Escape of a Small Molecule from Inside T4 Lysozyme by Multiple Pathways

WEDAP: A Python Package for Streamlined Plotting of Molecular Simulation Data

Given the growing interest in path sampling methods for extending the time scales of molecular dynamics (MD) simulations, there has been great interest in software tools that streamline the generation of plots for monitoring the progress of large-scale simulations. Here, we present the WEDAP Python package for simplifying the analysis of data generated from either conventional MD simulations or the weighted ensemble (WE) path sampling method, as implemented in the widely used WESTPA software package. WEDAP facilitates (i) the parsing of WE simulation data stored in highly compressed, hierarchical HDF5 files and (ii) incorporates trajectory weights from WE simulations into all generated plots. Our Python package consists of multiple user-friendly interfaces: a command-line interface, a graphical user interface, and a Python application programming interface. We demonstrate the plotting features of WEDAP through a series of examples using data from WE and conventional MD simulations that focus on the HIV-1 capsid protein's C-terminal domain dimer as a showcase system. The source code for WEDAP is freely available on GitHub at https://github.com/chonglab-pitt/wedap.

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.

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.

WEDAP: A Python Package for Streamlined Plotting of Molecular Simulation Data

Given the growing interest in path sampling methods for extending the timescales of molecular dynamics (MD) simulations, there has been great interest in software tools that streamline the generation of plots for monitoring the progress of large-scale simulations. Here, we present the WEDAP Python package for simplifying the analysis of data generated from either conventional MD simulations or the weighted ensemble (WE) path sampling method, as implemented in the widely used WESTPA software package. WEDAP facilitates (i) the parsing of WE simulation data stored in highly compressed, hierarchical HDF5 files, and (ii) incorporates trajectory weights from WE simulations into all generated plots. Our Python package consists of multiple user-friendly interfaces: a command-line interface, a graphical user interface, and a Python application programming interface. We demonstrate the plotting features of WEDAP through a series of examples using data from WE and conventional MD simulations that focus on the HIV-1 capsid protein C-terminal domain dimer as a showcase system. The source code for WEDAP is freely available on GitHub at https://github.com/chonglab-pitt/wedap .

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.

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.

Data-driven classification of ligand unbinding pathways

Studying the pathways of ligand-receptor binding is essential to understand the mechanism of target recognition by small molecules. The binding free energy and kinetics of protein-ligand complexes can be computed using molecular dynamics (MD) simulations, often in quantitative agreement with experiments. However, only a qualitative picture of the ligand binding/unbinding paths can be obtained through a conventional analysis of the MD trajectories. Besides, the higher degree of manual effort involved in analyzing pathways limits its applicability in large-scale drug discovery. Here, we address this limitation by introducing an automated approach for analyzing molecular transition paths with a particular focus on protein-ligand dissociation. Our method is based on the dynamic time-warping algorithm, originally designed for speech recognition. We accurately classified molecular trajectories using a very generic descriptor set of contacts or distances. Our approach outperforms manual classification by distinguishing between parallel dissociation channels, within the pathways identified by visual inspection. Most notably, we could compute exit-path-specific ligand-dissociation kinetics. The unbinding timescale along the fastest path agrees with the experimental residence time, providing a physical interpretation to our entirely data-driven protocol. In combination with appropriate enhanced sampling algorithms, this technique can be used for the initial exploration of ligand-dissociation pathways as well as for calculating path-specific thermodynamic and kinetic properties.

How Robust Is the Ligand Binding Transition State?

