Quantitatively characterizing the ligand binding mechanisms of choline binding protein using Markov state model analysis

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

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

Capturing the Effects of Single Atom Substitutions on the Inhibition Efficiency of Glycogen Synthase Kinase-3β Inhibitors via Markov State Modeling and Experiments

Small modifications in the chemical structure of ligands are known to dramatically change their ability to inhibit the activity of a protein. Unraveling the mechanisms that govern these dramatic changes requires scrutinizing the dynamics of protein-ligand binding and unbinding at the atomic level. As an exemplary case, we have studied Glycogen Synthase Kinase-3β (GSK-3β), a multifunctional kinase that has been implicated in a host of pathological processes. As such, there is a keen interest in identifying ligands that inhibit GSK-3β activity. One family of compounds that are highly selective and potent inhibitors of GSK-3β is exemplified by a molecule termed COB-187. COB-187 consists of a five-member heterocyclic ring with a thione at C2, a pyridine substituted methyl at N3, and a hydroxyl and phenyl at C4. We have studied the inhibition of GSK-3β by COB-187-related ligands that differ in a single heavy atom from each other (either in the location of nitrogen in their pyridine ring, or with the pyridine ring replaced by a phenyl ring), or in the length of the alkyl group joining the pyridine and the N3. The inhibition experiments show a large range of half-maximal inhibitory concentration (IC50) values from 10 nM to 10 μM, implying that these ligands exhibit vastly different propensities to inhibit GSK-3β. To explain these differences, we perform Markov State Modeling (MSM) using fully atomistic simulations. Our MSM results are in excellent agreement with the experiments in that they accurately capture differences in the binding propensities of the ligands. The simulations show that the binding propensities are related to the ligands' ability to attain a compact conformation where their two aromatic rings are spatially close. We rationalize this result by sampling numerous binding and unbinding events via funnel metadynamics simulations, which show that indeed while approaching the bound state, the ligands prefer to be in their compact conformation. We find that the presence of nitrogen in the aromatic ring increases the probability of attaining the compact conformation. Protein-ligand binding is understood to be dictated by the energetics of interactions and entropic factors, like the release of bound water from the binding pockets. This work shows that changes in the conformational distribution of ligands due to atom-level modifications in the structure play an important role in protein-ligand binding.

A Kinetic Transition Network Model Reveals the Diversity of Protein Dimer Formation Mechanisms

Protein homodimers have been classified as three-state or two-state dimers depending on whether a folded monomer forms before association, but the details of the folding-binding mechanisms are poorly understood. Kinetic transition networks of conformational states have provided insight into the folding mechanisms of monomeric proteins, but extending such a network to two protein chains is challenging as all the relative positions and orientations of the chains need to be included, greatly increasing the number of degrees of freedom. Here, we present a simplification of the problem by grouping all states of the two chains into two layers: a dissociated and an associated layer. We combined our two-layer approach with the Wako-Saito-Muñoz-Eaton method and used Transition Path Theory to investigate the dimer formation kinetics of eight homodimers. The analysis reveals a remarkable diversity of dimer formation mechanisms. Induced folding, conformational selection, and rigid docking are often simultaneously at work, and their contribution depends on the protein concentration. Pre-folded structural elements are always present at the moment of association, and asymmetric binding mechanisms are common. Our two-layer network approach can be combined with various methods that generate discrete states, yielding new insights into the kinetics and pathways of flexible binding processes.

Temperature Accelerated Sliced Sampling to Probe Ligand Dissociation from Protein

Modeling ligand unbinding in proteins to estimate the free energy of binding and probing the mechanism presents several challenges. They primarily pertain to the entropic bottlenecks resulting from protein and solvent conformations. While exploring the unbinding processes using enhanced sampling techniques, very long simulations are required to sample all of the conformational states as the system gets trapped in local free energy minima along transverse coordinates. Here, we demonstrate that temperature accelerated sliced sampling (TASS) is an ideal approach to overcome some of the difficulties faced by conventional sampling methods in studying ligand unbinding. Using TASS, we study the unbinding of avibactam inhibitor molecules from the Class C β-lactamase (CBL) active site. Extracting CBL-avibactam unbinding free energetics, unbinding pathways, and identifying critical interactions from the TASS simulations are demonstrated.

