Calculations of the Absolute Free Energies of Binding between RNA and Metal Ions Using Molecular Dynamics Simulations and Continuum Electrostatics

Absolute Binding Free Energy Calculations Using Molecular Dynamics Simulations with Restraining Potentials

The recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies, although highly desired, remains a challenging endeavour, mostly limited to small model cases. Here, we demonstrate accurate first principles based absolute binding free energy estimates for 128 pharmaceutically relevant targets. We use a novel rigorous method to generate protein-ligand ensembles for the ligand in its decoupled state. Not only do the calculations deliver accurate protein-ligand binding affinity estimates, but they also provide detailed physical insight into the structural determinants of binding. We identify subtle rotamer rearrangements between apo and holo states of a protein that are crucial for binding. When compared to relative binding free energy calculations, obtaining absolute binding free energies is considerably more challenging in large part due to the need to explicitly account for the protein in its apo state. In this work we present several approaches to obtain apo state ensembles for accurate absolute ΔG calculations, thus outlining protocols for prospective application of the methods for drug discovery.

Approximately 90% of the structures in the Protein Data Bank (PDB) were obtained by X-ray crystallography or electron microscopy. Whereas the overall quality of structure is considered high, thanks to a wide range of tools for structure validation, uncertainties may arise from density maps of small molecules, such as organic ligands, ions or water, which are non-covalently bound to the biomolecules. Even with some experience and chemical intuition, the assignment of such disconnected electron densities is often far from obvious. In this study, we suggest the use of molecular dynamics (MD) simulations and free energy calculations, which are well-established computational methods, to aid in the assignment of ambiguous disconnected electron densities. Specifically, estimates of (i) relative binding affinities, for instance between an ion and water, (ii) absolute binding free energies, i.e., free energies for transferring a solute from bulk solvent to a binding site, and (iii) stability assessments during equilibrium simulations may reveal the most plausible assignments. We illustrate this strategy using the crystal structure of the fluoride specific channel (Fluc), which contains five disconnected electron densities previously interpreted as four fluoride and one sodium ion. The simulations support the assignment of the sodium ion. In contrast, calculations of relative and absolute binding free energies as well as stability assessments during free MD simulations suggest that four of the densities represent water molecules instead of fluoride. The assignment of water is compatible with the loss of these densities in the non-conductive F82I/F85I mutant of Fluc. We critically discuss the role of the ion force fields for the calculations presented here. Overall, these findings indicate that MD simulations and free energy calculations are helpful tools for modeling water and ions into crystallographic density maps.

Apoptosis signal-regulating kinase 1 (ASK1), a key component of the mitogen-activated protein kinase (MAPK) cascades, has been identified as a promising therapeutic target owing to its critical role in signal transduction pathways. In this study, we proposed novel pyridin-2-yl urea inhibitors exhibiting favorable physicochemical properties. The potency of these compounds was validated through in vitro protein bioassays. The inhibition (IC50) of compound 2 was 1.55 ± 0.27 nM, which was comparable to the known clinical inhibitor, Selonsertib. To further optimize the hit compounds, two possible binding modes were initially predicted by molecular docking. Absolute binding free energy (BFE) calculations based on molecular dynamics simulations further discriminated the binding modes, presenting good tendency with bioassay results. This strategy, underpinned by BFE calculations, has the great potential to expedite the drug discovery process in the targeting of ASK1 kinase.

Recent advances in relative protein-ligand binding free energy calculations have shown the value of alchemical methods in drug discovery. Accurately assessing absolute binding free energies remains a challenging endeavour, mostly limited to small model cases. We demonstrate accurate absolute binding free energy estimates for 128 pharmaceutically relevant ligands across 7 proteins using a highly parallelizable non-equilibrium method. These calculations also provide detailed physical insight into the structural determinants of binding, identifying subtle rotamer rearrangements between protein apo and holo states that are crucial for binding. The challenge behind absolute binding free energy calculations stems in large part from the need to explicitly account for the protein’s apo state. In this work we present several approaches to obtain apo state ensembles, including a novel rigorous method to generate protein-ligand ensembles for the ligand in its decoupled state. Altogether, we present an effective open-source protocol for prospective application in drug discovery.

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.

