Free Energy Calculation Methods Research Articles

Characterizing the Cooperative Effect of PROTAC Systems with End-Point Binding Free Energy Calculation.

Proteolytic targeting chimeras (PROTACs), as an emerging type of drug, function by proximity-based modalities that narrow the distance between a target protein and the E3 ubiquitin ligase to facilitate the ubiquitination labeling of the target protein for degradation. Although it is evidenced that the cooperativity of the PROTAC ternary interaction is one of the key factors affecting the degradation rate of a target protein, PROTAC design utilizing this indicator is still challenging because of the complicated/flexible interactions in a target-PROTAC-E3 ternary system. Therefore, developing reliable and practicable computational methods is of great interest for PROTAC design. Hence, in this study, we investigate the feasibility of using the end-point binding free energy calculation method, represented by molecular mechanics/Poisson-Boltzmann (generalized-Born) surface area (MM/PB(GB)SA), for characterizing cooperativity (including the stabilization and hook effects) of the PROTAC systems. The result shows that MM/GBSA is a good predictor in characterizing these effects under a relatively long molecular dynamics adjustment (50-100 ns) and low dielectric constant (εin = 1), with the Pearson correlation coefficient (rp) > 0.5 and 0.6 for the stabilization and hook effect, respectively. This study provides a feasible strategy for characterizing the cooperativity of the PROTAC systems, facilitating the rational design of PROTAC molecules.

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

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

In vitro and in silico studies of the inclusion complexation of 8-bromobaicalein with β-cyclodextrins

Baicalein, a flavone derived from Scutellaria baicalensis Georgi, exhibits potent anti-inflammatory, antiviral, and anticancer properties. Its derivative, known as 8-bromobaicalein (BB), has been found to have strong cytotoxic effect on MCF-7 human breast cancer cells. However, its limited solubility in water has hindered its potential for wider applications. To address this issue, we investigated the use of cyclodextrins specifically βCD, 2,6-di-O-methyl-β-cyclodextrin (DMβCD), and hydroxypropyl-β-cyclodextrin (HPβCD) to improve the solubility of BB through inclusion complexation. During 250 ns molecular dynamics simulations, it was found that BB can form inclusion complexes with all βCDs. These complexes exhibit two distinct orientations: chromone group insertion (C-form) and phenyl group insertion (P-form). The formation of these complexes is primarily driven by van der Waals interactions. DMβCD has the highest number of atom contacts with BB and the lowest solvent accessibility in the hydrophobic cavity. These results coincide with the highest binding affinity from the MM/GBSA-based free energy calculation method. Experimental phase solubility diagrams revealed a 1:1 stoichiometric ratio (AL type) between BB and βCDs, in which BB/DMβCD showed the highest stability. The formation of inclusion complexes was confirmed by differential scanning calorimetry and scanning electron microscope methods. Additionally, the BB/DMβCD inclusion complex demonstrated significantly higher anticancer activity against MCF-7 human breast cancer cells compared to BB alone. These findings underscore the potential of DMβCD for formulating BB in pharmaceutical and medical applications.

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

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

Ligand Binding Affinity Prediction for Membrane Proteins with Alchemical Free Energy Calculation Methods.

Alchemical relative binding free energy (ΔΔG) calculations have shown high accuracy in predicting ligand binding affinity and have been used as important tools in computer-aided drug discovery and design. However, there has been limited research on the application of ΔΔG methods to membrane proteins despite the fact that these proteins represent a significant proportion of drug targets, play crucial roles in biological processes, and are implicated in numerous diseases. In this study, to predict the binding affinity of ligands to G protein-coupled receptors (GPCRs), we employed two ΔΔG calculation methods: thermodynamic integration (TI) with AMBER and the alchemical transfer method (AToM) with OpenMM. We calculated ΔΔG values for 53 transformations involving four class A GPCRs and evaluated the performance of AMBER-TI and AToM-OpenMM. In addition, we conducted tests using different numbers of windows and varying simulation times to achieve reliable ΔΔG results and to optimize resource utilization. Overall, both AMBER-TI and AToM-OpenMM show good agreement with the experimental data. Our results validate the applicability of AMBER-TI and AToM-OpenMM for optimization of lead compounds targeting membrane proteins.