Disease mutations and phosphorylation alter the allosteric pathways involved in autoinhibition of protein phosphatase 2A

Mutations in protein phosphatase 2A (PP2A) are connected to intellectual disability and cancer. It has been hypothesized that these mutations might disrupt the autoinhibition and phosphorylation-induced activation of PP2A. Since they are located far from both the active and substrate binding sites, it is unclear how they exert their effect. We performed allosteric pathway analysis based on molecular dynamics simulations and combined it with biochemical experiments to investigate the autoinhibition of PP2A. In the wild type (WT), the C-arm of the regulatory subunit B56δ obstructs the active and substrate binding sites exerting a dual autoinhibition effect. We find that the disease mutant, E198K, severely weakens the allosteric pathways that stabilize the C-arm in the WT. Instead, the strongest allosteric pathways in E198K take a different route that promotes exposure of the substrate binding site. To facilitate the allosteric pathway analysis, we introduce a path clustering algorithm for lumping pathways into channels. We reveal remarkable similarities between the allosteric channels of E198K and those in phosphorylation-activated WT, suggesting that the autoinhibition can be alleviated through a conserved mechanism. In contrast, we find that another disease mutant, E200K, which is in spatial proximity of E198, does not repartition the allosteric pathways leading to the substrate binding site; however, it may still induce exposure of the active site. This finding agrees with our biochemical data, allowing us to predict the activity of PP2A with the phosphorylated B56δ and provide insight into how disease mutations in spatial proximity alter the enzymatic activity in surprisingly different mechanisms.

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.

A litmus test for classifying recognition mechanisms of transiently binding proteins

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.

Structural Rearrangement of the Serotonin Transporter Intracellular Gate Induced by Thr276 Phosphorylation

The reuptake of the neurotransmitter serotonin from the synaptic cleft by the serotonin transporter, SERT, is essential for proper neurological signaling. Biochemical studies have shown that Thr276 of transmembrane helix 5 is a site of PKG-mediated SERT phosphorylation, which has been proposed to shift the SERT conformational equilibria to promote inward-facing states, thus enhancing 5-HT transport. Recent structural and simulation studies have provided insights into the conformation transitions during substrate transport but have not shed light on SERT regulation via post-translational modifications. Using molecular dynamics simulations and Markov state models, we investigate how Thr276 phosphorylation impacts the SERT mechanism and its role in enhancing transporter stability and function. Our simulations show that Thr276 phosphorylation alters the hydrogen-bonding network involving residues on transmembrane helix 5. This in turn decreases the free energy barriers for SERT to transition to the inward-facing state, thus facilitating 5-HT import. The results provide atomistic insights into in vivo SERT regulation and can be extended to other pharmacologically important transporters in the solute carrier family.

Dissecting the Protein Dynamics Coupled Ligand Binding with Kinetic Models and Single-Molecule FRET

Protein-ligand interactions are crucial to many biological processes. Ligand binding and dissociation are the basic steps that allow proteins to function. Protein conformational dynamics have been shown to play important roles in ligand binding and dissociation. However, it is challenging to determine the ligand binding kinetics of dynamic proteins. Here, we undertook comprehensive single-molecule FRET (smFRET) measurements and kinetic model analysis to characterize the conformational dynamics coupled ligand binding of glutamine-binding protein (GlnBP). We showed that hinge and T118A mutations of GlnBP affect its conformational dynamics as well as the ligand binding affinity. Based on smFRET measurements, the kinetic model of ligand-GlnBP interactions was constructed. Using experimentally measured parameters, we solved the rate equations of the model and obtained the undetectable parameters of the model which allowed us to understand the ligand binding kinetics fully. Our results demonstrate that modulation of the conformational dynamics of GlnBP affects the ligand binding and dissociation rates. This study provides insights into the binding kinetics of ligands, which are related to the protein function itself.

Multiscale Approach for Computing Gated Ligand Binding from Molecular Dynamics and Brownian Dynamics Simulations

We develop an approach to characterize the effects of gating by a multiconformation protein consisting of macrostate conformations that are either accessible or inaccessible to ligand binding. We first construct a Markov state model of the apo-protein from atomistic molecular dynamics simulations from which we identify macrostates and their conformations, compute their relative macrostate populations and interchange kinetics, and structurally characterize them in terms of ligand accessibility. We insert the calculated first-order rate constants for conformational transitions into a multistate gating theory from which we derive a gating factor γ that quantifies the degree of conformational gating. Applied to HIV-1 protease, our approach yields a kinetic network of three accessible (semi-open, open, and wide-open) and two inaccessible (closed and a newly identified, "parted") macrostate conformations. The parted conformation sterically partitions the active site, suggesting a possible role in product release. We find that the binding kinetics of drugs and drug-like inhibitors to HIV-1 protease falls in the slow gating regime. However, because γ = 0.75, conformational gating only modestly slows ligand binding. Brownian dynamics simulations of the diffusional association of eight inhibitors to the protease─having a wide range of experimental association constants (∼10⁴-10¹⁰ M^-1 s^-1)─yields gated rate constants in the range of ∼0.5-5.7 × 10⁸ M^-1 s^-1. This indicates that, whereas the association rate of some inhibitors could be described by the model, for many inhibitors either subsequent conformational transitions or alternate binding mechanisms may be rate-limiting. For systems known to be modulated by conformational gating, the approach could be scaled computationally efficiently to screen association kinetics for a large number of ligands.

