Predicting Biomolecular Binding Kinetics: A Review

Ligand Gaussian Accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional molecular dynamics (cMD), due to limited simulation time scales. Based on our previously developed ligand Gaussian accelerated molecular dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3″, in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding, and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as the model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 μs simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 were in agreement with the available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligands and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Incorporating Prior Knowledge in the Seeds of Adaptive Sampling Molecular Dynamics Simulations of Ligand Transport in Enzymes with Buried Active Sites

Because most proteins have buried active sites, protein tunnels or channels play a crucial role in the transport of small molecules into buried cavities for enzymatic catalysis. Tunnels can critically modulate the biological process of protein-ligand recognition. Various molecular dynamics methods have been developed for exploring and exploiting the protein-ligand conformational space to extract high-resolution details of the binding processes, a recent example being energetically unbiased high-throughput adaptive sampling simulations. The current study systematically contrasted the role of integrating prior knowledge while generating useful initial protein-ligand configurations, called seeds, for these simulations. Using a nontrivial system of a haloalkane dehalogenase mutant with multiple transport tunnels leading to a deeply buried active site, simulations were employed to derive kinetic models describing the process of association and dissociation of the substrate molecule. The most knowledge-based seed generation enabled high-throughput simulations that could more consistently capture the entire transport process, explore the complex network of transport tunnels, and predict equilibrium dissociation constants, koff/kon, on the same order of magnitude as experimental measurements. Overall, the infusion of more knowledge into the initial seeds of adaptive sampling simulations could render analyses of transport mechanisms in enzymes more consistent even for very complex biomolecular systems, thereby promoting drug development efforts and the rational design of enzymes with buried active sites.

Measuring the Adsorption Cross Section of YOYO-1 to Immobilized DNA Molecules

Many interactions between small molecules and particles occur in solutions. They are surrounded by other molecules that do not react, for example, biological processes in water, chemical reactions in gas or liquid solutions, and environmental reactions in air and water. However, predicting the rate of such diffusive interactions remains challenging, due to the random motion of molecules in solutions, as exampled by the famous Brownian motion of pollen particles. In this report, we experimentally confirmed that a disruptive rate equation we have published before can predict the association rate of typical adsorption at interfaces, which has a surprising fraction order of 4/3 that has not been considered before. This could be an important step toward a generalized method to predict the adsorption rate of many reactions.

Increased throughput in methods for simulating protein ligand binding and unbinding

By incorporating full flexibility and enabling the quantification of crucial parameters such as binding free energies and residence times, methods for investigating protein-ligand binding and unbinding via molecular dynamics provide details on the involved mechanisms at the molecular level. While these advancements hold promise for impacting drug discovery, a notable drawback persists: their relatively time-consuming nature limits throughput. Herein, we survey recent implementations which, employing a blend of enhanced sampling techniques, a clever choice of collective variables, and often machine learning, strive to enhance the efficiency of new and previously reported methods without compromising accuracy. Particularly noteworthy is the validation of these methods that was often performed on systems mirroring real-world drug discovery scenarios.

Understanding the impact of binding free energy and kinetics calculations in modern drug discovery

INTRODUCTION

For rational drug design, it is crucial to understand the receptor-drug binding processes and mechanisms. A new era for the use of computer simulations in predicting drug-receptor interactions at an atomic level has begun with remarkable advances in supercomputing and methodological breakthroughs.

AREAS COVERED

End-point free energy calculation methods such as Molecular Mechanics/Poisson Boltzmann Surface Area (MM/PBSA) or Molecular-Mechanics/Generalized Born Surface Area (MM/GBSA), free energy perturbation (FEP), and thermodynamic integration (TI) are commonly used for binding free energy calculations in drug discovery. In addition, kinetic dissociation and association rate constants (k off and k on ) play critical roles in the function of drugs. Nowadays, Molecular Dynamics (MD) and enhanced sampling simulations are increasingly being used in drug discovery. Here, the authors provide a review of the computational techniques used in drug binding free energy and kinetics calculations.

EXPERT OPINION

The applications of computational methods in drug discovery and design are expanding, thanks to improved predictions of the binding free energy and kinetic rates of drug molecules. Recent microsecond-timescale enhanced sampling simulations have made it possible to accurately capture repetitive ligand binding and dissociation, facilitating more efficient and accurate calculations of ligand binding free energy and kinetics.

