On the Role of Dewetting Transitions in Host-Guest Binding Free Energy Calculations

Comparison of Receptor-Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations

Alchemical absolute binding free energy calculations are of increasing interest in drug discovery. These calculations require restraints between the receptor and ligand to restrict their relative positions and, optionally, orientations. Boresch restraints are commonly used, but they must be carefully selected in order to sufficiently restrain the ligand and to avoid inherent instabilities. Applying multiple distance restraints between anchor points in the receptor and ligand provides an alternative framework without inherent instabilities which may provide convergence benefits by more strongly restricting the relative movements of the receptor and ligand. However, there is no simple method to calculate the free energy of releasing these restraints due to the coupling of the internal and external degrees of freedom of the receptor and ligand. Here, a method to rigorously calculate free energies of binding with multiple distance restraints by imposing intramolecular restraints on the anchor points is proposed. Absolute binding free energies for the human macrophage migration inhibitory factor/MIF180, system obtained using a variety of Boresch restraints and rigorous and nonrigorous implementations of multiple distance restraints are compared. It is shown that several multiple distance restraint schemes produce estimates in good agreement with Boresch restraints. In contrast, calculations without orientational restraints produce erroneously favorable free energies of binding by up to approximately 4 kcal mol-1. These approaches offer new options for the deployment of alchemical absolute binding free energy calculations.

Prediction of multiple dry-wet transition pathways with a mesoscale variational approach

Water fluctuates in a hydrophobic confinement, forming multiple dry and wet hydration states through evaporation and condensation. Transitions between such states are critical to both thermodynamics and kinetics of solute molecular processes, such as protein folding and protein-ligand binding and unbinding. To efficiently predict such dry-wet transition paths, we develop a hybrid approach that combines a variational implicit solvation model, a generalized string method for minimum free-energy paths, and the level-set numerical implementation. This approach is applied to three molecular systems: two hydrophobic plates, a carbon nanotube, and a synthetic host molecule Cucurbit[7]uril. Without an explicit description of individual water molecules, our mesoscale approach effectively captures multiple dry and wet hydration states, multiple dry-wet transition paths, such as those geometrically symmetric and asymmetric paths, and transition states, providing activation energy barriers between different states. Further analysis shows that energy barriers depend on mesoscopic lengths, such as the separation distance between the two plates and the cross section diameter of the nanotube, and that the electrostatic interactions strongly influence the dry-wet transitions. With the inclusion of solute atomic motion, general collective variables as reaction coordinates, and the finite-temperature string method, together with an improved treatment of continuum electrostatics, our approach can be further developed to sample an ensemble of transition paths, providing more accurate predictions of the transition kinetics.

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

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.

Overview of the SAMPL6 host-guest binding affinity prediction challenge

Accurately predicting the binding affinities of small organic molecules to biological macromolecules can greatly accelerate drug discovery by reducing the number of compounds that must be synthesized to realize desired potency and selectivity goals. Unfortunately, the process of assessing the accuracy of current computational approaches to affinity prediction against binding data to biological macromolecules is frustrated by several challenges, such as slow conformational dynamics, multiple titratable groups, and the lack of high-quality blinded datasets. Over the last several SAMPL blind challenge exercises, host-guest systems have emerged as a practical and effective way to circumvent these challenges in assessing the predictive performance of current-generation quantitative modeling tools, while still providing systems capable of possessing tight binding affinities. Here, we present an overview of the SAMPL6 host-guest binding affinity prediction challenge, which featured three supramolecular hosts: octa-acid (OA), the closely related tetra-endo-methyl-octa-acid (TEMOA), and cucurbit[8]uril (CB8), along with 21 small organic guest molecules. A total of 119 entries were received from ten participating groups employing a variety of methods that spanned from electronic structure and movable type calculations in implicit solvent to alchemical and potential of mean force strategies using empirical force fields with explicit solvent models. While empirical models tended to obtain better performance than first-principle methods, it was not possible to identify a single approach that consistently provided superior results across all host-guest systems and statistical metrics. Moreover, the accuracy of the methodologies generally displayed a substantial dependence on the system considered, emphasizing the need for host diversity in blind evaluations. Several entries exploited previous experimental measurements of similar host-guest systems in an effort to improve their physical-based predictions via some manner of rudimentary machine learning; while this strategy succeeded in reducing systematic errors, it did not correspond to an improvement in statistical correlation. Comparison to previous rounds of the host-guest binding free energy challenge highlights an overall improvement in the correlation obtained by the affinity predictions for OA and TEMOA systems, but a surprising lack of improvement regarding root mean square error over the past several challenge rounds. The data suggests that further refinement of force field parameters, as well as improved treatment of chemical effects (e.g., buffer salt conditions, protonation states), may be required to further enhance predictive accuracy.