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.

The Role of Calcium in Regulating the Conformational Dynamics of d-Galactose/d-Glucose-Binding Protein Revealed by Markov State Model Analysis

The d-glucose/d-galactose-binding protein (GGBP) from Escherichia coli is a substrate-binding protein (SBP) associated with sugar transport and chemotaxis. It is also a calcium-binding protein, which makes it unique in the SBP family. However, the functional importance of Ca²⁺ binding is not fully understood. Here, the calcium-dependent properties of GGBP were explored by all-atom molecular dynamics simulations and Markov state model (MSM) analysis as well as single-molecule Förster resonance energy transfer (smFRET) measurements. In agreement with previous experimental studies, we observed the structure stabilization effect of Ca²⁺ binding on the C-terminal domain of GGBP, especially the Ca²⁺-binding site. Interestingly, the MSMs of calcium-depleted GGBP and calcium-bound GGBP (GGBP/Ca²⁺) demonstrate that Ca²⁺ greatly stabilizes the open conformation, and smFRET measurements confirmed this result. Further analysis reveals that Ca²⁺ binding disturbs the local hydrogen bonding interactions and the conformational dynamics of the hinge region, thereby weakening the long-range interdomain correlations to favor the open conformation. These results suggest an active regulatory role of Ca²⁺ binding in GGBP, which finely tunes the conformational distribution. The work sheds new light on the study of calcium-binding proteins in prokaryotes.

Markov State Models to Elucidate Ligand Binding Mechanism

Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

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.

Enhanced Jarzynski free energy calculations using weighted ensemble

The free energy of transitions between stable states is the key thermodynamic quantity that governs the relative probabilities of the forward and reverse reactions and the ratio of state probabilities at equilibrium. The binding free energy of a drug and its receptor is of particular interest, as it serves as an optimization function for drug design. Over the years, many computational methods have been developed to calculate binding free energies, and while many of these methods have a long history, issues such as convergence of free energy estimates and the projection of a binding process onto order parameters remain. Over 20 years ago, the Jarzynski equality was derived with the promise to calculate equilibrium free energies by measuring the work applied to short nonequilibrium trajectories. However, these calculations were found to be dominated by trajectories with low applied work that occur with extremely low probability. Here, we examine the combination of weighted ensemble algorithms with the Jarzynski equality. In this combined method, an ensemble of nonequilibrium trajectories are run in parallel, and cloning and merging operations are used to preferentially sample low-work trajectories that dominate the free energy calculations. Two additional methods are also examined: (i) a novel weighted ensemble resampler that samples trajectories directly according to their importance to the work of work and (ii) the diffusion Monte Carlo method using the applied work as the selection potential. We thoroughly examine both the accuracy and efficiency of unbinding free energy calculations for a series of model Lennard-Jones atom pairs with interaction strengths ranging from 2 kcal/mol to 20 kcal/mol. We find that weighted ensemble calculations can more efficiently determine accurate binding free energies, especially for deeper Lennard-Jones well depths.

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.

Ligand-bound glutamine binding protein assumes multiple metastable binding sites with different binding affinities

Protein dynamics plays key roles in ligand binding. However, the microscopic description of conformational dynamics-coupled ligand binding remains a challenge. In this study, we integrate molecular dynamics simulations, Markov state model (MSM) analysis and experimental methods to characterize the conformational dynamics of ligand-bound glutamine binding protein (GlnBP). We show that ligand-bound GlnBP has high conformational flexibility and additional metastable binding sites, presenting a more complex energy landscape than the scenario in the absence of ligand. The diverse conformations of GlnBP demonstrate different binding affinities and entail complex transition kinetics, implicating a concerted ligand binding mechanism. Single molecule fluorescence resonance energy transfer measurements and mutagenesis experiments are performed to validate our MSM-derived structure ensemble as well as the binding mechanism. Collectively, our study provides deeper insights into the protein dynamics-coupled ligand binding, revealing an intricate regulatory network underlying the apparent binding affinity.

Zhang, Wu, Feng et al. show that ligand-bound glutamine binding protein assumes multiple metastable binding sites, presenting a more dynamic energy landscape than its ligand-free form. This study provides insights into the ligand-binding mechanisms coupled with protein dynamics that underly the apparent binding affinity.