Expanding the Available RNA Labeling Toolbox With CutA Nucleotidyltransferase for Efficient Transcript Labeling with Purine and Pyrimidine Nucleotide Analogs

RNA labeling is an invaluable tool for investigation of the function and localization of nucleic acids. Labels are commonly incorporated into 3' end of RNA and the primary enzyme used for this purpose is RNA poly(A) polymerase (PAP), which belongs to the class of terminal nucleotidyltransferases (NTases). However, PAP preferentially adds ATP analogs, thus limiting the number of available substrates. Here, we report the use of another NTase, CutA from the fungus Thielavia terrestris. Using this enzyme, we were able to incorporate into the 3' end of RNA not only purine analogs, but also pyrimidine analogs. We engaged strain-promoted azide-alkyl cycloaddition (SPAAC) to obtain fluorescently labeled or biotinylated transcripts from RNAs extended with azide analogs by CutA. Importantly, modified transcripts retained their biological properties. Furthermore, fluorescently labeled mRNAs were suitable for visualization in cultured mammalian cells. Finally, we demonstrate that either affinity studies or molecular dynamic (MD) simulations allow for rapid screening of NTase substrates, what opens up new avenues in the search for the optimal substrates for this class of enzymes.

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.

Ligand Gaussian accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional Molecular Dynamics (cMD), due to limited simulation timescales. Based on our previously developed Ligand Gaussian accelerated Molecular Dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3", in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 microsecond simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 agreed with available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligand and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

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.

Characterization of binding kinetics and intracellular signaling of new psychoactive substances targeting cannabinoid receptor using transition-based reweighting method

New psychoactive substances (NPS) targeting cannabinoid receptor 1 pose a significant threat to society as recreational abusive drugs that have pronounced physiological side effects. These greater adverse effects compared to classical cannabinoids have been linked to the higher downstream β-arrestin signaling. Thus, understanding the mechanism of differential signaling will reveal important structure-activity relationship essential for identifying and potentially regulating NPS molecules. In this study, we simulate the slow (un)binding process of NPS MDMB-Fubinaca and classical cannabinoid HU-210 from CB1 using multi-ensemble simulation to decipher the effects of ligand binding dynamics on downstream signaling. The transition-based reweighing method is used for the estimation of transition rates and underlying thermodynamics of (un)binding processes of ligands with nanomolar affinities. Our analyses reveal major interaction differences with transmembrane TM7 between NPS and classical cannabinoids. A variational autoencoder-based approach, neural relational inference (NRI), is applied to assess the allosteric effects on intracellular regions attributable to variations in binding pocket interactions. NRI analysis indicate a heightened level of allosteric control of NPxxY motif for NPS-bound receptors, which contributes to the higher probability of formation of a crucial triad interaction (Y7.53-Y5.58-T3.46) necessary for stronger β-arrestin signaling. Hence, in this work, MD simulation, data-driven statistical methods, and deep learning point out the structural basis for the heightened physiological side effects associated with NPS, contributing to efforts aimed at mitigating their public health impact.

Mechanism of Ligand Binding to Theophylline RNA Aptamer

Studying RNA-ligand interactions and quantifying their binding thermodynamics and kinetics are of particular relevance in the field of drug discovery. Here, we combined biochemical binding assays and accelerated molecular simulations to investigate ligand binding and dissociation in RNA using the theophylline-binding RNA as a model system. All-atom simulations using a Ligand Gaussian accelerated Molecular Dynamics method (LiGaMD) have captured repetitive binding and dissociation of theophylline and caffeine to RNA. Theophylline's binding free energy and kinetic rate constants align with our experimental data, while caffeine's binding affinity is over 10,000 times weaker, and its kinetics could not be determined. LiGaMD simulations allowed us to identify distinct low-energy conformations and multiple ligand binding pathways to RNA. Simulations revealed a "conformational selection" mechanism for ligand binding to the flexible RNA aptamer, which provides important mechanistic insights into ligand binding to the theophylline-binding model. Our findings suggest that compound docking using a structural ensemble of representative RNA conformations would be necessary for structure-based drug design of flexible RNA.

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.