Binding free energy calculations that make use of alchemical pathways are becoming increasingly feasible thanks to advances in hardware and algorithms. Although relative binding free energy (RBFE) calculations are starting to find widespread use, absolute binding free energy (ABFE) calculations are still being explored mainly in academic settings due to the high computational requirements and still uncertain predictive value. However, in some drug design scenarios, RBFE calculations are not applicable and ABFE calculations could provide an alternative. Computationally cheaper end-point calculations in implicit solvent, such as molecular mechanics Poisson–Boltzmann surface area (MMPBSA) calculations, could too be used if one is primarily interested in a relative ranking of affinities. Here, we compare MMPBSA calculations to previously performed absolute alchemical free energy calculations in their ability to correlate with experimental binding free energies for three sets of bromodomain–inhibitor pairs. Different MMPBSA approaches have been considered, including a standard single-trajectory protocol, a protocol that includes a binding entropy estimate, and protocols that take into account the ligand hydration shell. Despite the improvements observed with the latter two MMPBSA approaches, ABFE calculations were found to be overall superior in obtaining correlation with experimental affinities for the test cases considered. A difference in weighted average Pearson () and Spearman () correlations of 0.25 and 0.31 was observed when using a standard single-trajectory MMPBSA setup ( = 0.64 and = 0.66 for ABFE; = 0.39 and = 0.35 for MMPBSA). The best performing MMPBSA protocols returned weighted average Pearson and Spearman correlations that were about 0.1 inferior to ABFE calculations: = 0.55 and = 0.56 when including an entropy estimate, and = 0.53 and = 0.55 when including explicit water molecules. Overall, the study suggests that ABFE calculations are indeed the more accurate approach, yet there is also value in MMPBSA calculations considering the lower compute requirements, and if agreement to experimental affinities in absolute terms is not of interest. Moreover, for the specific protein–ligand systems considered in this study, we find that including an explicit ligand hydration shell or a binding entropy estimate in the MMPBSA calculations resulted in significant performance improvements at a negligible computational cost.

Binding free energy calculations predict the potency of compounds to protein binding sites in a physically rigorous manner and see broad application in prioritizing the synthesis of novel drug candidates. Relative binding free energy (RBFE) calculations have emerged as an industry-standard approach to achieve highly accurate rank-order predictions of the potency of related compounds; however, this approach requires that the ligands share a common scaffold and a common binding mode, restricting the methods' domain of applicability. This is a critical limitation since complex modifications to the ligands, especially core hopping, are very common in drug design. Absolute binding free energy (ABFE) calculations are an alternate method that can be used for ligands that are not congeneric. However, ABFE suffers from a known problem of long convergence times due to the need to sample additional degrees of freedom within each system, such as sampling rearrangements necessary to open and close the binding site. Here, we report on an alternative method for RBFE, called Separated Topologies (SepTop), which overcomes the issues in both of the aforementioned methods by enabling large scaffold changes between ligands with a convergence time comparable to traditional RBFE. Instead of only mutating atoms that vary between two ligands, this approach performs two absolute free energy calculations at the same time in opposite directions, one for each ligand. Defining the two ligands independently allows the comparison of the binding of diverse ligands without the artificial constraints of identical poses or a suitable atom-atom mapping. This approach also avoids the need to sample the unbound state of the protein, making it more efficient than absolute binding free energy calculations. Here, we introduce an implementation of SepTop. We developed a general and efficient protocol for running SepTop, and we demonstrated the method on four diverse, pharmaceutically relevant systems. We report the performance of the method, as well as our practical insights into the strengths, weaknesses, and challenges of applying this method in an industrial drug design setting. We find that the accuracy of the approach is sufficiently high to rank order ligands with an accuracy comparable to traditional RBFE calculations while maintaining the additional flexibility of SepTop.