On Calculating Free Energy Differences Using Ensembles of Transition Paths

The free energy of a process is the fundamental quantity that determines its spontaneity or propensity at a given temperature. In particular, the binding free energy of a drug candidate to its biomolecular target is used as an objective quantity in drug design. Recently, binding kinetics—rates of association (k_on) and dissociation (k_off)—have also demonstrated utility for their ability to predict efficacy and in some cases have been shown to be more predictive than the binding free energy alone. Some methods exist to calculate binding kinetics from molecular simulations, although these are typically more difficult to calculate than the binding affinity as they depend on details of the transition path ensemble. Assessing these rate constants can be difficult, due to uncertainty in the definition of the bound and unbound states, large error bars and the lack of experimental data. As an additional consistency check, rate constants from simulation can be used to calculate free energies (using the log of their ratio) which can then be compared to free energies obtained experimentally or using alchemical free energy perturbation. However, in this calculation it is not straightforward to account for common, practical details such as the finite simulation volume or the particular definition of the “bound” and “unbound” states. Here we derive a set of correction terms that can be applied to calculations of binding free energies using full reactive trajectories. We apply these correction terms to revisit the calculation of binding free energies from rate constants for a host-guest system that was part of a blind prediction challenge, where significant deviations were observed between free energies calculated with rate ratios and those calculated from alchemical perturbation. The correction terms combine to significantly decrease the error with respect to computational benchmarks, from 3.4 to 0.76 kcal/mol. Although these terms were derived with weighted ensemble simulations in mind, some of the correction terms are generally applicable to free energies calculated using physical pathways via methods such as Markov state modeling, metadynamics, milestoning, or umbrella sampling.

To probe the binding pathway of a selective compound (D089-0563) to c-MYC Pu24 G-quadruplex using free ligand binding simulations and Markov state model analysis

D089-0563 is a highly promising anti-cancer compound that selectively binds the transcription-silencing G-quadruplex element (Pu27) at the promoter region of the human c-MYC oncogene; however, its binding mechanism remains elusive.

Encounter complexes and hidden poses of kinase-inhibitor binding on the free-energy landscape

Modern drug discovery increasingly focuses on the drug-target binding kinetics which depend on drug (un)binding pathways. The conventional molecular dynamics simulation can observe only a few binding events even using the fastest supercomputer. Here, we develop 2D gREST/REUS simulation with enhanced flexibility of the ligand and the protein binding site. Simulation (43 μs in total) applied to an inhibitor binding to c-Src kinase covers 100 binding and unbinding events. On the statistically converged free-energy landscapes, we succeed in predicting the X-ray binding structure, including water positions. Furthermore, we characterize hidden semibound poses and transient encounter complexes on the free-energy landscapes. Regulatory residues distant from the catalytic core are responsible for the initial inhibitor uptake and regulation of subsequent bindings, which was unresolved by experiments. Stabilizing/blocking of either the semibound poses or the encounter complexes can be an effective strategy to optimize drug-target residence time.

Dynamic graphical models of molecular kinetics

Most current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be represented by a single global state (e.g., a Markov state in a Markov state model [MSM]). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small- to medium-sized proteins. However, this approach breaks down in frustrated systems and in large protein assemblies, where the number of global metastable states may grow exponentially with the system size. To address this problem, we here introduce dynamic graphical models (DGMs) that describe molecules as assemblies of coupled subsystems, akin to how spins interact in the Ising model. The change of each subsystem state is only governed by the states of itself and its neighbors. DGMs require fewer parameters than MSMs or other global state models; in particular, we do not need to observe all global system configurations to characterize them. Therefore, DGMs can predict previously unobserved molecular configurations. As a proof of concept, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.

Simulations of the regulatory ACT domain of human phenylalanine hydroxylase (PAH) unveil its mechanism of phenylalanine binding

Phenylalanine hydroxylase (PAH) regulates phenylalanine (Phe) levels in mammals to prevent neurotoxicity resulting from high Phe concentrations as observed in genetic disorders leading to hyperphenylalaninemia and phenylketonuria. PAH senses elevated Phe concentrations by transient allosteric Phe binding to a protein-protein interface between ACT domains of different subunits in a PAH tetramer. This interface is present in an activated PAH (A-PAH) tetramer and absent in a resting-state PAH (RS-PAH) tetramer. To investigate this allosteric sensing mechanism, here we used the GROMACS molecular dynamics simulation suite on the Folding@home computing platform to perform extensive molecular simulations and Markov state model (MSM) analysis of Phe binding to ACT domain dimers. These simulations strongly implicated a conformational selection mechanism for Phe association with ACT domain dimers and revealed protein motions that act as a gating mechanism for Phe binding. The MSMs also illuminate a highly mobile hairpin loop, consistent with experimental findings also presented here that the PAH variant L72W does not shift the PAH structural equilibrium toward the activated state. Finally, simulations of ACT domain monomers are presented, in which spontaneous transitions between resting-state and activated conformations are observed, also consistent with a mechanism of conformational selection. These mechanistic details provide detailed insight into the regulation of PAH activation and provide testable hypotheses for the development of new allosteric effectors to correct structural and functional defects in PAH.

