Good practices in free-energy calculations

Computational Screening of Hydrophobic Zeolites for the Removal of Emerging Organic Contaminants from Water

The pollution of water resources by pharmaceuticals and agents of personal care products (PPCPs) poses an increasingly pressing issue that has received considerable attention from scientists and government agencies alike. Hydrophobic zeolites can serve as selective adsorbents to remove these contaminants from aqueous solution. So far, the adsorption of PPCPs in zeolites has often been investigated in case studies focusing on a small number of contaminants and one or a few zeolites. We present a computational screening approach to investigate the interaction of 53 PPCPs with 14 all-silica zeolites, aiming at a more comprehensive understanding of factors that are beneficial for a strong host-guest interaction and thus an efficient adsorption. The systems are modelled on the classical force field level of theory, allowing for the efficient computational treatment of a large number of PPCP-zeolite combinations and evaluated in terms of the interaction energy between PPCP and zeolite framework. For selected PPCP-zeolite combinations additional Free Energy Perturbation simulations are employed to compute Free Energies of Transfer between the aqueous phase and the adsorbed state. These results can serve as a starting point for experimental studies of relevant PPCP-zeolite combination or more in-depth theoretical investigations.

Single Molecule Thermodynamic Penalties Applied to Enzymes by Whispering Gallery Mode Biosensors

Optical microcavities, particularly whispering gallery mode (WGM) microcavities enhanced by plasmonic nanorods, are emerging as powerful platforms for single-molecule sensing. However, the impact of optical forces from the plasmonic near field on analyte molecules is inadequately understood. Using a standard optoplasmonic WGM single-molecule sensor to monitor two enzymes, both of which undergo an open-to-closed-to-open conformational transition, the work done on an enzyme by the WGM sensor as atoms of the enzyme move through the electric field gradient of the plasmonic hotspot during conformational change has been quantified. As the work done by the sensor on analyte enzymes can be modulated by varying WGM intensity, the WGM microcavity system can be used to apply free energy penalties to regulate enzyme activity at the single-molecule level. The findings advance the understanding of optical forces in WGM single-molecule sensing, potentially leading to the capability to precisely manipulate enzyme activity at the single-molecule level through tailored optical modulation.

High throughput mutational scanning of a protein via alchemistry on a high-performance computing resource

Antibiotic resistance presents a significant challenge to public health, as bacteria can develop resistance to antibiotics through random mutations during their life cycles, making the drugs ineffective. Understanding how these mutations contribute to drug resistance at the molecular level is crucial for designing new treatment approaches. Recent advancements in molecular biology tools have made it possible to conduct comprehensive analyses of protein mutations. Computational methods for assessing molecular fitness, such as binding energies, are not as precise as experimental techniques like deep mutational scanning. Although full atomistic alchemical free energy calculations offer the necessary precision, they are seldom used to assess high throughput data as they require significantly more computational resources. We generated a computational library using deep mutational scanning for dihydrofolate reductase (DHFR), a protein commonly studied in antibiotic resistance research. Due to resource limitations, we analyzed 33 out of 159 positions, identifying 16 single amino acid replacements. Calculations were conducted for DHFR in its drug-free state and in the presence of two different inhibitors. We demonstrate the feasibility of such calculations, made possible due to the enhancements in computational resources and their optimized use.

Machine Learning Guided AQFEP: A Fast and Efficient Absolute Free Energy Perturbation Solution for Virtual Screening

Structure-based methods in drug discovery have become an integral part of the modern drug discovery process. The power of virtual screening lies in its ability to rapidly and cost-effectively explore enormous chemical spaces to select promising ligands for further experimental investigation. Relative free energy perturbation (RFEP) and similar methods are the gold standard for binding affinity prediction in drug discovery hit-to-lead and lead optimization phases, but have high computational cost and the requirement of a structural analog with a known activity. Without a reference molecule requirement, absolute FEP (AFEP) has, in theory, better accuracy for hit ID, but in practice, the slow throughput is not compatible with VS, where fast docking and unreliable scoring functions are still the standard. Here, we present an integrated workflow to virtually screen large and diverse chemical libraries efficiently, combining active learning with a physics-based scoring function based on a fast absolute free energy perturbation method. We validated the performance of the approach in the ranking of structurally related ligands, virtual screening hit rate enrichment, and active learning chemical space exploration; disclosing the largest reported collection of free energy simulations to date.

Machine Learning Approach to Vertical Energy Gap in Redox Processes

A straightforward approach to calculating the free energy change (ΔG) and reorganization energy of a redox process is linear response approximation (LRA). However, accurate prediction of redox properties is still challenging due to difficulties in conformational sampling and vertical energy-gap sampling. Expensive hybrid quantum mechanical/molecular mechanical (QM/MM) calculations are typically employed in sampling energy gaps using conformations from simulations. To alleviate the computational cost associated with the expensive QM method in the QM/MM calculation, we propose machine learning (ML) methods to predict the vertical energy gaps (VEGs). We tested several ML models to predict the VEGs and observed that simple models like linear regression show excellent performance (mean absolute error ∼0.1 eV) in predicting VEGs in all test systems, even when using features extracted from cheaper semiempirical methods. Our best ML model (extra trees regressor) shows a mean absolute error of around 0.1 eV while using features from the cheapest QM method. We anticipate our approach can be generalized to larger macromolecular systems with more complex redox centers.

Hit-to-Lead Optimization of Heterocyclic Carbonyloxycarboximidamides as Selective Antagonists at Human Adenosine A3 Receptor

Antagonism of the human adenosine A3 receptor (hA3R) has potential therapeutic application. Alchemical relative binding free energy calculations of K18 and K32 suggested that the combination of a 3-(2,6-dichlorophenyl)-isoxazolyl group with 2-pyridinyl at the ends of a carbonyloxycarboximidamide group should improve hA3R affinity. Of the 25 new analogues synthesized, 37 and 74 showed improved hA3R affinity compared to K18 (and K32). This was further improved through the addition of a bromine group to the 2-pyridinyl at the 5-position, generating compound 39. Alchemical relative binding free energy calculations, mutagenesis studies and MD simulations supported the compounds' binding pattern while suggesting that the bromine of 39 inserts deep into the hA3R orthosteric pocket, so highlighting the importance of rigidification of the carbonyloxycarboximidamide moiety. MD simulations highlighted the importance of rigidification of the carbonyloxycarboximidamide, while suggesting that the bromine of 39 inserts deep into the hA3R orthosteric pocket, which was supported through mutagenesis studies 39 also selectively antagonized endogenously expressed hA3R in nonsmall cell lung carcinoma cells, while pharmacokinetic studies indicated low toxicity enabling in vivo evaluation. We therefore suggest that 39 has potential for further development as a high-affinity hA3R antagonist.