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

A deep encoder-decoder framework for identifying distinct ligand binding pathways

The pathway(s) that a ligand would adopt en route to its trajectory to the native pocket of the receptor protein act as a key determinant of its biological activity. While Molecular Dynamics (MD) simulations have emerged as the method of choice for modeling protein-ligand binding events, the high dimensional nature of the MD-derived trajectories often remains a barrier in the statistical elucidation of distinct ligand binding pathways due to the stochasticity inherent in the ligand's fluctuation in the solution and around the receptor. Here, we demonstrate that an autoencoder based deep neural network, trained using an objective input feature of a large matrix of residue-ligand distances, can efficiently produce an optimal low-dimensional latent space that stores necessary information on the ligand-binding event. In particular, for a system of L99A mutant of T4 lysozyme interacting with its native ligand, benzene, this deep encoder-decoder framework automatically identifies multiple distinct recognition pathways, without requiring user intervention. The intermediates involve the spatially discrete location of the ligand in different helices of the protein before its eventual recognition of native pose. The compressed subspace derived from the autoencoder provides a quantitatively accurate measure of the free energy and kinetics of ligand binding to the native pocket. The investigation also recommends that while a linear dimensional reduction technique, such as time-structured independent component analysis, can do a decent job of state-space decomposition in cases where the intermediates are long-lived, autoencoder is the method of choice in systems where transient, low-populated intermediates can lead to multiple ligand-binding pathways.

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.

Unraveling the Abnormal Molecular Mechanism of Suicide Inhibition of Cytochrome P450 3A4

Suicide inhibition of the CYP3A4 enzyme by a drug inactivates the enzyme in the drug biotransformation process and often shows safety concerns about the drug. Despite extensive experimental studies, the abnormal molecular mechanism of a suicide inhibitor that forms a covalent bond with the residue far away from the catalytically active center of CYP3A4 inactivating the enzyme remains elusive. Here, the authors used molecular simulation approaches to study in detail how diquinone methide (DQR), the metabolite product of raloxifene, unbinds from CYP3A4 and inactivates the enzyme at the atomistic level. The results clearly indicate that in one of the intermediate states formed in its unbinding process, DQR covalently binds to Cys239, a residue far away from the catalytically active center of CYP3A4, and hinders the substrate from entering or leaving the enzyme. This work therefore provides an unprecedented way of clarifying the abnormal mechanism of suicide inhibition of the CYP3A4 enzyme.

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.

Drug Discovery by Automated Adaptation of Chemical Structure and Identity

Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.

Markov State Study of Electrostatic Channeling within the Tricarboxylic Acid Cycle Supercomplex

The high efficiency of cascade reactions in supramolecular enzyme nanoassemblies, known as metabolons, has attracted substantial attention in various fields ranging from fundamental biochemistry and molecular biology to recent applications in biofuel cells, biosensors, and chemical synthesis. One reason for the high efficiency of metabolons is the structures formed by sequential enzymes that allow the direct transport of intermediates between consecutive active sites. The supercomplex of malate dehydrogenase (MDH) and citrate synthase (CS) is an ideal example of the controlled transport of intermediates via electrostatic channeling. Here, using a combination of molecular dynamics (MD) simulations and a Markov state model (MSM), we examined the transport process of the intermediate oxaloacetate (OAA) from MDH to CS. The MSM enables the identification of the dominant transport pathways of OAA from MDH to CS. Analysis of all pathways using a hub score approach reveals a small set of residues that control OAA transport. This set includes an arginine residue previously identified experimentally. MSM analysis of a mutated complex, where the identified arginine is replaced by alanine, led to a 2-fold decrease in transfer efficiency, also consistent with experimental results. This work provides a molecular-level understanding of the electrostatic channeling mechanism and will enable the further design of catalytic nanostructures utilizing electrostatic channeling.

Flow-regulated nucleation protrusion theory for collapsed polymers

The globular-stretch transition of a collapsed polymer in low strain rate elongational flow is studied using polymeric protrusion kinetics scaling laws and numerical simulation. Results demonstrate the influence of fluid flow on the occurrence probability of long-length thermally nucleated polymeric protrusions, which regulate collapsed polymer unfolding in low strain rate flows. Further, we estimate that the globular-stretch transition rate (k_{s}) in low strain rate (∈[over ̇]) elongational flows varies as k_{s}∼e^{-α∈[over ̇]^{-1}}. Results here reveal that the existing approach of neglecting the effects of fluid flow on thermally nucleated protrusions distribution is not valid for analyzing polymer unfolding behavior in low strain rate flows. Neglecting such an effect overestimates the constant α in the scaling law of transition rate (k_{s}∼e^{-α∈[over ̇]^{-1}}) by a factor of 2.

