems with extensive phase spaces including protein folding, protein−protein docking, and protein design.
Authors: Z. Zheng, M. N. Ucisik, and K. M. Merz, Jr.