Methodological and force field effects in the molecular dynamics-based prediction of binding free energies of host-guest systems

As a contribution to the understanding and rationalization of methodological and modeling effects in recent host-guest SAMPL challenges, using an alchemical molecular dynamics technique we have examined the impact of force field parameterization and ionic strength in connection with guest charge neutralization on computed dissociation free energies in two typical SAMPL heavily charged macrocyclic hosts encapsulating small protonated amines with disparate binding affinities. We have shown that the methodological treatment for host neutralization, with explicit ions or with the background neutralizing plasma in the context of alchemical calculations under periodic boundary conditions, has a moderate effect on the calculated affinities. On the other hand, we have shown that seemingly small differences in the force field parameterization in highly symmetric hosts can produce systematic effects on the structural features that can have a significant impact on the predicted binding affinities.

The thermodynamics of self-assembled monolayer formation: a computational and experimental study of thiols on a flat gold surface

A methodology based on molecular dynamics simulations is presented to determine the chemical potential of thiol self-assembled monolayers on a gold surface. The thiol de-solvation and then the monolayer formation are described by thermodynamic integration with a gradual decoupling of one molecule from the environment, with the necessary corrections to account for standard state changes. The procedure is applied both to physisorbed undissociated thiol molecules and to chemisorbed dissociated thiyl radicals, considering in the latter case the possible chemical potential of the produced hydrogen. We considered monolayers formed by either 7-mercapto-4-methylcoumarin (MMC) or 3-mercapto-propanoic acid (MPA) on a flat gold surface: the free energy profiles with respect to the monolayer density are consistent with a transition from a very stable lying-down phase at low densities to a standing-up phase at higher densities, as expected. The maximum densities of thermodynamically stable monolayers are compared to experimental measures performed with reference-free grazing-incidence X-ray fluorescence (RF-GIXRF) on the same systems, finding a better agreement in the case of chemisorbed thiyl radicals.

Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols

The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. We derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.

Improved Highly Mobile Membrane Mimetic Model for Investigating Protein-Cholesterol Interactions

Cholesterol (CHL) plays an integral role in modulating the function and activity of various mammalian membrane proteins. Due to the slow dynamics of lipids, conventional computational studies of protein-CHL interactions rely on either long-time scale atomistic simulations or coarse-grained approximations to sample the process. A highly mobile membrane mimetic (HMMM) has been developed to enhance lipid diffusion and thus used to facilitate the investigation of lipid interactions with peripheral membrane proteins and, with customized in silico solvents to replace phospholipid tails, with integral membrane proteins. Here, we report an updated HMMM model that is able to include CHL, a nonphospholipid component of the membrane, henceforth called HMMM-CHL. To this end, we had to optimize the effect of the customized solvents on CHL behavior in the membrane. Furthermore, the new solvent is compatible with simulations using force-based switching protocols. In the HMMM-CHL, both improved CHL dynamics and accelerated lipid diffusion are integrated. To test the updated model, we have applied it to the characterization of protein-CHL interactions in two membrane protein systems, the human β2-adrenergic receptor (β2AR) and the mitochondrial voltage-dependent anion channel 1 (VDAC-1). Our HMMM-CHL simulations successfully identified CHL binding sites and captured detailed CHL interactions in excellent consistency with experimental data as well as other simulation results, indicating the utility of the improved model in applications where an enhanced sampling of protein-CHL interactions is desired.

Convergence criteria for single-step free-energy calculations: the relation between the Π bias measure and the sample variance

Free energy calculations play a crucial role in simulating chemical processes, enzymatic reactions, and drug design. However, assessing the reliability and convergence of these calculations remains a challenge. This study focuses on single-step free-energy calculations using thermodynamic perturbation. It explores how the sample distributions influence the estimated results and evaluates the reliability of various convergence criteria, including Kofke's bias measure Π and the standard deviation of the energy difference ΔU, σ ΔU . The findings reveal that for Gaussian distributions, there is a straightforward relationship between Π and σ ΔU , free energies can be accurately approximated using a second-order cumulant expansion, and reliable results are attainable for σ ΔU up to 25 kcal mol-1. However, interpreting non-Gaussian distributions is more complex. If the distribution is skewed towards more positive values than a Gaussian, converging the free energy becomes easier, rendering standard convergence criteria overly stringent. Conversely, distributions that are skewed towards more negative values than a Gaussian present greater challenges in achieving convergence, making standard criteria unreliable. We propose a practical approach to assess the convergence of estimated free energies.

Calculating Binding Free Energies in Model Host-Guest Systems with Unrestrained Advanced Sampling

Host-guest interactions are important to the design of pharmaceuticals and, more broadly, to soft materials as they can enable targeted, strong, and specific interactions between molecules. The binding process between the host and guest may be classified as a "rare event" when viewing the system at atomic scales, such as those explored in molecular dynamics simulations. To obtain equilibrium binding conformations and dissociation constants from these simulations, it is essential to resolve these rare events. Advanced sampling methods such as the adaptive biasing force (ABF) promote the occurrence of less probable configurations in a system, therefore facilitating the sampling of essential collective variables that characterize the host-guest interactions. Here, we present the application of ABF to a rod-cavitand coarse-grained model of host-guest systems to acquire the potential of mean force. We show that the employment of ABF enables the computation of the configurational and thermodynamic properties of bound and unbound states, including the free energy landscape. Moreover, we identify important dynamic bottlenecks that limit sampling and discuss how these may be addressed in more general systems.

Adaptive lambda schemes for efficient relative binding free energy calculation

The relative free energy perturbation (RFEP) calculation is one of the most theoretically sound computational chemistry approaches for the binding affinity prediction. However, its application is often hindered by the complexity of the calculation choices and the requirement of expertise in the field. Improper lambda scheme of RFEP may result in deviations from an accurate description of the perturbation process and is prone to erroneous affinity predictions. To address such challenges, an automated adaptive lambda method is proposed where the adaptive lambda schemes are obtained through a split-and-merge algorithm based on the pilot runs. The newly established workflow along with a series of improvements to the perturbation settings increases the consistency of the RFEP calculation results. Comparing the pilot and adaptive lambda schemes, the latter demonstrated improvements in convergence and reproducibility and lowered the mean unsigned error and the root-mean-square error. Overall, the adaptive lambda method is a reliable and robust choice to predict small molecule relative binding free energy and can be capitalized to benefit routine RFEP calculations for drug discovery projects.

Why Does the E1219V Mutation Expand T-Rich PAM Recognition in Cas9 from Streptococcus pyogenes?

