Computer Simulations of the Dissociation Mechanism of Gleevec from Abl Kinase with Milestoning

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.

Comparison of Accuracy and Efficiency of Milestoning Variants: Introducing Buffer Milestoning

The Milestoning algorithm is a method for long-time molecular dynamics simulations. It enables the sampling of rare events. The precise calculations of observables depend on accurately determining the first hitting point distribution (FHPD) for each milestone. There is no analytical expression for FHPD, which is estimated numerically. Several variants of Milestoning offer approximations to the FHPD. Here, we examine in detail the FHPD of an exact calculation and Milestoning variants. We also introduce a new version of the Milestoning algorithm, buffer Milestoning, with a comparable cost to conventional Milestoning but higher accuracy. We use the mean first passage time and the free energy to assess the simulation quality, and we compare the accuracy and efficiency of buffer Milestoning to exact calculations, conventional Milestoning, local-passage-time-weighted Milestoning, Markovian Milestoning with Voronoi tessellation, and exact Milestoning. Conventional Milestoning requires milestone decorrelation. If this condition is not satisfied, it is the least accurate approach of all the techniques we examined. We conclude that for a small increase in cost compared to conventional Milestoning, buffer Milestoning provides accurate results for a range of problems, including more correlated milestones and is, therefore, versatile compared to other variants. Local-passage-time-weighted Milestoning provides accuracy similar to that of buffer Milestoning but at an increased simulation cost. Markovian Milestoning with Voronoi tessellation is the most accurate compared with other approximations, but it is less stable for high barriers and more expensive.

Allo-targeting of the kinase domain: Insights from in silico studies and comparison with experiments

The eukaryotic protein kinase domain has been a broadly explored target for drug discovery, despite limitations imposed by its high sequence conservation as a shared modular domain and the development of resistance to drugs. One way of addressing those limitations has been to target its potential allosteric sites, shortly called allo-targeting, in conjunction with, or separately from, its conserved catalytic/orthosteric site that has been widely exploited. Allosteric regulation has gained importance as an alternative to overcome the drawbacks associated with the indiscriminate effect of targeting the active site, and it turned out to be particularly useful for these highly promiscuous and broadly shared kinase domains. Yet, allo-targeting often faces challenges as the allosteric sites are not as clearly defined as its orthosteric sites, and the effect on the protein function may not be unambiguously assessed. A robust understanding of the consequence of site-specific allo-targeting on the conformational dynamics of the target protein is essential to design effective allo-targeting strategies. Recent years have seen important advances in in silico identification of druggable sites and distinguishing among them those sites expected to allosterically mediate conformational switches essential to signal transmission. The present opinion underscores the utility of such computational approaches applied to the kinase domain, with the help of comparison between computational predictions and experimental observations.

15 Years of molecular simulation of drug-binding kinetics

INTRODUCTION

Drug-binding kinetics has been increasingly recognized as an important factor to be considered in drug discovery. Long residence time could prolong the action of some drugs while produce toxicity on others. Early evaluation of the binding kinetics of drug candidates could reduce attrition rate late in the drug discovery process. Computational prediction of drug-binding kinetics is useful as compounds can be evaluated even before they are made. However, simulation of drug-binding kinetics is a challenging problem because of the long-time scale involved. Nevertheless, significant progress has been made.

AREAS COVERED

This review illustrates the rapid evolution of qualitative to quantitative molecular dynamics-based methods that have been developed over the last 15 years.

EXPERT OPINION

The development of new methods based on molecular dynamics simulations now enables computation of absolute association/dissociation rate constants. Cheaper methods capable of identifying candidates with fast or slow binding kinetics, or rank-ordering rate constants are also available. Together, these methods have generated useful insights into the molecular mechanisms of drug-binding kinetics, and the design of drug candidates with therapeutically favorable kinetics. Although predicting absolute rate constants is still expensive and challenging, rapid improvement is expected in the coming years with the continuing refinement of current technologies, development of new methodologies, and the utilization of machine learning.

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.

