Can One Trust Kinetic and Thermodynamic Observables from Biased Metadynamics Simulations?: Detailed Quantitative Benchmarks on Millimolar Drug Fragment Dissociation

Reconstruction of the unbinding pathways of new inhibitors of the SARS-CoV-2 papain-like protease using molecular dynamics simulation

Developing novel antiviral drugs against the SARS-CoV-2 virus and COVID-19 disease is imperative as the vaccines may not offer absolute protection. PLpro plays a crucial role in the viral life cycle, making it an attractive target for drug development. Several PLpro inhibitors have been developed, and their 3D structures in complex with PLpro are available. In this work, we employed Supervised Molecular Dynamics (SuMD), a specific Unbiased Molecular Dynamics (UMD) method, to investigate unbinding pathways of the novel inhibitors of PLpro (PDB IDs: 7LBR, 7RZC, 7SDR and 7E35) and GRL0617 (PDB ID: 7JRN) as a reference. We conducted three simulations for each ligand and achieved unbinding events in the nanosecond timescale in all simulations. We found that unbinding events are commonly affected by altering the conformation of the BL2 loop, which is caused by the natural fluctuations of the loop that are required to trap the substrate and throw out the product. BL2 loop is crucial for keeping the ligand and unbinding and acts as a double-edged sword. Any inhibitor designed to be effective must prevent the loop's natural fluctuations. We perceived that increasing ligands interactions with the binding pocket interior and the BL2 loop will help prevent natural fluctuation of the BL2 loop, Although the interactions with the binding pocket's inner side are more critical than the BL2 loop. These findings may be helpful in developing more potent inhibitors against SARS-CoV-2.Communicated by Ramaswamy H. Sarma.

Calculating Protein-Ligand Residence Times through State Predictive Information Bottleneck Based Enhanced Sampling

Understanding drug residence times in target proteins is key to improving drug efficacy and understanding target recognition in biochemistry. While drug residence time is just as important as binding affinity, atomic-level understanding of drug residence times through molecular dynamics (MD) simulations has been difficult primarily due to the extremely long time scales. Recent advances in rare event sampling have allowed us to reach these time scales, yet predicting protein-ligand residence times remains a significant challenge. Here we present a semi-automated protocol to calculate the ligand residence times across 12 orders of magnitude of time scales. In our proposed framework, we integrate a deep learning-based method, the state predictive information bottleneck (SPIB), to learn an approximate reaction coordinate (RC) and use it to guide the enhanced sampling method metadynamics. We demonstrate the performance of our algorithm by applying it to six different protein-ligand complexes with available benchmark residence times, including the dissociation of the widely studied anticancer drug Imatinib (Gleevec) from both wild-type Abl kinase and drug-resistant mutants. We show how our protocol can recover quantitatively accurate residence times, potentially opening avenues for deeper insights into drug development possibilities and ligand recognition mechanisms.

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.

Calculating Protein-Ligand Residence Times Through State Predictive Information Bottleneck based Enhanced Sampling

Understanding drug residence times in target proteins is key to improving drug efficacy and understanding target recognition in biochemistry. While drug residence time is just as important as binding affinity, atomic-level understanding of drug residence times through molecular dynamics (MD) simulations has been difficult primarily due to the extremely long timescales. Recent advances in rare event sampling have allowed us to reach these timescales, yet predicting protein-ligand residence times remains a significant challenge. Here we present a semi-automated protocol to calculate the ligand residence times across 12 orders of magnitudes of timescales. In our proposed framework, we integrate a deep learning-based method, the state predictive information bottleneck (SPIB), to learn an approximate reaction coordinate (RC) and use it to guide the enhanced sampling method metadynamics. We demonstrate the performance of our algorithm by applying it to six different protein-ligand complexes with available benchmark residence times, including the dissociation of the widely studied anti-cancer drug Imatinib (Gleevec) from both wild-type Abl kinase and drug-resistant mutants. We show how our protocol can recover quantitatively accurate residence times, potentially opening avenues for deeper insights into drug development possibilities and ligand recognition mechanisms.

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.

