Implementing and Assessing an Alchemical Method for Calculating Protein-Protein Binding Free Energy

Application of an alchemical free energy method for the prediction of thermostable DuraPETase variants

Non-equilibrium (NEQ) alchemical free energy calculations are an emerging tool for accurately predicting changes in protein folding free energy resulting from amino acid mutations. In this study, this method in combination with the Rosetta ddg monomer tool was applied to predict more thermostable variants of the polyethylene terephthalate (PET) degrading enzyme DuraPETase. The Rosetta ddg monomer tool efficiently enriched promising mutations prior to more accurate prediction by NEQ alchemical free energy calculations. The relative change in folding free energy of 96 single amino acid mutations was calculated by NEQ alchemical free energy calculation. Experimental validation of ten of the highest scoring variants identified two mutations (DuraPETaseS61M and DuraPETaseS223Y) that increased the melting temperature (Tm) of the enzyme by up to 1 °C. The calculated relative change in folding free energy showed an excellent correlation with experimentally determined Tm resulting in a Pearson's correlation coefficient of r =  - 0.84. Limitations in the prediction of strongly stabilizing mutations were, however, encountered and are discussed. Despite these challenges, this study demonstrates the practical applicability of NEQ alchemical free energy calculations in prospective enzyme engineering projects. KEY POINTS: • Rosetta ddg monomer enriches stabilizing mutations in a library of DuraPETase variants • NEQ free energy calculations accurately predict changes in Tm of DuraPETase • The DuraPETase variants S223Y, S42M, and S61M have increased Tm.

In Vitro and In Silico Explorations of the Protein Conformational Changes of Corynebacterium glutamicum MshA, a Model Retaining GT-B Glycosyltransferase

MshA is a GT-B glycosyltransferase catalyzing the first step in the biosynthesis of mycothiol. While many GT-B enzymes undergo an open-to-closed transition, MshA is unique because its 97° rotation is beyond the usual range of 10-25°. Molecular dynamics (MD) simulations were carried out for MshA in both ligand bound and unbound states to investigate the effect of ligand binding on localized protein dynamics and its conformational free energy landscape. Simulations showed that both the unliganded "opened" and liganded "closed" forms of the enzyme sample a wide degree of dihedral angles and interdomain distances with relatively low overlapping populations. Calculation of the free energy surface using replica exchange MD for the apo "opened" and an artificial generated apo "closed" structure revealed overlaps in the geometries sampled, allowing calculation of a barrier of 2 kcal/mol for the open-to-closed transition in the absence of ligands. MD simulations of fully liganded MshA revealed a smaller sampling of the dihedral angles. The localized protein fluctuation changes suggest that UDP-GlcNAc binding activates the motions of loops in the 1-l-myo-inositol-1-phosphate (I1P)-binding site despite little change in the interactions with UDP-GlcNAc. Circular dichroism, intrinsic fluorescence spectroscopy, and mutagenesis studies were used to confirm the ligand-induced structural changes in MshA. The results support a proposed mechanism where UDP-GlcNAc binds with rigid interactions to the C-terminal domain of MshA and activates flexible loops in the N-terminal domain for binding and positioning of I1P. This model can be used for future structure-based drug development of inhibitors of the mycothiol biosynthetic pathway.

Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

Comparing Supervised Learning and Rigorous Approach for Predicting Protein Stability upon Point Mutations in Difficult Targets

Accurate prediction of protein stability upon a point mutation has important applications in drug discovery and personalized medicine. It remains a challenging issue in computational biology. Existing computational prediction methods, which range from mechanistic to supervised learning approaches, have experienced limited progress over the last few decades. This stagnation is largely due to their heavy reliance on both the quantity and quality of the training data. This is evident in recent state-of-the-art methods that continue to yield substantial errors on two challenging blind test sets: frataxin and p53, with average root-mean-square errors exceeding 3 and 1.5 kcal/mol, respectively, which is still above the theoretical 1 kcal/mol prediction barrier. Rigorous approaches, on the other hand, offer greater potential for accuracy without relying on training data but are computationally demanding and require both wild-type and mutant structure information. Although they showed high accuracy for conserving mutations, their performance is still limited for charge-changing mutation cases. This might be due to the lack of an available mutant structure, often represented by a simplified capped peptide. The recent advances in protein structure prediction methods now make it possible to obtain structures comparable to experimental ones, including complete mutant structure information. In this work, we compare the performance of supervised learning-based methods and rigorous approaches for predicting protein stability on point mutations in difficult targets: frataxin and p53. The rigorous alchemical method significantly surpasses state-of-the-art techniques in terms of both the root-mean-squared error and Pearson correlation coefficient in these two challenging blind test sets. Additionally, we propose an improved alchemical method that employs the pmx double-system/single-box approach to accurately predict the folding free energy change upon both conserving and charge-changing mutations. The enhanced protocol can accurately predict both types of mutations, thereby outperforming existing state-of-the-art methods in overall performance.