Improving the productivity of monodisperse polyhedral cages by the rational design of kinetic self-assembly pathways

Hollow polyhedral cages hold great potential for application in nanotechnological and biomedical fields. Understanding the formation mechanism of these self-assembled structures could provide guidance for the rational design of the desired polyhedral cages. Here, by constructing kinetic network models from extensive coarse-grained molecular dynamics simulations, we elucidated the formation mechanism of the dodecahedral cage, which is formed by the self-assembly of patchy particles. We found that the dodecahedral cage is formed through increasing the aggregate size followed by structure rearrangement. Based on this mechanistic understanding, we improved the productivity of the dodecahedral cage through the rational design of the patch arrangement of patchy particles, which promotes the structural rearrangement process. Our results demonstrate that it should be a feasible strategy to achieve the rational design of the desired nanostructures via the kinetic analysis. We anticipate that this methodology could be extended to other self-assembly systems for the fabrication of functional nanomaterials.

Harnessing complexity in molecular self-assembly using computer simulations

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit time scale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule has never been formally proved. In this work, we present analytical results for the slowest time scale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit time scale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit time scale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit time scale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest time scales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.

Bridging Microscopic and Macroscopic Mechanisms of p53-MDM2 Binding with Kinetic Network Models

Under normal cellular conditions, the tumor suppressor protein p53 is kept at low levels in part due to ubiquitination by MDM2, a process initiated by binding of MDM2 to the intrinsically disordered transactivation domain (TAD) of p53. Many experimental and simulation studies suggest that disordered domains such as p53 TAD bind their targets nonspecifically before folding to a tightly associated conformation, but the microscopic details are unclear. Toward a detailed prediction of binding mechanisms, pathways, and rates, we have performed large-scale unbiased all-atom simulations of p53-MDM2 binding. Markov state models (MSMs) constructed from the trajectory data predict p53 TAD binding pathways and on-rates in good agreement with experiment. The MSM reveals that two key bound intermediates, each with a nonnative arrangement of hydrophobic residues in the MDM2 binding cleft, control the overall on-rate. Using microscopic rate information from the MSM, we parameterize a simple four-state kinetic model to 1) determine that induced-fit pathways dominate the binding flux over a large range of concentrations, and 2) predict how modulation of residual p53 helicity affects binding, in good agreement with experiment. These results suggest new ways in which microscopic models of peptide binding, coupled with simple few-state binding flux models, can be used to understand biological function in physiological contexts.

The Isomeric Preference of an Atypical Dopamine Transporter Inhibitor Contributes to Its Selection of the Transporter Conformation

Cocaine, a widely abused psychostimulant, inhibits the dopamine transporter (DAT) by trapping the protein in an outward-open conformation, whereas atypical DAT inhibitors such as benztropine have low abuse liability and prefer less outward-open conformations. Here, we use a spectrum of computational modeling and simulation approaches to obtain the underlying molecular mechanism in atomistic detail. Interestingly, our quantum mechanical calculations and molecular dynamics (MD) simulations suggest that a benztropine derivative JHW007 prefers a different stereoisomeric conformation of tropane in binding to DAT compared to that of a cocaine derivative, CFT. To further investigate the different inhibition mechanisms of DAT, we carried out MD simulations in combination with Markov state modeling analysis of wild-type and Y156F DAT in the absence of any ligand or the presence of CFT or JHW007. Our results indicate that the Y156F mutation and CFT shift the conformational equilibrium toward an outward-open conformation, whereas JHW007 prefers an inward-occluded conformation. Our findings reveal the mechanistic details of DAT inhibition by JHW007 at the atomistic level, which provide clues for rational design of atypical inhibitors.

Chinese Herbal Medicine Meets Biological Networks of Complex Diseases: A Computational Perspective

With the rapid development of cheminformatics, computational biology, and systems biology, great progress has been made recently in the computational research of Chinese herbal medicine with in-depth understanding towards pharmacognosy. This paper summarized these studies in the aspects of computational methods, traditional Chinese medicine (TCM) compound databases, and TCM network pharmacology. Furthermore, we chose arachidonic acid metabolic network as a case study to demonstrate the regulatory function of herbal medicine in the treatment of inflammation at network level. Finally, a computational workflow for the network-based TCM study, derived from our previous successful applications, was proposed.