Structure-Kinetic Relationship for Drug Design Revealed by a PLS Model with Retrosynthesis-Based Pre-Trained Molecular Representation and Molecular Dynamics Simulation

Drug design based on kinetic properties is growing in application. Here, we applied retrosynthesis-based pre-trained molecular representation (RPM) in machine learning (ML) to train 501 inhibitors of 55 proteins and successfully predicted the dissociation rate constant (k_off) values of 38 inhibitors from an independent dataset for the N-terminal domain of heat shock protein 90α (N-HSP90). Our RPM molecular representation outperforms other pre-trained molecular representations such as GEM, MPG, and general molecular descriptors from RDKit. Furthermore, we optimized the accelerated molecular dynamics to calculate the relative retention time (RT) for the 128 inhibitors of N-HSP90 and obtained the protein-ligand interaction fingerprints (IFPs) on their dissociation pathways and their influencing weights on the k_off value. We observed a high correlation among the simulated, predicted, and experimental -log(k_off) values. Combining ML, molecular dynamics (MD) simulation, and IFPs derived from accelerated MD helps design a drug for specific kinetic properties and selectivity profiles to the target of interest. To further validate our k_off predictive ML model, we tested our model on two new N-HSP90 inhibitors, which have experimental k_off values and are not in our ML training dataset. The predicted k_off values are consistent with experimental data, and the mechanism of their kinetic properties can be explained by IFPs, which shed light on the nature of their selectivity against N-HSP90 protein. We believe that the ML model described here is transferable to predict k_off of other proteins and will enhance the kinetics-based drug design endeavor.

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.

Complete reconstruction of dasatinib unbinding pathway from c-Src kinase by supervised molecular dynamics simulation method; assessing efficiency and trustworthiness of the method

Over the past years, rational drug design has gained lots of attention since employing it gave the world targeted therapy and more effective treatment solutions. Structure-based drug design (SBDD) is an excellent tool in rational drug design that takes advantage of accurate methods such as unbiased molecular dynamics (UMD) simulation for designing and optimizing molecular entities by understanding the binding and unbinding pathways of the binders. Supervised molecular dynamics (SuMD) simulation is a branch of UMD in which long-duration simulations are turned into short simulations, called replica, and a specific parameter is monitored throughout the simulation. In this work, we utilized this strategy to reconstruct the unbinding pathway of the anticancer drug dasatinib from its target protein, the c-Src kinase. Several unbinding events with valuable details were achieved. Then, to assess the efficiency and trustworthiness of the SuMD method, the unbinding pathway was also reconstructed by conventional UMD simulation, which uncovered some of the limitations of this method, such as limited sampling of the active site and finding the metastable states in the unbinding pathway. Furthermore, in times like these, when the world is desperate to find treatments for the Covid-19 disease, we think these methods are of exceptional value.Communicated by Ramaswamy H. Sarma.

Effect of nitrogen molecules on the growth kinetics at the interface between a (111) plane of cubic ice and water

The molecular-scale growth kinetics of ice from water in the presence of air molecules are still poorly understood, despite their importance for understanding ice particle formation in nature. In this study, a molecular dynamics simulation is conducted to elucidate the molecular-scale growth kinetics at the interface between a (111) plane of cubic ice and water in the presence of N2 molecules. Two potential models of N2 molecules with and without atomic charges are examined. For both models, N2 molecules bind stably to the interface for a period of 1 ns or longer, and the stability of the binding is higher for the charged model than for the noncharged model. Free-energy surfaces of an N2 molecule along the interface and along an ideal (111) plane surface of cubic ice suggest that for both models, the position where an N2 molecule binds stably is different at the interface and on the ideal plane surface, and the stability of the binding is much higher for the interface than for the ideal plane surface. For both models, stacking-disordered ice grows at the interface, and the formation probability of a hexagonal ice layer in the stacking-disordered ice is higher for the charged model than for the uncharged model. The formation probability for the hexagonal ice layer in the stacking-disordered ice depends not only on the stability of binding but also on the positions where N2 molecules bind on the underlying ice, and the number of N2 molecules that bind stably to the underlying ice.

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

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.

Stable Binding Conformations of Polymaleic and Polyacrylic Acids at a Calcite Surface in the Presence of Countercations: A Metadynamics Study

Elucidating the stable binding conformations of additives at the surface of CaCO3 crystals is essential to biomineralization, scale inhibition, and materials technology. However, accomplishing this by experimental means is rather difficult. In this study, molecular dynamics simulations based on a metadynamics approach were conducted to elucidate the stable binding conformations of a deprotonated polymaleic acid (PMA) additive and two deprotonated poly(acrylic acid) (PAA) additives with different polymerization degrees in the presence of various countercations at a hydrated calcite (104) surface. The simulated free-energy surfaces suggested the existence of several slightly different stable binding conformations for each additive. The appearance of these distinct binding conformations is speculated to originate from different balances of interactions between the additive, the calcite surface, and the countercations. The binding conformations and binding stabilities at the calcite surface were affected by the countercations, with Ca2+ ions producing a more pronounced effect than Na+ ions. Furthermore, the simulation results suggested that the binding stability at the calcite surface was higher for the PMA additive than for the PAA additives, and the PAA additive with a polymerization degree of 10 displayed a binding stability that was similar to or lower than that of the PAA additive with a polymerization degree of 5. The present simulation method provides a new strategy for analyzing the binding conformations of complex additives at material surfaces, developing additives that stably bind to these surfaces, and designing additives to control crystal growth.