Classification of GTP-dependent K-Ras4B active and inactive conformational states

Classifying reliably active and inactive molecular conformations of wildtype (WT) and mutated oncogenic proteins is a key, ongoing challenge in molecular cancer studies. Here, we probe the GTP-bound K-Ras4B conformational dynamics using long-time atomistic molecular dynamics (MD) simulations. We extract and analyze the detailed underlying free energy landscape of WT K-Ras4B. We use two key reaction coordinates, labeled d₁ and d₂ (i.e., distances coordinating the P_β atom of the GTP ligand with two key residues, T35 and G60), shown to correlate closely with activities of WT and mutated K-Ras4B. However, our new K-Ras4B conformational kinetics study reveals a more complex network of equilibrium Markovian states. We show that a new reaction coordinate is required to account for the orientation of acidic K-Ras4B sidechains such as D38 with respect to the interface with binding effector RAF1 and rationalize the activation/inactivation propensities and the corresponding molecular binding mechanisms. We use this understanding to unveil how a relatively conservative mutation (i.e., D33E, in the switch I region) can lead to significantly different activation propensities compared with WT K-Ras4B. Our study sheds new light on the ability of residues near the K-Ras4B-RAF1 interface to modulate the network of salt bridges at the binding interface with the RAF1 downstream effector and, thus, to influence the underlying GTP-dependent activation/inactivation mechanism. Altogether, our hybrid MD-docking modeling approach enables the development of new in silico methods for quantitative assessment of activation propensity changes (e.g., due to mutations or local binding environment). It also unveils the underlying molecular mechanisms and facilitates the rational design of new cancer drugs.

Milestoning simulation of ligand dissociation from the glycogen synthase kinase 3β

As drug-binding kinetics has become an important factor to be considered in modern drug discovery, this work evaluated the ability of the Milestoning method in computing the absolute dissociation rate of a ligand from the serine-threonine kinase, glycogen synthase kinase 3β, which is a target for designing drugs to treat diseases such as neurodegenerative disorders and diabetes. We found that the Milestoning method gave good agreement with experiment with modest computational costs. Although the time scale for dissociation lasted tens of seconds, the collective molecular dynamics simulations total less than 1μs. Computing the committor function helped to identify the transition states (TSs), in which the ligand moved substantially away from the binding pocket. The glycine-rich loop with a serine residue attaching to its tips was found to undergo large movement from the bound to the TSs and might play a role in controlling drug-dissociation kinetics.

Advances in computational methods for ligand binding kinetics

Binding kinetic parameters can be correlated with drug efficacy, which in recent years led to the development of various computational methods for predicting binding kinetic rates and gaining insight into protein-drug binding paths and mechanisms. In this review, we introduce and compare computational methods recently developed and applied to two systems, trypsin-benzamidine and kinase-inhibitor complexes. Methods involving enhanced sampling in molecular dynamics simulations or machine learning can be used not only to predict kinetic rates, but also to reveal factors modulating the duration of residence times, selectivity, and drug resistance to mutations. Methods which require less computational time to make predictions are highlighted, and suggestions to reduce the error of computed kinetic rates are presented.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

Simulation of ligand dissociation kinetics from the protein kinase PYK2

Early-stage drug discovery projects often focus on equilibrium binding affinity to the target alongside selectivity and other pharmaceutical properties. The kinetics of drug binding are ignored but can have significant influence on drug efficacy. Therefore, increasing attention has been paid on evaluating drug-binding kinetics early in a drug discovery process. Simulating drug-binding kinetics at the atomic level is challenging for the long time scale involved. Here, we used the transition-based reweighting analysis method (TRAM) with the Markov state model to study the dissociation of a ligand from the protein kinase PYK2. TRAM combines biased and unbiased simulations to reduce computational costs. This work used the umbrella sampling technique for the biased simulations. Although using the potential of mean force from umbrella sampling simulations with the transition-state theory over-estimated the dissociation rate by three orders of magnitude, TRAM gave a dissociation rate within an order of magnitude of the experimental value.

Protein Flexibility and Dissociation Pathway Differentiation Can Explain Onset of Resistance Mutations in Kinases

Understanding how mutations render a drug ineffective is a problem of immense relevance. Often the mechanism through which mutations cause drug resistance can be explained purely through thermodynamics. However, the more perplexing situation is when two proteins have the same drug binding affinities but different residence times. In this work, we demonstrate how all-atom molecular dynamics simulations using recent developments grounded in statistical mechanics can provide a detailed mechanistic rationale for such variances. We discover dissociation mechanisms for the anti-cancer drug Imatinib (Gleevec) against wild-type and the N368S mutant of Abl kinase. We show how this point mutation triggers far-reaching changes in the protein's flexibility and leads to a different, much faster, drug dissociation pathway. We believe that this work marks an efficient and scalable approach to obtain mechanistic insight into resistance mutations in biomolecular receptors that are hard to explain using a structural perspective.

