Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

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.

Quantum mechanical-based strategies in drug discovery: Finding the pace to new challenges in drug design

The expansion of the chemical space to tangible libraries containing billions of synthesizable molecules opens exciting opportunities for drug discovery, but also challenges the power of computer-aided drug design to prioritize the best candidates. This directly hits quantum mechanics (QM) methods, which provide chemically accurate properties, but subject to small-sized systems. Preserving accuracy while optimizing the computational cost is at the heart of many efforts to develop high-quality, efficient QM-based strategies, reflected in refined algorithms and computational approaches. The design of QM-tailored physics-based force fields and the coupling of QM with machine learning, in conjunction with the computing performance of supercomputing resources, will enhance the ability to use these methods in drug discovery. The challenge is formidable, but we will undoubtedly see impressive advances that will define a new era.

Microbial Synthetic Epigenetic Tools Design and Applications

Microbial synthetic epigenetics offers significant opportunities for the design of synthetic biology tools by leveraging reversible gene control mechanisms without altering DNA sequences. However, limited understanding and a lack of technologies for thorough analysis of the mechanisms behind epigenetic modifications have hampered their utilization in biotechnological applications. In this review, we explore advancements in developing epigenetic-based synthetic gene regulatory tools at both transcriptional and post-transcriptional levels. Furthermore, we examine strategies developed to construct epigenetic-based circuits that provide controllable and stable gene regulation, aiming to boost the performance of microbial chassis cells. Finally, we discuss the current challenges and perspectives in the development of synthetic epigenetic tools.

How exascale computing can shape drug design: A perspective from multiscale QM/MM molecular dynamics simulations and machine learning-aided enhanced sampling algorithms

Molecular simulations are an essential asset in the first steps of drug design campaigns. However, the requirement of high-throughput limits applications mainly to qualitative approaches with low computational cost, but also low accuracy. Unlocking the potential of more rigorous quantum mechanical/molecular mechanics (QM/MM) models combined with molecular dynamics-based free energy techniques could have a tremendous impact. Indeed, these two relatively old techniques are emerging as promising methods in the field. This has been favored by the exponential growth of computer power and the proliferation of powerful data-driven methods. Here, we briefly review recent advances and applications, and give our perspective on the impact that QM/MM and free-energy methods combined with machine learning-aided algorithms can have on drug design.

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.

All-Atom Biomolecular Simulation in the Exascale Era

Exascale supercomputers have opened the door to dynamic simulations, facilitated by AI/ML techniques, that model biomolecular motions over unprecedented length and time scales. This new capability holds the potential to revolutionize our understanding of fundamental biological processes. Here we report on some of the major advances that were discussed at a recent CECAM workshop in Pisa, Italy, on the topic with a primary focus on atomic-level simulations. First, we highlight examples of current large-scale biomolecular simulations and the future possibilities enabled by crossing the exascale threshold. Next, we discuss challenges to be overcome in optimizing the usage of these powerful resources. Finally, we close by listing several grand challenge problems that could be investigated with this new computer architecture.

QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations

Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.

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.

New Insights into the Cooperativity and Dynamics of Dimeric Enzymes

A survey of protein databases indicates that the majority of enzymes exist in oligomeric forms, with about half of those found in the UniProt database being homodimeric. Understanding why many enzymes are in their dimeric form is imperative. Recent developments in experimental and computational techniques have allowed for a deeper comprehension of the cooperative interactions between the subunits of dimeric enzymes. This review aims to succinctly summarize these recent advancements by providing an overview of experimental and theoretical methods, as well as an understanding of cooperativity in substrate binding and the molecular mechanisms of cooperative catalysis within homodimeric enzymes. Focus is set upon the beneficial effects of dimerization and cooperative catalysis. These advancements not only provide essential case studies and theoretical support for comprehending dimeric enzyme catalysis but also serve as a foundation for designing highly efficient catalysts, such as dimeric organic catalysts. Moreover, these developments have significant implications for drug design, as exemplified by Paxlovid, which was designed for the homodimeric main protease of SARS-CoV-2.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

Dissociation Rate Calculation via Constant-Force Steered Molecular Dynamics Simulation

Steered molecular dynamics (SMD) simulations are used to study molecular dissociation events by applying a harmonic force to the molecules and pulling them at a constant velocity. Instead of constant-velocity pulling, we use a constant force: the constant-force SMD (CF-SMD) simulation. The CF-SMD simulation employs a constant force to reduce the activation barrier of molecular dissociation, thereby enhancing the dissociation event. Here, we present the capability of the CF-SMD simulation to estimate the dissociation time at equilibrium. We performed all-atom CF-SMD simulations for NaCl and protein-ligand systems, producing dissociation time at various forces. We extrapolated these values to the dissociation rate without a constant force using Bell's model or the Dudko-Hummer-Szabo model. We demonstrate that the CF-SMD simulations with the models predicted the dissociation time in equilibrium. A CF-SMD simulation is a powerful tool for estimating the dissociation rate in a direct and computationally efficient manner.

