Advances in computational methods for ligand binding kinetics

Characterization of the Bottlenecks and Pathways for Inhibitor Dissociation from [NiFe] Hydrogenase

[NiFe] hydrogenases can act as efficient catalysts for hydrogen oxidation and biofuel production. However, some [NiFe] hydrogenases are inhibited by gas molecules present in the environment, such as O2 and CO. One strategy to engineer [NiFe] hydrogenases and achieve O2- and CO-tolerant enzymes is by introducing point mutations to block the access of inhibitors to the catalytic site. In this work, we characterized the unbinding pathways of CO in the complex with the wild-type and 10 different mutants of [NiFe] hydrogenase from Desulfovibrio fructosovorans using τ-random accelerated molecular dynamics (τRAMD) to enhance the sampling of unbinding events. The ranking provided by the relative residence times computed with τRAMD is in agreement with experiments. Extensive data analysis of the simulations revealed that from the two bottlenecks proposed in previous studies for the transit of gas molecules (residues 74 and 122 and residues 74 and 476), only one of them (residues 74 and 122) effectively modulates diffusion and residence times for CO. We also computed pathway probabilities for the unbinding of CO, O2, and H2 from the wild-type [NiFe] hydrogenase, and we observed that while the most probable pathways are the same, the secondary pathways are different. We propose that introducing mutations to block the most probable paths, in combination with mutations to open the main secondary path used by H2, can be a feasible strategy to achieve CO and O2 resistance in the [NiFe] hydrogenase from Desulfovibrio fructosovorans.

Quantitative Prediction of Dissociation Rates of PYK2 Ligands Using Umbrella Sampling and Milestoning

We used umbrella sampling and the milestoning simulation method to study the dissociation of multiple ligands from protein kinase PYK2. The activation barriers obtained from the potential of mean force of the umbrella sampling simulations correlated well with the experimental dissociation rates. Using the zero-temperature string method, we obtained optimized paths along the free-energy surfaces for milestoning simulations of three ligands with a similar structure. The milestoning simulations gave an absolute dissociation rate within 2 orders of magnitude of the experimental value for two ligands but at least 3 orders of magnitude too high for the third. Despite the similarity in their structures, the ligands took different pathways to exit from the binding site of PYK2, making contact with different sets of residues. In addition, the protein experienced different conformational changes for dissociation of the three ligands.

Accurate Characterization of Binding Kinetics and Allosteric Mechanisms for the HSP90 Chaperone Inhibitors Using AI-Augmented Integrative Biophysical Studies

The binding kinetics of drugs to their targets are gradually being recognized as a crucial indicator of the efficacy of drugs in vivo, leading to the development of various computational methods for predicting the binding kinetics in recent years. However, compared with the prediction of binding affinity, the underlying structure and dynamic determinants of binding kinetics are more complicated. Efficient and accurate methods for predicting binding kinetics are still lacking. In this study, quantitative structure-kinetics relationship (QSKR) models were developed using 132 inhibitors targeting the ATP binding domain of heat shock protein 90α (HSP90α) to predict the dissociation rate constant (koff), enabling a direct assessment of the drug-target residence time. These models demonstrated good predictive performance, where hydrophobic and hydrogen bond interactions significantly influence the koff prediction. In subsequent applications, our models were used to assist in the discovery of new inhibitors for the N-terminal domain of HSP90α (N-HSP90α), demonstrating predictive capabilities on an experimental validation set with a new scaffold. In X-ray crystallography experiments, the loop-middle conformation of apo N-HSP90α was observed for the first time (previously, the loop-middle conformation had only been observed in holo-N-HSP90α structures). Interestingly, we observed different conformations of apo N-HSP90α simultaneously in an asymmetric unit, which was also observed in a holo-N-HSP90α structure, suggesting an equilibrium of conformations between different states in solution, which could be one of the determinants affecting the binding kinetics of the ligand. Different ligands can undergo conformational selection or alter the equilibrium of conformations, inducing conformational rearrangements and resulting in different effects on binding kinetics. We then used molecular dynamics simulations to describe conformational changes of apo N-HSP90α in different conformational states. In summary, the study of the binding kinetics and molecular mechanisms of N-HSP90α provides valuable information for the development of more targeted therapeutic approaches.

