Determination of free energy profiles by repository based adaptive umbrella sampling: bridging nonequilibrium and quasiequilibrium simulations

Effective prediction model and determination of binding residues influential for inhibitors targeting HIV-1 integrase-LEDGF/p75 interface by employing solvent accessible surface area energy as key determinant

Development of a highly accurate prediction model for protein-ligand inhibition has been a major challenge in drug discovery. Herein, we describe a novel predictive model for the inhibition of HIV-1 integrase (IN)-LEDGF/p75 protein-protein interaction. The model was constructed using energy parameters approximated from molecular dynamics (MD) simulations and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) calculations. Chemometric analysis using partial least squares (PLS) regression revealed that solvent accessible surface area energy (ΔG_SASA) is the major determinant parameter contributing greatly to the prediction accuracy. PLS prediction model on the ΔG_SASA values collected from 41 complexes yielded a strong correlation between the predicted and the actual inhibitory activities (R² = 0.9666, RMSEC of pIC₅₀ values = 0.0890). Additionally, for the test set of 14 complexes, the model performed satisfactorily with very low pIC₅₀ errors (Q² = 0.5168, RMSEP = 0.3325). A strong correlation between the buried surface areas on the IN protein, when bound with IN-LEDGF/p75 inhibitors, and the respective ΔG_SASA values was also obtained. Furthermore, the current method could identify 'hot spots'of amino acid residues highly influential to the inhibitory activity prediction. This could present fruitful implications in binding site determination and future inhibitor developments targeting protein-protein interactions.Communicated by Ramaswamy H. Sarma.

Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: quantum mechanical/molecular mechanical free energy simulations

The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid-base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mechanical/molecular mechanical free energy simulations and pKa calculations, as well as experimental measurements of the rate constant for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calculations suggest that an external base deprotonates either G40(N1) or possibly A-1(O2'), which would be followed by proton transfer from G40(N1) to A-1(O2'). After this initial deprotonation, A-1(O2') starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2') to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2') to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calculated rate constant for the favored mechanism is in agreement with the experimental rate constant measured at biological Mg(2+) ion concentration. According to these calculations, catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa's of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.

Quantum mechanical/molecular mechanical free energy simulations of the self-cleavage reaction in the hepatitis delta virus ribozyme

The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg²⁺ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na⁺ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2′ nucleophile by deprotonation and orientation is less favorable with Na⁺ ions than with Mg²⁺ ions. To explore this hypothesis, we experimentally measure the pK_a of O2′ by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg²⁺ ion may play three key roles: assisting in the activation of the O2′ nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it.

Roadmaps through free energy landscapes calculated using the multi-dimensional vFEP approach

The variational free energy profile (vFEP) method is extended to two dimensions and tested with molecular simulation applications. The proposed 2D-vFEP approach effectively addresses the two major obstacles to constructing free energy profiles from simulation data using traditional methods: the need for overlap in the re-weighting procedure and the problem of data representation. This is especially evident as these problems are shown to be more severe in two dimensions. The vFEP method is demonstrated to be highly robust and able to provide stable, analytic free energy profiles with only a paucity of sampled data. The analytic profiles can be analyzed with conventional search methods to easily identify stationary points (e.g. minima and first-order saddle points) as well as the pathways that connect these points. These "roadmaps" through the free energy surface are useful not only as a post-processing tool to characterize mechanisms, but can also serve as a basis from which to direct more focused "on-the-fly" sampling or adaptive force biasing. Test cases demonstrate that 2D-vFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct stable, converged analytic free energy profiles. In a classic test case, the two dimensional free energy profile of the backbone torsion angles of alanine dipeptide, 2D-vFEP needs less than 1% of the original data set to reach a sampling accuracy of 0.5 kcal/mol in free energy shifts between windows. A new software tool for performing one and two dimensional vFEP calculations is herein described and made publicly available.

A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations

A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.

Introducing sampling entropy in repository based adaptive umbrella sampling

Determining free energy surfaces along chosen reaction coordinates is a common and important task in simulating complex systems. Due to the complexity of energy landscapes and the existence of high barriers, one widely pursued objective to develop efficient simulation methods is to achieve uniform sampling among thermodynamic states of interest. In this work, we have demonstrated sampling entropy (SE) as an excellent indicator for uniform sampling as well as for the convergence of free energy simulations. By introducing SE and the concentration theorem into the biasing-potential-updating scheme, we have further improved the adaptivity, robustness, and applicability of our recently developed repository based adaptive umbrella sampling (RBAUS) approach [H. Zheng and Y. Zhang, J. Chem. Phys. 128, 204106 (2008)]. Besides simulations of one dimensional free energy profiles for various systems, the generality and efficiency of this new RBAUS-SE approach have been further demonstrated by determining two dimensional free energy surfaces for the alanine dipeptide in gas phase as well as in water.

Increasing the time step with mass scaling in Born-Oppenheimer ab initio QM/MM molecular dynamics simulations

Born-Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state-of-the-art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass-scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born-Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass-scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles.