Direct validation of the single step classical to quantum free energy perturbation

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

A Monte Carlo Resampling approach for the calculation of hybrid classical and quantum free energies

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 post-processed 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 semi-empirical 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

Ligand binding free energies with adaptive water networks: two-dimensional grand canonical alchemical perturbations

Computational methods to calculate ligand binding affinities are increasing in popularity, due to improvements in simulation algorithms, computational resources, and easy-to-use software. However, issues can arise in relative ligand binding free energy simulations if the ligands considered have different active site water networks, as simulations are typically performed with a predetermined number of water molecules (fixed N ensembles) in preassigned locations. If an alchemical perturbation is attempted where the change should result in a different active site water network, the water molecules may not be able to adapt appropriately within the time scales of the simulations - particularly if the active site is occluded. By combining the grand canonical ensemble (μVT) to sample active site water molecules, with conventional alchemical free energy methods, the water network is able to dynamically adapt to the changing ligand. We refer to this approach as grand canonical alchemical perturbation (GCAP). In this work we demonstrate GCAP for two systems; Scytalone Dehydratase (SD) and Adenosine A2A receptor. For both systems, GCAP is shown to perform well at reproducing experimental binding affinities. Calculating the relative binding affinities with a nalve, conventional attempt to solvate the active site illustrates how poor results can be if proper consideration of water molecules in occluded pockets is neglected. GCAP results are shown to be consistent with time-consuming double decoupling simulations. In addition, by obtaining the free energy surface for ligand perturbations, as a function of both the free energy coupling parameter and water chemical potential, it is possible to directly deconvolute the binding energetics in terms of protein-ligand direct interactions and protein binding site hydration.</p

A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies

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 <i>ab initio</i> 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

Replica-Exchange and Standard State Binding Free Energies with Grand Canonical Monte Carlo

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 of the precision of standard state water binding free energies as calculated with grand canonical integration, which has allowed us to address a missing standard state correction

Preparation for commissioning of materials detritiation facility at Culham Science Centre

The Materials Detritiation Facility has been designed to thermally treat solid non-combustible radioactive waste produced during operations of the Joint European Torus (JET) that is classified as Intermediate Level Waste in the UK due to its tritium inventory (> 12 kBq/g). The waste will be thermally treated in a retort furnace at temperatures up to 1000 degrees C under a flowing air atmosphere to reduce its tritium inventory sufficiently to allow its disposal at a lower waste category via existing disposal routes. The gaseous flow from the furnace will be processed via a bubbler system, where released tritium will be trapped in water. Commissioning of the facility will be divided into two main parts: inactive and active. The main purpose of the inactive commissioning is to verify that all components and safety systems of the facility are installed, tested and operated properly and within their operational limits. Several trials of the furnace with non-radioactive materials will be performed to verify its temperature profile, and to verify operation of the gaseous process line. During the active commissioning, small amounts of tritium-contaminated material will be introduced into the facility and used for active trials. The tritium inventory in this material has been selected based on the As low as reasonably practicable (ALARP) principle, to ensure that the activity levels are sufficient to fully test the control instrumentation and pose minimal risk to operators during commissioning. Overall, four active trials will be performed with carbon-based and Inconel materials with total tritium inventories of 1MBq, 3GBq, 20GBq and 26GBq. Tritium levels in the bubblers as well as in aerial discharge from the facility will be monitored. Furthermore, all materials used in the active trials will be sampled and analyzed to verify the performance of the process and confirm that a major part of tritium inventory can be removed from materials by the process