Discovery of an EP300 Inhibitor using Structure-based Virtual Screening and Bioactivity Evaluation.

EP300 (E1A binding protein p300) played a significant role in serial diseases such as cancer, neurodegenerative disease. Therefore, it became a significant target. Targeting EP300 discovery of a novel drug to alleviate these diseases. In this paper, 17 candidate compounds were obtained using a structure-based virtual screening approach, 4449-0460, with an IC50 of 5.89 ± 2.08 uM, which was identified by the EP300 bioactivity test. 4449-0460 consisted of three rings. The middle benzene ring connected the 5-ethylideneimidazolidine-2,4-dione group and the 3-F-Phenylmethoxy group. Furthermore, the interaction mechanism between 4449-0460 and EP300 was explored by combining molecular dynamics (MD) simulations and binding free energy calculation methods. The binding free energy of EP300 with 4449-0460 was -10.93 kcal/mol, and mainly came from the nonpolar energy term (ΔGnonpolar). Pro1074, Phe1075, Val1079, Leu1084, and Val1138 were the key residues in EP300/4449-0460 binding with more -1 kcal/mol energy contribution. 4449-0460 was a promising inhibitor targeting EP300, which had implications for the development of drugs for EP300-related diseases.

A simple and accurate method to determine fluid-crystal phase boundaries from direct coexistence simulations.

One method for computationally determining phase boundaries is to explicitly simulate a direct coexistence between the two phases of interest. Although this approach works very well for fluid-fluid coexistences, it is often considered to be less useful for fluid-crystal transitions, as additional care must be taken to prevent the simulation boundaries from imposing unwanted strains on the crystal phase. Here, we present a simple adaptation to the direct coexistence method that nonetheless allows us to obtain highly accurate predictions of fluid-crystal coexistence conditions, assuming that a fluid-crystal interface can be readily simulated. We test our approach on hard spheres, the screened Coulomb potential, and a 2D patchy-particle model. In all cases, we find excellent agreement between the direct coexistence approach and (much more cumbersome) free-energy calculation methods. Moreover, the method is sufficiently accurate to resolve the (tiny) free-energy difference between the face-centered cubic and hexagonally close-packed crystal of hard spheres in the thermodynamic limit. The simplicity of this method also ensures that it can be trivially implemented in essentially any simulation method or package. Hence, this approach provides an excellent alternative to free-energy based methods for the precise determination of phase boundaries.

Comprehensive, Open-Source, and Automated Workflow for Multisite λ-Dynamics in Lead Optimization.

Multisite λ-dynamics (MSLD) is a highly efficient binding free energy calculation method that samples multiple ligands in a single round by assigning different λ values to the alchemical part of each ligand. This method holds great promise for lead optimization (LO) in drug discovery. However, the complex data preparation and simulation process limits its widespread application in diverse protein-ligand systems. To address this challenge, we developed a comprehensive, open-source, and automated workflow for MSLD calculations based on the BLaDE dynamics engine. This workflow incorporates the Ligand Internal and Cartesian coordinate reconstruction-based alignment algorithm (LIC-align) and an optimized maximum common substructure (MCS) search algorithm to accurately generate MSLD multiple topologies with ideal perturbation patterns. Furthermore, our workflow is highly modularized, allowing straightforward integration and extension of various simulation techniques, and is highly accessible to nonexperts. This workflow was validated by calculating the relative binding free energies of large-scale congeneric ligands, many of which have large perturbing groups. The agreement between the calculations and experiments was excellent, with an average unsigned error of 1.08 ± 0.47 kcal/mol. More than 57.1% of the ligands had an error of less than 1.0 kcal/mol, and the perturbations of 6 targets were fully connected via the calculations, while those of 2 targets were connected via both calculations and experimental data. The Pearson correlation coefficient reached 0.88, indicating that the MSLD workflow provides accurate predictions that can guide lead optimization in drug discovery. We also examined the impact of single-site versus multisite perturbations, ligand grouping by perturbing group size, and the position of the anchor atom on the MSLD performance. By integrating our proposed LIC-align and optimized MCS search algorithm along with the coping strategies to handle challenging molecular substructures, our workflow can handle many realistic scenarios more reasonably than all previously published methods. Moreover, we observed that our MSLD workflow achieved similar accuracy to free energy perturbation (FEP) while improving computational efficiency by over 1 order of magnitude in speedup. These findings provide valuable insights and strategies for further MSLD development, making MSLD a competitive tool for lead optimization.