Popular RNA-guided DNA endonuclease Cas9 from Streptococcus pyogenes (SpCas9) recognizes the canonical 5'-NGG-3' protospacer adjacent motif (PAM) and triggers double-stranded DNA cleavage activity. Mutations in SpCas9 were demonstrated to expand the PAM readability and hold promise for therapeutic and genome editing applications. However, the energetics of the PAM recognition and its relation to the atomic structure remain unknown. Using the X-ray structure (precatalytic SpCas9:sgRNA:dsDNA) as a template, we calculated the change in the PAM binding affinity in response to SpCas9 mutations using computer simulations. The E1219V mutation in SpCas9 fine-tunes the water accessibility in the PAM binding pocket and promotes new interactions in the SpCas9:noncanonical T-rich PAM, thus weakening the PAM stringency. The nucleotide-specific interaction of two arginine residues (i.e., R1333 and R1335 of SpCas9) ensured stringent 5'-NGG-3' PAM recognition. R1335A substitution (SpCas9R1335A) completely disrupts the direct interaction between SpCas9 and PAM sequences (canonical or noncanonical), accounting for the loss of editing activity. Interestingly, the double mutant (SpCas9R1335A,E1219V) boosts DNA binding affinity by favoring protein:PAM electrostatic contact in a desolvated pocket. The underlying thermodynamics explain the varied DNA cleavage activity of SpCas9 variants. A direct link between the energetics, structures, and activity is highlighted, which can aid in the rational design of improved SpCas9-based genome editing tools.

Reweighting from Molecular Mechanics Force Fields to the ANI-2x Neural Network Potential

To achieve chemical accuracy in free energy calculations, it is necessary to accurately describe the system's potential energy surface and efficiently sample configurations from its Boltzmann distribution. While neural network potentials (NNPs) have shown significantly higher accuracy than classical molecular mechanics (MM) force fields, they have a limited range of applicability and are considerably slower than MM potentials, often by orders of magnitude. To address this challenge, Rufa et al. [Rufa et al. bioRxiv 2020, 10.1101/2020.07.29.227959.] suggested a two-stage approach that uses a fast and established MM alchemical energy protocol, followed by reweighting the results using NNPs, known as endstate correction or indirect free energy calculation. This study systematically investigates the accuracy and robustness of reweighting from an MM reference to a neural network target potential (ANI-2x) for an established data set in vacuum, using single-step free-energy perturbation (FEP) and nonequilibrium (NEQ) switching simulation. We assess the influence of longer switching lengths and the impact of slow degrees of freedom on outliers in the work distribution and compare the results to those of multistate equilibrium free energy simulations. Our results demonstrate that free energy calculations between NNPs and MM potentials should be preferably performed using NEQ switching simulations to obtain accurate free energy estimates. NEQ switching simulations between the MM potentials and NNPs are efficient, robust, and trivial to implement.

Adenine Methylation Enhances the Conformational Flexibility of an RNA Hairpin Tetraloop

The N6-methyladenosine modification is one of the most abundant post-transcriptional modifications in ribonucleic acid (RNA) molecules. Using molecular dynamics simulations and alchemical free-energy calculations, we studied the structural and energetic implications of incorporating this modification in an adenine mononucleotide and an RNA hairpin structure. At the mononucleotide level, we found that the syn configuration is more favorable than the anti configuration by 2.05 ± 0.15 kcal/mol. The unfavorable effect of methylation was due to the steric overlap between the methyl group and a nitrogen atom in the purine ring. We then probed the effect of methylation in an RNA hairpin structure containing an AUCG tetraloop, which is recognized by a "reader" protein (YTHDC1) to promote transcriptional silencing of long noncoding RNAs. While methylation had no significant conformational effect on the hairpin stem, the methylated tetraloop showed enhanced conformational flexibility compared to the unmethylated tetraloop. The increased flexibility was associated with the outward flipping of two bases (A6 and U7) which formed stacking interactions with each other and with the C8 and G9 bases in the tetraloop, leading to a conformation similar to that in the RNA/reader protein complex. Therefore, methylation-induced conformational flexibility likely facilitates RNA recognition by the reader protein.

Toward physics-based precision medicine: Exploiting protein dynamics to design new therapeutics and interpret variants

The goal of precision medicine is to utilize our knowledge of the molecular causes of disease to better diagnose and treat patients. However, there is a substantial mismatch between the small number of food and drug administration (FDA)-approved drugs and annotated coding variants compared to the needs of precision medicine. This review introduces the concept of physics-based precision medicine, a scalable framework that promises to improve our understanding of sequence-function relationships and accelerate drug discovery. We show that accounting for the ensemble of structures a protein adopts in solution with computer simulations overcomes many of the limitations imposed by assuming a single protein structure. We highlight studies of protein dynamics and recent methods for the analysis of structural ensembles. These studies demonstrate that differences in conformational distributions predict functional differences within protein families and between variants. Thanks to new computational tools that are providing unprecedented access to protein structural ensembles, this insight may enable accurate predictions of variant pathogenicity for entire libraries of variants. We further show that explicitly accounting for protein ensembles, with methods like alchemical free energy calculations or docking to Markov state models, can uncover novel lead compounds. To conclude, we demonstrate that cryptic pockets, or cavities absent in experimental structures, provide an avenue to target proteins that are currently considered undruggable. Taken together, our review provides a roadmap for the field of protein science to accelerate precision medicine.

Addressing Suboptimal Poses in Nonequilibrium Alchemical Calculations

Alchemical transformations can be used to quantitatively estimate absolute binding free energies at a reasonable computational cost. However, most of the approaches currently in use require knowledge of the correct (crystallographic) pose. In this paper, we present a combined Hamiltonian replica exchange nonequilibrium alchemical method that allows us to reliably calculate absolute binding free energies, even when starting from suboptimal initial binding poses. Performing a preliminary Hamiltonian replica exchange enhances the sampling of slow degrees of freedom of the ligand and the target, allowing the system to populate the correct binding pose when starting from an approximate docking pose. We apply the method on 6 ligands of the first bromodomain of the BRD4 bromodomain-containing protein. For each ligand, we start nonequilibrium alchemical transformations from both the crystallographic pose and the top-scoring docked pose that are often significantly different. We show that the method produces statistically equivalent binding free energies, making it a useful tool for computational drug discovery pipelines.