Computational Chemistry in Structure-Based Solute Carrier Transporter Drug Design: Recent Advances and Future Perspectives

Solute carrier transporters (SLCs) are a class of important transmembrane proteins that are involved in the transportation of diverse solute ions and small molecules into cells. There are approximately 450 SLCs within the human body, and more than a quarter of them are emerging as attractive therapeutic targets for multiple complex diseases, e.g., depression, cancer, and diabetes. However, only 44 unique transporters (∼9.8% of the SLC superfamily) with 3D structures and specific binding sites have been reported. To design innovative and effective drugs targeting diverse SLCs, there are a number of obstacles that need to be overcome. However, computational chemistry, including physics-based molecular modeling and machine learning- and deep learning-based artificial intelligence (AI), provides an alternative and complementary way to the classical drug discovery approach. Here, we present a comprehensive overview on recent advances and existing challenges of the computational techniques in structure-based drug design of SLCs from three main aspects: (i) characterizing multiple conformations of the proteins during the functional process of transportation, (ii) identifying druggability sites especially the cryptic allosteric ones on the transporters for substrates and drugs binding, and (iii) discovering diverse small molecules or synthetic protein binders targeting the binding sites. This work is expected to provide guidelines for a deep understanding of the structure and function of the SLC superfamily to facilitate rational design of novel modulators of the transporters with the aid of state-of-the-art computational chemistry technologies including artificial intelligence.

Binding and unbinding of potent melatonin receptor ligands: Mechanistic simulations and experimental evidence

The labeled ligand commonly employed in competition binding studies for melatonin receptor ligands, 2-[125I]iodomelatonin, showed slow dissociation with different half-lives at the two receptor subtypes. This may affect the operational measures of affinity constants, which at short incubation times could not be obtained in equilibrium conditions, and structure-activity relationships, as the Ki values of tested ligands could depend on either interaction at the binding site or the dissociation path. To address these issues, the kinetic and saturation binding parameters of 2-[125I]iodomelatonin as well as the competition constants for a series of representative ligands were measured at a short (2 h) and a long (20 h) incubation time. Concurrently, we simulated by molecular modeling the dissociation path of 2-iodomelatonin from MT1 and MT2 receptors and investigated the role of interactions at the binding site on the stereoselectivity observed for the enantiomers of the subtype-selective ligand UCM1014. We found that equilibrium conditions for 2-[125I]iodomelatonin binding can be reached only with long incubation times, particularly for the MT2 receptor subtype, for which a time of 20 h approximates this condition. On the other hand, measured Ki values for a set of ligands including agonists, antagonists, nonselective, and subtype-selective compounds were not significantly affected by the length of incubation, suggesting that structure-activity relationships based on data collected at shorter time reflect different interactions at the binding site. Molecular modeling simulations evidenced that the slower dissociation of 2-iodomelatonin from the MT2 receptor can be related to the restricted mobility of a gatekeeper tyrosine along a lipophilic path from the binding site to the membrane bilayer. The enantiomers of the potent, MT2-selective agonist UCM1014 were separately synthesized and tested. Molecular dynamics simulations of the receptor-ligand complexes provided an explanation for their stereoselectivity as due to the preference shown by the eutomer at the binding site for the most abundant axial conformation adopted by the ligand in solution. These results suggest that, despite the slow-binding kinetics occurring for the labeled ligand, affinity measures at shorter incubation times give robust results consistent with known structure-activity relationships and with interactions taken at the receptor binding site.

Computational Workflow for Refining AlphaFold Models in Drug Design Using Kinetic and Thermodynamic Binding Calculations: A Case Study for the Unresolved Inactive Human Adenosine A3 Receptor