Energy penalties enhance flexible receptor docking in a model cavity

Protein flexibility remains a major challenge in library docking because of difficulties in sampling conformational ensembles with accurate probabilities. Here, we use the model cavity site of T4 lysozyme L99A to test flexible receptor docking with energy penalties from molecular dynamics (MD) simulations. Crystallography with larger and smaller ligands indicates that this cavity can adopt three major conformations: open, intermediate, and closed. Since smaller ligands typically bind better to the cavity site, we anticipate an energy penalty for the cavity opening. To estimate its magnitude, we calculate conformational preferences from MD simulations. We find that including a penalty term is essential for retrospective ligand enrichment; otherwise, high-energy states dominate the docking. We then prospectively docked a library of over 900,000 compounds for new molecules binding to each conformational state. Absent a penalty term, the open conformation dominated the docking results; inclusion of this term led to a balanced sampling of ligands against each state. High ranked molecules were experimentally tested by Tm upshift and X-ray crystallography. From 33 selected molecules, we identified 18 ligands and determined 13 crystal structures. Most interesting were those bound to the open cavity, where the buried site opens to bulk solvent. Here, highly unusual ligands for this cavity had been predicted, including large ligands with polar tails; these were confirmed both by binding and by crystallography. In docking, incorporating protein flexibility with thermodynamic weightings may thus access new ligand chemotypes. The MD approach to accessing and, crucially, weighting such alternative states may find general applicability.

Ligand unbinding mechanisms and kinetics for T4 lysozyme mutants from τRAMD simulations

The protein-ligand residence time, τ, influences molecular function in biological networks and has been recognized as an important determinant of drug efficacy. To predict τ, computational methods must overcome the problem that τ often exceeds the timescales accessible to conventional molecular dynamics (MD) simulation. Here, we apply the τ-Random Acceleration Molecular Dynamics (τRAMD) method to a set of kinetically characterized complexes of T4 lysozyme mutants with small, engineered binding cavities. τRAMD yields relative ligand dissociation rates in good accordance with experiments across this diverse set of complexes that differ with regard to measurement temperature, ligand identity, protein mutation and binding cavity. τRAMD thereby allows a comprehensive characterization of the ligand egress routes and determinants of τ. Although ligand dissociation by multiple egress routes is observed, we find that egress via the predominant route determines the value of τ. We also find that the presence of a greater number of metastable states along egress pathways leads to slower protein-ligand dissociation. These physical insights could be exploited in the rational optimization of the kinetic properties of drug candidates.

•

Relative residence times are computed for T4 lysozyme mutant-ligand complexes.

•

τ-Random Acceleration Molecular Dynamics provide efficient sampling of unbinding.

•

Computed dissociation rates show good agreement with all available measured values.

•

Ligand egress via the predominant route determines the value of the residence time.

•

The presence of metastable states along egress pathways slows down dissociation.

Predicting pathological von Willebrand factor unraveling in elongational flow

The globular-to-unraveled conformation transition of von Willebrand factor (vWF), a large polymeric glycoprotein in human blood plasma, is a crucial step in the process of clotting at sites of vascular injury. However, unraveling of vWF multimers in uninjured vasculature can lead to pathology (i.e., thrombus formation or degradation of vWF proteins by enzyme ADAMTS13, making them nonfunctional). To identify blood flow conditions that might induce pathological unraveling of vWF multimers, here we have computed the globular-to-unraveled transition rate of vWF multimers subjected to varying strain rate elongational flow by employing an enhanced sampling technique, the weighted ensemble method. Weighted ensemble sampling was employed instead of standard brute-force simulations because pathological blood flow conditions can induce undesired vWF unraveling on timescales potentially inaccessible to standard simulation methods. Results here indicate that brief but periodic exposure of vWF to the elongational flow of strain rate greater than or equal to 2500 s^-1 represents a source of possible pathology caused by the undesired unraveling of vWF multimers.