PopShift: A Thermodynamically Sound Approach to Estimate Binding Free Energies by Accounting for Ligand-Induced Population Shifts from a Ligand-Free Markov State Model

Obtaining accurate binding free energies from in silico screens has been a long-standing goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking─producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation─and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

Reference-Quality Free Energy Barriers in Catalysis from Machine Learning Thermodynamic Perturbation Theory

For the first time, we report calculations of the free energies of activation of cracking and isomerization reactions of alkenes that combine several different electronic structure methods with molecular dynamics simulations. We demonstrate that the use of a high level of theory (here Random Phase Approximation-RPA) is necessary to bridge the gap between experimental and computed values. These transformations, catalyzed by zeolites and proceeding via cationic intermediates and transition states, are building blocks of many chemical transformations for valorization of long chain paraffins originating, e.g., from plastic waste, vegetable oils, Fischer-Tropsch waxes or crude oils. Compared with the free energy barriers computed at the PBE+D2 production level of theory via constrained ab initio molecular dynamics, the barriers computed at the RPA level by the application of Machine Learning thermodynamic Perturbation Theory (MLPT) show a significant decrease for isomerization reaction and an increase of a similar magnitude for cracking, yielding an unprecedented agreement with the results obtained by experiments and kinetic modeling.

Accurate calculation of affinity changes to the close state of influenza A M2 transmembrane domain in response to subtle structural changes of adamantyl amines using free energy perturbation methods in different lipid bilayers

Experimental binding free energies of 27 adamantyl amines against the influenza M2(22-46) WT tetramer, in its closed form at pH 8, were measured by ITC in DPC micelles. The measured Kd's range is ~44 while the antiviral potencies (IC50) range is ~750 with a good correlation between binding free energies computed with Kd and IC50 values (r = 0.76). We explored with MD simulations (ff19sb, CHARMM36m) the binding profile of complexes with strong, moderate and weak binders embedded in DMPC, DPPC, POPC or a viral mimetic membrane and using different experimental starting structures of M2. To predict accurately differences in binding free energy in response to subtle changes in the structure of the ligands, we performed 18 alchemical perturbative single topology FEP/MD NPT simulations (OPLS2005) using the BAR estimator (Desmond software) and 20 dual topology calculations TI/MD NVT simulations (ff19sb) using the MBAR estimator (Amber software) for adamantyl amines in complex with M2(22-46) WT in DMPC, DPPC, POPC. We observed that both methods with all lipids show a very good correlation between the experimental and calculated relative binding free energies (r = 0.77-0.87, mue = 0.36-0.92 kcal mol-1) with the highest performance achieved with TI/MBAR and lowest performance with FEP/BAR in DMPC bilayers. When antiviral potencies are used instead of the Kd values for computing the experimental binding free energies we obtained also good performance with both FEP/BAR (r = 0.83, mue = 0.75 kcal mol-1) and TI/MBAR (r = 0.69, mue = 0.77 kcal mol-1).

Free-energy measuring nanopore device

Free energies (FEs) in molecular sciences can be used to quantify the stability of folded molecules. In this article, we introduce nanopores for measuring FEs. We pull DNA hairpin-forming molecules through a nanopore, measure work, and estimate the FE change in the slow limit, and with the Jarzynski fluctuation theorem (FT) at fast pulling times. We also pull our molecule with optical tweezers, compare it to nanopores, and explore how sampling single molecules from equilibrium or a folded ensemble affects the FE estimate via the FT. The nanopore experiment helps us address and overcome the conceptual problem of equilibrium sampling in single-molecule pulling experiments. Only when molecules are sampled from an equilibrium ensemble do nanopore and tweezer FE estimates mutually agree. We demonstrate that nanopores are very useful tools for comparing FEs of two molecules at finite times and we propose future applications.

Molecular Dynamics Simulations on Spike Protein Mutants Binding with Human β Defensin Type 2

Human β defensin type 2 (hBD-2), a cationic cysteine-rich peptide secreted from the human innate immune system, can bind Spike-RBD at the same site as receptor ACE2, thus blocking viral entry into ACE2-expressing cells. In order to find out the impact of CoV-2 mutations on hBD-2's antiviral activity, it is important to investigate the binding and interaction of hBD-2 with RBD mutants. All-atom molecular dynamics simulations were conducted on typical RBD mutants, including N501Y, E484K, P479S, T478I, S477N, N439K, K417N, and N501Y-E484K-K417N, binding with hBD-2. Starting from the stable binding structure of hBD-2 and wt-RBD and ClusPro and HADDOCK docking-predicted initial structures, the RBD variants bound with hBD-2 simulations were set up, and NAMD simulations were conducted. Based on the structure and dynamics analysis, it was found that most RBD variants can still form a similar number of hydrogen bonds with hBD-2, in addition to having a similar-sized buried surface area (BSA) and a similar binding interface to the RBD wildtype. However, the RBD triple mutant formed a less stable binding structure with hBD-2 than other variants. Additionally, the free energy perturbation (FEP) method was applied to calculate the contribution of key mutant residues to the binding and the free energy change caused by the mutations. The result shows that N439K, K417N, and the trimutation increase the binding free energy of RBD with hBD-2; thus, RBD should bind less stably with hBD-2. E484K decreases the binding free energy, thus it should bind more stably with hBD-2, while N501Y, S477N, T478I, and P479S almost do not change the binding free energy with hBD-2. The MM-GBSA method predicted the binding interaction energy which shows that the trimutant should be able to escape the binding with hBD-2 but N501Y should not. The result can provide insight into understanding the functional mechanism of hBD-2 combating SARS-CoV-2 mutants.

Fluctuation Relations to Calculate Protein Redox Potentials from Molecular Dynamics Simulations

The tunable design of protein redox potentials promises to open a range of applications in biotechnology and catalysis. Here, we introduce a method to calculate redox potential changes by combining fluctuation relations with molecular dynamics simulations. It involves the simulation of reduced and oxidized states, followed by the instantaneous conversion between them. Energy differences introduced by the perturbations are obtained using the Kubo-Onsager approach. Using a detailed fluctuation relation coupled with Bayesian inference, these are postprocessed into estimates for the redox potentials in an efficient manner. This new method, denoted MD + CB, is tested on a de novo four-helix bundle heme protein (the m4D2 "maquette") and five designed mutants, including some mutants characterized experimentally in this work. The MD + CB approach is found to perform reliably, giving redox potential shifts with reasonably good correlation (0.85) to the experimental values for the mutants. The MD + CB approach also compares well with redox potential shift predictions using a continuum electrostatic method. The estimation method employed within the MD + CB approach is straightforwardly transferable to standard equilibrium MD simulations and holds promise for redox protein engineering and design applications.