Molecular Dynamics Simulations of the Conformational Plasticity in the Active Pocket of Salt-Inducible Kinase 2 (SIK2) Multi-State Binding with Bosutinib

The kinase domain is highly conserved among protein kinases 'in terms of both sequence and structure. Conformational rearrangements of the kinase domain are affected by the phosphorylation of residues and the binding of kinase inhibitors. Interestingly, the conformational rearrangement of the active pocket plays an important role in kinase activity and can be used to design novel kinase inhibitors. We characterized the conformational plasticity of the active pocket when bosutinib was bound to salt-inducible kinase 2 (SIK2) using homology modeling and molecular dynamics simulations. Ten different initial complex models were constructed using the Morph server, ranging from open to closed conformations of SIK2 binding with bosutinib. Our simulation showed that bosutinib binds SIK2 with up or down conformations of the P-loop and with all the conformations of the activation loop. In addition, the αC-helix conformation was induced by the conformation of the activation loop, and the salt bridge formed only with its open conformation. The binding affinity of the models was also determined using the molecular mechanics generalized Born surface area method. Bosutinib was found to form a strong binding model with SIK2 and hydrophobic interactions were the dominant factor. This discovery may help guide the design of novel SIK2 inhibitors.

Practical Protocols for Efficient Sampling of Kinase-Inhibitor Binding Pathways Using Two-Dimensional Replica-Exchange Molecular Dynamics

Molecular dynamics (MD) simulations are increasingly used to study various biological processes such as protein folding, conformational changes, and ligand binding. These processes generally involve slow dynamics that occur on the millisecond or longer timescale, which are difficult to simulate by conventional atomistic MD. Recently, we applied a two-dimensional (2D) replica-exchange MD (REMD) method, which combines the generalized replica exchange with solute tempering (gREST) with the replica-exchange umbrella sampling (REUS) in kinase-inhibitor binding simulations, and successfully observed multiple ligand binding/unbinding events. To efficiently apply the gREST/REUS method to other kinase-inhibitor systems, we establish modified, practical protocols with non-trivial simulation parameter tuning. The current gREST/REUS simulation protocols are tested for three kinase-inhibitor systems: c-Src kinase with PP1, c-Src kinase with Dasatinib, and c-Abl kinase with Imatinib. We optimized the definition of kinase-ligand distance as a collective variable (CV), the solute temperatures in gREST, and replica distributions and umbrella forces in the REUS simulations. Also, the initial structures of each replica in the 2D replica space were prepared carefully by pulling each ligand from and toward the protein binding sites for keeping stable kinase conformations. These optimizations were carried out individually in multiple short MD simulations. The current gREST/REUS simulation protocol ensures good random walks in 2D replica spaces, which are required for enhanced sampling of inhibitor dynamics around a target kinase.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Mutation in Abl kinase with altered drug-binding kinetics indicates a novel mechanism of imatinib resistance

Protein kinase inhibitors are potent anticancer therapeutics. For example, the Bcr-Abl kinase inhibitor imatinib decreases mortality for chronic myeloid leukemia by 80%, but 22 to 41% of patients acquire resistance to imatinib. About 70% of relapsed patients harbor mutations in the Bcr-Abl kinase domain, where more than a hundred different mutations have been identified. Some mutations are located near the imatinib-binding site and cause resistance through altered interactions with the drug. However, many resistance mutations are located far from the drug-binding site, and it remains unclear how these mutations confer resistance. Additionally, earlier studies on small sets of patient-derived imatinib resistance mutations indicated that some of these mutant proteins were in fact sensitive to imatinib in cellular and biochemical studies. Here, we surveyed the resistance of 94 patient-derived Abl kinase domain mutations annotated as disease relevant or resistance causing using an engagement assay in live cells. We found that only two-thirds of mutations weaken imatinib affinity by more than twofold compared to Abl wild type. Surprisingly, one-third of mutations in the Abl kinase domain still remain sensitive to imatinib and bind with similar or higher affinity than wild type. Intriguingly, we identified three clinical Abl mutations that bind imatinib with wild type-like affinity but dissociate from imatinib considerably faster. Given the relevance of residence time for drug efficacy, mutations that alter binding kinetics could cause resistance in the nonequilibrium environment of the body where drug export and clearance play critical roles.