Accurate Estimation of Protein-ligand Binding Free Energies Based on Geometric Restraints

Abstract

Binding free energy is the most crucial physical quantity for describing recognition-association of protein-ligand hybrids. Accurate estimation of protein-ligand binding free energies is of paramount importance in the field of drug design and biological engineering. However, the association process of protein-ligand hybrids is usually coupled with complex conformational changes of molecular objects, which is not amenable to the timescale of classical molecular simulations. This limitation makes it difficult to accurately estimate the protein-ligand binding free energies using classical free-energy calculation strategies. An effective solution is to apply geometric restraints to reduce the configurational space needed to be sampled, so as to boost up the convergence rate of simulations, and then calculate and deduct the contribution of these restraints to the binding free energy by post-processing. In this review, we firstly introduce the recent developments of three geometric restraints, namely, funnel, spherical, and seven-degree-of-freedom restraints, used in accurate binding free-energy calculations, with emphasis on the latest progress of the third one. Specifically, the theoretically rigorous seven-degree-of-freedom restraint describes translational, orientational, rotational, and conformational degrees of freedom by means of a center-of-mass distance, spherical angles, Euler angles and the root-mean-square deviation. Moreover, we demonstrate the theoretical backgrounds and methods of how to achieve accurate protein-ligand binding free-energy estimation by combination of geometric restraints and importance-sampling or alchemical algorithms. In the geometric routes, the degrees of freedom of the relative movement of the protein-ligand complex are addressed in a stepwise fashion by one-dimensional importance-sampling simulations. In the alchemical routes, a special thermodynamics cycle is designed, in which additional simulations are performed to address the contribution of the restraints. A general suggestion for how to choose a suitable strategy for a given molecular assembly based on our experience is provided. Last but not least, we discuss the applications and challenges of using accurate protein-ligand binding free-energy calculation methods in fields such as drug design, and present the possibility of extending these methods for investigating complex protein-protein interaction.