Mechanistic insights of key host proteins and potential repurposed inhibitors regulating SARS-CoV-2 pathway

The emergence of pandemic situations originated from severe acute respiratory syndrome (SARS)‐CoV‐2 and its new variants created worldwide medical emergencies. Due to the non‐availability of efficient drugs and vaccines at these emergency hours, repurposing existing drugs can effectively treat patients critically infected by SARS‐CoV‐2. Finding a suitable repurposing drug with inhibitory efficacy to a host‐protein is challenging. A detailed mechanistic understanding of the kinetics, (dis)association pathways, key protein residues facilitating the entry–exit of the drugs with targets are fundamental in selecting these repurposed drugs. Keeping this target as the goal of the paper, the potential repurposing drugs, Nafamostat, Camostat, Silmitasertib, Valproic acid, and Zotatifin with host‐proteins HDAC2, CSK22, eIF4E2 are studied to elucidate energetics, kinetics, and dissociation pathways. From an ensemble of independent simulations, we observed the presence of single or multiple dissociation pathways with varying host‐proteins‐drug systems and quantitatively estimated the probability of unbinding through these specific pathways. We also explored the crucial gateway residues facilitating these dissociation mechanisms. Interestingly, the residues we obtained for HDAC2 and CSK22 are also involved in the catalytic activity. Our results demonstrate how these potential drugs interact with the host machinery and the specific target residues, showing involvement in the mechanism. Most of these drugs are in the preclinical phase, and some are already being used to treat severe COVID‐19 patients. Hence, the mechanistic insight presented in this study is envisaged to support further findings of clinical studies and eventually develop efficient inhibitors to treat SARS‐CoV‐2.

Assessing models of force-dependent unbinding rates via infrequent metadynamics

Protein–ligand interactions are crucial for a wide range of physiological processes. Many cellular functions result in these non-covalent “bonds” being mechanically strained, and this can be integral to proper cellular function. Broadly, two classes of force dependence have been observed—slip bonds, where the unbinding rate increases, and catch bonds, where the unbinding rate decreases. Despite much theoretical work, we cannot predict for which protein–ligand pairs, pulling coordinates, and forces a particular rate dependence will appear. Here, we assess the ability of MD simulations combined with enhanced sampling techniques to probe the force dependence of unbinding rates. We show that the infrequent metadynamics technique correctly produces both catch and slip bonding kinetics for model potentials. We then apply it to the well-studied case of a buckyball in a hydrophobic cavity, which appears to exhibit an ideal slip bond. Finally, we compute the force-dependent unbinding rate of biotin–streptavidin. Here, the complex nature of the unbinding process causes the infrequent metadynamics method to begin to break down due to the presence of unbinding intermediates, despite the use of a previously optimized sampling coordinate. Allowing for this limitation, a combination of kinetic and free energy computations predicts an overall slip bond for larger forces consistent with prior experimental results although there are substantial deviations at small forces that require further investigation. This work demonstrates the promise of predicting force-dependent unbinding rates using enhanced sampling MD techniques while also revealing the methodological barriers that must be overcome to tackle more complex targets in the future.

Unbinding of hACE2 and inhibitors from the receptor binding domain of SARS-CoV-2 spike protein

The first direful biomolecular event leading to COVID-19 disease is the SARS-CoV-2 virus surface spike (S) protein-mediated interaction with the human transmembrane protein, angiotensin-converting enzyme 2 (hACE2). Prevention of this interaction presents an attractive alternative to thwart SARS-CoV-2 replications. The development of monoclonal antibodies (mAbs) in the convalescent plasma treatment, nanobody, and designer peptides, which recognizes epitopes that overlap with hACE2 binding sites in the receptor-binding domain (RBD) of S protein (S/RBD) and thereby blocking the infection has been the center stage of therapeutic research. Here we report atomistic and reliable in silico structure-energetic features of the S/RBD interactions with hACE2 and its two inhibitors (convalescent mAb, B38, and an alpaca nanobody, Ty1). The discovered potential of mean forces exhibits free energy basin and barriers along the interaction pathways, providing sufficient molecular insights to design a B38 mutant and a Ty1-based peptide with higher binding capacity. While the mutated B38 forms a 60-fold deeper free energy minimum, the designer peptide (Ty1-based) constitutes 38 amino acids and is found to form a 100-fold deeper free energy minimum in the first binding basin than their wild-type variants in complex with S/RBD. Our strategy may help to design more efficacious biologics towards therapeutic intervention against the current raging pandemic.Communicated by Ramaswamy H. Sarma.