Evaluation of Ochratoxin Recognition by Peptides Using Explicit Solvent Molecular Dynamics

Biosensing platforms based on peptide recognition provide a cost-effective and stable alternative to antibody-based capture and discrimination of ochratoxin-A (OTA) vs. ochratoxin-B (OTB) in monitoring bioassays. Attempts to engineer peptides with improved recognition efficacy require thorough structural and thermodynamic characterization of the binding-competent conformations. Classical molecular dynamics (MD) approaches alone do not provide a thorough assessment of a peptide's recognition efficacy. In this study, in-solution binding properties of four different peptides, a hexamer (SNLHPK), an octamer (CSIVEDGK), NFO4 (VYMNRKYYKCCK), and a 13-mer (GPAGIDGPAGIRC), which were previously generated for OTA-specific recognition, were evaluated using an advanced MD simulation approach involving accelerated configurational search and predictive modeling. Peptide configurations relevant to ochratoxin binding were initially generated using biased exchange metadynamics and the dynamic properties associated with the in-solution peptide-ochratoxin binding were derived from Markov State Models. Among the various peptides, NFO4 shows superior in-solution OTA sensing and also shows superior selectivity for OTA vs. OTB due to the lower penalty associated with solvating its bound complex. Advanced MD approaches provide structural and energetic insights critical to the hapten-specific recognition to aid the engineering of peptides with better sensing efficacies.

Estimation of kinetic and thermodynamic ligand-binding parameters using computational strategies

Kinetic and thermodynamic ligand–protein binding parameters are gaining growing importance as key information to consider in drug discovery. The determination of the molecular structures, using particularly x-ray and NMR techniques, is crucial for understanding how a ligand recognizes its target in the final binding complex. However, for a better understanding of the recognition processes, experimental studies of ligand–protein interactions are needed. Even though several techniques can be used to investigate both thermodynamic and kinetic profiles for a ligand–protein complex, these procedures are very often laborious, time consuming and expensive. In the last 10 years, computational approaches have enormous potential in providing insights into each of the above effects and in parsing their contributions to the changes in both kinetic and thermodynamic binding parameters. The main purpose of this review is to summarize the state of the art of computational strategies for estimating the kinetic and thermodynamic parameters of a ligand–protein binding.

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

In heme proteins, the efficient transport of ligands such as NO or O₂ to the binding site is achieved via ligand migration networks. A quantitative assessment of ligand diffusion in these networks is thus essential for a better understanding of the function of these proteins. For this, Xe migration in truncated hemoglobin N (trHbN) of Mycobacterium Tuberculosis was studied using molecular dynamics simulations. Transitions between pockets of the migration network and intra-pocket relaxation occur on similar time scales (10 ps and 20 ps), consistent with low free energy barriers (1-2 kcal/mol). Depending on the pocket from where Xe enters a particular transition, the conformation of the side chains lining the transition region differs which highlights the coupling between ligand and protein degrees of freedom. Furthermore, comparison of transition probabilities shows that Xe migration in trHbN is a non-Markovian process. Memory effects arise due to protein rearrangements and coupled dynamics as Xe moves through it.

Binding and transport of ligands in proteins is essential, in particular in globular proteins which often exhibit internal cavities. In truncated Hemoglobin N (trHbN) these cavities are arranged as a network with particular connectivities. The present work supports the notion that ligand diffusion in trHbN is an active process and coupled to the protein dynamics. Furthermore, transition probabilities between neighboring pockets depend on the location from where the ligand entered the transition, which is typical for non-Markovian processes. Hence, ligand migration in trHbN exhibits memory effects due to dynamical coupling between the protein and ligand motion.

Rate Constants and Mechanisms of Protein-Ligand Binding

Whereas protein-ligand binding affinities have long-established prominence, binding rate constants and binding mechanisms have gained increasing attention in recent years. Both new computational methods and new experimental techniques have been developed to characterize the latter properties. It is now realized that binding mechanisms, like binding rate constants, can and should be quantitatively determined. In this review, we summarize studies and synthesize ideas on several topics in the hope of providing a coherent picture of and physical insight into binding kinetics. The topics include microscopic formulation of the kinetic problem and its reduction to simple rate equations; computation of binding rate constants; quantitative determination of binding mechanisms; and elucidation of physical factors that control binding rate constants and mechanisms.

Protein-ligand (un)binding kinetics as a new paradigm for drug discovery at the crossroad between experiments and modelling

In the last three decades, protein and nucleic acid structure determination and comprehension of the mechanisms, leading to their physiological and pathological functions, have become a cornerstone of biomedical sciences. A deep understanding of the principles governing the fates of cells and tissue at the molecular level has been gained over the years, offering a solid basis for the rational design of drugs aimed at the pharmacological treatment of numerous diseases. Historically, affinity indicators (i.e. Kd and IC50/EC50) have been assumed to be valid indicators of the in vivo efficacy of a drug. However, recent studies pointed out that the kinetics of the drug-receptor binding process could be as important or even more important than affinity in determining the drug efficacy. This eventually led to a growing interest in the characterisation and prediction of the rate constants of protein-ligand association and dissociation. For instance, a drug with a longer residence time can kinetically select a given receptor over another, even if the affinity for both receptors is comparable, thus increasing its therapeutic index. Therefore, understanding the molecular features underlying binding and unbinding processes is of central interest towards the rational control of drug binding kinetics. In this review, we report the theoretical framework behind protein-ligand association and highlight the latest advances in the experimental and computational approaches exploited to investigate the binding kinetics.