SAMPL6 host-guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

On the fly estimation of host-guest binding free energies using the movable type method: participation in the SAMPL5 blind challenge

We review our performance in the SAMPL5 challenge for predicting host-guest binding affinities using the movable type (MT) method. The challenge included three hosts, acyclic Cucurbit[2]uril and two octa-acids with and without methylation at the entrance to their binding cavities. Each host was associated with 6-10 guest molecules. The MT method extrapolates local energy landscapes around particular molecular states and estimates the free energy by Monte Carlo integration over these landscapes. Two blind submissions pairing MT with variants of the KECSA potential function yielded mean unsigned errors of 1.26 and 1.53 kcal/mol for the non-methylated octa-acid, 2.83 and 3.06 kcal/mol for the methylated octa-acid, and 2.77 and 3.36 kcal/mol for Cucurbit[2]uril host. While our results are in reasonable agreement with experiment, we focused on particular cases in which our estimates gave incorrect results, particularly with regard to association between the octa-acids and an adamantane derivative. Working on the hypothesis that differential solvation effects play a role in effecting computed binding affinities for the parent octa-acid and the methylated octa-acid and that the ligands bind inside the pockets (rather than on the surface) we devised a new solvent accessible surface area term to better quantify solvation energy contributions in MT based studies. To further explore this issue a, molecular dynamics potential of mean force (PMF) study indicates that, as found by our docking calculations, the stable binding mode for this ligand is inside (rather than surface bound) the octa-acid cavity whether the entrance is methylated or not. The PMF studies also obtained the correct order for the methylation-induced change in binding affinities and associated the difference, to a large extent to differential solvation effects. Overall, the SAMPL5 challenge yielded in improvements our solvation modeling and also demonstrated the need for thorough validation of input data integrity prior to any computational analysis.

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the "normal velocity" that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

A self-consistent phase-field approach to implicit solvation of charged molecules with Poisson-Boltzmann electrostatics

Dielectric boundary based implicit-solvent models provide efficient descriptions of coarse-grained effects, particularly the electrostatic effect, of aqueous solvent. Recent years have seen the initial success of a new such model, variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett. 96, 087802 (2006) and J. Chem. Phys. 124, 084905 (2006)], in capturing multiple dry and wet hydration states, describing the subtle electrostatic effect in hydrophobic interactions, and providing qualitatively good estimates of solvation free energies. Here, we develop a phase-field VISM to the solvation of charged molecules in aqueous solvent to include more flexibility. In this approach, a stable equilibrium molecular system is described by a phase field that takes one constant value in the solute region and a different constant value in the solvent region, and smoothly changes its value on a thin transition layer representing a smeared solute-solvent interface or dielectric boundary. Such a phase field minimizes an effective solvation free-energy functional that consists of the solute-solvent interfacial energy, solute-solvent van der Waals interaction energy, and electrostatic free energy described by the Poisson-Boltzmann theory. We apply our model and methods to the solvation of single ions, two parallel plates, and protein complexes BphC and p53/MDM2 to demonstrate the capability and efficiency of our approach at different levels. With a diffuse dielectric boundary, our new approach can describe the dielectric asymmetry in the solute-solvent interfacial region. Our theory is developed based on rigorous mathematical studies and is also connected to the Lum-Chandler-Weeks theory (1999). We discuss these connections and possible extensions of our theory and methods.

Parameterization of an effective potential for protein-ligand binding from host-guest affinity data

Force field accuracy is still one of the "stalemates" in biomolecular modeling. Model systems with high quality experimental data are valuable instruments for the validation and improvement of effective potentials. With respect to protein-ligand binding, organic host-guest complexes have long served as models for both experimental and computational studies because of the abundance of binding affinity data available for such systems. Binding affinity data collected for cyclodextrin (CD) inclusion complexes, a popular model for molecular recognition, is potentially a more reliable resource for tuning energy parameters than hydration free energy measurements. Convergence of binding free energy calculations on CD host-guest systems can also be obtained rapidly, thus offering the opportunity to assess the robustness of these parameters. In this work, we demonstrate how implicit solvent parameters can be developed using binding affinity experimental data and the binding energy distribution analysis method (BEDAM) and validated using the Grid Inhomogeneous Solvation Theory analysis. These new solvation parameters were used to study protein-ligand binding in two drug targets against the HIV-1 virus and improved the agreement between the calculated and the experimental binding affinities. This work illustrates how benchmark sets of high quality experimental binding affinity data and physics-based binding free energy models can be used to evaluate and optimize force fields for protein-ligand systems. Copyright © 2015 John Wiley & Sons, Ltd.