Ligand-binding affinity prediction for membrane proteins with alchemical free-energy calculation methods

Ligand-binding affinity prediction for membrane proteins with alchemical free-energy calculation methods

Binding Free Energy Calculation Based on the Fragment Molecular Orbital Method and Its Application in Designing Novel SHP-2 Allosteric Inhibitors.

The accurate prediction of binding free energy is a major challenge in structure-based drug design. Quantum mechanics (QM)-based approaches show promising potential in predicting ligand-protein binding affinity by accurately describing the behavior and structure of electrons. However, traditional QM calculations face computational limitations, hindering their practical application in drug design. Nevertheless, the fragment molecular orbital (FMO) method has gained widespread application in drug design due to its ability to reduce computational costs and achieve efficient ab initio QM calculations. Although the FMO method has demonstrated its reliability in calculating the gas phase potential energy, the binding of proteins and ligands also involves other contributing energy terms, such as solvent effects, the 'deformation energy' of a ligand's bioactive conformations, and entropy. Particularly in cases involving ionized fragments, the calculation of solvation free energy becomes particularly crucial. We conducted an evaluation of some previously reported implicit solvent methods on the same data set to assess their potential for improving the performance of the FMO method. Herein, we develop a new QM-based binding free energy calculation method called FMOScore, which enhances the performance of the FMO method. The FMOScore method incorporates linear fitting of various terms, including gas-phase potential energy, deformation energy, and solvation free energy. Compared to other widely used traditional prediction methods such as FEP+, MM/PBSA, MM/GBSA, and Autodock vina, FMOScore showed good performance in prediction accuracies. By constructing a retrospective case study, it was observed that incorporating calculations for solvation free energy and deformation energy can further enhance the precision of FMO predictions for binding affinity. Furthermore, using FMOScore-guided lead optimization against Src homology-2-containing protein tyrosine phosphatase 2 (SHP-2), we discovered a novel and potent allosteric SHP-2 inhibitor (compound 8).

Identification of novel LRRK2 inhibitors by structure-based virtual screening and alchemical free energy calculation.

The Leucine-rich repeat kinase 2 (LRRK2) target has been identified as a promising drug target for Parkinson's disease (PD) treatment. This study focuses on optimizing the activity of LRRK2 inhibitors using alchemical relative binding free energy (RBFE) calculations. Initially, we assessed various free energy calculation methods across different LRRK2 kinase inhibitor scaffolds. The results indicate that alchemical free energy calculations are promising for prospective predictions on LRRK2 inhibitors, especially for the aminopyrimidine scaffold with an RMSE of 1.15 kcal mol-1 and Rp of 0.83. Following this, we optimized a potent LRRK2 kinase inhibitor identified from previous virtual screenings, featuring a novel scaffold. Guided by RBFE predictions using alchemical methods, this optimization led to the discovery of compound LY2023-001. This compound, with a [1,2,4]triazolo[5,6-b]indole scaffold, exhibited enhanced inhibitory activity against G2019S LRRK2 (IC50 = 12.9 nM). Molecular dynamics (MD) simulations revealed that LY2023-001 formed stable hydrogen bonds with Glu1948, and Ala1950 in the G2019S LRRK2 protein. Additionally, its phenyl substituents engage in strong electrostatic interactions with Lys1906 and van der Waals interactions with Leu1885, Phe1890, Val1893, Ile1933, Met1947, Leu1949, Leu2001, Ala2016, and Asp2017. Our findings underscore the potential of computational methods in the successful optimization of small molecules, offering important insights for the development of novel LRRK2 inhibitors.