Elucidating Mechanisms of Molecular Recognition Between Human Argonaute and miRNA Using Computational Approaches

MicroRNA (miRNA) and Argonaute (AGO) protein together form the RNA-induced silencing complex (RISC) that plays an essential role in the regulation of gene expression. Elucidating the underlying mechanism of AGO-miRNA recognition is thus of great importance not only for the in-depth understanding of miRNA function but also for inspiring new drugs targeting miRNAs. In this chapter we introduce a combined computational approach of molecular dynamics (MD) simulations, Markov state models (MSMs), and protein-RNA docking to investigate AGO-miRNA recognition. Constructed from MD simulations, MSMs can elucidate the conformational dynamics of AGO at biologically relevant timescales. Protein-RNA docking can then efficiently identify the AGO conformations that are geometrically accessible to miRNA. Using our recent work on human AGO2 as an example, we explain the rationale and the workflow of our method in details. This combined approach holds great promise to complement experiments in unraveling the mechanisms of molecular recognition between large, flexible, and complex biomolecules.

Adaptive partitioning by local density-peaks: An efficient density-based clustering algorithm for analyzing molecular dynamics trajectories

We present an efficient density-based adaptive-resolution clustering method APLoD for analyzing large-scale molecular dynamics (MD) trajectories. APLoD performs the k-nearest-neighbors search to estimate the density of MD conformations in a local fashion, which can group MD conformations in the same high-density region into a cluster. APLoD greatly improves the popular density peaks algorithm by reducing the running time and the memory usage by 2-3 orders of magnitude for systems ranging from alanine dipeptide to a 370-residue Maltose-binding protein. In addition, we demonstrate that APLoD can produce clusters with various sizes that are adaptive to the underlying density (i.e., larger clusters at low-density regions, while smaller clusters at high-density regions), which is a clear advantage over other popular clustering algorithms including k-centers and k-medoids. We anticipate that APLoD can be widely applied to split ultra-large MD datasets containing millions of conformations for subsequent construction of Markov State Models. © 2016 Wiley Periodicals, Inc.

Understanding the core of RNA interference: The dynamic aspects of Argonaute-mediated processes

At the core of RNA interference, the Argonaute proteins (Ago) load and utilize small guide nucleic acids to silence mRNAs or cleave foreign nucleic acids in a sequence specific manner. In recent years, based on extensive structural studies of Ago and its interaction with the nucleic acids, considerable progress has been made to reveal the dynamic aspects of various Ago-mediated processes. Here we review these novel insights into the guide-strand loading, duplex unwinding, and effects of seed mismatch, with a focus on two representative Agos, the human Ago 2 (hAgo2) and the bacterial Thermus thermophilus Ago (TtAgo). In particular, comprehensive molecular simulation studies revealed that although sharing similar overall structures, the two Agos have vastly different conformational landscapes and guide-strand loading mechanisms because of the distinct rigidity of their L1-PAZ hinge. Given the central role of the PAZ motions in regulating the exposure of the nucleic acid binding channel, these findings exemplify the importance of protein motions in distinguishing the overlapping, yet distinct, mechanisms of Ago-mediated processes in different organisms.

Conformational Heterogeneity in the Michaelis Complex of Lactate Dehydrogenase: An Analysis of Vibrational Spectroscopy Using Markov and Hidden Markov Models

Lactate dehydrogenase (LDH) catalyzes the interconversion of pyruvate and lactate. Recent isotope-edited IR spectroscopy suggests that conformational heterogeneity exists within the Michaelis complex of LDH, and this heterogeneity affects the propensity toward the on-enzyme chemical step for each Michaelis substate. By combining molecular dynamics simulations with Markov and hidden Markov models, we obtained a detailed kinetic network of the substates of the Michaelis complex of LDH. The ensemble-average electric fields exerted onto the vibrational probe were calculated to provide a direct comparison with the vibrational spectroscopy. Structural features of the Michaelis substates were also analyzed on atomistic scales. Our work not only clearly demonstrates the conformational heterogeneity in the Michaelis complex of LDH and its coupling to the reactivities of the substates, but it also suggests a methodology to simultaneously resolve kinetics and structures on atomistic scales, which can be directly compared with the vibrational spectroscopy.