Protocols utilizing constant pH molecular dynamics to compute pH-dependent binding free energies

In protein–ligand binding, the electrostatic environments of the two binding partners may vary significantly in bound and unbound states, which may lead to protonation changes upon binding. In cases where ligand binding results in a net uptake or release of protons, the free energy of binding is pH-dependent. Nevertheless, conventional free energy calculations and molecular docking protocols typically do not rigorously account for changes in protonation that may occur upon ligand binding. To address these shortcomings, we present a simple methodology based on Wyman’s binding polynomial formalism to account for the pH dependence of binding free energies and demonstrate its use on cucurbit[7]uril (CB[7]) host–guest systems. Using constant pH molecular dynamics and a reference binding free energy that is taken either from experiment or from thermodynamic integration computations, the pH-dependent binding free energy is determined. This computational protocol accurately captures the large pK_a shifts observed experimentally upon CB[7]:guest association and reproduces experimental binding free energies at different levels of pH. We show that incorrect assignment of fixed protonation states in free energy computations can give errors of >2 kcal/mol in these host–guest systems. Use of the methods presented here avoids such errors, thus suggesting their utility in computing proton-linked binding free energies for protein–ligand complexes.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Does cation break the cyano bond? A critical evaluation of nitrile-cation interaction

DFT and G4 results reveal that cations display the following trends in imparting its positive charge to acrylonitrile; H⁺ > Li⁺ > Na⁺ > K⁺ for group I and Be²⁺ > Mg²⁺ > Ca²⁺ for group II. Solvation by water molecules and interaction with cation make the cyano bond more polarized and exhibits ketene-imine character. Bond order in nitrile-cation complexes has been predicted based on the s character of the covalent bond orbitals. Mulliken, CHELPG, and NPA charges are in good agreement in predicting positive charge buildup and GIAO nuclear deshileding on C1. G4 enthalpies show that Mg²⁺ is more strongly bound to acrylonitrile than to acetonitrile by 3 kcal mol⁻¹, and the proton affinity of the former is higher by 0.8 kcal mol⁻¹. G4 enthalpies of reductions support prior experimental observation that metalated conjugated nitriles show enhanced reactivity toward weak nucleophiles to afford Michael addition products.

Variational Implicit Solvation with Poisson-Boltzmann Theory

We incorporate the Poisson-Boltzmann (PB) theory of electrostatics into our variational implicit-solvent model (VISM) for the solvation of charged molecules in an aqueous solvent. In order to numerically relax the VISM free-energy functional by our level-set method, we develop highly accurate methods for solving the dielectric PB equation and for computing the dielectric boundary force. We also apply our VISM-PB theory to analyze the solvent potentials of mean force and the effect of charges on the hydrophobic hydration for some selected molecular systems. These include some single ions, two charged particles, two charged plates, and the host-guest system Cucurbit[7]uril and Bicyclo[2.2.2]octane. Our computational results show that VISM with PB theory can capture well the sensitive response of capillary evaporation to the charge in hydrophobic confinement and the polymodal hydration behavior and can provide accurate estimates of binding affinity of the host-guest system. We finally discuss several issues for further improvement of VISM.

Converging free energies of binding in cucurbit[7]uril and octa-acid host-guest systems from SAMPL4 using expanded ensemble simulations

Molecular containers such as cucurbit[7]uril (CB7) and the octa-acid (OA) host are ideal simplified model test systems for optimizing and analyzing methods for computing free energies of binding intended for use with biologically relevant protein-ligand complexes. To this end, we have performed initially blind free energy calculations to determine the free energies of binding for ligands of both the CB7 and OA hosts. A subset of the selected guest molecules were those included in the SAMPL4 prediction challenge. Using expanded ensemble simulations in the dimension of coupling host-guest intermolecular interactions, we are able to show that our estimates in most cases can be demonstrated to fully converge and that the errors in our estimates are due almost entirely to the assigned force field parameters and the choice of environmental conditions used to model experiment. We confirm the convergence through the use of alternative simulation methodologies and thermodynamic pathways, analyzing sampled conformations, and directly observing changes of the free energy with respect to simulation time. Our results demonstrate the benefits of enhanced sampling of multiple local free energy minima made possible by the use of expanded ensemble molecular dynamics and may indicate the presence of significant problems with current transferable force fields for organic molecules when used for calculating binding affinities, especially in non-protein chemistries.