The prediction of protein-ligand unbinding for modern drug discovery

INTRODUCTION

Drug-target thermodynamic and kinetic information have perennially important roles in drug design. The prediction of protein-ligand unbinding, which can provide important kinetic information, in experiments continues to face great challenges. Uncovering protein-ligand unbinding through molecular dynamics simulations has become efficient and inexpensive with the progress and enhancement of computing power and sampling methods.

AREAS COVERED

In this review, various sampling methods for protein-ligand unbinding and their basic principles are firstly briefly introduced. Then, their applications in predicting aspects of protein-ligand unbinding, including unbinding pathways, dissociation rate constants, residence time and binding affinity, are discussed.

EXPERT OPINION

Although various sampling methods have been successfully applied in numerous systems, they still have shortcomings and deficiencies. Most enhanced sampling methods require researchers to possess a wealth of prior knowledge of collective variables or reaction coordinates. In addition, most systems studied at present are relatively simple, and the study of complex systems in real drug research remains greatly challenging. Through the combination of machine learning and enhanced sampling methods, prediction accuracy can be further improved, and some problems encountered in complex systems also may be solved.

Machine Learning and Enhanced Sampling Simulations for Computing the Potential of Mean Force and Standard Binding Free Energy

Computational capabilities are rapidly increasing, primarily because of the availability of GPU-based architectures. This creates unprecedented simulative possibilities for the systematic and robust computation of thermodynamic observables, including the free energy of a drug binding to a target. In contrast to calculations of relative binding free energy, which are nowadays widely exploited for drug discovery, we here push the boundary of computing the binding free energy and the potential of mean force. We introduce a novel protocol that leverages enhanced sampling, machine learning, and ad hoc algorithms to limit human intervention, computing time, and free parameters in free energy calculations. We first validate the method on a host-guest system, and then we apply the protocol to glycogen synthase kinase 3 beta, a protein kinase of pharmacological interest. Overall, we obtain a good correlation with experimental values in relative and absolute terms. While we focus on protein-ligand binding, the strategy is of broad applicability to any complex event that can be described with a path collective variable. We systematically discuss key details that influence the final result. The parameters and simulation settings are available at PLUMED-NEST to allow full reproducibility.

Metadynamics-based enhanced sampling protocol for virtual screening: case study for 3CLpro protein for SARS-CoV-2

In recent times, computational methods played an important role in the down selection of chemical compounds, which could be a potential drug candidate with a high affinity to target proteins. However, the screening methodologies, including docking, often fails to identify the most effective compound, which could be a ligand for the target protein. To solve that, here we have integrated meta-dynamics, an enhanced sampling molecular simulation method, with all-atom molecular dynamics to determine a specific compound that could target the main protease of novel severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). This combined computational approach uses the enhanced sampling to explore the free energy surface associated with the protein's binding site (including the ligand) in an explicit solvent. We have implemented this method to find new chemical entities that exhibit high specificity of binding to the 3-chymotrypsin-like cysteine protease (3CLpro) present in the SARS-CoV-2 and segregated to the most strongly bound ligands based on free energy and scoring functions (defined and implemented) from a set of 17 ligands which were prescreened for synthesizability and druggability. Additionally, we have compared these 17 ligands' affinities against controls, N3 and 13b α-ketoamide inhibitors, for which experimental crystal structures are available. Based on our results and analysis from the combined molecular simulation approach, we could identify the best compound which could be further taken as a potential candidate for experimental validation.Communicated by Ramaswamy H. Sarma.

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics

Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.