Pepsin-like aspartic proteases (PAPs) as model systems for combining biomolecular simulation with biophysical experiments

Pepsin-like aspartic proteases (PAPs) are a class of aspartic proteases which shares tremendous structural similarity with human pepsin. One of the key structural features of PAPs is the presence of a β-hairpin motif otherwise known as flap. The biological function of the PAPs is highly dependent on the conformational dynamics of the flap region. In apo PAPs, the conformational dynamics of the flap is dominated by the rotational degrees of freedom associated with χ1 and χ2 angles of conserved Tyr (or Phe in some cases). However it is plausible that dihedral order parameters associated with several other residues might play crucial roles in the conformational dynamics of apo PAPs. Due to their size, complexities associated with conformational dynamics and clinical significance (drug targets for malaria, Alzheimer's disease etc.), PAPs provide a challenging testing ground for computational and experimental methods focusing on understanding conformational dynamics and molecular recognition in biomolecules. The opening of the flap region is necessary to accommodate substrate/ligand in the active site of the PAPs. The BIG challenge is to gain atomistic details into how reversible ligand binding/unbinding (molecular recognition) affects the conformational dynamics. Recent reports of kinetics (K i, K d) and thermodynamic parameters (ΔH, TΔS, and ΔG) associated with macro-cyclic ligands bound to BACE1 (belongs to PAP family) provide a perfect challenge (how to deal with big ligands with multiple torsional angles and select optimum order parameters to study reversible ligand binding/unbinding) for computational methods to predict binding free energies and kinetics beyond typical test systems e.g. benzamide-trypsin. In this work, i reviewed several order parameters which were proposed to capture the conformational dynamics and molecular recognition in PAPs. I further highlighted how machine learning methods can be used as order parameters in the context of PAPs. I then proposed some open ideas and challenges in the context of molecular simulation and put forward my case on how biophysical experiments e.g. NMR, time-resolved FRET etc. can be used in conjunction with biomolecular simulation to gain complete atomistic insights into the conformational dynamics of PAPs.

Qualitative Prediction of Ligand Dissociation Kinetics from Focal Adhesion Kinase Using Steered Molecular Dynamics

Most early-stage drug discovery projects focus on equilibrium binding affinity to the target alongside selectivity and other pharmaceutical properties. Since many approved drugs have nonequilibrium binding characteristics, there has been increasing interest in optimizing binding kinetics early in the drug discovery process. As focal adhesion kinase (FAK) is an important drug target, we examine whether steered molecular dynamics (SMD) can be useful for identifying drug candidates with the desired drug-binding kinetics. In simulating the dissociation of 14 ligands from FAK, we find an empirical power–law relationship between the simulated time needed for ligand unbinding and the experimental rate constant for dissociation, with a strong correlation depending on the SMD force used. To improve predictions, we further develop regression models connecting experimental dissociation rate with various structural and energetic quantities derived from the simulations. These models can be used to predict dissociation rates from FAK for related compounds.

Molecular Dynamics Simulations in Drug Discovery and Pharmaceutical Development

Molecular dynamics (MD) simulations have become increasingly useful in the modern drug development process. In this review, we give a broad overview of the current application possibilities of MD in drug discovery and pharmaceutical development. Starting from the target validation step of the drug development process, we give several examples of how MD studies can give important insights into the dynamics and function of identified drug targets such as sirtuins, RAS proteins, or intrinsically disordered proteins. The role of MD in antibody design is also reviewed. In the lead discovery and lead optimization phases, MD facilitates the evaluation of the binding energetics and kinetics of the ligand-receptor interactions, therefore guiding the choice of the best candidate molecules for further development. The importance of considering the biological lipid bilayer environment in the MD simulations of membrane proteins is also discussed, using G-protein coupled receptors and ion channels as well as the drug-metabolizing cytochrome P450 enzymes as relevant examples. Lastly, we discuss the emerging role of MD simulations in facilitating the pharmaceutical formulation development of drugs and candidate drugs. Specifically, we look at how MD can be used in studying the crystalline and amorphous solids, the stability of amorphous drug or drug-polymer formulations, and drug solubility. Moreover, since nanoparticle drug formulations are of great interest in the field of drug delivery research, different applications of nano-particle simulations are also briefly summarized using multiple recent studies as examples. In the future, the role of MD simulations in facilitating the drug development process is likely to grow substantially with the increasing computer power and advancements in the development of force fields and enhanced MD methodologies.