The SAMPL4 host-guest blind prediction challenge: an overview

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options.

Recovery of dilute aqueous acetone, butanol, and ethanol with immobilized calixarene cavities

Macrocyclic calixarene molecules were modified with functional groups of different polarities at the upper rim and subsequently grafted to mesoporous silica supports through a single Si atom linker. The resulting materials were characterized by thermogravimetric analysis, UV-visible spectroscopy, nitrogen physisorption, and solid-state NMR spectroscopy. Materials were then used to separate acetone, n-butanol, and ethanol from dilute aqueous solution, as may be useful in the recovery of fermentation-based biofuels. For the purpose of modeling batch adsorption isotherms, the materials were considered to have one strong adsorption site per calixarene molecule and a larger number of weak adsorption sites on the silica surface and external to the calixarene cavity. The magnitude of the net free energy change of adsorption varied from approximately 15 to 20 kJ/mol and was found to decrease as upper-rim calixarene functional groups became more electron-withdrawing. Adsorption appears to be driven by weak van der Waals interactions with the calixarene cavity and, particularly for butanol, minimizing contacts with solvent water. In addition to demonstrating potentially useful new sorbents, these materials provide some of the first experimental estimates of the energy of interaction between aqueous solutes and hydrophobic calixarenes, which have previously been inaccessible because of the insolubility of most nonionic calixarene species in water.

Prediction of Small Molecule Hydration Thermodynamics with Grid Cell Theory

An efficient methodology has been developed to quantify water energetics by analysis of explicit solvent molecular simulations of organic and biomolecular systems. The approach, grid cell theory (GCT), relies on a discretization of the cell theory methodology on a three-dimensional grid to spatially resolve the density, enthalpy, and entropy of water molecules in the vicinity of solute(s) of interest. Entropies of hydration are found to converge more efficiently than enthalpies of hydration. GCT predictions of free energies of hydration on a data set of small molecules are strongly correlated with thermodynamic integration predictions. Agreement with the experiment is comparable for both approaches. A key advantage of GCT is its ability to provide from a single simulation insightful graphical analyses of spatially resolved components of the enthalpies and entropies of hydration.

Variational Implicit-Solvent Modeling of Host-Guest Binding: A Case Study on Cucurbit[7]uril|

The synthetic host cucurbit[7]uril (CB[7]) binds aromatic guests or metal complexes with ultrahigh affinity compared with that typically displayed in protein–ligand binding. Due to its small size, CB[7] serves as an ideal receptor–ligand system for developing computational methods for molecular recognition. Here, we apply the recently developed variational implicit-solvent model (VISM), numerically evaluated by the level-set method, to study hydration effects in the high-affinity binding of the B2 bicyclo[2.2.2]octane derivative to CB[7]. For the unbound host, we find that the host cavity favors the hydrated state over the dry state due to electrostatic effects. For the guest binding, we find reasonable agreement to experimental binding affinities. Dissection of the individual VISM free-energy contributions shows that the major driving forces are water-mediated hydrophobic interactions and the intrinsic (vacuum) host–guest van der Waals interactions. These findings are in line with recent experiments and molecular dynamics simulations with explicit solvent. It is expected that the level-set VISM, with further refinement on the electrostatic descriptions, can efficiently predict molecular binding and recognition in a wide range of future applications.

The electrostatic response of water to neutral polar solutes: implications for continuum solvent modeling

Continuum solvation models are widely used to estimate the hydration free energies of small molecules and proteins, in applications ranging from drug design to protein engineering, and most such models are based on the approximation of a linear dielectric response by the solvent. We used explicit-water molecular dynamics simulations with the TIP3P water model to probe this linear response approximation in the case of neutral polar molecules, using miniature cucurbituril and cyclodextrin receptors and protein side-chain analogs as model systems. We observe supralinear electrostatic solvent responses, and this nonlinearity is found to result primarily from waters' being drawn closer and closer to the solutes with increased solute-solvent electrostatic interactions; i.e., from solute electrostriction. Dielectric saturation and changes in the water-water hydrogen bonding network, on the other hand, play little role. Thus, accounting for solute electrostriction may be a productive approach to improving the accuracy of continuum solvation models.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.