Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

Force-Field-Based Computational Study of the Thermodynamics of a Large Set of Aqueous Alkanolamine Solvents for Post-Combustion CO2 Capture

The ability to predict the thermodynamic properties of amine species in CO₂-loaded aqueous solutions, including their deprotonation (pK_a) and carbamate to bicarbonate reversion (pK_c) equilibrium constants and their corresponding standard reaction enthalpies, is of critical importance for the design of improved carbon capture solvents. In this study, we used isocoulombic forms of both reactions to determine these quantities for a large set of aqueous alkanolamine solvent systems. Our hybrid approach involves using classical molecular dynamics simulations with the general amber force field (GAFF) and semi-empirical AM1-BCC charges (GAFF/AM1-BCC) in the solution phase, combined with high-level composite quantum chemical ideal-gas calculations. We first determined a new force field (FF) for the hydronium ion (H₃O⁺) by matching to the single experimental pK_a data point for the well-known monoethanolamine system at 298.15 K. We then used this FF to predict the pK_a values for 76 other amines at 298.15 K and for all 77 amines at elevated temperatures. Additionally, we indirectly relate the H₃O⁺ hydration free energy to that of H⁺ and provide expressions for intrinsic hydration free energy and enthalpy of the proton. Using the derived H₃O⁺ FF, we predicted the pK_a values of a diverse set of alkanolamines with an overall average absolute deviation of less than 0.72 pK_a units. Furthermore, the derived H₃O⁺ FF is able to predict the protonation enthalpy of these amines when used with the GAFF. We also predicted the carbamate reversion constants of the primary and secondary amine species in the data set and their corresponding standard heats of reaction, which we compared with the scarcely available experimental data, which are often subject to significant uncertainty. Finally, we also described the influence of electronic and steric effects of different molecular fragments/groups on the stabilities of the carbamates.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

On the convergence of multi-scale free energy simulations

In this work we employ simple model systems to evaluate the relative performance of two of the most important free energy methods: The Zwanzig equation (also known as "Free energy perturbation") and Bennett's acceptance ratio method (BAR). Although our examples should be transferable to other kinds of free energy simulations, we focus on applications of multi-scale free energy simulations. Such calculations are especially complex, since they connect two different levels of theory with very different requirements in terms of speed, accuracy, sampling and parallelizability. We try to reconcile all those different factors by developing some simple criteria to guide the early stages of the development of a free energy protocol. This is accomplished by quantifying how many λ intermediate steps and how many potential energy evaluations are necessary in order to reach a certain level of convergence.

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.

Calculating binding free energies of host-guest systems using the AMOEBA polarizable force field

Molecular recognition is of paramount interest in many applications. Here we investigate a series of host-guest systems previously used in the SAMPL4 blind challenge by using molecular simulations and the AMOEBA polarizable force field. The free energy results computed by Bennett's acceptance ratio (BAR) method using the AMOEBA polarizable force field ranked favorably among the entries submitted to the SAMPL4 host-guest competition [Muddana, et al., J. Comput.-Aided Mol. Des., 2014, 28, 305-317]. In this work we conduct an in-depth analysis of the AMOEBA force field host-guest binding thermodynamics by using both BAR and the orthogonal space random walk (OSRW) methods. The binding entropy-enthalpy contributions are analyzed for each host-guest system. For systems of inordinate binding entropy-enthalpy values, we further examine the hydrogen bonding patterns and configurational entropy contribution. The binding mechanism of this series of host-guest systems varies from ligand to ligand, driven by enthalpy and/or entropy changes. Convergence of BAR and OSRW binding free energy methods is discussed. Ultimately, this work illustrates the value of molecular modelling and advanced force fields for the exploration and interpretation of binding thermodynamics.