Investigating the role of dispersion corrections and anharmonic effects on the phase transition in SrZrS3: A systematic analysis from AIMD free energy calculations

A thermally driven needle-like (NL) to distorted perovskite (DP) phase transition in SrZrS3 was investigated by means of ab initio free energy calculations accelerated by machine learning. As a first step, a systematic screening of the methods to include long-range interactions in semilocal density functional theory Perdew-Burke-Ernzerhof calculations was performed. Out of the ten correction schemes tested, the Tkatchenko-Scheffler method with iterative Hirshfeld partitioning method was found to yield the best match between calculated and experimental lattice geometries, while predicting the correct order of stability of NL and DP phases at zero temperature. This method was then used in free energy calculations, performed using several approaches, so as to determine the effect of various anharmonicity contributions, such as the anisotropic thermal lattice expansion or the thermally induced internal structure changes, on the phase transition temperature (TNP→DP). Accounting for the full anharmonicity by combining the NPT molecular dynamics data with thermodynamic integration with harmonic reference provided our best estimate of TNL→DP = 867 K. Although this result is ∼150 K lower than the experimental value, it still provides an improvement by nearly 300 K compared to the previous theoretical report by Koocher et al. [Inorg. Chem. 62, 11134-11141 (2023)].

OGRe: Optimal Grid Refinement Protocol for Accurate Free Energy Surfaces and Its Application in Proton Hopping in Zeolites and 2D COF Stacking

While free energy surfaces are the crux of our understanding of many chemical and biological processes, their accuracy is generally unknown. Moreover, many developments to improve their accuracy are often complicated, limiting their general use. Luckily, several tools and guidelines are already in place to identify these shortcomings, but they are typically lacking in flexibility or fail to systematically determine how to improve the accuracy of the free energy calculation. To overcome these limitations, this work introduces OGRe, a Python package for optimal grid refinement in an arbitrary number of dimensions. OGRe is based on three metrics that gauge the confinement, consistency, and overlap of each simulation in a series of umbrella sampling (US) simulations, an enhanced sampling technique ubiquitously adopted to construct free energy surfaces for hindered processes. As these three metrics are fundamentally linked to the accuracy of the weighted histogram analysis method adopted to generate free energy surfaces from US simulations, they facilitate the systematic construction of accurate free energy profiles, where each metric is driven by a specific umbrella parameter. This allows for the derivation of a consistent and optimal collection of umbrellas for each simulation, largely independent of the initial values, thereby dramatically increasing the ease-of-use toward accurate free energy surfaces. As such, OGRe is particularly suited to determine complex free energy surfaces with large activation barriers and shallow minima, which underpin many physical and chemical transformations and hence to further our fundamental understanding of these processes.

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.

Dealing with Induced Fit, Conformational Selection, and Secondary Poses in Molecular Dynamics Simulations for Reliable Free Energy Predictions

In this study, we have tested the performance of standard molecular dynamics (MD) simulations, replicates of shorter standard MD simulations, and Hamiltonian Replica Exchange (HREM) simulations for the sampling of two macrocyclic hosts for guest delivery, characterized by induced fit (phenyl-based host) and conformation selection (naphthyl-based host) and of the ODR-BRD4(I) drug-receptor system where the ligand can assume two main poses. For the optimization of the HREM simulation, we have proposed and tested an on-the-fly iterative scheme for equalizing the acceptance ratio along the replica progression at a constant replica number resulting in a moderate impact of the sampling efficiency. Concerning standard MD, we have found that, while splitting the total allocated simulation time in short MD replicates can reproduce the sampling efficiency of HREM in the phenyl-based host and in the ODR-BRD4(I) complex, in the naphthyl-based macrocycle, characterized by long-lived metastable states, enhanced sampling techniques are the only viable alternative for a reliable canonical sampling of the rugged conformational landscape.

Introducing the Automated Ligand Searcher

The Automated Ligand Searcher (ALISE) is designed as an automated computational drug discovery tool. To approximate the binding free energy of ligands to a receptor, ALISE includes a three-stage workflow, with each stage involving an increasingly sophisticated computational method: molecular docking, molecular dynamics, and free energy perturbation, respectively. To narrow the number of potential ligands, poorly performing ligands are gradually segregated out. The performance and usability of ALISE are benchmarked for a case study containing known active ligands and decoys for the HIV protease. The example illustrates that ALISE filters the decoys successfully and demonstrates that the automation, comprehensiveness, and user-friendliness of the software make it a valuable tool for improved and faster drug development workflows.

Discovery of Nirmatrelvir Resistance Mutations in SARS-CoV-2 3CLpro: A Computational-Experimental Approach

The COVID-19 pandemic has emphasized the urgency for effective antiviral therapies against SARS-CoV-2. Targeting the main protease (3CLpro) of the virus has emerged as a promising approach, and nirmatrelvir (PF-07321332), the active component of Pfizer's oral drug Paxlovid, has demonstrated remarkable clinical efficacy. However, the emergence of resistance mutations poses a challenge to its continued success. In this study, we employed alchemical free energy perturbation (FEP) alanine scanning to identify nirmatrelvir-resistance mutations within SARS-CoV-2 3CLpro. FEP identified several mutations, which were validated through in vitro IC50 experiments and found to result in 8- and 72-fold increases in nirmatrelvir IC50 values. Additionally, we constructed SARS-CoV-2 omicron replicons containing these mutations, and one of the mutants (S144A/E166A) displayed a 20-fold increase in EC50, confirming the role of FEP in identifying drug-resistance mutations. Our findings suggest that FEP can be a valuable tool in proactively monitoring the emergence of resistant strains and guiding the design of future inhibitors with reduced susceptibility to drug resistance. As nirmatrelvir is currently widely used for treating COVID-19, this research has important implications for surveillance efforts and antiviral development.

Molecular dynamics and free energy calculations of clozapine bound to D2 and H1 receptors reveal a cardiometabolic mitigated derivative

Most atypical antipsychotics derive from a high dropout of drug treatments due to adverse cardiometabolic side effects. These side effects are caused, in part, by the H1 receptor blockade. The current work sought a clozapine derivative with a reduced affinity for the H1 receptor while maintaining its therapeutic effect linked to D2 receptor binding. Explicit molecular dynamics simulations and end-point free energy calculations of clozapine in complex with the D2 and H1 receptors embedded in cholesterol-rich lipid bilayers were performed to analyze the intermolecular interactions and address the relevance of clozapine-functional groups. Based on that, free energy perturbation calculations were performed to measure the change in free energy of clozapine structural modifications. Our results indicate the best clozapine derivative is the iodine atom substitution for chlorine. The latter is mainly due to electrostatic interaction loss for the H1 receptor, while the halogen orientation out of the D2 active site reduces the impact on the affinity.Communicated by Ramaswamy H. Sarma.

