The ability of grand canonical Monte Carlo (GCMC) to create and annihilate molecules in a given region greatly aids the identification of water sites and water binding free energies in protein cavities. However, acceptance rates without the application of biased moves can be low, resulting in large variations in the observed water occupancies. Here, we show that replica-exchange of the chemical potential significantly reduces the variance of the GCMC data. This improvement comes at a negligible increase in computational expense when simulations comprise of runs at different chemical potentials. Replica-exchange GCMC is also found to substantially increase the precision of water binding free energies as calculated with grand canonical integration, which has allowed us to address a missing standard state correction.

Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are postprocessed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation, however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semiempirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.

Hydration free energy (HFE) calculations are often used to assess the performance of biomolecular force fields and the quality of assigned parameters. The AMOEBA polarizable force field moves beyond traditional pairwise additive models of electrostatics and may be expected to improve upon predictions of thermodynamic quantities such as HFEs over and above fixed-point-charge models. The recent SAMPL4 challenge evaluated the AMOEBA polarizable force field in this regard but showed substantially worse results than those using the fixed-point-charge GAFF model. Starting with a set of automatically generated AMOEBA parameters for the SAMPL4 data set, we evaluate the cumulative effects of a series of incremental improvements in parametrization protocol, including both solute and solvent model changes. Ultimately, the optimized AMOEBA parameters give a set of results that are not statistically significantly different from those of GAFF in terms of signed and unsigned error metrics. This allows us to propose a number of guidelines for new molecule parameter derivation with AMOEBA, which we expect to have benefits for a range of biomolecular simulation applications such as protein–ligand binding studies.

Water molecules play integral roles in the formation of many protein–ligand complexes, and recent computational efforts have been focused on predicting the thermodynamic properties of individual waters and how they may be exploited in rational drug design. However, when water molecules form highly coupled hydrogen-bonding networks, there is, as yet, no method that can rigorously calculate the free energy to bind the entire network or assess the degree of cooperativity between waters. In this work, we report theoretical and methodological developments to the grand canonical Monte Carlo simulation technique. Central to our results is a rigorous equation that can be used to calculate efficiently the binding free energies of water networks of arbitrary size and complexity. Using a single set of simulations, our methods can locate waters, estimate their binding affinities, capture the cooperativity of the water network, and evaluate the hydration free energy of entire protein binding sites. Our techniques have been applied to multiple test systems and compare favorably to thermodynamic integration simulations and experimental data. The implications of these methods in drug design are discussed.

The use of the Zwanzig equation in the calculation of single-step perturbations to provide first-principles (ab initio) quantum mechanics (QM) correction terms to molecular mechanics (MM) free energy cycles is well established. A rigorous test of the ability to converge such calculations would be very useful in this context. In this work, we perform a direct assessment of the convergence of the MM to QM perturbation, by attempting the reverse QM to MM perturbation. This required the generation of extensive QM molecular dynamics trajectories, using density functional theory (DFT), within the representative biological system of a DNA adenosine–thymidine dimer. Over 100 ps of dynamics with the PBE functional and 6.25 ps with the LDA functional were generated. We demonstrate that calculations with total potential energies are very poorly convergent due to a lack of overlap of phase space distributions between ensembles. While not theoretically rigorous, the use of interaction energies provides far superior convergence, despite the presence of nonclassical charge transfer effects within the DFT trajectories. The source of poor phase space overlap for total energies is diagnosed, the approximate quantification of overlaps suggesting that even for the comparatively simple system considered here convergence of total energy calculations within a reasonable simulation time is unfeasible.

We present a molecular simulation protocol to compute free energies of binding, which combines a QM/MM correction term with rigorous classical free energy techniques, thereby accounting for electronic polarization effects. Relative free energies of binding are first computed using classical force fields, Monte Carlo sampling, and replica exchange thermodynamic integration. Snapshots of the configurations at the end points of the perturbation are then subjected to DFT-QM/MM single-point calculations using the B3LYP functional and a range of basis sets. The resulting quantum mechanical energies are then processed using the Zwanzig equation to give free energies incorporating electronic polarization. Our approach is conceptually simple and does not require tightly coupled QM and MM software. The method has been validated by calculating the relative free energies of hydration of methane and water and the relative free energy of binding of two inhibitors of cyclooxygenase-2. Closed thermodynamic cycles are obtained across different pathways, demonstrating the correctness of the technique, although significantly more sampling is required for the protein−ligand system. Our method offers a simple and effective way to incorporate quantum mechanical effects into computed free energies of binding.

The unassisted permeation process of β-blocker drugs (alprenolol, atenolol, pindolol) and steroid hormones (progesterone, testosterone) through a lipid membrane is simulated by a novel dual-resolution molecular dynamics approach. The lipid and water molecules are described by simple and efficient coarse-grain models, whereas the drug and hormone permeants are represented by traditional atomistic models. Our hybrid method is about two orders of magnitude faster than standard atomic-level counterparts. For each permeant, we calculate the transfer free energy as a function of depth inside the bilayer; these data indicate the location across the membrane where the solutes preferentially partition. Using the free energy profiles, we develop a simple expression that proves remarkably accurate in predicting experimental permeability rankings; the proposed permeation model highlights and addresses potentially problematic aspects of the standard solubility-diffusion theory. We also calculate the diffusion coefficients of the permeants, and track their lateral motion to study their diffusive patterns. Furthermore, we show the drugs' perturbing effect on the bilayer structure and quantify the steroids' preferred orientations. The results obtained compare favourably with experimental measurements and traditional atomic-level simulation data reported in the literature. Promising potential applications of our methodology to areas such as drug design and membrane-protein modelling are discussed.