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals

First principles prediction of the structure, thermodynamics and solubility of organic molecular crystals, which play a central role in chemical, material, pharmaceutical and engineering sciences, challenges both potential energy functions and sampling methodologies. Here we calculate absolute crystal deposition thermodynamics using a novel dual force field approach whose goal is to maintain the accuracy of advanced multipole force fields (e.g. the polarizable AMOEBA model) while performing more than 95% of the sampling in an inexpensive fixed charge (FC) force field (e.g. OPLS-AA). Absolute crystal sublimation/deposition phase transition free energies were determined using an alchemical path that grows the crystalline state from a vapor reference state based on sampling with the OPLS-AA force field, followed by dual force field thermodynamic corrections to change between FC and AMOEBA resolutions at both end states (we denote the three step path as AMOEBA/FC). Importantly, whereas the phase transition requires on the order of 200 ns of sampling per compound, only 5 ns of sampling was needed for the dual force field thermodynamic corrections to reach a mean statistical uncertainty of 0.05 kcal mol-1. For five organic compounds, the mean unsigned error between direct use of AMOEBA and the AMOEBA/FC dual force field path was only 0.2 kcal mol-1 and not statistically significant. Compared to experimental deposition thermodynamics, the mean unsigned error for AMOEBA/FC (1.4 kcal mol-1) was more than a factor of two smaller than uncorrected OPLS-AA (3.2 kcal mol-1). Overall, the dual force field thermodynamic corrections reduced condensed phase sampling in the expensive force field by a factor of 40, and may prove useful for protein stability or binding thermodynamics in the future.

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

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.

Using docking and alchemical free energy approach to determine the binding mechanism of eEF2K inhibitors and prioritizing the compound synthesis

A-484954 is a known eEF2K inhibitor with submicromolar IC₅₀ potency. However, the binding mechanism and the crystal structure of the kinase remains unknown. Here, we employ a homology eEF2K model, docking and alchemical free energy simulations to probe the binding mechanism of eEF2K, and in turn, guide the optimization of potential lead compounds. The inhibitor was docked into the ATP-binding site of a homology model first. Three different binding poses, hypothesis 1, 2, and 3, were obtained and subsequently applied to molecular dynamics (MD) based alchemical free energy simulations. The calculated relative binding free energy of the analogs of A-484954 using the binding pose of hypothesis 1 show a good correlation with the experimental IC₅₀ values, yielding an r² coefficient of 0.96 after removing an outlier (compound 5). Calculations using another two poses show little correlation with experimental data, (r² of less than 0.5 with or without removing any outliers). Based on hypothesis 1, the calculated relative free energy suggests that bigger cyclic groups, at R1 e.g., cyclobutyl and cyclopentyl promote more favorable binding than smaller groups, such as cyclopropyl and hydrogen. Moreover, this study also demonstrates the ability of the alchemical free energy approach in combination with docking and homology modeling to prioritize compound synthesis. This can be an effective means of facilitating structure-based drug design when crystal structures are not available.

Efficiently computing pathway free energies: New approaches based on chain-of-replica and Non-Boltzmann Bennett reweighting schemes

BACKGROUND

Accurately modeling condensed phase processes is one of computation's most difficult challenges. Include the possibility that conformational dynamics may be coupled to chemical reactions, where multiscale (i.e., QM/MM) methods are needed, and this task becomes even more daunting.

METHODS

Free energy simulations (i.e., molecular dynamics), multiscale modeling, and reweighting schemes.

RESULTS

Herein, we present two new approaches for mitigating the aforementioned challenges. The first is a new chain-of-replica method (off-path simulations, OPS) for computing potentials of mean force (PMFs) along an easily defined reaction coordinate. This development is coupled with a new distributed, highly-parallel replica framework (REPDstr) within the CHARMM package. Validation of these new schemes is carried out on two processes that undergo conformational changes. First is the simple torsional rotation of butane, while a much more challenging glycosidic rotation (in vacuo and solvated) is the second. Additionally, a new approach that greatly improves (i.e., possibly an order of magnitude) the efficiency of computing QM/MM PMFs is introduced and compared to standard schemes. Our efforts are grounded in the recently developed method for efficiently computing QM-based free energies (i.e., QM-Non-Boltzmann Bennett, QM-NBB). Again, we validate this new technique by computing the QM/MM PMF of butane's torsional rotation.

CONCLUSIONS

The OPS-REPDstr method is a promising new approach that overcomes many limitations of standard pathway simulations in CHARMM. The combination of QM-NBB with pathway techniques is very promising as it offers significant advantages over current procedures.

GENERAL SIGNIFICANCE

Efficiently computing potentials of mean force is a major, unresolved, area of interest. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems

Characterizing large-scale structural transitions in biomolecular systems poses major technical challenges to both experimental and computational approaches. On the computational side, efficient sampling of the configuration space along the transition pathway remains the most daunting challenge. Recognizing this issue, we introduce a knowledge-based computational approach toward describing large-scale conformational transitions using (i) nonequilibrium, driven simulations combined with work measurements and (ii) free energy calculations using empirically optimized biasing protocols. The first part is based on designing mechanistically relevant, system-specific reaction coordinates whose usefulness and applicability in inducing the transition of interest are examined using knowledge-based, qualitative assessments along with nonequilirbrium work measurements which provide an empirical framework for optimizing the biasing protocol. The second part employs the optimized biasing protocol resulting from the first part to initiate free energy calculations and characterize the transition quantitatively. Using a biasing protocol fine-tuned to a particular transition not only improves the accuracy of the resulting free energies but also speeds up the convergence. The efficiency of the sampling will be assessed by employing dimensionality reduction techniques to help detect possible flaws and provide potential improvements in the design of the biasing protocol. Structural transition of a membrane transporter will be used as an example to illustrate the workings of the proposed approach.

