Accurate Free Energy Calculations Research Articles

Effect of Protein-Polarized Ligand Charges on Relative Protein Ligand Binding Affinities.

A major challenge in computer-aided drug design is predicting relative binding energies of different molecules to a target protein using fast and accurate free-energy calculation methods. Free-energy calculations are primarily computed by utilizing classical molecular dynamics simulations based on all-atom force fields (FF) to model the interactions in the system. The present standard classical all-atom FFs contain fixed partial charges on the atoms, and hence electrostatic interactions are modeled between them. The parametrization process to determine these partial charges usually relies on quantum mechanics or semiempirical calculations of the molecule in the gas phase or homogeneous water surrounding. These present standard parametrization schemes of the partial charges neglect, therefore, polarization effects from the protein surrounding. The absence of protein polarization effects can lead to significant errors in free-energy calculations in proteins. We present a parametrization scheme for the partial charges of ligands, named protein-induced polarization (PIP) charges, which account for the electrostatic polarization due to the protein surrounding. The scheme involves single-point quantum mechanics/molecular mechanics calculations of the ligand charges in the protein/water surrounding. Using PIP ligand partial charges, we have calculated the relative binding free energies (RBFEs) of well-studied protein-ligand systems. We show here that RBFEs computed with PIP charges are either significantly improved or at least comparable to those computed with nonpolarized standard GAFF charges. Overall, we present a simple-to-use parametrization scheme to include protein polarization in any type of binding free-energy calculations. The parametrization scheme increases the accuracy in RBFE calculations, while it does not add significant computation time to standard parametrization procedures.

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models.

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.

QM, molecular docking and molecular dynamics investigation on acidic phospholipase A2 2 protein and acidic phospholipase A2 3 protein with silane dimethyl

Phytochemicals and non-nutritive plant substances can protect humans from various diseases by possessing anti-inflammatory or anti-disease properties. The Andrographis Paniculata species has been the primary focus of extensive pharmacological and phytochemical research. QM concepts are being applied scientifically in chemical and biological problems, with molecular docking and molecular dynamics techniques being crucial in-silico drug development. Absorptions in Andrographis Paniculata come from charge transfer due to visible light's energy emissions, with GCMS– results indicating its chemical components possess antibacterial properties. The PES concept aids in the intuitive understanding of mathematical concepts, while RDG recreates the complete distribution of electronic pairings, including interatomic bonding regions, lone pairs, and cores. Molecular dynamics is crucial for protein-ligand docking due to its accurate binding free energy calculations and profound understanding of the dynamic nature of protein-ligand interactions.

Efficient and accurate binding free energy calculation of Aβ9-40 protofilament propagation.

Self-assembled aggregation of peptides and proteins into regular amyloid fibrils is associated with several neurodegenerative diseases. In case of Alzheimer's disease proteolytic cleavage products of the amyloid precursor protein form pathological amyloid-beta fibrils in a nucleation and propagation phase. The molecular details and thermodynamic driving forces of amyloid formation are not well understood, but are of high relevance for potential pharmacological interference. We used atomistic binding free energy simulations to calculate the free energy of protofilament propagation by an additional Aβ9-40 peptide binding to the protofilament tip. It requires sampling of relevant conformational transitions which is challenging since the monomeric Aβ9-40 peptide is intrinsically disordered. However, the convergence of umbrella simulations can be enhanced by applying additional restraining potentials on the axial, orientational and conformational degrees of freedom. The improved convergence leads to a much closer agreement with experimental binding free energy data compared to unrestrained umbrella sampling. Moreover, the restraining approach results in a separation of contributions to the total binding free energy. The calculated contributions indicate that the free energy change associated with the restriction of conformational freedom upon propagation makes a large opposing contribution of higher magnitude than the total binding free energy. Finally, optimization of the approach leads to further significant reduction of the computational demand which is crucial for systematic studies on mutations, denaturants and inhibitors in the fibril propagation step.