HIV-1 protease performs a vital step in the propagation of the HIV virus and is therefore an important drug target in the treatment of AIDS. It consists of a homodimer, with access to the active site limited by two protein flaps. NMR studies have identified two time scales of motions that occur in these flaps, and it is thought that the slower of these is responsible for a conformational change that makes the protein ligand-accessible. This motion occurs on a time scale outside that achievable using traditional molecular dynamics simulations. Reversible Digitally Filtered Molecular Dynamics (RDFMD) is a method that amplifies low frequency motions associated with conformational change and has recently been applied to, among others, E. coli dihydrofolate reductase, inducing a conformational change between known crystal structures. In this paper, the conformational motions of HIV-1 protease produced during MD and RDFMD simulations are presented, including movement between the known semiopen and closed conformations, and the opening and closing of the protein flaps.

The HIV-1 IN enzyme is one of three crucial virally encoded enzymes (HIV-1 IN, HIV-1 PR, and HIV-1 RT) involved in the life-cycle of the HIV-1 virus, making it an attractive target in the development of drugs against the AIDS virus. The structure and mechanism of the HIV-1 IN enzyme is the least understood of the three enzymes due to the lack of three-dimensional structural information. X-ray cystallographic studies have not yet been able to resolve the full-length structure, and studies have been mainly focused on the catalytic domain. This central domain possesses an important catalytic loop observed to overhang the active site, and experimental studies have shown that its dynamics affects the catalytic activity of mutant HIV-1 IN enzymes. In this study, the enhanced sampling technique, Reversible Digitally Filtered Molecular Dynamics (RDFMD), has been applied to the catalytic domain of the WT and G140A/G149A HIV-1 IN enzymes and has highlighted significant differences between the behavior of the catalytic loop which may explain the decrease of activity observed in experimental studies for this mutant.

The transmembrane permeation of eight small (molecular weight <100) organic molecules across a phospholipid bilayer is investigated by multiscale molecular dynamics simulation. The bilayer and hydrating water are represented by simplified, efficient coarse-grain models, whereas the permeating molecules are described by a standard atomic-level force-field. Permeability properties are obtained through a refined version of the z-constraint algorithm. By constraining each permeant at selected depths inside the bilayer, we have sampled free energy differences and diffusion coefficients across the membrane. These data have been combined, according to the inhomogeneous solubility−diffusion model, to yield the permeability coefficients. The results are generally consistent with previous atomic-level calculations and available experimental data. Computationally, our multiscale approach proves 2 orders of magnitude faster than traditional atomic-level methods.

One of the factors preventing the general application of free energy methods in rational drug design remains the lack of sufficient computational resources. Many nonequilibrium (NE) free energy methods, however, are easily made embarrassingly parallel in comparison to equilibrium methods and may be conveniently run on desktop computers using distributed computing software. In recent years, there has been a proliferation of NE methods, but the general applicability of these approaches has not been determined. In this study, a subset including only those NE methods which are easily parallelised were considered for examination, with a view to their application to the prediction of protein−ligand binding affinities. A number of test systems were examined, including harmonic oscillator (HO) systems and the calculation of relative free energies of hydration of water−methane. The latter system uses identical potentials to the protein ligand case and is therefore an appropriate model system on which methods may be tested. As well as investigating existing protocols, a replica exchange NE approach was developed, which was found to offer advantages over conventional methods. It was found that Rosenbluth-based approaches to optimizing the NE work values used in NE free energy estimates were not consistent in the improvements in accuracy achieved and that, given their computational cost, the simple approach of taking each work value in an unbiased way is to be preferred. Of the two free energy estimators examined, Bennett’s acceptance ratio was the most consistent and is, therefore, to be preferred over the Jarzynski estimator. The recommended protocols may be run very efficiently within a distributed computing environment and are of similar accuracy and precision to equilibrium free energy methods.

Nonequilibrium (NE) free energy methods are embarrassingly parallel and may be very conveniently run on desktop computers using distributed computing software. In recent years there has been a proliferation of NE methods, but these approaches have barely, if at all, been used in the context of calculating protein−ligand binding free energies. In a recent study by these authors, different combinations of NE methods with various test systems were compared and protocols identified which yielded results as accurate as replica exchange thermodynamic integration (RETI). The NE approaches, however, lend themselves to extensive parallelization through the use of distributed computing.(1) Here the best performing of those NE protocols, a replica exchange method using Bennett’s acceptance ratio as the free energy estimator (RENE), is applied to two sets of congeneric inhibitors bound to neuraminidase and cyclooxygenase-2. These protein−ligand systems were originally studied with RETI,(2) giving results to which NE and RENE simulations are compared. These NE calculations were carried out on a large, highly distributed group of low-performance desktop computers which are part of a Condor pool.(3) RENE was found to produce results of a predictive quality at least as good as RETI in less than half the wall clock time. However, non-RE NE results were found to be far less predictive. In addition, the RENE method successfully identified a localized region of rapidly changing free energy gradients without the need for prior investigation. These results suggest that the RENE protocol is appropriate for use in the context of predicting protein−ligand binding free energies and that it can offer advantages over conventional, equilibrium approaches.

The identification of lead molecules using computational modeling often relies on approximate, high-throughput approaches, of limited accuracy. We show here that, with a methodology we recently developed, it is possible to predict the relative binding free energies of structurally diverse ligands of the estrogen receptor-α using a rigorous statistical thermodynamics approach. Predictions obtained from the simulations with an explicit solvation model are in good qualitative agreement with experimental data, while simulations with implicit solvent models or rank ordering by empirical scoring functions yield predictions of lower quality. In addition, it is shown that free energy techniques can be used to select the most likely binding mode from a set of possible orientations generated by a docking program. It is suggested that the free energy techniques outlined in this study can be used to rank-order, by potency, structurally diverse compounds identified by virtual screening, de novo design or scaffold hopping programs.