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.

Unbinding Kinetics of Muscarinic M3 Receptor Antagonists Explained by Metadynamics Simulations

The residence time (RT), the time for which a drug remains bound to its biological target, is a critical parameter for drug design. The prediction of this key kinetic property has been proven to be challenging and computationally demanding in the framework of atomistic simulations. In the present work, we setup and applied two distinct metadynamics protocols to estimate the RTs of muscarinic M3 receptor antagonists. In the first method, derived from the conformational flooding approach, the kinetics of unbinding is retrieved from a physics-based parameter known as the acceleration factor α (i.e., the running average over time of the potential deposited in the bound state). Such an approach is expected to recover the absolute RT value for a compound of interest. In the second method, known as the t_META-D approach, a qualitative estimation of the RT is given by the time of simulation required to drive the ligand from the binding site to the solvent bulk. This approach has been developed to reproduce the change of experimental RTs for compounds targeting the same target. Our analysis shows that both computational protocols are able to rank compounds in agreement with their experimental RTs. Quantitative structure-kinetics relationship (SKR) models can be identified and employed to predict the impact of a chemical modification on the experimental RT once a calibration study has been performed.

Selectivity and Ranking of Tight-Binding JAK-STAT Inhibitors Using Markovian Milestoning with Voronoi Tessellations

Janus kinases (JAK), a group of proteins in the nonreceptor tyrosine kinase (NRTKs) family, play a crucial role in growth, survival, and angiogenesis. They are activated by cytokines through the Janus kinase-signal transducer and activator of a transcription (JAK-STAT) signaling pathway. JAK-STAT signaling pathways have significant roles in the regulation of cell division, apoptosis, and immunity. Identification of the V617F mutation in the Janus homology 2 (JH2) domain of JAK2 leading to myeloproliferative disorders has stimulated great interest in the drug discovery community to develop JAK2-specific inhibitors. However, such inhibitors should be selective toward JAK2 over other JAKs and display an extended residence time. Recently, novel JAK2/STAT5 axis inhibitors (N-(1H-pyrazol-3-yl)pyrimidin-2-amino derivatives) have displayed extended residence times (hours or longer) on target and adequate selectivity excluding JAK3. To facilitate a deeper understanding of the kinase-inhibitor interactions and advance the development of such inhibitors, we utilize a multiscale Markovian milestoning with Voronoi tessellations (MMVT) approach within the Simulation-Enabled Estimation of Kinetic Rates v.2 (SEEKR2) program to rank order these inhibitors based on their kinetic properties and further explain the selectivity of JAK2 inhibitors over JAK3. Our approach investigates the kinetic and thermodynamic properties of JAK-inhibitor complexes in a user-friendly, fast, efficient, and accurate manner compared to other brute force and hybrid-enhanced sampling approaches.

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.

Ligand Gaussian Accelerated Molecular Dynamics 2 (LiGaMD2): Improved Calculations of Ligand Binding Thermodynamics and Kinetics with Closed Protein Pocket

Ligand binding thermodynamics and kinetics are critical parameters for drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics from molecular simulations due to limited simulation timescales. Protein dynamics, especially in the ligand binding pocket, often plays an important role in ligand binding. Based on our previously developed Ligand Gaussian accelerated molecular dynamics (LiGaMD), here we present LiGaMD2 in which a selective boost potential was applied to both the ligand and protein residues in the binding pocket to improve sampling of ligand binding and dissociation. To validate the performance of LiGaMD2, the T4 lysozyme (T4L) mutants with open and closed pockets bound by different ligands were chosen as model systems. LiGaMD2 could efficiently capture repetitive ligand dissociation and binding within microsecond simulations of all T4L systems. The obtained ligand binding kinetic rates and free energies agreed well with available experimental values and previous modeling results. Therefore, LiGaMD2 provides an improved approach to sample opening of closed protein pockets for ligand dissociation and binding, thereby allowing for efficient calculations of ligand binding thermodynamics and kinetics.

Sampling rare event energy landscapes via birth-death augmented dynamics

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time scales. Many enhanced sampling methods have been developed to address this sampling problem and more efficiently sample rare event systems. An interesting idea, coming from the field of statistics, was introduced in a recent work [Lu, Lu, and Nolen, Accelerating Langevin sampling with birth-death, arXiv:1905.09863] in the form of a novel sampling algorithm that augments overdamped Langevin dynamics with a birth-death process. In this work, we expand on this idea and show that this birth-death sampling scheme can efficiently sample prototypical rare event energy landscapes, and that the speed of equilibration is independent of the barrier height. We amend a crucial shortcoming of the original algorithm that leads to incorrect sampling of barrier regions by introducing an alternative approximation of the birth-death term. We establish important theoretical properties of the modified algorithm and prove mathematically that the relevant convergence results still hold. We investigate via numerical simulations the effect of various parameters, and we investigate ways to reduce the computational effort of the sampling scheme. We show that the birth-death mechanism can be used to accelerate sampling in the more general case of underdamped Langevin dynamics that is more commonly used in simulating physical systems. Our results show that this birth-death scheme is a promising method for sampling rare event energy landscapes.