Roles of Accelerated Molecular Dynamics Simulations in Predictions of Binding Kinetic Parameters

Rational predictions on binding kinetics parameters of drugs to targets play significant roles in future drug designs. Full conformational samplings of targets are requisite for accurate predictions of binding kinetic parameters. In this review, we mainly focus on the applications of enhanced sampling technologies in calculations of binding kinetics parameters and residence time of drugs. The methods involved in molecular dynamics simulations are applied to not only probe conformational changes of targets but also reveal calculations of residence time that is significant for drug efficiency. For this review, special attention are paid to accelerated molecular dynamics (aMD) and Gaussian aMD (GaMD) simulations that have been adopted to predict the association or disassociation rate constant. We also expect that this review can provide useful information for future 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.

Kinetics from Metadynamics: Principles, Applications, and Outlook

Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein-ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.

A multiscale predictive digital twin for neurocardiac modulation

Cardiac function is tightly regulated by the autonomic nervous system (ANS). Activation of the sympathetic nervous system increases cardiac output by increasing heart rate and stroke volume, while parasympathetic nerve stimulation instantly slows heart rate. Importantly, imbalance in autonomic control of the heart has been implicated in the development of arrhythmias and heart failure. Understanding of the mechanisms and effects of autonomic stimulation is a major challenge because synapses in different regions of the heart result in multiple changes to heart function. For example, nerve synapses on the sinoatrial node (SAN) impact pacemaking, while synapses on contractile cells alter contraction and arrhythmia vulnerability. Here, we present a multiscale neurocardiac modelling and simulator tool that predicts the effect of efferent stimulation of the sympathetic and parasympathetic branches of the ANS on the cardiac SAN and ventricular myocardium. The model includes a layered representation of the ANS and reproduces firing properties measured experimentally. Model parameters are derived from experiments and atomistic simulations. The model is a first prototype of a digital twin that is applied to make predictions across all system scales, from subcellular signalling to pacemaker frequency to tissue level responses. We predict conditions under which autonomic imbalance induces proarrhythmia and can be modified to prevent or inhibit arrhythmia. In summary, the multiscale model constitutes a predictive digital twin framework to test and guide high-throughput prediction of novel neuromodulatory therapy. KEY POINTS: A multi-layered model representation of the autonomic nervous system that includes sympathetic and parasympathetic branches, each with sparse random intralayer connectivity, synaptic dynamics and conductance based integrate-and-fire neurons generates firing patterns in close agreement with experiment. A key feature of the neurocardiac computational model is the connection between the autonomic nervous system and both pacemaker and contractile cells, where modification to pacemaker frequency drives initiation of electrical signals in the contractile cells. We utilized atomic-scale molecular dynamics simulations to predict the association and dissociation rates of noradrenaline with the β-adrenergic receptor. Multiscale predictions demonstrate how autonomic imbalance may increase proclivity to arrhythmias or be used to terminate arrhythmias. The model serves as a first step towards a digital twin for predicting neuromodulation to prevent or reduce disease.

Application of Molecular Dynamics Simulations to Determine Interactions between Canary Seed (Phalaris canariensis L.) Bioactive Peptides and Skin-Aging Enzymes

Food bioactive peptides are well recognized for their health benefits such as antimicrobial, antioxidant, and antihypertensive benefits, among others. Their drug-like behavior has led to their potential use in targeting skin-related aging factors like the inhibition of enzymes related with the skin-aging process. In this study, canary seed peptides (CSP) after simulated gastrointestinal digestion (<3 kDa) were fractioned by RP-HPLC and their enzyme-inhibition activity towards elastase and tyrosinase was evaluated in vitro. CSP inhibited elastase (IC50 = 6.2 mg/mL) and tyrosinase (IC50 = 6.1 mg/mL), while the hydrophobic fraction-VI (0.2 mg/mL) showed the highest inhibition towards elastase (93%) and tyrosinase (67%). The peptide fraction with the highest inhibition was further characterized by a multilevel in silico workflow, including physicochemical descriptor calculations, antioxidant activity predictions, and molecular dynamics-ensemble docking towards elastase and tyrosinase. To gain insights into the skin permeation process during molecular dynamics simulations, based on their docking scores, five peptides (GGWH, VPPH, EGLEPNHRVE, FLPH, and RPVNKYTPPQ) were identified to have favorable intermolecular interactions, such as hydrogen bonding of polar residues (W, H, and K) to lipid polar groups and 2-3 Å van der Waals close contact of hydrophobic aliphatic residues (P, V, and L). These interactions can play a critical role for the passive insertion of peptides into stratum corneum model skin-membranes, suggesting a promising application of CSP for skin-aging treatments.

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.