Free and internal energies for the adsorption of short alkanes into the zeolite SSZ-13 from ab initio molecular dynamics simulations

Electronic structure calculations have become a valuable tool in understanding chemical reactions of hydrocarbons in zeolite pores. However, commonly applied approaches to calculate free energies based on static electronic structure calculations significantly overestimate the entropic penalty for molecular adsorption into zeolite pores. Here, we use ab initio molecular dynamics (AIMD) simulations to model the adsorption of methane, ethane, and propane to purely siliceous and protonated SSZ-13. In our analyses we focus on the internal and Helmholtz free energies of adsorption of each molecule and compare our results to various approaches for the calculation of free energies based on static calculations. We find that only an approach that retains two thirds of the translational entropy of the adsorbate upon adsorption compares favorably with AIMD simulations. However, comparison to experimental measurements of Gibbs free energies of adsorption reported in the literature implies that we might not have captured the full complexity of alkane adsorption in our model. We expect that results in this work will help to develop a better understanding of alkane adsorption in zeolites, and that the provided data will serve as a benchmark for free energy calculations of alkane adsorption in zeolites in the future.

Computed Protein-Protein Enthalpy Signatures as a Tool for Identifying Conformation Sampling Problems

Understanding the thermodynamic signature of protein-peptide binding events is a major challenge in computational chemistry. The complexity generated by both components possessing many degrees of freedom poses a significant issue for methods that attempt to directly compute the enthalpic contribution to binding. Indeed, the prevailing assumption has been that the errors associated with such approaches would be too large for them to be meaningful. Nevertheless, we currently have no indication of how well the present methods would perform in terms of predicting the enthalpy of binding for protein-peptide complexes. To that end, we carefully assembled and curated a set of 11 protein-peptide complexes where there is structural and isothermal titration calorimetry data available and then computed the absolute enthalpy of binding. The initial "out of the box" calculations were, as expected, very modest in terms of agreement with the experiment. However, careful inspection of the outliers allows for the identification of key sampling problems such as distinct conformations of peptide termini not being sampled or suboptimal cofactor parameters. Additional simulations guided by these aspects can lead to a respectable correlation with isothermal titration calorimetry (ITC) experiments (R2 of 0.88 and an RMSE of 1.48 kcal/mol overall). Although one cannot know prospectively whether computed ITC values will be correct or not, this work shows that if experimental ITC data are available, then this in conjunction with computed ITC, can be used as a tool to know if the ensemble being simulated is representative of the true ensemble or not. That is important for allowing the correct interpretation of the detailed dynamics of the system with respect to the measured enthalpy. The results also suggest that computational calorimetry is becoming increasingly feasible. We provide the data set as a resource for the community, which could be used as a benchmark to help further progress in this area.

Structure, dynamics and free energy studies on the effect of point mutations on SARS-CoV-2 spike protein binding with ACE2 receptor

The ongoing COVID-19 pandemic continues to infect people worldwide, and the virus continues to evolve in significant ways which can pose challenges to the efficiency of available vaccines and therapeutic drugs and cause future pandemic. Therefore, it is important to investigate the binding and interaction of ACE2 with different RBD variants. A comparative study using all-atom MD simulations was conducted on ACE2 binding with 8 different RBD variants, including N501Y, E484K, P479S, T478I, S477N, N439K, K417N and N501Y-E484K-K417N on RBD. Based on the RMSD, RMSF, and DSSP results, overall the binding of RBD variants with ACE2 is stable, and the secondary structure of RBD and ACE2 are consistent after the point mutation. Besides that, a similar buried surface area, a consistent binding interface and a similar amount of hydrogen bonds formed between RBD and ACE2 although the exact residue pairs on the binding interface were modified. The change of binding free energy from point mutation was predicted using the free energy perturbation (FEP) method. It is found that N501Y, N439K, and K417N can strengthen the binding of RBD with ACE2, while E484K and P479S weaken the binding, and S477N and T478I have negligible effect on the binding. Point mutations modified the dynamic correlation of residues in RBD based on the dihedral angle covariance matrix calculation. Doing dynamic network analysis, a common intrinsic network community extending from the tail of RBD to central, then to the binding interface region was found, which could communicate the dynamics in the binding interface region to the tail thus to the other sections of S protein. The result can supply unique methodology and molecular insight on studying the molecular structure and dynamics of possible future pandemics and design novel drugs.

On the Path to Optimal Alchemistry

Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.

Learned mappings for targeted free energy perturbation between peptide conformations

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. [J. Chem. Phys. 153, 144112 (2020)] demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to the free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases and different spring centers. When the neural network is trained until "early stopping"-when the loss value of the test set increases-we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å. For more distant thermodynamic states, the mapping does not produce structures representative of the target state, and the method does not reproduce reference calculations.

Effect of Spacer Length Modification of the Cationic Side Chain on the Energetics of Antimicrobial Peptide Binding to Membrane-Mimetic Bilayers

Understanding the mechanism of action of the antimicrobial peptide (AMP) in terms of its structure and energetics is the key to designing new potent and selective AMPs. Recently, we reported a membranolytic 14-residue-long lysine-rich cationic antimicrobial peptide (LL-14: NH3+-LKWLKKLLKWLKKL-CONH2) against Pseudomonas aeruginosa, Klebsiella pneumoniae, and Staphylococcus aureus, which is limited by cytotoxicity and expected to undergo facile protease degradation. Aliphatic side-chain-length modification of the cationic amino-acid residues (Lys and Arg) is a popular strategy for designing protease-resistant AMPs. However, the effect of the peptide side-chain length modifications on the membrane binding affinity and its relation to the atomic structure remain an unsolved problem. We report computer simulations that quantitatively calculated the difference in peptide binding affinity to membrane-mimetic-bilayer models (bacterial: 1-palmitoyl-2-oleoyl-phosphatidylethanolamine (POPE)/1-palmitoyl-2-oleoyl-phosphatidylglycerol (POPG) bilayer and mammalian: 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer) upon decreasing or increasing the spacer length of the cationic lysine residues of LL-14 (as well as their arginine analogues). We show that the peptide/bilayer interaction energetics varies drastically in response to spacer length modification. The strength of peptide discrimination depends strongly on the nature of the bilayer (bacterial or mammalian mimetic model). An increase in the lysine spacer length by one carbon (i.e., homolysine analogue of LL-14) is weakly/strongly disfavored by the bacterial/mammalian-membrane-mimetic bilayer. Recently, we have demonstrated an excellent correlation between the antimicrobial activity of the membranolytic cationic peptides and their binding affinity to membrane-mimetic-bilayer models. Thus, the homolysine analogue of LL-14 is a promising noncytotoxic AMP with conserved activity. On the other hand, homoarginine analogue (arginine spacer length increment by a single carbon) was preferred by both the bacteria and the mammalian mimetic bilayers and displayed the strongest affinity for the former among the peptides studied in this work. Thus, the promising most potent homoarginine analogue is likely to be cytotoxic. Shortening the Lys/Arg side chain to a three-carbon spacer (Dab/Agb) improves the binding affinity to bacterial and mammalian-membrane-mimetic bilayers. Arginine and arginine-derivative peptides exhibited stronger binding affinity to the bilayers relative to the lysine analogue. The results provide a plausible explanation to the previous experimental observations, viz., superior antimicrobial activity of the arginine peptides relative to Lys peptides and the improvement of antimicrobial activity upon substitution of Lys with Dab in the cationic peptides. The simulations revealed that the small change in the peptide hydrophobicity by Lys/Arg spacer length modification could drastically alter the energetics of peptide/bilayer binding by fine-tuning the electrostatic interactions. The energetics underlying the peptide selectivity by simple membrane-mimetic bilayer models may be beneficial for designing new selective and protease-resistant AMPs.