The calculation of binding free energies of charged species to a target molecule is a frequently encountered problem in molecular dynamics studies of (bio-)chemical thermodynamics. Many important endogenous receptor-binding molecules, enzyme substrates, or drug molecules have a nonzero net charge. Absolute binding free energies, as well as binding free energies relative to another molecule with a different net charge will be affected by artifacts due to the used effective electrostatic interaction function and associated parameters (e.g., size of the computational box). In the present study, charging contributions to binding free energies of small oligoatomic ions to a series of model host cavities functionalized with different chemical groups are calculated with classical atomistic molecular dynamics simulation. Electrostatic interactions are treated using a lattice-summation scheme or a cutoff-truncation scheme with Barker–Watts reaction-field correction, and the simulations are conducted in boxes of different edge lengths. It is illustrated that the charging free energies of the guest molecules in water and in the host strongly depend on the applied methodology and that neglect of correction terms for the artifacts introduced by the finite size of the simulated system and the use of an effective electrostatic interaction function considerably impairs the thermodynamic interpretation of guest-host interactions. Application of correction terms for the various artifacts yields consistent results for the charging contribution to binding free energies and is thus a prerequisite for the valid interpretation or prediction of experimental data via molecular dynamics simulation. Analysis and correction of electrostatic artifacts according to the scheme proposed in the present study should therefore be considered an integral part of careful free-energy calculation studies if changes in the net charge are involved. © 2013 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Advanced free energy perturbation molecular dynamics (FEP/MD) simulation methods are available to accurately calculate absolute binding free energies of protein-ligand complexes. However, these methods rely on several sophisticated command scripts implementing various biasing energy restraints to enhance the convergence of the FEP/MD calculations, which must all be handled properly to yield correct results. Here, we present a user-friendly Web interface, CHARMM-GUI Ligand Binder ( http://www.charmm-gui.org/input/gbinding ), to provide standardized CHARMM input files for calculations of absolute binding free energies using the FEP/MD simulations. A number of features are implemented to conveniently set up the FEP/MD simulations in highly customizable manners, thereby permitting an accelerated throughput of this important class of computations while decreasing the possibility of human errors. The interface and a series of input files generated by the interface are tested with illustrative calculations of absolute binding free energies of three nonpolar aromatic ligands to the L99A mutant of T4 lysozyme and three FK506-related ligands to FKBP12. Statistical errors within individual calculations are found to be small (~1 kcal/mol), and the calculated binding free energies generally agree well with the experimental measurements and the previous computational studies (within ~2 kcal/mol). Therefore, CHARMM-GUI Ligand Binder provides a convenient and reliable way to set up the ligand binding free energy calculations and can be applicable to pharmaceutically important protein-ligand systems.

Accurate, routine calculation of absolute binding free energies (ABFEs) for protein-ligand complexes remains a key goal of computer-aided drug design since it can enable screening and optimization of drug candidates. For development and testing of related methods, it is important to have high-quality datasets. To this end, from our own experimental studies, we have selected a set of 16 inhibitors of the SARS-CoV-2 main protease (Mpro) with structural diversity and well-distributed BFEs covering a 5 kcal/mol range. There is also minimal structural uncertainty since X-ray crystal structures have been deposited for 12 of the compounds. For methods testing, we report ABFE results from 2 μs molecular dynamics (MD) simulations using free energy perturbation (FEP) theory. The correlation of experimental and computed results is encouraging, with a Pearson's r2 of 0.58 and a Kendall τ of 0.24. The results indicate that current FEP-based ABFE calculations can be used for identification of active compounds (hits). While their accuracy for lead optimization is not yet sufficient, this activity remains addressable in separate lead series by relative BFE calculations.

We recently introduced a method called conveyor belt (CB) thermodynamic integration (TI) for the calculation of alchemical free-energy differences based on molecular dynamics simulations. In the present work, the CBTI approach is generalized to conformational free-energy changes, i.e., to the determination of the potential of mean force (PMF) along a conformational coordinate ξ of interest. The proposed conveyor belt umbrella sampling (CBUS) scheme relies on the parallel simulation of K replicas k = 0,1, ..., K - 1 of the system, with K even. For each replica k, the instantaneous value of ξ is restrained to an anchor value λk. The latter anchor points are equally spaced along a forward-turn-backward-turn path (i.e., a CB) between two extreme values defining the ξ-range of interest. The rotation of the CB is controlled by a variable Λ (range from 0 to 2π) which evolves dynamically along the simulation. The evolution of Λ results from the forces exerted by the restraining potentials on the anchor points, taken equal and opposite to those they exert on the replicas. Because these forces tend to cancel out along the CB, the dynamics of Λ is essentially diffusive, and the continuous distribution of ξ-values sampled by the replica system is automatically close to homogeneous. The latter feature represents an advantage over direct counting (DCNT) and traditional umbrella sampling (TRUS), shared to some extent with replica-exchange umbrella sampling (REUS). In this work, the CBUS scheme is introduced and compared to the three latter schemes in the calculation of 45 standard absolute binding free energies. These correspond to the binding of five alkali cations to three crown ethers in three solvents. Different free-energy estimators are considered for the PMF calculation, and the calculated values are also compared to those of a previous study relying on an alchemical path, as well as to experimental data.