Assessing the performance of MM/PBSA and MM/GBSA methods. 10. Prediction reliability of binding affinities and binding poses for RNA-ligand complexes.

Ribonucleic acid (RNA)-ligand interactions play a pivotal role in a wide spectrum of biological processes, ranging from protein biosynthesis to cellular reproduction. This recognition has prompted the broader acceptance of RNA as a viable candidate for drug targets. Delving into the atomic-scale understanding of RNA-ligand interactions holds paramount importance in unraveling intricate molecular mechanisms and further contributing to RNA-based drug discovery. Computational approaches, particularly molecular docking, offer an efficient way of predicting the interactions between RNA and small molecules. However, the accuracy and reliability of these predictions heavily depend on the performance of scoring functions (SFs). In contrast to the majority of SFs used in RNA-ligand docking, the end-point binding free energy calculation methods, such as molecular mechanics/generalized Born surface area (MM/GBSA) and molecular mechanics/Poisson Boltzmann surface area (MM/PBSA), stand as theoretically more rigorous approaches. Yet, the evaluation of their effectiveness in predicting both binding affinities and binding poses within RNA-ligand systems remains unexplored. This study first reported the performance of MM/PBSA and MM/GBSA with diverse solvation models, interior dielectric constants (εin) and force fields in the context of binding affinity prediction for 29 RNA-ligand complexes. MM/GBSA is based on short (5 ns) molecular dynamics (MD) simulations in an explicit solvent with the YIL force field; the GBGBn2 model with higher interior dielectric constant (εin = 12, 16 or 20) yields the best correlation (Rp = -0.513), which outperforms the best correlation (Rp = -0.317, rDock) offered by various docking programs. Then, the efficacy of MM/GBSA in identifying the near-native binding poses from the decoys was assessed based on 56 RNA-ligand complexes. However, it is evident that MM/GBSA has limitations in accurately predicting binding poses for RNA-ligand systems, particularly compared with notably proficient docking programs like rDock and PLANTS. The best top-1 success rate achieved by MM/GBSA rescoring is 39.3%, which falls below the best results given by docking programs (50%, PLNATS). This study represents the first evaluation of MM/PBSA and MM/GBSA for RNA-ligand systems and is expected to provide valuable insights into their successful application to RNA targets.

Structural and molecular investigation of the impact of S30L and D88N substitutions in G9R protein on coupling with E4R from Monkeypox virus (MPXV)

Understanding the pathogenesis mechanism of the Monkeypox virus (MPXV) is essential to guide therapeutic development against the Monkeypox virus. In the current study, we investigated the impact of the only two reported substitutions, S30L, D88N, and S30L-D88N on the G9R of the replication complex in 2022 with E4R using structural modeling, simulation, and free energy calculation methods. From the molecular docking and dissociation constant (KD) results, it was observed that the binding affinity did not increase in the mutants, but the interaction paradigm was altered by these substitutions. Molecular simulation data revealed that these mutations are responsible for destabilization, changes in protein packing, and internal residue fluctuations, which can cause functional variance. Additionally, hydrogen bonding analysis revealed that the estimated number of hydrogen bonds are almost equal among the wild-type G9R and each mutant. The total binding free energy for the wild-type G9R with E4R was −85.00 kcal/mol while for the mutants the TBE was −42.75 kcal/mol, −43.68 kcal/mol, and −48.65 kcal/mol respectively. This shows that there is no direct impact of these two reported mutations on the binding with E4R, or it may affect the whole replication complex or any other mechanism involved in pathogenesis. To explore these variations further, we conducted PCA and FEL analyses. Based on our findings, we speculate that within the context of interaction with E4R, the mutations in the G9R protein might be benign, potentially leading to functional diversity associated with other proteins. Communicated by Ramaswamy H. Sarma