Accurate and Efficient Multilevel Free Energy Simulations with Neural Network-Assisted Enhanced Sampling

Free energy differences (ΔF) are essential to quantitative characterization and understanding of chemical and biological processes. Their direct estimation with an accurate quantum mechanical potential is of great interest and yet impractical due to high computational cost and incompatibility with typical alchemical free energy protocols. One promising solution is the multilevel free energy simulation in which the estimate of ΔF at an inexpensive low level of theory is combined with the correction toward a higher level of theory. The poor configurational overlap generally expected between the two levels of theory, however, presents a major challenge. We overcome this challenge by using a deep neural network model and enhanced sampling simulations. An adversarial autoencoder is used to identify a low-dimensional (latent) space that compactly represents the degrees of freedom that encode the distinct distributions at the two levels of theory. Enhanced sampling in this latent space is then used to drive the sampling of configurations that predominantly contribute to the free energy correction. Results for both gas phase and condensed phase systems demonstrate that this data-driven approach offers high accuracy and efficiency with great potential for scalability to complex systems.

Kinetic Barrier to Enzyme Inhibition Is Manipulated by Dynamical Local Interactions in E. coli DHFR

Dihydrofolate reductase (DHFR) is an important drug target and a highly studied model protein for understanding enzyme dynamics. DHFR's crucial role in folate synthesis renders it an ideal candidate to understand protein function and protein evolution mechanisms. In this study, to understand how a newly proposed DHFR inhibitor, 4'-deoxy methyl trimethoprim (4'-DTMP), alters evolutionary trajectories, we studied interactions that lead to its superior performance over that of trimethoprim (TMP). To elucidate the inhibition mechanism of 4'-DTMP, we first confirmed, both computationally and experimentally, that the relative binding free energy cost for the mutation of TMP and 4'-DTMP is the same, pointing the origin of the characteristic differences to be kinetic rather than thermodynamic. We then employed an interaction-based analysis by focusing first on the active site and then on the whole enzyme. We confirmed that the polar modification in 4'-DTMP induces additional local interactions with the enzyme, particularly, the M20 loop. These changes are propagated to the whole enzyme as shifts in the hydrogen bond networks. To shed light on the allosteric interactions, we support our analysis with network-based community analysis and show that segmentation of the loop domain of inhibitor-bound DHFR must be avoided by a successful inhibitor.

Bridging semiempirical and ab initio QM/MM potentials by Gaussian process regression and its sparse variants for free energy simulation

Free energy simulations that employ combined quantum mechanical and molecular mechanical (QM/MM) potentials at ab initio QM (AI) levels are computationally highly demanding. Here, we present a machine-learning-facilitated approach for obtaining AI/MM-quality free energy profiles at the cost of efficient semiempirical QM/MM (SE/MM) methods. Specifically, we use Gaussian process regression (GPR) to learn the potential energy corrections needed for an SE/MM level to match an AI/MM target along the minimum free energy path (MFEP). Force modification using gradients of the GPR potential allows us to improve configurational sampling and update the MFEP. To adaptively train our model, we further employ the sparse variational GP (SVGP) and streaming sparse GPR (SSGPR) methods, which efficiently incorporate previous sample information without significantly increasing the training data size. We applied the QM-(SS)GPR/MM method to the solution-phase SN2 Menshutkin reaction, NH3+CH3Cl→CH3NH3++Cl-, using AM1/MM and B3LYP/6-31+G(d,p)/MM as the base and target levels, respectively. For 4000 configurations sampled along the MFEP, the iteratively optimized AM1-SSGPR-4/MM model reduces the energy error in AM1/MM from 18.2 to 4.4 kcal/mol. Although not explicitly fitting forces, our method also reduces the key internal force errors from 25.5 to 11.1 kcal/mol/Å and from 30.2 to 10.3 kcal/mol/Å for the N-C and C-Cl bonds, respectively. Compared to the uncorrected simulations, the AM1-SSGPR-4/MM method lowers the predicted free energy barrier from 28.7 to 11.7 kcal/mol and decreases the reaction free energy from -12.4 to -41.9 kcal/mol, bringing these results into closer agreement with their AI/MM and experimental benchmarks.

Assessing the performance of docking, FEP, and MM/GBSA methods on a series of KLK6 inhibitors

Kallikrein 6 (KLK6) is an attractive drug target for the treatment of neurological diseases and for various cancers. Herein, we explore the accuracy and efficiency of different computational methods and protocols to predict the free energy of binding (ΔG_bind) for a series of 49 inhibitors of KLK6. We found that the performance of the methods varied strongly with the tested system. For only one of the three KLK6 datasets, the docking scores obtained with rDock were in good agreement (R² ≥ 0.5) with experimental values of ΔG_bind. A similar result was obtained with MM/GBSA (using the ff14SB force field) calculations based on single minimized structures. Improved binding affinity predictions were obtained with the free energy perturbation (FEP) method, with an overall MUE and RMSE of 0.53 and 0.68 kcal/mol, respectively. Furthermore, in a simulation of a real-world drug discovery project, FEP was able to rank the most potent compounds at the top of the list. These results indicate that FEP can be a promising tool for the structure-based optimization of KLK6 inhibitors.

Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of Paxlovid, a drug approved by the U.S. Food and Drug Administration for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here, we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggest that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weaken the nirmatrelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intelligence approaches, and together with biochemical experiments, they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the optimization of antiviral drugs. The presented approach, in general, can be applied to characterize mutation effects on any protein drug targets.

Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls

In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.