SparseRNAfolD: optimized sparse RNA pseudoknot-free folding with dangle consideration

MotivationComputational RNA secondary structure prediction by free energy minimization is indispensable for analyzing structural RNAs and their interactions. These methods find the structure with the minimum free energy (MFE) among exponentially many possible structures and have a restrictive time and space complexity (O(n3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^3)$$\\end{document} time and O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} space for pseudoknot-free structures) for longer RNA sequences. Furthermore, accurate free energy calculations, including dangle contributions can be difficult and costly to implement, particularly when optimizing for time and space requirements.ResultsHere we introduce a fast and efficient sparsified MFE pseudoknot-free structure prediction algorithm, SparseRNAFolD, that utilizes an accurate energy model that accounts for dangle contributions. While the sparsification technique was previously employed to improve the time and space complexity of a pseudoknot-free structure prediction method with a realistic energy model, SparseMFEFold, it was not extended to include dangle contributions due to the complexity of computation. This may come at the cost of prediction accuracy. In this work, we compare three different sparsified implementations for dangle contributions and provide pros and cons of each method. As well, we compare our algorithm to LinearFold, a linear time and space algorithm, where we find that in practice, SparseRNAFolD has lower memory consumption across all lengths of sequence and a faster time for lengths up to 1000 bases.ConclusionOur SparseRNAFolD algorithm is an MFE-based algorithm that guarantees optimality of result and employs the most general energy model, including dangle contributions. We provide a basis for applying dangles to sparsified recursion in a pseudoknot-free model that has the potential to be extended to pseudoknots.

Achieving Accurate Standard Protein-Protein Binding Free Energy Calculations through the Geometrical Route and Ergodic Sampling.

A new strategy for the prediction of binding free energies of protein-protein complexes is reported in the present article. By combining an ergodic-sampling algorithm with the so-called "geometrical route", which introduces a series of geometrical restraints as a preamble to the physical separation of the two partners, we achieve accurate binding free energy calculations for medium-sized protein-protein complexes within the microsecond timescale. The ergodic-sampling algorithm, namely, Gaussian-accelerated molecular dynamics (GaMD), implicitly helps explore the conformational change of the two binding partners as they associate reversibly by raising the energy wells. Therefore, independent simulations capturing the isomerization of proteins are no longer needed, reducing both the computational cost and human effort. Numerical applications indicate errors on the order of 0.1 kcal/mol for the Abl-SH3 domain binding a decapeptide, of 2.6 kcal/mol for the barnase-barstar complex, and of 0.2 kcal/mol for human leukocyte elastase binding the third domain of the turkey ovomucoid inhibitor. Compared with the classical geometrical route, which resorts to collective variables to describe the isomerization of proteins, our new strategy possesses remarkable convergence properties and robustness for protein-protein complexes owing to improved ergodic sampling. We are confident that the strategy presented in this study will have a broad range of applications, helping us understand recognition-association phenomena in the areas of physical, biological, and medicinal chemistry.

Advancing drug discovery with accurate and reliable protein-ligand binding free energy calculations.

Drug discovery is a very expensive and time-consuming process, with the average cost to bring a drug molecule into market reaching $2.5B in 2016. Computational modeling can significantly accelerate the preclinical discovery process and reduce the cost. In this presentation, I am going to discuss how computational modeling, particularly the accurate and reliable protein-ligand binding free energy calculations through FEP+, can help to address some of the challenges in preclinical drug discovery, and present a few real-life drug discovery projects demonstrating the various ways these computational models were able to impact the discovery process.

Role of lipids in hydrophobic gating and blocker affinity in BK channels.