Wepy: A Flexible Software Framework for Simulating Rare Events with Weighted Ensemble Resampling

Here, we introduce the open-source software framework wepy (https://github.com/ADicksonLab/wepy) which is a toolkit for running and analyzing weighted ensemble (WE) simulations. The wepy toolkit is in pure Python and as such is highly portable and extensible, making it an excellent platform to develop and use new WE resampling algorithms such as WExplore, REVO, and others while leveraging the entire Python ecosystem. In addition, wepy simplifies WE-specific analyses by defining out-of-core tree-like data structures using the cross-platform HDF5 file format. In this paper, we discuss the motivations and challenges for simulating rare events in biomolecular systems. As has previously been shown, high-dimensional WE resampling algorithms such as WExplore and REVO have been successful at these tasks, especially for rare events that are difficult to describe by one or two collective variables. We explain in detail how wepy facilitates implementation of these algorithms, as well as aids in analyzing the unique structure of WE simulation results. To explain how wepy and WE work in general, we describe the mathematical formalism of WE, an overview of the architecture of wepy, and provide code examples of how to construct, run, and analyze simulation results for a protein-ligand system (T4 Lysozyme in an implicit solvent). This paper is written with a variety of readers in mind, including (1) those curious about how to leverage WE rare-event simulations for their domain, (2) current WE users who want to begin using new high-dimensional resamplers such as WExplore and REVO, and (3) expert users who would like to prototype or implement their own algorithms that can be easily adopted by others.

Ranking of Ligand Binding Kinetics Using a Weighted Ensemble Approach and Comparison with a Multiscale Milestoning Approach

To improve lead optimization efforts in finding the right ligand, pharmaceutical industries need to know the ligand's binding kinetics, such as binding and unbinding rate constants, which often correlate with the ligand's efficacy in vivo. To predict binding kinetics efficiently, enhanced sampling methods, such as milestoning and the weighted ensemble (WE) method, have been used in molecular dynamics (MD) simulations of these systems. However, a comparison of these enhanced sampling methods in ranking ligands has not been done. Hence, a WE approach called the concurrent adaptive sampling (CAS) algorithm that uses MD simulations was used to rank seven ligands for β-cyclodextrin, a system in which a multiscale milestoning approach called simulation enabled estimation of kinetic rates (SEEKR) was also used, which uses both MD and Brownian dynamics simulations. Overall, the CAS algorithm can successfully rank ligands using the unbinding rate constant k_off values and binding free energy ΔG values, as SEEKR did, with reduced computational cost that is about the same as SEEKR. We compare the CAS algorithm simulations with different parameters and discuss the impact of parameters in ranking ligands and obtaining rate constant and binding free energy estimates. We also discuss similarities and differences and advantages and disadvantages of SEEKR and the CAS algorithm for future use.

Recent progress in molecular simulation methods for drug binding kinetics

Due to the contribution of drug-target binding kinetics to drug efficacy, there is a high level of interest in developing methods to predict drug-target binding kinetic parameters. During the review period, a wide range of enhanced sampling molecular dynamics simulation-based methods has been developed for computing drug-target binding kinetics and studying binding and unbinding mechanisms. Here, we assess the performance of these methods considering two benchmark systems in detail: mutant T4 lysozyme-ligand complexes and a large set of N-HSP90-inhibitor complexes. The results indicate that some of the simulation methods can already be usefully applied in drug discovery or lead optimization programs but that further studies on more high-quality experimental benchmark datasets are necessary to improve and validate computational methods.

