Binding Affinity Estimation From Restrained Umbrella Sampling Simulations

Abstract

The protein-ligand binding affinity quantifies the binding strength between a protein and its ligand. Computer modeling and simulations can be used to estimate the binding affinity or binding free energy using data- or physics-driven methods or a combination thereof. Here, we discuss a purely physics-based sampling approach based on biased molecular dynamics (MD) simulations, which in spirit is similar to the stratification strategy suggested previously by Woo and Roux. The proposed methodology uses umbrella sampling (US) simulations with additional restraints based on collective variables such as the orientation of the ligand. The novel extension of this strategy presented here uses a simplified and more general scheme that can be easily tailored for any system of interest. We estimate the binding affinity of human fibroblast growth factor 1 (hFGF1) to heparin hexasaccharide based on the available crystal structure of the complex as the initial model and four different variations of the proposed method to compare against the experimentally determined binding affinity obtained from isothermal calorimetry (ITC) experiments. Our results indicate that enhanced sampling methods that sample along the ligand-protein distance without restraining other degrees of freedom do not perform as well as those with additional restraint. In particular, restraining the orientation of the ligands plays a crucial role in reaching a reasonable estimate for binding affinity. The general framework presented here provides a flexible scheme for designing practical binding free energy estimation methods.