The large-conductance, calcium-activated potassium (BK) channel lacks the classic intracellular bundle-crossing gate observed in most other ion channels of the 6TM family. This observation, initially inferred from closed-pore accessibility experiments and recently corroborated by a cryo-EM structure of the non-conductive state, raises naturally a puzzling question: how can gating occur in absence of steric hindrance? To answer this question, we combined electrophysiology and molecular simulations and investigated the kinetics BK inhibition by two pore-blockers. The crux of our strategy was to leverage the state-dependent affinity of the binders to probe the physical properties of the pore. We thus combined kinetic modeling with a series of accurate free energy calculations to obtain a microscopic picture of the sequence of events taking place during the open-to-closed transition and giving rise to a nonconductive state. Our results highlight an unexpected role for annular lipids, which turn out to be an integral part of the gating machinery. Due to the presence of fenestrations, the closed-state pore is transiently occupied by some of the methyl groups from the lipid alkyl chains. This dynamic and intermittent occupancy triggers liquid-vapor oscillations and thus dewetting of the pore. Importantly, this lipid-mediated hydrophobic gating rationalizes several seemingly problematic experimental observations, including the state-dependent pore accessibility of blockers.

Combined ab initio and experimental screening of phase stabilities in the Ce-Fe-Ti- X system ( X=3d and 4d metals)

One of the main challenges for the synthesis and application of the promising hard-magnetic compound $\mathrm{Ce}{\mathrm{Fe}}_{11}\mathrm{Ti}$ is the formation of Laves phases that are detrimental for their thermodynamic stability and magnetic properties. In this paper, we present an ab initio based approach to modify the stability of these phases in the Ce-Fe-Ti system by additions of $3d$ and $4d$ elements. We combine highly accurate free-energy calculations with an efficient screening technique to determine the critical annealing temperature for the formation of $\mathrm{Ce(Fe,X)}{}_{11}\mathrm{Ti}$. The central findings are the dominant role of the formation enthalpy at $T=0$ K on chemical trends and the major relevance of partial chemical decompositions. Based on these insights, promising transition metals to promote the stability of the hard-magnetic phase, such as Zn and Tc, were predicted. The comparison with suction casting and reactive crucible melting experiments for Ce-Fe-Ti-X (X = Cu, Ga, Co, and Cr) highlights the relevance of additional phases and quaternary elements.

Absolute Binding Free Energy Calculations for Buried Water Molecules.

Water often plays a key role in mediating protein-ligand interactions. Understanding contributions from active-site water molecules to binding thermodynamics of a ligand is important in predicting binding free energies for ligand optimization. In this work, we tested a non-equilibrium switching method for absolute binding free energy calculations on water molecules in binding sites of 13 systems. We discuss the lessons we learned about identified issues that affected our calculations and ways to address them. This work fits with our larger focus on how to do accurate ligand binding free energy calculations when water rearrangements are very slow, such as rearrangements due to ligand modification (as in relative free energy calculations) or ligand binding (as in absolute free energy calculations). The method studied in this work can potentially be used to account for limited water sampling via providing endpoint corrections to free energy calculations using our calculated binding free energy of water.

Probing Factor Xa Protein-Ligand Interactions: Accurate Free Energy Calculations and Experimental Validations of Two Series of High-Affinity Ligands.

The accurate prediction of protein-ligand binding affinity belongs to one of the central goals in computer-based drug design. Molecular dynamics (MD)-based free energy calculations have become increasingly popular in this respect due to their accuracy and solid theoretical basis. Here, we present a combined study which encompasses experimental and computational studies on two series of factor Xa ligands, which enclose a broad chemical space including large modifications of the central scaffold. Using this integrated approach, we identified several new ligands with different heterocyclic scaffolds different from the previously identified indole-2-carboxamides that show superior or similar affinity. Furthermore, the so far underexplored terminal alkyne moiety proved to be a suitable non-classical bioisosteric replacement for the higher halogen-π aryl interactions. With this challenging example, we demonstrated the ability of the MD-based non-equilibrium free energy calculation approach for guiding crucial modifications in the lead optimization process, such as scaffold replacement and single-site modifications at molecular interaction hot spots.

