Enhanced Monte Carlo Methods for Modeling Proteins Including Computation of Absolute Free Energies of Binding

Abstract

The generation of a complete ensemble of geometrical configurations is required to obtain reliable estimations of absolute binding free energies by alchemical free energy methods. Molecular dynamics (MD) is the most popular sampling method, but the representation of large biomolecular systems may be incomplete owing to energetic barriers that impede efficient sampling of the configurational space. Monte Carlo (MC) methods can possibly overcome this issue by adapting the attempted movement sizes to facilitate transitions between alternative local-energy minima. In this study, we present an MC statistical mechanics algorithm to explore the protein-ligand conformational space with emphasis on the motions of the protein backbone and side chains. The parameters for each MC move type were optimized to better reproduce conformational distributions of 18 dipeptides and the well-studied T4-lysozyme L99A protein. Next, the performance of the improved MC algorithms was evaluated by computing absolute free energies of binding for L99A lysozyme with benzene and seven analogs. Results for benzene with L99A lysozyme from MD and the optimized MC protocol were found to agree within 0.6 kcal/mol, while a mean unsigned error of 1.2 kcal/mol between MC results and experiment was obtained for the seven benzene analogs. Significant advantages in computation speed are also reported with MC over MD for similar extents of configurational sampling.

Correcting electrostatic artifacts due to net‐charge changes in the calculation of ligand binding free energies

“…One of the major challenges in modern computational biochemistry is the accurate and reliable calculation of affinities between proteins and associated binding partners . A very prominent method to calculate free‐energy changes upon a ligand binding to a host protein or DNA is to simulate a nonphysical path where the ligand is alchemically perturbed in the protein and free in solution .…”

“…One of the major challenges in modern computational biochemistry is the accurate and reliable calculation of affinities between proteins and associated binding partners. [1][2][3][4][5][6][7][8] A very prominent method to calculate free-energy changes upon a ligand binding to a host protein or DNA is to simulate a nonphysical path where the ligand is alchemically perturbed in the protein and free in solution. [9] In combination with the employment of a thermodynamic cycle, the free-energy change along the nonphysical path is the same as the free-energy change along the physical path.…”

The SAMPL6 SAMPLing challenge: Assessing the reliability and efficiency of binding free energy calculations

“…In a reproducibility study involving four different implementations of relative hydration free energy calculations, the authors found in many cases statistically significant ΔΔ differences on the order of 0.2 kcal/mol [27]. Systematic differences of the same order of magnitude were detected in a recent study comparing Monte Carlo and Molecular Dynamics sampling for binding free energy calculations [24], although, in this case, differences in water models and periodic boundary conditions might confound the analysis.…”

“…Secondly, changing the potential energy of the system used to simulate the bound and unbound states means changing the theoretical free energy Δ , which makes it harder to detect systematic biases introduced by the methodologies. There are several examples in the literature noting differences in binding free energy predictions between different methods, but in which it was impossible to determine whether this was due to other differences in the model or system preparation, insufficient sampling, or shortcomings of the methodology [22][23][24][25]. Consequently, it is important to test the methods on the same set of molecular systems, using the same model.…”

“…On the other hand, the efficiency of sampling strategies in the context of free energy calculations has been evaluated in many different ways in the past. In some cases, one or more system-specific collective variables associated with a slow degree of freedom can be directly inspected to verify thorough sampling [24,32,33]. This strategy requires extensive knowledge of the system and is not generally applicable to arbitrary receptor-ligand systems.…”