Alchemical Calculation of Relative Free Energies for Charge-Changing Mutations at Protein-Protein Interfaces Considering Fixed and Variable Protonation States

The calculation of relative free energies (ΔΔG) for charge-changing mutations at protein-protein interfaces through alchemical methods remains challenging due to variations in the system's net charge during charging steps, the possibility of mutated and contacting ionizable residues occurring in various protonation states, and undersampling issues. In this study, we present a set of strategies, collectively termed TIRST/TIRST-H+, to address some of these challenges. Our approaches combine thermodynamic integration (TI) with the prediction of pKa shifts to calculate ΔΔG values. Moreover, special sets of restraints are employed to keep the alchemically transformed molecules separated. The accuracy of the devised approaches was assessed on a large and diverse data set comprising 164 point mutations of charged residues (Asp, Glu, Lys, and Arg) to Ala at the protein-protein interfaces of complexes with known three-dimensional structures. Mean absolute and root-mean-square errors ranging from 1.38 to 1.66 and 1.89 to 2.44 kcal/mol, respectively, and Pearson correlation coefficients of ∼0.6 were obtained when testing the approaches on the selected data set using the GPU-TI module of Amber18 suite and the ff14SB force field. Furthermore, the inclusion of variable protonation states for the mutated acid residues improved the accuracy of the predicted ΔΔG values. Therefore, our results validate the use of TIRST/TIRST-H+ in prospective studies aimed at evaluating the impact of charge-changing mutations to Ala on the stability of protein-protein complexes.

Identifying and Overcoming the Sampling Challenges in Relative Binding Free Energy Calculations of a Model Protein:Protein Complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

A FRET-Based Assay for the Identification of PCNA Inhibitors

Proliferating cell nuclear antigen (PCNA) is the key regulator of human DNA metabolism. One important interaction partner is p15, involved in DNA replication and repair. Targeting the PCNA-p15 interaction is a promising therapeutic strategy against cancer. Here, a Förster resonance energy transfer (FRET)-based assay for the analysis of the PCNA-p15 interaction was developed. Next to the application as screening tool for the identification and characterization of PCNA-p15 interaction inhibitors, the assay is also suitable for the investigation of mutation-induced changes in their affinity. This is particularly useful for analyzing disease associated PCNA or p15 variants at the molecular level. Recently, the PCNA variant C148S has been associated with Ataxia-telangiectasia-like disorder type 2 (ATLD2). ATLD2 is a neurodegenerative disease based on defects in DNA repair due to an impaired PCNA. Incubation time dependent FRET measurements indicated no effect on PCNA^C148S-p15 affinity, but on PCNA stability. The impaired stability and increased aggregation behavior of PCNA^C148S was confirmed by intrinsic tryptophan fluorescence, differential scanning fluorimetry (DSF) and asymmetrical flow field-flow fractionation (AF4) measurements. The analysis of the disease associated PCNA variant demonstrated the versatility of the interaction assay as developed.

Free Energy Perturbation Calculations of Mutation Effects on SARS-CoV-2 RBD::ACE2 Binding Affinity

The strength of binding between human angiotensin converting enzyme 2 (ACE2) and the receptor binding domain (RBD) of viral spike protein plays a role in the transmissibility of the SARS-CoV-2 virus. In this study we focus on a subset of RBD mutations that have been frequently observed in infected individuals and probe binding affinity changes to ACE2 using surface plasmon resonance (SPR) measurements and free energy perturbation (FEP) calculations. Our SPR results are largely in accord with previous studies but discrepancies do arise due to differences in experimental methods and to protocol differences even when a single method is used. Overall, we find that FEP performance is superior to that of other computational approaches examined as determined by agreement with experiment and, in particular, by its ability to identify stabilizing mutations. Moreover, the calculations successfully predict the observed cooperative stabilization of binding by the Q498R N501Y double mutant present in Omicron variants and offer a physical explanation for the underlying mechanism. Overall, our results suggest that despite the significant computational cost, FEP calculations may offer an effective strategy to understand the effects of interfacial mutations on protein-protein binding affinities and, hence, in a variety of practical applications such as the optimization of neutralizing antibodies.

Identifying and overcoming the sampling challenges in relative binding free energy calculations of a model protein:protein complex

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a GPU-accelerated opensource relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches-alchemical replica exchange and alchemical replica exchange with solute tempering-for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally-determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and available at https://github.com/choderalab/perses .

Predicting binding affinity changes from long-distance mutations using molecular dynamics simulations and Rosetta

Computationally modeling how mutations affect protein-protein binding not only helps uncover the biophysics of protein interfaces, but also enables the redesign and optimization of protein interactions. Traditional high-throughput methods for estimating binding free energy changes are currently limited to mutations directly at the interface due to difficulties in accurately modeling how long-distance mutations propagate their effects through the protein structure. However, the modeling and design of such mutations is of substantial interest as it allows for greater control and flexibility in protein design applications. We have developed a method that combines high-throughput Rosetta-based side-chain optimization with conformational sampling using classical molecular dynamics simulations, finding significant improvements in our ability to accurately predict long-distance mutational perturbations to protein binding. Our approach uses an analytical framework grounded in alchemical free energy calculations while enabling exploration of a vastly larger sequence space. When comparing to experimental data, we find that our method can predict internal long-distance mutational perturbations with a level of accuracy similar to that of traditional methods in predicting the effects of mutations at the protein-protein interface. This work represents a new and generalizable approach to optimize protein free energy landscapes for desired biological functions.