Solution-Phase Conformational/Vibrational Anharmonicity in Comonomer Incorporation Polyolefin Catalysis.

The prediction of comonomer incorporation statistics in polyolefin catalysis necessitates an accurate calculation of free energies corresponding to monomer binding and insertion, often requiring sub-kcal/mol resolution to resolve experimental free energies. Batch reactor experiments are used to probe incorporation statistics of ethene and larger α-olefins for three constrained geometry complexes which are employed as model systems. Herein, over 6 ns of quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is performed in combination with the zero-temperature string method to characterize the solution-phase insertion barrier and to analyze the contributions from conformational and vibrational anharmonicity arising both in vacuum and in solution. Conformational sampling in the solution-phase results in 0-2 kcal/mol corrections to the insertion barrier which are on the same scale necessary to resolve experimental free energies. Anharmonic contributions from conformational sampling in the solution phase are crucial energy contributions missing from static density functional theory calculations and implicit solvation models, and the accurate calculation of these contributions is a key step toward the quantitative prediction of comonomer incorporation statistics.

Assessing the Performance of Screening MM/PBSA in Protein-Ligand Interactions.

Accurate calculation of the binding free energies between a protein and a ligand is the primary objective of structure-based drug design, but it still remains a challenging problem. In this work, we apply the screening molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) method to calculate the binding affinity of protein-ligand interactions. Our results show that the performance of the screening MM/PBSA is better than that of the standard MM/PBSA, especially in a charged-ligand system. In addition, we also investigate the effect of the solute dielectric constant on the results, and find that the optimal solute dielectric constants are different between the neutral-ligand system and the charged-ligand system. Moreover, we also evaluate the effect of the atomic-charge methods on the performance of the screening MM/PBSA. The present study demonstrates that the screening MM/PBSA should be a reliable method for calculating binding energy of biosystems.

A highly accurate metadynamics-based Dissociation Free Energy method to calculate protein\u2013protein and protein\u2013ligand binding potencies

Although seeking to develop a general and accurate binding free energy calculation method for protein–protein and protein–ligand interactions has been a continuous effort for decades, only limited successes have been obtained so far. Here, we report the development of a metadynamics-based procedure that calculates Dissociation Free Energy (DFE) and its application to 19 non-congeneric protein–protein complexes and hundreds of protein–ligand complexes covering eight targets. We achieved very high correlations in comparison to experimental binding free energies for these diverse sets of systems, demonstrating the generality and accuracy of the method. Since structures of most proteins are available owing to the recent success of prediction by artificial intelligence, a general free energy method such as DFE, combined with other methods, can make structure-based drug design a widely viable and reliable solution to develop both traditional small molecule drugs and biologic drugs as well as PROTACS.

Potency- and Selectivity-Enhancing Mutations of Conotoxins for Nicotinic Acetylcholine Receptors Can Be Predicted Using Accurate Free-Energy Calculations.