Alchemical Free Energy and Hamiltonian Replica Exchange Molecular Dynamics to Compute Hydrofluorocarbon Isotherms in Imidazolium-Based Ionic Liquids

Ionic liquids (ILs) have shown promise for applications that leverage differential gas solubility in an IL solvent, e.g., gas separations. Although most available literature provides Henry's law constants, the ability to efficiently estimate full isotherms is important for engineering design calculations. Molecular simulation can be used as a tool to predict full isotherms of gas in ILs. However, particle insertions or deletions in a charge-dense IL medium and the sluggish conformational dynamics of ILs present two sampling challenges for these systems. We therefore devised a method that uses Hamiltonian replica exchange (HREX) molecular dynamics (MD) combined with alchemical free energy calculations to compute full solubility isotherms of two different hydrofluorocarbons (HFCs) in imidazolium-based IL binary mixtures. This workflow is significantly faster than the Gibbs ensemble Monte Carlo (GEMC) simulations which fail to deal with the slow conformational relaxation caused by the sluggish dynamics of ILs. Multiple free energy estimators, including thermodynamic integration, free energy perturbation, and multistate Bennett acceptance ratio method, provided consistent results. Overall, the simulated Henry's law constant, isotherm curvature, and solubility trends match experimental results reasonably well. We close by calculating the full solubility isotherms of two HFCs in IL mixtures that have not been reported in the literature, demonstrating the potential of this method to be used for solubility prediction and setting the stage for future computational screening studies that search for the "best" IL to separate azeotropic HFC mixtures.

Exploring Routes to Enhance the Calculation of Free Energy Differences via Non-Equilibrium Work SQM/MM Switching Simulations Using Hybrid Charge Intermediates between MM and SQM Levels of Theory or Non-Linear Switching Schemes

Non-equilibrium work switching simulations and Jarzynski's equation are a reliable method for computing free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly become very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment such as explicit solvent water. We find that even for relatively simple solute-water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with an emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges, which resembles the charge distribution of the desired high level, makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., a faster convergence for all systems. To understand these findings, we analyzed the solutes' properties as a function of the partial charges used and the number of water molecules in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute's charge distribution.

NE-RDFE: A protocol and toolkit for computing relative dissociation free energies with GROMACS between dissimilar molecules using bidirectional nonequilibrium dual topology schemes

We describe a step-by-step protocol and toolkit for the computation of the relative dissociation free energy (RDFE) with the GROMACS molecular dynamics package, based on a novel bidirectional nonequilibrium alchemical approach. The proposed methodology does not require any intervention on the code and allows computing with good accuracy the RDFE between small molecules with arbitrary differences in volume, charge, and chemical topology. The procedure is illustrated for the challenging SAMPL9 batch of host-guest pairs. The article is supplemented by a detailed online tutorial, available at https://procacci.github.io/vdssb_gromacs/NE-RDFE and by a public Zenodo repository available at https://zenodo.org/record/6982932.

Study of SQ109 analogs binding to mycobacterium MmpL3 transporter using MD simulations and alchemical relative binding free energy calculations

N-geranyl-N΄-(2-adamantyl)ethane-1,2-diamine (SQ109) is a tuberculosis drug that has high potency against Mycobacterium tuberculosis (Mtb) and may function by blocking cell wall biosynthesis. After the crystal structure of MmpL3 from Mycobacterium smegmatis in complex with SQ109 became available, it was suggested that SQ109 inhibits Mmpl3 mycolic acid transporter. Here, we showed using molecular dynamics (MD) simulations that the binding profile of nine SQ109 analogs with inhibitory potency against Mtb and alkyl or aryl adducts at C-2 or C-1 adamantyl carbon to MmpL3 was consistent with the X-ray structure of MmpL3 - SQ109 complex. We showed that rotation of SQ109 around carbon-carbon bond in the monoprotonated ethylenediamine unit favors two gauche conformations as minima in water and lipophilic solvent using DFT calculations as well as inside the transporter's binding area using MD simulations. The binding assays in micelles suggested that the binding affinity of the SQ109 analogs was increased for the larger, more hydrophobic adducts, which was consistent with our results from MD simulations of the SQ109 analogues suggesting that sizeable C-2 adamantyl adducts of SQ109 can fill a lipophilic region between Y257, Y646, F260 and F649 in MmpL3. This was confirmed quantitatively by our calculations of the relative binding free energies using the thermodynamic integration coupled with MD simulations method with a mean assigned error of 0.74 kcal mol^-1 compared to the experimental values.

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH₃ group rotation in ethane, a nucleophilic substitution of CH₃Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Quality over quantity: Sampling high probability rare events with the weighted ensemble algorithm

The prediction of (un)binding rates and free energies is of great significance to the drug design process. Although many enhanced sampling algorithms and approaches have been developed, there is not yet a reliable workflow to predict these quantities. Previously we have shown that free energies and transition rates can be calculated by directly simulating the binding and unbinding processes with our variant of the WE algorithm "Resampling of Ensembles by Variation Optimization", or "REVO". Here, we calculate binding free energies retrospectively for three SAMPL6 host-guest systems and prospectively for a SAMPL9 system to test a modification of REVO that restricts its cloning behavior in quasi-unbound states. Specifically, trajectories cannot clone if they meet a physical requirement that represents a high likelihood of unbinding, which in the case of this work is a center-of-mass to center-of-mass distance. The overall effect of this change was difficult to predict, as it results in fewer unbinding events each of which with a much higher statistical weight. For all four systems tested, this new strategy produced either more accurate unbinding free energies or more consistent results between simulations than the standard REVO algorithm. This approach is highly flexible, and any feature of interest for a system can be used to determine cloning eligibility. These findings thus constitute an important improvement in the calculation of transition rates and binding free energies with the weighted ensemble method.

QSAR via Multisite λ-Dynamics in the Orphaned TSSK1B Kinase

Multisite λ-dynamics (MSλD) is a novel method for the calculation of relative free energies of binding for ligands to their targeted receptors. It can be readily used to examine a large number of molecules with multiple functional groups at multiple sites around a common core. This makes MSλD a powerful tool in structure-based drug design. In the present study, MSλD is applied to calculate the relative binding free energies of 1296 inhibitors to the testis specific serine kinase 1B (TSSK1B), a validated target for male contraception. For this system, MSλD requires significantly fewer computational resources compared to traditional free energy methods like free energy perturbation or thermodynamic integration. From MSλD simulations, we examined whether modifications of a ligand at two different sites are coupled or not. Based on our calculations, we established a quantitative structure-activity relationship (QSAR) for this set of molecules and identified a site in the ligand where further modification, such as adding more polar groups, may lead to increased binding affinity. This article is protected by copyright. All rights reserved.