Kinetics and free energy of ligand dissociation using weighted ensemble milestoning

We consider the recently developed weighted ensemble milestoning (WEM) scheme [D. Ray and I. Andricioaei, J. Chem. Phys. 152, 234114 (2020)] and test its capability of simulating ligand-receptor dissociation dynamics. We performed WEM simulations on the following host-guest systems: Na⁺/Cl^- ion pair and 4-hydroxy-2-butanone ligand with FK506 binding protein. As a proof of principle, we show that the WEM formalism reproduces the Na⁺/Cl^- ion pair dissociation timescale and the free energy profile obtained from long conventional MD simulation. To increase the accuracy of WEM calculations applied to kinetics and thermodynamics in protein-ligand binding, we introduced a modified WEM scheme called weighted ensemble milestoning with restraint release (WEM-RR), which can increase the number of starting points per milestone without adding additional computational cost. WEM-RR calculations obtained a ligand residence time and binding free energy in agreement with experimental and previous computational results. Moreover, using the milestoning framework, the binding time and rate constants, dissociation constants, and committor probabilities could also be calculated at a low computational cost. We also present an analytical approach for estimating the association rate constant (k_on) when binding is primarily diffusion driven. We show that the WEM method can efficiently calculate multiple experimental observables describing ligand-receptor binding/unbinding and is a promising candidate for computer-aided inhibitor design.

A combination of machine learning and infrequent metadynamics to efficiently predict kinetic rates, transition states, and molecular determinants of drug dissociation from G protein-coupled receptors

Determining the drug-target residence time (RT) is of major interest in drug discovery given that this kinetic parameter often represents a better indicator of in vivo drug efficacy than binding affinity. However, obtaining drug-target unbinding rates poses significant challenges, both computationally and experimentally. This is particularly palpable for complex systems like G Protein-Coupled Receptors (GPCRs) whose ligand unbinding typically requires very long timescales oftentimes inaccessible by standard molecular dynamics simulations. Enhanced sampling methods offer a useful alternative, and their efficiency can be further improved by using machine learning tools to identify optimal reaction coordinates. Here, we test the combination of two machine learning techniques, automatic mutual information noise omission and reweighted autoencoded variational Bayes for enhanced sampling, with infrequent metadynamics to efficiently study the unbinding kinetics of two classical drugs with different RTs in a prototypic GPCR, the μ-opioid receptor. Dissociation rates derived from these computations are within one order of magnitude from experimental values. We also use the simulation data to uncover the dissociation mechanisms of these drugs, shedding light on the structures of rate-limiting transition states, which, alongside metastable poses, are difficult to obtain experimentally but important to visualize when designing drugs with a desired kinetic profile.

Combining Monte Carlo and Molecular Dynamics Simulations for Enhanced Binding Free Energy Estimation through Markov State Models

We present a multistep protocol, combining Monte Carlo and molecular dynamics simulations, for the estimation of absolute binding free energies, one of the most significant challenges in computer-aided drug design. The protocol is based on an initial short enhanced Monte Carlo simulation, followed by clustering of the ligand positions, which serve to identify the most relevant states of the unbinding process. From these states, extensive molecular dynamics simulations are run to estimate an equilibrium probability distribution obtained with Markov State Models, which is subsequently used to estimate the binding free energy. We tested the procedure on two different protein systems, the Plasminogen kringle domain 1 and Urokinase, each with multiple ligands, for an aggregated molecular dynamics length of 760 μs. Our results indicate that the initial sampling of the unbinding events largely facilitates the convergence of the subsequent molecular dynamics exploration. Moreover, the protocol is capable to properly rank the set of ligands examined, albeit with a significant computational cost for the, more realistic, Urokinase complexes. Overall, this work demonstrates the usefulness of combining enhanced sampling methods with regular simulation techniques as a way to obtain more reliable binding affinity estimates.

Pathways for the formation of ice polymorphs from water predicted by a metadynamics method

The mechanism of how ice crystal form has been extensively studied by many researchers but remains an open question. Molecular dynamics (MD) simulations are a useful tool for investigating the molecular-scale mechanism of crystal formation. However, the timescale of phenomena that can be analyzed by MD simulations is typically restricted to microseconds or less, which is far too short to explore ice crystal formation that occurs in real systems. In this study, a metadynamics (MTD) method was adopted to overcome this timescale limitation of MD simulations. An MD simulation combined with the MTD method, in which two discrete oxygen–oxygen radial distribution functions represented by Gaussian window functions were used as collective variables, successfully reproduced the formation of several different ice crystals when the Gaussian window functions were set at appropriate oxygen–oxygen distances: cubic ice, stacking disordered ice consisting of cubic ice and hexagonal ice, high-pressure ice VII, layered ice with an ice VII structure, and layered ice with an unknown structure. The free-energy landscape generated by the MTD method suggests that the formation of each ice crystal occurred via high-density water with a similar structure to the formed ice crystal. The present method can be used not only to study the mechanism of crystal formation but also to search for new crystals in real systems.

Dynamical reweighting methods for Markov models

Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.