Nicotinic acetylcholine receptor (nAChR) subtypes are key drug targets, but it is challenging to pharmacologically differentiate between them because of their highly similar sequence identities. Furthermore, α-conotoxins (α-CTXs) are naturally selective and competitive antagonists for nAChRs and hold great potential for treating nAChR disorders. Identifying selectivity-enhancing mutations is the chief aim of most α-CTX mutagenesis studies, although doing so with traditional docking methods is difficult due to the lack of α-CTX/nAChR crystal structures. Here, we use homology modeling to predict the structures of α-CTXs bound to two nearly identical nAChR subtypes, α3β2 and α3β4, and use free-energy perturbation (FEP) to re-predict the relative potency and selectivity of α-CTX mutants at these subtypes. First, we use three available crystal structures of the nAChR homologue, acetylcholine-binding protein (AChBP), and re-predict the relative affinities of twenty point mutations made to the α-CTXs LvIA, LsIA, and GIC, with an overall root mean square error (RMSE) of 1.08 ± 0.15 kcal/mol and an R2 of 0.62, equivalent to experimental uncertainty. We then use AChBP as a template for α3β2 and α3β4 nAChR homology models bound to the α-CTX LvIA and re-predict the potencies of eleven point mutations at both subtypes, with an overall RMSE of 0.85 ± 0.08 kcal/mol and an R2 of 0.49. This is significantly better than the widely used molecular mechanics—generalized born/surface area (MM-GB/SA) method, which gives an RMSE of 1.96 ± 0.24 kcal/mol and an R2 of 0.06 on the same test set. Next, we demonstrate that FEP accurately classifies α3β2 nAChR selective LvIA mutants while MM-GB/SA does not. Finally, we use FEP to perform an exhaustive amino acid mutational scan of LvIA and predict fifty-two mutations of LvIA to have greater than 100X selectivity for the α3β2 nAChR. Our results demonstrate the FEP is well-suited to accurately predict potency- and selectivity-enhancing mutations of α-CTXs for nAChRs and to identify alternative strategies for developing selective α-CTXs.

A replica exchange umbrella sampling (REUS) approach to predict host\u2013guest binding free energies in SAMPL8 challenge

In this study, we report binding free energy calculations of various drugs-of-abuse to Cucurbit-[8]-uril as part of the SAMPL8 blind challenge. Force-field parameters were obtained from force-matching with different quantum mechanical levels of theory. The Replica Exchange Umbrella Sampling (REUS) approach was used with a cylindrical restraint to enhance the sampling of host–guest binding. Binding free energy was calculated by pulling the guest molecule from one side of the symmetric and cylindrical host, then into and through the host, and out the other side (bidirectional) as compared to pulling only to the bound pose inside the cylindrical host (unidirectional). The initial results with force-matched MP2 parameter set led to RMSE of 4.68 {text{kcal}}/{text{mol}} from experimental values. However, the follow-up study with CHARMM generalized force field parameters and force-matched PM6-D3H4 parameters resulted in RMSEs from experiment of 2.65 and 1.72 {text{kcal}}/{text{mol}}, respectively, which demonstrates the potential of REUS for accurate binding free energy calculation given a more suitable description of energetics. Moreover, we compared the free energies for the so called bidirectional and unidirectional free energy approach and found that the binding free energies were highly similar. However, one issue in the bidirectional approach is the asymmetry of profile on the two sides of the host. This is mainly due to the insufficient sampling for these larger systems and can be avoided by longer sampling simulations. Overall REUS shows great promise for binding free energy calculations.

Ab initio anharmonic thermodynamic properties of cubic CaSiO3 perovskite

We present an $\textit{ab initio}$ study of the thermodynamic properties of cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of the Earth's lower mantle. We compute the anharmonic phonon dispersions throughout the Brillouin zone by utilizing the phonon quasiparticle approach, which characterizes the intrinsic temperature dependence of phonon frequencies and, in principle, captures full anharmonicity. Such temperature-dependent phonon dispersions are used to calculate $\textit{ab initio}$ free energy in the thermodynamic limit ($N \rightarrow \infty$) within the framework of the phonon gas model. Accurate free energy calculations enable us to investigate cubic CaPv's thermodynamic properties and thermal equation of state, where anharmonic effects are demonstrated. The present methodology provides an important theoretical approach for exploring phase boundaries, thermodynamic, and thermoelastic properties of strongly anharmonic materials at high pressures and temperatures.

Potency-Enhancing Mutations of Gating Modifier Toxins for the Voltage-Gated Sodium Channel NaV1.7 Can Be Predicted Using Accurate Free-Energy Calculations.