Protein-ligand binding with the coarse-grained Martini model

The detailed understanding of the binding of small molecules to proteins is the key for the development of novel drugs or to increase the acceptance of substrates by enzymes. Nowadays, computer-aided design of protein–ligand binding is an important tool to accomplish this task. Current approaches typically rely on high-throughput docking essays or computationally expensive atomistic molecular dynamics simulations. Here, we present an approach to use the recently re-parametrized coarse-grained Martini model to perform unbiased millisecond sampling of protein–ligand interactions of small drug-like molecules. Remarkably, we achieve high accuracy without the need of any a priori knowledge of binding pockets or pathways. Our approach is applied to a range of systems from the well-characterized T4 lysozyme over members of the GPCR family and nuclear receptors to a variety of enzymes. The presented results open the way to high-throughput screening of ligand libraries or protein mutations using the coarse-grained Martini model.

Computer-aided design of protein-ligand binding is important for the development of novel drugs. Here authors present an approach to use the recently re-parametrized coarse-grained Martini model to perform unbiased millisecond sampling of protein-ligand binding interactions of small drug-like molecules.

Capturing Protein-Ligand Recognition Pathways in Coarse-Grained Simulation

Protein-ligand recognition is dynamic and complex. A key approach in deciphering the mechanism underlying the recognition process is to capture the kinetic process of the ligand in its act of binding to its designated protein cavity. Toward this end, ultralong all-atom molecular dynamics simulation has recently emerged as a popular method of choice because of its ability to record these events at high spatial and temporal resolution. However, success via this route comes at an exorbitant computational cost. Herein, we demonstrate that coarse-grained models of the protein, when systematically optimized to maintain its tertiary fold, can capture the complete process of spontaneous protein-ligand binding from bulk media to the cavity at crystallographic precision and within wall clock time that is orders of magnitude shorter than that of all-atom simulations. The exhaustive sampling of ligand exploration in protein and solvent, harnessed by coarse-grained simulation, leads to elucidation of new ligand recognition pathways and discovery of non-native binding poses.

Flexible Fitting of Small Molecules into Electron Microscopy Maps Using Molecular Dynamics Simulations with Neural Network Potentials

Despite significant advances in resolution, the potential for cryo-electron microscopy (EM) to be used in determining the structures of protein-drug complexes remains unrealized. Determination of accurate structures and coordination of bound ligands necessitates simultaneous fitting of the models into the density envelopes, exhaustive sampling of the ligand geometries, and, most importantly, concomitant rearrangements in the side chains to optimize the binding energy changes. In this article, we present a flexible-fitting pipeline where molecular dynamics flexible fitting (MDFF) is used to refine structures of protein-ligand complexes from 3 to 5 Å electron density data. Enhanced sampling is employed to explore the binding pocket rearrangements. To provide a model that can accurately describe the conformational dynamics of the chemically diverse set of small-molecule drugs inside MDFF, we use QM/MM and neural-network potential (NNP)/MM models of protein-ligand complexes, where the ligand is represented using the QM or NNP model, and the protein is represented using established molecular mechanical force fields (e.g., CHARMM). This pipeline offers structures commensurate to or better than recently submitted high-resolution cryo-EM or X-ray models, even when given medium to low-resolution data as input. The use of the NNPs makes the algorithm more robust to the choice of search models, offering a radius of convergence of 6.5 Å for ligand structure determination. The quality of the predicted structures was also judged by density functional theory calculations of ligand strain energy. This strain potential energy is found to systematically decrease with better fitting to density and improved ligand coordination, indicating correct binding interactions. A computationally inexpensive protocol for computing strain energy is reported as part of the model analysis protocol that monitors both the ligand fit as well as model quality.

From Brazil to Germany: Challenges and Advantages

Moving to a new country, with a different culture and a new environment, is not an easy decision. In this perspective, I present some reasons that made me, a Brazilian computational biochemist, move abroad to do postdoctoral research and some of the challenges I faced before and after moving.

