Adaptive Biasing Combined with Hamiltonian Replica Exchange to Improve Umbrella Sampling Free Energy Simulations

Abstract

The accurate calculation of potentials of mean force for ligand-receptor binding is one of the most important applications of molecular simulation techniques. Typically, the separation distance between ligand and receptor is chosen as a reaction coordinate along which a PMF can be calculated with the aid of umbrella sampling (US) techniques. In addition, restraints can be applied on the relative position and orientation of the partner molecules to reduce accessible phase space. An approach combining such phase space reduction with flattening of the free energy landscape and configurational exchanges has been developed, which significantly improves the convergence of PMF calculations in comparison with standard umbrella sampling. The free energy surface along the reaction coordinate is smoothened by iteratively adapting biasing potentials corresponding to previously calculated PMFs. Configurations are allowed to exchange between the umbrella simulation windows via the Hamiltonian replica exchange method. The application to a DNA molecule in complex with a minor groove binding ligand indicates significantly improved convergence and complete reversibility of the sampling along the pathway. The calculated binding free energy is in excellent agreement with experimental results. In contrast, the application of standard US resulted in large differences between PMFs calculated for association and dissociation pathways. The approach could be a useful alternative to standard US for computational studies on biomolecular recognition processes.

P-loop Conformation Governed Crizotinib Resistance in G2032R-Mutated ROS1 Tyrosine Kinase: Clues from Free Energy Landscape

“…The final structures were submitted to the metadynamics simulations. In the well-tempered metadynamics, the heavy atoms out of 15 Å of crizotinib in proteins were constrained with 5 kcal/mol·Å 2 to prevent drifting issues [70]. The initial hill height ( ω ) was set to 1, and the deposition rate of the added biasing potential was set to 1 kcal/mol·ps with the bias-factor parameter of 10 at 310 K of the simulation temperature.…”

“…Roux and co-workers have developed a well-characterized and well-tested absolute binding free energy calculation scheme by using various restrains, including conformational, rotational, and translational restrains, to the investigated systems, which significantly accelerated the convergence due to the constriction of the relative external degrees of freedom of the systems [30], [70], [97]–[104]. In the spirit of Woo and Roux's scheme [30], the absolute binding free energy could be obtained by calculating the reaction equilibrium constant ( K bind ) with restrains at the biased molecule's conformation (corresponding to and ), orientation (corresponding to , , , and ), and translation (corresponding to , and ), as shown in equations (4) and (5): where Δ G bind-US is the absolute binding free energy calculated based on umbrella sampling simulation, and S * and I * are associated with the angular and translational restrains in bulk and separation PMF depth, respectively [30].…”

Efficient calculation of relative binding free energies by umbrella sampling perturbation

“…Hamiltonian Replica Exchange US simulations (H-REMD-US) [5,16,27,28] were performed along the center of mass separation of molecules W1 and W2 for all systems. To cover the range between 2.0 and 7.0 Å, six windows with an intermediate spacing of 1.0 Å were used.…”

“…[2][3][4][5] Typically, a series of simulations is set up with different harmonic potentials added to the force field to achieve an efficient free energy sampling in selected regions of the reaction coordinate. In many cases, a detailed investigation of the effects due to specific modifications of systems, such as the substitution of single atoms, chemical groups, or force field parameters, by means of PMF calculations is of interest for a mechanistic understanding or molecular design applications.…”

Orthogonal sampling in free-energy calculations of residue mutations in a tripeptide: TI versusλ-LEUS

“…For example, the calculation of an absolute (or a relative) host‐guest binding free energy is often advantageously performed using the double‐decoupling approach, where the perturbation from the guest to a dummy skeleton (or to another ligand) is performed separately either within the host or free in the solvent. The sampling of the two separate unphysical processes is typically far easier than the sampling of the physical association process, which involves determining the potential of mean force (PMF) along a variation of the host‐guest distance …”