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.

Multiscale Modeling of Phosphate···π Contacts in RNA U-Turns Exposes Differences between Quantum-Chemical and AMBER Force Field Descriptions

Phosphate···π, also called anion···π, contacts occur between nucleobases and anionic phosphate oxygens (OP2) in r(GNRA) and r(UNNN) U-turn motifs (N = A,G,C,U; R = A,G). These contacts were investigated using state-of-the-art quantum-chemical methods (QM) to characterize their physicochemical properties and to serve as a reference to evaluate AMBER force field (AFF) performance. We found that phosphate···π interaction energies calculated with the AFF for dimethyl phosphate···nucleobase model systems are less stabilizing in comparison with double-hybrid DFT and that minimum contact distances are larger for all nucleobases. These distance stretches are also observed in large-scale AFF vs QM/MM computations and classical molecular dynamics (MD) simulations on several r(gcGNRAgc) tetraloop hairpins when compared to experimental data extracted from X-ray/cryo-EM structures (res. ≤ 2.5 Å) using the WebFR3D bioinformatic tool. MD simulations further revealed shifted OP2/nucleobase positions. We propose that discrepancies between the QM and AFF result from a combination of missing polarization in the AFF combined with too large AFF Lennard-Jones (LJ) radii of nucleobase carbon atoms in addition to an exaggerated short-range repulsion of the r^-12 LJ repulsive term. We compared these results with earlier data gathered on lone pair···π contacts in CpG Z-steps occurring in r(UNCG) tetraloops. In both instances, charge transfer calculations do not support any significant n → π* donation effects. We also investigated thiophosphate···π contacts that showed reduced stabilizing interaction energies when compared to phosphate···π contacts. Thus, we challenge suggestions that the experimentally observed enhanced thermodynamic stability of phosphorothioated r(GNRA) tetraloops can be explained by larger London dispersion.

Free energy and kinetic rate calculation via non-equilibrium molecular simulation: application to biomolecules

Non-equilibrium molecular dynamics (NEMD) simulation has been recognized as a powerful tool for examining biomolecules and provides fruitful insights into not only non-equilibrium but also equilibrium processes. We review recent advances in NEMD simulation and relevant, fundamental results of non-equilibrium statistical mechanics. We first introduce Crooks fluctuation theorem and Jarzynski equality that relate free energy difference to work done on a physical system during a non-equilibrium process. The theorems are beneficial for the analysis of NEMD trajectories. We then describe rate theory, a framework to calculate molecular kinetics from a non-equilibrium process; this theoretical framework enables us to calculate a reaction time-mean-first passage time-from NEMD trajectories. We, in turn, present recent NEMD techniques that apply an external force to a system to enhance molecular dissociation and introduce their application to biomolecules. Lastly, we show the current status of an appropriate selection of reaction coordinates for NEMD simulation.

Estimation of Drug-Target Residence Time by Targeted Molecular Dynamics Simulations

Drug-target residence time has emerged as a key selection factor in drug discovery since the binding duration of a drug molecule to its protein target can significantly impact its in vivo efficacy. The challenge in studying the residence time, in early drug discovery stages, lies in how to cost-effectively determine the residence time for the systematic assessment of compounds. Currently, there is still a lack of computational protocols to quickly estimate such a measure, particularly for large and flexible protein targets and drugs. Here, we report an efficient computational protocol, based on targeted molecular dynamics, to rank drug candidates by their residence time and to obtain insights into ligand-target dissociation mechanisms. The method was assessed on a dataset of 10 arylpyrazole inhibitors of CDK8, a large, flexible, and clinically important target, for which the experimental residence time of the inhibitors ranges from minutes to hours. The compounds were correctly ranked according to their estimated residence time scores compared to their experimental values. The analysis of protein-ligand interactions along the dissociation trajectories highlighted the favorable contribution of hydrophobic contacts to residence time and revealed key residues that strongly affect compound residence time.

Rare Event Kinetics from Adaptive Bias Enhanced Sampling

We introduce a novel enhanced sampling approach named on-the-fly probability enhanced sampling (OPES) flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the OPES approach [Invernizzi and Parrinello, J. Phys. Chem. Lett. 2020, 11, 7, 2731-2736], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double-well potential, conformational transition in the alanine dipeptide in the gas phase, and the folding and unfolding of the chignolin polypeptide in an aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.