Elucidation of the Dynamics of Transcription Elongation by RNA Polymerase II using Kinetic Network Models

RNA polymerase II (Pol II) is an essential enzyme that catalyzes transcription with high efficiency and fidelity in eukaryotic cells. During transcription elongation, Pol II catalyzes the nucleotide addition cycle (NAC) to synthesize mRNA using DNA as the template. The transitions between the states of the NAC require conformational changes of both the protein and nucleotides. Although X-ray structures are available for most of these states, the dynamics of the transitions between states are largely unknown. Molecular dynamics (MD) simulations can predict structure-based molecular details and shed light on the mechanisms of these dynamic transitions. However, the employment of MD simulations on a macromolecule (tens to hundreds of nanoseconds) such as Pol II is challenging due to the difficulty of reaching biologically relevant timescales (tens of microseconds or even longer). For this challenge to be overcome, kinetic network models (KNMs), such as Markov State Models (MSMs), have become a popular approach to access long-timescale conformational changes using many short MD simulations. We describe here our application of KNMs to characterize the molecular mechanisms of the NAC of Pol II. First, we introduce the general background of MSMs and further explain procedures for the construction and validation of MSMs by providing some technical details. Next, we review our previous studies in which we applied MSMs to investigate the individual steps of the NAC, including translocation and pyrophosphate ion release. In particular, we describe in detail how we prepared the initial conformations of Pol II elongation complex, performed MD simulations, extracted MD conformations to construct MSMs, and further validated them. We also summarize our major findings on molecular mechanisms of Pol II elongation based on these MSMs. In addition, we have included discussions regarding various key points and challenges for applications of MSMs to systems as large as the Pol II elongation complex. Finally, to study the overall NAC, we combine the individual steps of the NAC into a five-state KNM based on a nonbranched Brownian ratchet scheme to explain the single-molecule optical tweezers experimental data. The studies complement experimental observations and provide molecular mechanisms for the transcription elongation cycle. In the long term, incorporation of sequence-dependent kinetic parameters into KNMs has great potential for identifying error-prone sequences and predicting transcription dynamics in genome-wide transcriptomes.

Dynamic Modelling Reveals 'Hotspots' on the Pathway to Enzyme-Substrate Complex Formation

Dihydrodipicolinate synthase (DHDPS) catalyzes the first committed step in the diaminopimelate pathway of bacteria, yielding amino acids required for cell wall and protein biosyntheses. The essentiality of the enzyme to bacteria, coupled with its absence in humans, validates DHDPS as an antibacterial drug target. Conventional drug design efforts have thus far been unsuccessful in identifying potent DHDPS inhibitors. Here, we make use of contemporary molecular dynamics simulation and Markov state models to explore the interactions between DHDPS from the human pathogen Staphylococcus aureus and its cognate substrate, pyruvate. Our simulations recover the crystallographic DHDPS-pyruvate complex without a priori knowledge of the final bound structure. The highly conserved residue Arg140 was found to have a pivotal role in coordinating the entry of pyruvate into the active site from bulk solvent, consistent with previous kinetic reports, indicating an indirect role for the residue in DHDPS catalysis. A metastable binding intermediate characterized by multiple points of intermolecular interaction between pyruvate and key DHDPS residue Arg140 was found to be a highly conserved feature of the binding trajectory when comparing alternative binding pathways. By means of umbrella sampling we show that these binding intermediates are thermodynamically metastable, consistent with both the available experimental data and the substrate binding model presented in this study. Our results provide insight into an important enzyme-substrate interaction in atomistic detail that offers the potential to be exploited for the discovery of more effective DHDPS inhibitors and, in a broader sense, dynamic protein-drug interactions.

Interactions between proteins and ligands underpin many important biological processes, such as binding of substrates to their cognate enzymes in the process of catalysis. These interactions are complex, often requiring several intermediate steps to fully transition into the bound state. Here, we have used computational simulation to study binding of pyruvate to Dihydrodipicolinate synthase (DHDPS), an enzyme in the bacterial diaminopimelate pathway. In bacteria, such as the human pathogen S. aureus, DHDPS functions to make building blocks necessary for protein and bacterial cell wall biosyntheses. As the enzyme is absent in humans, yet essential for bacterial growth, DHDPS is a valid target for broad-range antibiotics. However, known DHDPS inhibitors show poor potency. One avenue that has not yet been taken into consideration for inhibitor design is the dynamics of DHDPS’s interaction with its reaction substrates (e.g. pyruvate). Using molecular dynamics simulation, we find that pyruvate binding to DHDPS must pass through a transition intermediate ‘hotspot’ in which the substrate is held in place by a dense network of noncovalent bonds. Given that many of the protein residues involved in this interaction are also shared by DHDPS from many pathogenic bacteria, this binding intermediate ‘hotspot’ may help in development of better broad-range DHDPS inhibitors.