A structure-based drug design pipeline that considers both thermodynamic and kinetic binding data of ligands against a receptor will enable the computational design of improved drug molecules. For unresolved GPCR-ligand complexes, a workflow that can apply both thermodynamic and kinetic binding data in combination with alpha-fold (AF)-derived or other homology models and experimentally resolved binding modes of relevant ligands in GPCR-homologs needs to be tested. Here, as test case, we studied a congeneric set of ligands that bind to a structurally unresolved G protein-coupled receptor (GPCR), the inactive human adenosine A3 receptor (hA3R). We tested three available homology models from which two have been generated from experimental structures of hA1R or hA2AR and one model was a multistate alphafold 2 (AF2)-derived model. We applied alchemical calculations with thermodynamic integration coupled with molecular dynamics (TI/MD) simulations to calculate the experimental relative binding free energies and residence time (τ)-random accelerated MD (τ-RAMD) simulations to calculate the relative residence times (RTs) for antagonists. While the TI/MD calculations produced, for the three homology models, good Pearson correlation coefficients, correspondingly, r = 0.74, 0.62, and 0.67 and mean unsigned error (mue) values of 0.94, 1.31, and 0.81 kcal mol-1, the τ-RAMD method showed r = 0.92 and 0.52 for the first two models but failed to produce accurate results for the multistate AF2-derived model. With subsequent optimization of the AF2-derived model by reorientation of the side chain of R1735.34 located in the extracellular loop 2 (EL2) that blocked ligand's unbinding, the computational model showed r = 0.84 for kinetic data and improved performance for thermodynamic data (r = 0.81, mue = 0.56 kcal mol-1). Overall, after refining the multistate AF2 model with physics-based tools, we were able to show a strong correlation between predicted and experimental ligand relative residence times and affinities, achieving a level of accuracy comparable to an experimental structure. The computational workflow used can be applied to other receptors, helping to rank candidate drugs in a congeneric series and enabling the prioritization of leads with stronger binding affinities and longer residence times.

How Robust Is the Ligand Binding Transition State?

For many drug targets, it has been shown that the kinetics of drug binding (e.g., on rate and off rate) is more predictive of drug efficacy than thermodynamic quantities alone. This motivates the development of predictive computational models that can be used to optimize compounds on the basis of their kinetics. The structural details underpinning these computational models are found not only in the bound state but also in the short-lived ligand binding transition states. Although transition states cannot be directly observed experimentally due to their extremely short lifetimes, recent successes have demonstrated that modeling the ligand binding transition state is possible with the help of enhanced sampling molecular dynamics methods. Previously, we generated unbinding paths for an inhibitor of soluble epoxide hydrolase (sEH) with a residence time of 11 min. Here, we computationally modeled unbinding events with the weighted ensemble method REVO (resampling of ensembles by variation optimization) for five additional inhibitors of sEH with residence times ranging from 14.25 to 31.75 min, with average prediction accuracy within an order of magnitude. The unbinding ensembles are analyzed in detail, focusing on features of the ligand binding transition state ensembles (TSEs). We find that ligands with similar bound poses can show significant differences in their ligand binding TSEs, in terms of their spatial distribution and protein-ligand interactions. However, we also find similarities across the TSEs when examining more general features such as ligand degrees of freedom. Together these findings show significant challenges for rational, kinetics-based drug design.

Elucidating protein-ligand binding kinetics based on returning probability theory

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

Predicting Protein-Ligand Binding and Unbinding Kinetics with Biased MD Simulations and Coarse-Graining of Dynamics: Current State and Challenges

The prediction of drug-target binding and unbinding kinetics that occur on time scales between milliseconds and several hours is a prime challenge for biased molecular dynamics simulation approaches. This Perspective gives a concise summary of the theory and the current state-of-the-art of such predictions via biased simulations, of insights into the molecular mechanisms defining binding and unbinding kinetics as well as of the extraordinary challenges predictions of ligand kinetics pose in comparison to binding free energy predictions.

Predicting Biomolecular Binding Kinetics: A Review

Biomolecular binding kinetics including the association (k_on) and dissociation (k_off) rates are critical parameters for therapeutic design of small-molecule drugs, peptides, and antibodies. Notably, the drug molecule residence time or dissociation rate has been shown to correlate with their efficacies better than binding affinities. A wide range of modeling approaches including quantitative structure-kinetic relationship models, Molecular Dynamics simulations, enhanced sampling, and Machine Learning has been developed to explore biomolecular binding and dissociation mechanisms and predict binding kinetic rates. Here, we review recent advances in computational modeling of biomolecular binding kinetics, with an outlook for future improvements.