Hydration Free Energy from Orthogonal Space Random Walk and Polarizable Force Field

The orthogonal space random walk (OSRW) method has shown enhanced sampling efficiency in free energy calculations from previous studies. In this study, the implementation of OSRW in accordance with the polarizable AMOEBA force field in TINKER molecular modeling software package is discussed and subsequently applied to the hydration free energy calculation of 20 small organic molecules, among which 15 are positively charged and five are neutral. The calculated hydration free energies of these molecules are compared with the results obtained from the Bennett acceptance ratio method using the same force field, and overall an excellent agreement is obtained. The convergence and the efficiency of the OSRW are also discussed and compared with BAR. Combining enhanced sampling techniques such as OSRW with polarizable force fields is very promising for achieving both accuracy and efficiency in general free energy calculations.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.

Computational insights for the discovery of non-ATP competitive inhibitors of MAP kinases

Due to their role in cellular signaling mitogen activated protein (MAP) kinases represent targets of pharmaceutical interest. However, the majority of known MAP kinase inhibitors compete with cellular ATP and target an ATP binding pocket that is highly conserved in the 500 plus representatives of the human protein kinase family. Here we review progress toward the development of non-ATP competitive MAP kinase inhibitors for the extracellular signal regulated kinases (ERK1/2), the c-jun N-terminal kinases (JNK1/2/3) and the p38 MAPKs (α, β, γ, and δ). Special emphasis is placed on the role of computational methods in the drug discovery process for MAP kinases. Topics include recent advances in X-ray crystallography theory that improve the MAP kinase structures essential to structurebased drug discovery, the use of molecular dynamics to understand the conformational heterogeneity of the activation loop and inhibitors discovered by virtual screening. The impact of an advanced polarizable force field such as AMOEBA used in conjunction with sophisticated kinetic and thermodynamic simulation methods is also discussed.

λ-Meta Dynamics Approach To Compute Absolute Solvation Free Energy

We present a new approach to combine λ dynamics with meta-dynamics (named λ-meta dynamics) to compute free energy surface with respect to λ. Particularly, the λ-meta dynamics method extends meta-dynamics to a single virtual variable λ, i.e., the coupling parameter between solute and solvent, to compute absolute solvation free energy as an exemplary application. We demonstrate that λ-meta dynamics simulations can recover the accurate potential of mean force surface with respect to λ compared to the benchmark results from traditional λ-dynamics with umbrella sampling. The solvation free energy results for five small organic molecules from λ-meta dynamics simulations using the same filling scheme show that the statistical errors are within ±0.5 kcal/mol. The new λ-meta dynamics method is general and other variables such as order parameters to describe conformational changes can be easily combined with λ-meta dynamics. This should allow for efficient samplings on high-dimension free energy landscapes.

Enhancing QM/MM molecular dynamics sampling in explicit environments via an orthogonal-space-random-walk-based strategy

Accurate prediction of molecular conformations in explicit environments, such as aqueous solution and protein interiors, can facilitate our understanding of various molecular recognition processes. Most computational approaches are limited as a result of their compromised choices between the underlying energy model and the sampling length. Taking advantage of a recent second-order generalized ensemble scheme [e.g., the orthogonal space random walk (OSRW) strategy], which can synergistically accelerate the motion of a focused region and its coupled environmental response, we are presenting a QM/MM (combined quantum mechanical/molecular mechanical)-based molecular dynamics sampling technique to explore molecular conformational landscapes in explicit environments. The present QM/MM potential scaling-based OSRW sampling scheme is employed to study the binding of DMSO to the FKBP12 protein, the conformation distribution of a novel mercaptosulfonamide inhibitor in aqueous solution, and its binding poses in zinc-containing matrix metalloproteinase-9 (MMP-9). As demonstrated, the present QM/MM second-order generalized ensemble sampling technique enables feasible usage of the QM/MM model to sample molecular conformations in condensed environments.