Exploring PROTAC Cooperativity with Coarse-Grained Alchemical Methods

Proteolysis targeting chimera (PROTAC) is a novel drug modality that facilitates the degradation of a target protein by inducing proximity with an E3 ligase. In this work, we present a new computational framework to model the cooperativity between PROTAC-E3 binding and PROTAC-target binding principally through protein-protein interactions (PPIs) induced by the PROTAC. Due to the scarcity and low resolution of experimental measurements, the physical and chemical drivers of these non-native PPIs remain to be elucidated. We develop a coarse-grained (CG) approach to model interactions in the target-PROTAC-E3 complexes, which enables converged thermodynamic estimations using alchemical free energy calculation methods despite an unconventional scale of perturbations. With minimal parametrization, we successfully capture fundamental principles of cooperativity, including the optimality of intermediate PROTAC linker lengths that originates from configurational entropy. We qualitatively characterize the dependency of cooperativity on PROTAC linker lengths and protein charges and shapes. Minimal inclusion of sequence- and conformation-specific features in our current force field, however, limits quantitative modeling to reproduce experimental measurements, but further development of the CG model may allow for efficient computational screening to optimize PROTAC cooperativity.

Assessment of a Computational Approach to Predict Drug Resistance Mutations for HIV, HBV and SARS-CoV-2

Viral resistance is a worldwide problem mitigating the effectiveness of antiviral drugs. Mutations in the drug-targeting proteins are the primary mechanism for the emergence of drug resistance. It is essential to identify the drug resistance mutations to elucidate the mechanism of resistance and to suggest promising treatment strategies to counter the drug resistance. However, experimental identification of drug resistance mutations is challenging, laborious and time-consuming. Hence, effective and time-saving computational structure-based approaches for predicting drug resistance mutations are essential and are of high interest in drug discovery research. However, these approaches are dependent on accurate estimation of binding free energies which indirectly correlate to the computational cost. Towards this goal, we developed a computational workflow to predict drug resistance mutations for any viral proteins where the structure is known. This approach can qualitatively predict the change in binding free energies due to mutations through residue scanning and Prime MM-GBSA calculations. To test the approach, we predicted resistance mutations in HIV-RT selected by (-)-FTC and demonstrated accurate identification of the clinical mutations. Furthermore, we predicted resistance mutations in HBV core protein for GLP-26 and in SARS-CoV-2 3CLpro for nirmatrelvir. Mutagenesis experiments were performed on two predicted resistance and three predicted sensitivity mutations in HBV core protein for GLP-26, corroborating the accuracy of the predictions.

Correction Schemes for Absolute Binding Free Energies Involving Lipid Bilayers

Absolute binding free-energy (ABFE) calculations are playing an increasing role in drug design, especially as they can be performed on a range of disparate compounds and direct comparisons between them can be made. It is, however, especially important to ensure that they are as accurate as possible, as unlike relative binding free-energy (RBFE) calculations, one does not benefit as much from a cancellation of errors during the calculations. In most modern implementations of ABFE calculations, a particle mesh Ewald scheme is typically used to treat the electrostatic contribution to the free energy. A central requirement of such schemes is that the box preserves neutrality throughout the calculation. There are many ways to deal with this problem that have been discussed over the years ranging from a neutralizing plasma with a post hoc correction term through to a simple co-alchemical ion within the same box. The post hoc correction approach is the most widespread. However, the vast majority of these studies have been applied to a soluble protein in a homogeneous solvent (water or salt solution). In this work, we explore which of the more common approaches would be the most suitable for a simulation box with a lipid bilayer within it. We further develop the idea of the so-called Rocklin correction for lipid-bilayer systems and show how such a correction could work. However, we also show that it will be difficult to make this generalizable in a practical way and thus we conclude that the use of a “co-alchemical ion” is the most useful approach for simulations involving lipid membrane systems.

Thermodynamics and kinetics in antibody resistance of the 501Y.V2 SARS-CoV-2 variant

Understanding the thermodynamics and kinetics of the binding process of an antibody to the SARS-CoV-2 receptor-binding domain (RBD) of the spike protein is very important for the development of COVID-19 vaccines. In particular, it is essential to understand how the binding mechanism may change under the effects of RBD mutations. In this context, we have demonstrated that the South African variant (B1.351 or 501Y.V2) can resist the neutralizing antibody (NAb). Three substitutions in the RBD including K417N, E484K, and N501Y alter the free energy landscape, binding pose, binding free energy, binding kinetics, hydrogen bonding, nonbonded contacts, and unbinding pathway of RBD + NAb complexes. The low binding affinity of NAb to 501Y.V2 RBD confirms the antibody resistance of the South African variant. Moreover, the fragment of NAb + RBD can be used as an affordable model to investigate changes in the binding process between the mutated RBD and antibodies.

Increasing FEL minima of 501Y.V2 RBD + antibody in comparison with the WT RBD systems imply that the complex 501Y.V2 RBD + antibody is more unstable than the WT one.