Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix

Can Free Energy Perturbation Simulations Coupled with Replica-Exchange Molecular Dynamics Study Ligands with Distributed Binding Sites?

Free energy perturbation coupled with replica exchange with solute tempering (FEP/REST) offers a rigorous approach to compute relative free energy changes for ligands. To determine the applicability of FEP/REST for the ligands with distributed binding poses, we considered two alchemical transformations involving three putative inhibitors I0, I1, and I2 of the Venezuelan equine encephalitis virus nuclear localization signal sequence binding to the importin-α (impα) transporter protein. I0 → I1 and I0 → I2 transformations, respectively, increase or decrease the polarity of the parent molecule. Our objective was three-fold─(i) to verify FEP/REST technical performance and convergence, (ii) to estimate changes in binding free energy ΔΔG, and (iii) to determine the utility of FEP/REST simulations for conformational binding analysis. Our results are as follows. First, our FEP/REST implementation properly follows FEP/REST formalism and produces converged ΔΔG estimates. Due to ligand inherent unbinding, the better FEP/REST strategy lies in performing multiple independent trajectories rather than extending their length. Second, I0 → I1 and I0 → I2 transformations result in overall minor changes in inhibitor binding free energy, slightly strengthening the affinity of I1 and weakening that of I2. Electrostatic interactions dominate binding interactions, determining the enthalpic changes. The two transformations cause opposite entropic changes, which ultimately govern binding affinities. Importantly, we confirm the validity of FEP/REST free energy estimates by comparing them with our previous REST simulations, directly probing binding of three ligands to impα. Third, we established that FEP/REST simulations can sample binding ensembles of ligands. Thus, FEP/REST can be applied (i) to study the energetics of the ligand binding without defined poses and showing minor differences in affinities |ΔΔG| ≲ 0.5 kcal/mol and (ii) to collect ligand binding conformational ensembles.

Structure-based virtual screening workflow to identify antivirals targeting HIV-1 capsid

We have identified novel HIV-1 capsid inhibitors targeting the PF74 binding site. Acting as the building block of the HIV-1 capsid core, the HIV-1 capsid protein plays an important role in the viral life cycle and is an attractive target for antiviral development. A structure-based virtual screening workflow for hit identification was employed, which includes docking 1.6 million commercially-available drug-like compounds from the ZINC database to the capsid dimer, followed by applying two absolute binding free energy (ABFE) filters on the 500 top-ranked molecules from docking. The first employs the Binding Energy Distribution Analysis Method (BEDAM) in implicit solvent. The top-ranked compounds are then refined using the Double Decoupling method in explicit solvent. Both docking and BEDAM refinement were carried out on the IBM World Community Grid as part of the FightAIDS@Home project. Using this virtual screening workflow, we identified 24 molecules with calculated binding free energies between − 6 and − 12 kcal/mol. We performed thermal shift assays on these molecules to examine their potential effects on the stability of HIV-1 capsid hexamer and found that two compounds, ZINC520357473 and ZINC4119064 increased the melting point of the latter by 14.8 °C and 33 °C, respectively. These results support the conclusion that the two ZINC compounds are primary hits targeting the capsid dimer interface. Our simulations also suggest that the two hit molecules may bind at the capsid dimer interface by occupying a new sub-pocket that has not been exploited by existing CA inhibitors. The possible causes for why other top-scored compounds suggested by ABFE filters failed to show measurable activity are discussed.

PyAutoFEP: An Automated Free Energy Perturbation Workflow for GROMACS Integrating Enhanced Sampling Methods

