Broadening the Scope of Binding Free Energy Calculations Using a Separated Topologies Approach.

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.

Noncovalent Host-Guest Complexes of Artemisinin with α-, ß-, and γ- Cyclodextrin Examined by Structural Mass Spectrometry Strategies.

Cyclodextrins (CDs) are a family of macrocyclic oligosaccharides with amphiphilic properties, which can improve the stability, solubility, and bioavailability of therapeutic compounds. There has been growing interest in the advancement of efficient and reliable analytical methods that assist with elucidating CD host-guest drug complexation. In this study, we investigate the noncovalent ion complexes formed between naturally occurring dextrins (αCD, ßCD, γCD, and maltohexaose) with the poorly water-soluble antimalarial drug, artemisinin, using a combination of ion mobility-mass spectrometry (IM-MS), tandem MS/MS, and theoretical modeling approaches. This study aims to determine if the drug can complex within the core dextrin cavity forming an inclusion complex or nonspecifically bind to the periphery of the dextrins. We explore the use of group I alkali earth metal additives to promote the formation of various noncovalent gas-phase ion complexes with different drug/dextrin stoichiometries (1:1, 1:2, 1:3, 1:4, and 2:1). Broad IM-MS collision cross section (CCS) mapping (n > 300) and power-law regression analysis were used to confirm the stoichiometric assignments. The 1:1 drug:αCD and drug:ßCD complexes exhibited strong preferences for Li+ and Na+ charge carriers, whereas drug:γCD complexes preferred forming adducts with the larger alkali metals, K+, Rb+, and Cs+. Although the ion-measured CCS increased with cation size for the unbound artemisinin and CDs, the 1:1 drug:dextrin complexes exhibit near-identical CCS values regardless of the cation, suggesting these are inclusion complexes. Tandem MS/MS survival yield curves of the [artemisinin:ßCD + X]+ ion (X = H, Li, Na, K) showed a decreased stability of the ion complex with increasing cation size. Empirical CCS measurements of the [artemisinin:ßCD + Li]+ ion correlated with predicted CCS values from the low-energy theoretical structures of the drug incorporated within the ßCD cavity, providing further evidence that gas-phase inclusion complexes are formed in these experiments. Taken together, this work demonstrates the utility of combining analytical information from IM-MS, MS/MS, and computational approaches in interpreting the presence of gas-phase inclusion phenomena.

Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams.

Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.

Generalized Temporal Acceleration Scheme for Kinetic Monte Carlo Simulations of Surface Catalytic Processes by Scaling the Rates of Fast Reactions.

A novel algorithm is presented that achieves temporal acceleration during kinetic Monte Carlo (KMC) simulations of surface catalytic processes. This algorithm allows for the direct simulation of reaction networks containing kinetic processes occurring on vastly disparate time scales which computationally overburden standard KMC methods. Previously developed methods for temporal acceleration in KMC were designed for specific systems and often require a priori information from the user such as identifying the fast and slow processes. In the approach presented herein, quasi-equilibrated processes are identified automatically based on previous executions of the forward and reverse reactions. Temporal acceleration is achieved by automatically scaling the intrinsic rate constants of the quasi-equilibrated processes, bringing their rates closer to the time scales of the slow kinetically relevant nonequilibrated processes. All reactions are still simulated directly, although with modified rate constants. Abrupt changes in the underlying dynamics of the reaction network are identified during the simulation, and the reaction rate constants are rescaled accordingly. The algorithm was utilized here to model the Fischer-Tropsch synthesis reaction over ruthenium nanoparticles. This reaction network has multiple time-scale-disparate processes which would be intractable to simulate without the aid of temporal acceleration. The accelerated simulations are found to give reaction rates and selectivities indistinguishable from those calculated by an equivalent mean-field kinetic model. The computational savings of the algorithm can span many orders of magnitude in realistic systems, and the computational cost is not limited by the magnitude of the time scale disparity in the system processes. Furthermore, the algorithm has been designed in a generic fashion and can easily be applied to other surface catalytic processes of interest.

Effects of a More Accurate Polarizable Hamiltonian on Polymorph Free Energies Computed Efficiently by Reweighting Point-Charge Potentials.

We examine the free energies of three benzene polymorphs as a function of temperature in the point-charge OPLS-AA and GROMOS54A7 potentials as well as the polarizable AMOEBA09 potential. For this system, using a polarizable Hamiltonian instead of the cheaper point-charge potentials is shown to have a significantly smaller effect on the stability at 250 K than on the lattice energy at 0 K. The benzene I polymorph is found to be the most stable crystal structure in all three potentials examined and at all temperatures examined. For each potential, we report the free energies over a range of temperatures and discuss the added value of using full free energy methods over the minimized lattice energy to determine the relative crystal stability at finite temperatures. The free energies in the polarizable Hamiltonian are efficiently calculated using samples collected in a cheaper point-charge potential. The polarizable free energies are estimated from the point-charge trajectories using Boltzmann reweighting with MBAR. The high configuration-space overlap necessary for efficient Boltzmann reweighting is achieved by designing point-charge potentials with intramolecular parameters matching those in the expensive polarizable Hamiltonian. Finally, we compare the computational cost of this indirect reweighted free energy estimate to the cost of simulating directly in the expensive polarizable Hamiltonian.

Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials.

We examine methods to reweight classical molecular mechanics solvation calculations to more expensive QM/MM energy functions. We first consider the solvation free energy difference between ethane and methanol in a QM/MM Hamiltonian from configurations generated in a cheaper MM potential. The solute molecules in the QM/MM Hamiltonian are treated with B3LYP/6-31G*, and the solvent water molecules are treated classically. The free energy difference in the QM/MM Hamiltonian is estimated using Boltzmann reweighting with both the non-Boltzmann Bennett method (NBB) and the multistate Bennett acceptance ratio (MBAR), and the variance of each method is directly compared for an identical data set. For this system, MBAR-derived methods are found to produce smaller overall uncertainties than NBB-based methods. Additionally, we show that to reduce the variance in the overall free energy difference estimate in this system for a fixed amount of QM/MM calculations, the energy re-evaluations in the Boltzmann reweighting step should be concentrated on the physical MM states with the highest overlap to the QM/MM states, rather than allocated equally over all sampled MM states. We also show that reallocating the QM/MM re-evaluations can be used to diagnose poor overlap between the sampled and target state. The solvation free energies for molecules in the SAMPL4 solvation data set are also calculated in the QM/MM Hamiltonian with NBB and MBAR, and the variances are marginally smaller for MBAR. Overall, NBB and MBAR produce similar variances for systems with poor sampling efficiency, and MBAR provides smaller variances than NBB in systems with high sampling efficiency. Both NBB and MBAR converge to identical solvation free energy estimates in the QM/MM Hamiltonian, and the RMSD to experimental values for molecules in the SAMPL4 solvation data set decreases by approximately 28% when switching from the MM Hamiltonian to the QM/MM Hamiltonian.