Gating modifier toxins (GMTs) isolated from venomous organisms such as Protoxin-II (ProTx-II) and Huwentoxin-IV (HwTx-IV) that inhibit the voltage-gated sodium channel NaV1.7 by binding to its voltage-sensing domain II (VSDII) have been extensively investigated as non-opioid analgesics. However, reliably predicting how a mutation to a GMT will affect its potency for NaV1.7 has been challenging. Here, we hypothesize that structure-based computational methods can be used to predict such changes. We employ free-energy perturbation (FEP), a physics-based simulation method for predicting the relative binding free energy (RBFE) between molecules, and the cryo electron microscopy (cryo-EM) structures of ProTx-II and HwTx-IV bound to VSDII of NaV1.7 to re-predict the relative potencies of forty-seven point mutants of these GMTs for NaV1.7. First, FEP predicted these relative potencies with an overall root mean square error (RMSE) of 1.0 ± 0.1 kcal/mol and an R2 value of 0.66, equivalent to experimental uncertainty and an improvement over the widely used molecular-mechanics/generalized born-surface area (MM-GB/SA) RBFE method that had an RMSE of 3.9 ± 0.8 kcal/mol. Second, inclusion of an explicit membrane model was needed for the GMTs to maintain stable binding poses during the FEP simulations. Third, MM-GB/SA and FEP were used to identify fifteen non-standard tryptophan mutants at ProTx-II[W24] predicted in silico to have a at least a 1 kcal/mol gain in potency. These predicted potency gains are likely due to the displacement of high-energy waters as identified by the WaterMap algorithm for calculating the positions and thermodynamic properties of water molecules in protein binding sites. Our results expand the domain of applicability of FEP and set the stage for its prospective use in biologics drug discovery programs involving GMTs and NaV1.7.

Force Field Optimization Guided by Small Molecule Crystal Lattice Data Enables Consistent Sub-Angstrom Protein-Ligand Docking.

Accurate and rapid calculation of protein-small molecule interaction free energies is critical for computational drug discovery. Because of the large chemical space spanned by drug-like molecules, classical force fields contain thousands of parameters describing atom-pair distance and torsional preferences; each parameter is typically optimized independently on simple representative molecules. Here, we describe a new approach in which small molecule force field parameters are jointly optimized guided by the rich source of information contained within thousands of available small molecule crystal structures. We optimize parameters by requiring that the experimentally determined molecular lattice arrangements have lower energy than all alternative lattice arrangements. Thousands of independent crystal lattice-prediction simulations were run on each of 1386 small molecule crystal structures, and energy function parameters of an implicit solvent energy model were optimized, so native crystal lattice arrangements had the lowest energy. The resulting energy model was implemented in Rosetta, together with a rapid genetic algorithm docking method employing grid-based scoring and receptor flexibility. The success rate of bound structure recapitulation in cross-docking on 1112 complexes was improved by more than 10% over previously published methods, with solutions within <1 Å in over half of the cases. Our results demonstrate that small molecule crystal structures are a rich source of information for guiding molecular force field development, and the improved Rosetta energy function should increase accuracy in a wide range of small molecule structure prediction and design studies.

The Variationally Derived Intermediates Method to Calculate Free Energy Differences

Accurate and fast free energy calculations, based on atomistic simulations, are key to a first principles understanding of many-particle systems in biophysics, and enable quantitative descriptions of molecular recognition processes, drug binding, transmembrane transport, or functional conformational motions of proteins or complexes. To this aim, alchemical methods, such as the Free Energy Perturbation or the Bennett Acceptance Ratio method, require ‘morphing’ between the Hamiltonians of the involved molecular end states, typically in terms of a linear interpolation. However, linear transformations and soft-core variants thereof are still a very special case amongst all possible transformations. Here, we present the Variationally Derived Intermediates (VI) method that generalizes this approach and yields, under the assumption of uncorrelated sampling points, the intermediates with optimal sampling accuracy, which differ markedly from the established ones. We present applications to the challenging case of solvation free energies, yielding improved accuracies for decoupling electrostatic interactions, and similar ones for Lennard-Jones interactions, compared to state of the art soft-core transformations.