Free energy perturbation (FEP) calculations are now routinely used in drug discovery to estimate the relative FEB (RFEB) of small molecules to a biomolecular target of interest. Using enhanced sampling can improve the correlation between predictions and experimental data, especially in systems with conformational changes. Due to the large number of perturbations required in drug discovery campaigns, the manual setup of FEP calculations is no longer viable. Here, we introduce PyAutoFEP, a flexible and open-source tool to aid the setup of RFEB FEP. PyAutoFEP is written in Python3, and automates the generation of perturbation maps, dual topologies, system building and molecular dynamics (MD), and analysis. PyAutoFEP supports multiple force fields, incorporates replica exchange with solute tempering (REST) and replica exchange with solute scaling (REST2) enhanced sampling methods, and allows flexible λ values along perturbation windows. To validate PyAutoFEP, it was applied to a set of 14 Farnesoid X receptor ligands, a system included in the drug design data resource grand challenge 2. An 88% mean correct sign prediction was achieved, and 75% of the predictions had an error below 1.5 kcal/mol. Results using Amber03/GAFF, CHARMM36m/CGenFF, and OPLS-AA/M/LigParGen had Pearson's r values of 0.71 ± 0.13, 0.30 ± 0.27, and 0.66 ± 0.20, respectively. The Amber03/GAFF and OPLS-AA/M/LigParGen results were on par with the top grand challenge 2 submissions. Applying REST2 improved the results using CHARMM36m/CGenFF (Pearson's r = 0.43 ± 0.21) but had little impact on the other force fields. CHARMM36-YF and CHARMM36-WYF modifications did not yield improved predictions compared to CHARMM36m. Finally, we estimated the probability of finding a molecule 1 pK_i better than a lead when using PyAutoFEP to screen 10 or 100 analogues. The probabilities, when compared to random sampling, increased up to sevenfold when 100 molecules were to be screened, suggesting that PyAutoFEP would likely be useful for lead optimization. PyAutoFEP is available on GitHub at https://github.com/lmmpf/PyAutoFEP.

Extension of the Variational Free Energy Profile and Multistate Bennett Acceptance Ratio Methods for High-Dimensional Potential of Mean Force Profile Analysis

We redevelop the variational free energy profile (vFEP) method using a cardinal B-spline basis to extend the method for analyzing free energy surfaces (FESs) involving three or more reaction coordinates. We also implemented software for evaluating high-dimensional profiles based on the multistate Bennett acceptance ratio (MBAR) method which constructs an unbiased probability density from global reweighting of the observed samples. The MBAR method takes advantage of a fast algorithm for solving the unbinned weighted histogram (UWHAM)/MBAR equations which replaces the solution of simultaneous equations with a nonlinear optimization of a convex function. We make use of cardinal B-splines and multiquadric radial basis functions to obtain smooth, differentiable MBAR profiles in arbitrary high dimensions. The cardinal B-spline vFEP and MBAR methods are compared using three example systems that examine 1D, 2D, and 3D profiles. Both methods are found to be useful and produce nearly indistinguishable results. The vFEP method is found to be 150 times faster than MBAR when applied to periodic 2D profiles, but the MBAR method is 4.5 times faster than vFEP when evaluating unbounded 3D profiles. In agreement with previous comparisons, we find the vFEP method produces superior FESs when the overlap between umbrella window simulations decreases. Finally, the associative reaction mechanism of hammerhead ribozyme is characterized using 3D, 4D, and 6D profiles, and the higher-dimensional profiles are found to have smaller reaction barriers by as much as 1.5 kcal/mol. The methods presented here have been implemented into the FE-ToolKit software package along with new methods for network-wide free energy analysis in drug discovery.

Variational Method for Networkwide Analysis of Relative Ligand Binding Free Energies with Loop Closure and Experimental Constraints

We describe an efficient method for the simultaneous solution of all free energies within a relative binding free-energy (RBFE) network with cycle closure and experimental/reference constraint conditions using Bennett Acceptance Ratio (BAR) and Multistate BAR (MBAR) analysis. Rather than solving the BAR or MBAR equations for each transformation independently, the simultaneous solution of all transformations are obtained by performing a constrained minimization of a global objective function. The nonlinear optimization of the objective function is subjected to affine linear constraints that couple the free energies between the network edges. The constraints are used to enforce the closure of thermodynamic cycles within the RBFE network, and to enforce an additional set of linear constraint conditions demonstrated here to be subsets of (1 or 2) experimental values. We describe details of the practical implementation of the network BAR/MBAR procedure, including use of generalized coordinates in the minimization of the free-energy objective function, propagation of bootstrap errors from those coordinates, and performance and memory optimization. In some cases it is found that use of restraints in the optimization is more practical than use of generalized coordinates for enforcing constraint conditions. The fast BARnet and MBARnet methods are used to analyze the RBFEs of six prototypical protein-ligand systems, and it is shown that enforcement of cycle closure conditions reduces the error in the predictions only modestly, and further reduction in errors can be achieved when one or two experimental RBFEs are included in the optimization procedure. These methods have been implemented into FE-ToolKit, a new free-energy analysis toolkit. The BARnet/MBARnet framework presented here opens the door to new, more efficient and robust free-energy analysis with enhanced predictive capability for drug discovery applications.