Exploring the conformational dynamics and thermodynamics of EGFR S768I and G719X + S768I mutations in non-small cell lung cancer: An in silico approaches.

Non-small cell lung cancer (NSCLC) is often driven by mutations in the epidermal growth factor receptor (EGFR) gene. However, rare mutations such as G719X and S768I lack standard anti-EGFR targeted therapies. Understanding the structural differences between wild-type EGFR and these rare mutants is crucial for developing EGFR-targeted drugs. We performed a systematic analysis using molecular dynamics simulations, essential dynamics (ED), molecular mechanics Poisson-Boltzmann surface area, and free energy calculation methods to compare the kinetic properties, molecular motion, and free energy distribution between wild-type EGFR and the rare mutants' structures G719X-EGFR, S768I-EGFR, and G719X + S768I-EGFR. Our results showed that S768I-EGFR and G719X + S768I-EGFR have higher global and local conformational flexibility and lower thermal and global structural stability than WT-EGFR. ED analysis revealed different molecular motion patterns between S768I-EGFR, G719X + S768I-EGFR, and WT-EGFR. The A-loop and αC-helix, crucial structural elements related to the active state, showed a tendency toward active state development, providing a molecular mechanism explanation for NSCLC caused by EGFR S768I and EGFR G719C + S768I mutations. The present study may be helpful in the development of new EGFR-targeted drugs based on the structure of rare mutations. Our findings may aid in developing new targeted treatments for patients with EGFR S768I and EGFR G719X + S768I mutations.

Camellia Sinensis Çaylarındaki Moleküllerin NLRP3 NACHT Domainine İn Siliko Bağlanma Afiniteleri

NLRP3 inflammasome secretes proinflammatory cytokines in response to microbial infection and cellular damage, induces pyroptotic cell death, and triggers many pathological conditions. For this reason, it is important to determine the products that can inhibit the NLRP3 protein. In this study, the affinities of 27 molecules in Camellia sinensis tea species to ADP and inhibitor cavities in the NACHT domain of NLRP3 were analyzed in silico using molecular docking, molecular dynamics simulation, and free energy calculation method MM/GBSA. Among the components, theaflavic acid, (-)-epicatechin gallate and (-)-epigallocatechin gallate gave better binding affinities. It was concluded that it would be beneficial to conduct advanced studies on whether these three compounds contribute to the preventability of NLRP3-mediated inflammatory diseases.

Molecular dynamics simulation of the inhibition mechanism of factor XIa by Milvexian-like macrocyclic inhibitors

Factor XIa is an important coagulation factor in the coagulation cascade, and its inhibitors have become a hot topic of research for their potential to block thrombus formation without increasing the risk of bleeding. In this paper, molecular dynamics simulation and binding free energy calculation methods were used to study the inhibition mechanism of five macrocyclic competitive inhibitors, which are the same as the Milvexian nucleus. And the reasons for the different inhibitory abilities of the inhibitors with different substituents in the nucleus were summarized. When the inhibitor has a triazole at the head or a carbamate at the tail, it can enhance the hydrogen bonding or electrostatic interaction with its nearby polar residues. The inhibitor 8 with –CH3 in the tail interacts less with its surrounding residues than the inhibitors 13 and 17 with -CHF2 when both heads carry triazoles. The triazole of inhibitor 17 bears a Cl atom, which can form a strong hydrophobic interaction with the nearby disulfide bond. In addition, the nitrogen atom on the ketone ring of this inhibitor can also increase its interaction with nearby residues. Therefore, inhibitor 17 has the strongest affinity to the protein. The present work has implications for the design of more efficient anticoagulant drugs for FXIa macrocyclic inhibitors.