In Silico Reoptimization of Binding Affinity and Drug-Resistance Circumvention Ability in Kinase Inhibitors: A Case Study with RL-45 and Src Kinase

A major bottleneck in the development of kinase inhibitors has been the onset of drug resistance around the gatekeeper residues of Src kinase. Although recent times have seen the reports of certain second-generation kinase inhibitors which are capable of bypassing the drug resistance by circumventing kinase mutation, their kinase-binding efficacy has remained considerably weaker than that of the classical adenosine 5'-triphosphate-competitive kinase inhibitors. Using a recently synthesized second-generation kinase inhibitor RL-45 as a template, the current work integrates fragment-based drug discovery and quantitative structure-activity relationship study with enhanced molecular dynamics simulation approaches, namely, metadynamics and replica exchange free-energy perturbation, and demonstrates how one can optimally redesign and assess novel Src kinase inhibitors, by minimal introduction of new functional moieties around template kinase inhibitor. Interestingly, unlike many synthetic kinase inhibitors, these in silico optimized small-molecule derivatives of RL-45 are found to be potentially capable of serving dual purposes, crucial for efficacy of an ideal kinase inhibitor: (a) circumventing gatekeeper residue mutation-related drug resistance in Src kinase, unlike many commercial kinase inhibitors and (b) manifesting superior resilience against unbinding from the kinase active site. The computer simulation, boosted by enhanced sampling techniques, further reveals that these designed inhibitors bring about key interactions in the form of significantly long-standing hydrogen bonds and hydrophobic pocket otherwise weak in the template bioactive kinase inhibitor, which enhance the binding efficacy of these newly designed ligands in the kinase-binding pocket.

Exhaustive Search of Ligand Binding Pathways via Volume-Based Metadynamics

Determining the complete set of ligands' binding-unbinding pathways is important for drug discovery and for rational interpretation of mutation data. Here we have developed a metadynamics-based technique that addresses this issue and allows estimating affinities in the presence of multiple escape pathways. Our approach is shown on a lysozyme T4 variant in complex with a benzene molecule. The calculated binding free energy is in agreement with experimental data. Remarkably, not only were we able to find all the previously identified ligand binding pathways, but also we identified three pathways previously not identified as such. These results were obtained at a small computational cost, making this approach valuable for practical applications, such as screening of small compound libraries.

Computational Estimation of Microsecond to Second Atomistic Folding Times

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 μs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 μs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Mechanisms for Benzene Dissociation through the Excited State of T4 Lysozyme L99A Mutant

The atomic-level mechanisms that coordinate ligand release from protein pockets are only known for a handful of proteins. Here, we report results from accelerated molecular dynamics simulations for benzene dissociation from the buried cavity of the T4 lysozyme Leu99Ala mutant (L99A). In these simulations, benzene is released through a previously characterized, sparsely populated room-temperature excited state of the mutant, explaining the coincidence for experimentally measured benzene off rate and apo protein slow-timescale NMR relaxation rates between ground and excited states. The path observed for benzene egress is a multistep ligand migration from the buried cavity to ultimate release through an opening between the F/G-, H-, and I-helices and requires a number of cooperative multiresidue and secondary-structure rearrangements within the C-terminal domain of L99A. These rearrangements are identical to those observed along the ground state to excited state transitions characterized by molecular dynamic simulations run on the Anton supercomputer. Analyses of the molecular properties of the residues lining the egress path suggest that protein surface electrostatic potential may play a role in the release mechanism. Simulations of wild-type T4 lysozyme also reveal that benzene-egress-associated dynamics in the L99A mutant are potentially exaggerations of the substrate-processivity-related dynamics of the wild type.

Kinetics of Ligand-Protein Dissociation from All-Atom Simulations: Are We There Yet?

Large parallel gains in the development of both computational resources and sampling methods have now made it possible to simulate dissociation events in ligand-protein complexes with all-atom resolution. Such encouraging progress, together with the inherent spatiotemporal resolution associated with molecular simulations, has left their use for investigating dissociation processes brimming with potential, both in rational drug design, where it can be an invaluable tool for determining the mechanistic driving forces behind dissociation rate constants, and in force-field development, where it can provide a catalog of transient molecular structures with which to refine force fields. Although much progress has been made in making force fields more accurate, reducing their error for transient structures along a transition path could yet prove to be a critical development helping to make kinetic predictions much more accurate. In what follows, we will provide a state-of-the-art compilation of the enhanced sampling methods based on molecular dynamics (MD) simulations used to investigate the kinetics and mechanisms of ligand-protein dissociation processes. Due to the time scales of such processes being slower than what is accessible using straightforward MD simulations, several ingenious schemes are being devised at a rapid rate to overcome this obstacle. Here we provide an up-to-date compendium of such methods and their achievements and shortcomings in extracting mechanistic insight into ligand-protein dissociation. We conclude with a critical and provocative appraisal attempting to answer the title of this Perspective.