Understanding the enzymatic mechanism that cellulases employ to degrade cellulose is critical to efforts to efficiently utilize plant biomass as a sustainable energy resource. A key component of cellulase action on cellulose is product inhibition from monosaccharide and disaccharides in the product site of cellulase tunnel. The absolute binding free energy of cellobiose and glucose to the product site of the catalytic tunnel of the Family 7 cellobiohydrolase (Cel7A) of Trichoderma reesei (Hypocrea jecorina) was calculated using two different approaches: steered molecular dynamics (SMD) simulations and alchemical free energy perturbation molecular dynamics (FEP/MD) simulations. For the SMD approach, three methods based on Jarzynski's equality were used to construct the potential of mean force from multiple pulling trajectories. The calculated binding free energies, −14.4 kcal/mol using SMD and −11.2 kcal/mol using FEP/MD, are in good qualitative agreement. Analysis of the SMD pulling trajectories suggests that several protein residues (Arg-251, Asp-259, Asp-262, Trp-376, and Tyr-381) play key roles in cellobiose and glucose binding to the catalytic tunnel. Five mutations (R251A, D259A, D262A, W376A, and Y381A) were made computationally to measure the changes in free energy during the product expulsion process. The absolute binding free energies of cellobiose to the catalytic tunnel of these five mutants are −13.1, −6.0, −11.5, −7.5, and −8.8 kcal/mol, respectively. The results demonstrated that all of the mutants tested can lower the binding free energy of cellobiose, which provides potential applications in engineering the enzyme to accelerate the product expulsion process and improve the efficiency of biomass conversion.

The binding of proteins and ligands is generally associated with the loss of translational, rotational, and conformational entropy. In many cases, however, the net entropy change due to binding is positive. To develop a deeper understanding of the energetics of entropically driven protein-ligand binding, we calculated the absolute binding free energies and binding entropies for two HIV-1 protease inhibitors Nelfinavir and Amprenavir using the double-decoupling method with molecular dynamics simulations in explicit solvent. For both ligands, the calculated absolute binding free energies are in general agreement with experiments. The statistical error in the computed ΔG(bind) due to convergence problem is estimated to be ≥2 kcal/mol. The decomposition of free energies indicates that, although the binding of Nelfinavir is driven by nonpolar interaction, Amprenavir binding benefits from both nonpolar and electrostatic interactions. The calculated absolute binding entropies show that (1) Nelfinavir binding is driven by large entropy change and (2) the entropy of Amprenavir binding is much less favorable compared with that of Nelfinavir. Both results are consistent with experiments. To obtain qualitative insights into the entropic effects, we decomposed the absolute binding entropy into different contributions based on the temperature dependence of free energies along different legs of the thermodynamic pathway. The results suggest that the favorable entropic contribution to binding is dominated by the ligand desolvation entropy. The entropy gain due to solvent release from binding site appears to be more than offset by the reduction of rotational and vibrational entropies upon binding.

The calculation of absolute binding free energies (ABFEs) for protein-ligand systems has long been a challenge. Recently, refined force fields and algorithms have improved the quality of the ABFE calculations. However, achieving the level of accuracy required to inform drug discovery efforts remains difficult. Here, we present a transferable enhanced sampling strategy to accurately calculate absolute binding free energies using OneOPES with simple geometric collective variables. We tested the strategy on two protein targets, BRD4 and Hsp90, complexed with a total of 17 chemically diverse ligands, including both molecular fragments and drug-like molecules. Our results show that OneOPES accurately predicts protein-ligand binding affinities with a mean unsigned error within 1 kcal mol-1 of experimentally determined free energies, without the need to tailor the collective variables to each system. Furthermore, our strategy effectively samples different ligand binding modes and consistently matches the experimentally determined structures regardless of the initial protein-ligand configuration. Our results suggest that the proposed OneOPES strategy can be used to inform lead optimization campaigns in drug discovery and to study protein-ligand binding and unbinding mechanisms.