Structure-based design of promising natural products to inhibit thymidylate kinase from Monkeypox virus and validation using free energy calculations

Monkeypox (MPXV) is a globally growing public health concern with 80,328 active cases and 53 deaths have been reported. No specific vaccine or drug is available for the treatment of MPXV. Hence, the current study also employed structure-based drug designing, molecular simulation, and free energy calculation methods to identify potential hit molecules against the TMPK of MPXV, which is a replicatory protein that helps the virus to replicate its DNA and increase the number of DNAs in the host cell. The 3D structure of TMPK was modeled with AlphaFold and screening of multiple natural products libraries (4,71,470 compounds) identified TCM26463, TCM2079, and TCM29893 from traditional Chinese medicines database (TCM), SANC00240, SANC00984, and SANC00986 South African natural compounds database (SANCDB), NPC474409, NPC278434 and NPC158847 from NPASS (natural product activity and species source database) while CNP0404204, CNP0262936, and CNP0289137 were shortlisted from coconut database (collection of open natural products) as the best hits. These compounds interact with the key active site residues through hydrogen bonds, salt bridges, and pie-pie interactions. The structural dynamics and binding free energy results further revealed that these compounds possess stable dynamics with excellent binding free energy scores. Moreover, the dissociation constant (KD) and bioactivity analysis revealed stronger activity of these compounds exhibit stronger biological activity against MPXV and may inhibit it in in vitro conditions. All the results demonstrated that the designed novel compounds possess stronger inhibitory activity than the control complex (TPD-TMPK) from the vaccinia virus. The current study is the first to design small molecule inhibitors for the replication protein of MPXV which may help in controlling the current epidemic and also overcome the challenge of vaccine evasion.

Switching of Redox Levels Leads to High Reductive Stability in Water-in-Salt Electrolytes.

Developing nonflammable electrolytes with wide electrochemical windows is of great importance for energy storage devices. Water-in-salt electrolytes (WiSE) have attracted great interests due to their widely opened electrochemical windows and high stability. Previous theoretical investigations have revealed changes in solvation shell of water molecules result in opening of HOMO-LUMO gaps of water, leading to the formation of an anion-derived solid-electrolyte-interphase (SEI) in WiSE. However, how solvation structures affect electrochemical windows at atomic level is still a puzzle, which hinders optimization and design of aqueous electrolytes. Herein, machine learning molecular dynamics and free energy calculation method are applied to compute redox potentials of anions of Li-salts and water of aqueous electrolytes at a range of salt concentrations. Furthermore, an analysis based on local solvation structures is employed to demonstrate the structure-property relations. Our calculation shows that the hydrogen evolution reaction is impeded in WiSE due to switching of the order of redox levels of the anion and H2O, leading to formation of SEI and high reductive stability. Level switching is caused by the special solvation environments of isolated water molecules. Our work provides new insight into the electrochemistry of aqueous electrolytes which would benefit the electrolyte design in energy storage devices.

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.

Free energy calculations and unbiased molecular dynamics targeting the liquid-liquid transition in water no man's land.

The existence of a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) form of supercooled water has been a central and highly debated issue of physics and chemistry for the last three decades. We present a computational study that allows us to determine the free-energy landscapes of supercooled water over a wide range of pressure and temperature conditions using the TIP4P/2005 force field. Our approach combines topology-based structural transformation coordinates, state-of-the-art free-energy calculation methods, and extensive unbiased molecular dynamics. All our diverse simulations cannot detect any barrier within the investigated timescales and system size, for a discontinuous transition between the LDL and HDL forms throughout the so-called "no man's land," until the onset of the solid, non-diffusive amorphous forms.