Toward Achieving Efficient and Accurate Ligand-Protein Unbinding with Deep Learning and Molecular Dynamics through RAVE

In this work, we demonstrate how to leverage our recent iterative deep learning-all atom molecular dynamics (MD) technique "Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)" (Ribeiro, Bravo, Wang, Tiwary, J. Chem. Phys. 2018, 149, 072301) for investigating ligand-protein unbinding mechanisms and calculating absolute binding free energies, Δ G_b, when plagued with difficult to sample rare events. In order to do so, we introduce a simple but powerful extension to RAVE that allows learning a reaction coordinate expressed as a piecewise function that is linear over all intervals. Such an approach allows us to retain the physical interpretation of a RAVE-derived reaction coordinate while making the method more applicable to a wider range of complex biophysical problems. As we will demonstrate, using as our test-case the slow dissociation of benzene from the L99A variant of lysozyme, the RAVE extension led to observing an unbinding event in 100% of the independent all-atom MD simulations, all within 3-50 ns for a process that takes on an average close to few hundred milliseconds, which reflects a 7 orders of magnitude acceleration relative to straightforward MD. Furthermore, we will show that without the use of time-dependent biasing, clear back-and-forth movement between metastable intermediates was achieved during the various simulations, demonstrating the caliber of the RAVE-derived piecewise reaction coordinate and bias potential, which together drive efficient and accurate sampling of the ligand-protein dissociation event. Last, we report the results for Δ G_b, which via very short MD simulations, can form a strict lower-bound that is ∼2-3 kcal/mol off from experiments. We believe that RAVE, together with its multidimensional extension that we introduce here, will be a useful tool for simulating the slow unbinding process of practical ligand-protein complexes in an automated manner with minimal use of human intuition.

Atomic resolution mechanism of ligand binding to a solvent inaccessible cavity in T4 lysozyme

Ligand binding sites in proteins are often localized to deeply buried cavities, inaccessible to bulk solvent. Yet, in many cases binding of cognate ligands occurs rapidly. An intriguing system is presented by the L99A cavity mutant of T4 Lysozyme (T4L L99A) that rapidly binds benzene (~106 M-1s-1). Although the protein has long served as a model system for protein thermodynamics and crystal structures of both free and benzene-bound T4L L99A are available, the kinetic pathways by which benzene reaches its solvent-inaccessible binding cavity remain elusive. The current work, using extensive molecular dynamics simulation, achieves this by capturing the complete process of spontaneous recognition of benzene by T4L L99A at atomistic resolution. A series of multi-microsecond unbiased molecular dynamics simulation trajectories unequivocally reveal how benzene, starting in bulk solvent, diffuses to the protein and spontaneously reaches the solvent inaccessible cavity of T4L L99A. The simulated and high-resolution X-ray derived bound structures are in excellent agreement. A robust four-state Markov model, developed using cumulative 60 μs trajectories, identifies and quantifies multiple ligand binding pathways with low activation barriers. Interestingly, none of these identified binding pathways required large conformational changes for ligand access to the buried cavity. Rather, these involve transient but crucial opening of a channel to the cavity via subtle displacements in the positions of key helices (helix4/helix6, helix7/helix9) leading to rapid binding. Free energy simulations further elucidate that these channel-opening events would have been unfavorable in wild type T4L. Taken together and via integrating with results from experiments, these simulations provide unprecedented mechanistic insights into the complete ligand recognition process in a buried cavity. By illustrating the power of subtle helix movements in opening up multiple pathways for ligand access, this work offers an alternate view of ligand recognition in a solvent-inaccessible cavity, contrary to the common perception of a single dominant pathway for ligand binding.