Mechanisms of protein-ligand association and its modulation by protein mutations

Dynamics of receptor activation by agonists

How do agonists turn on receptors? The model system we have used to address this question is the adult-type skeletal muscle nicotinic acetylcholine receptor. This ligand-gated ion channel has two orthosteric sites (for neurotransmitters) in the extracellular domain linked to an allosteric site (a gate) in the transmembrane domain. The goal of this perspective is to summarize how measurements of agonist binding energy reveal the dynamics of the neurotransmitter sites and the fundamental link between binding and gating.

Diffusion-Controlled Reactions: An Overview

We review the milestones in the century-long development of the theory of diffusion-controlled reactions. Starting from the seminal work by von Smoluchowski, who recognized the importance of diffusion in chemical reactions, we discuss perfect and imperfect surface reactions, their microscopic origins, and the underlying mathematical framework. Single-molecule reaction schemes, anomalous bulk diffusions, reversible binding/unbinding kinetics, and many other extensions are presented. An alternative encounter-based approach to diffusion-controlled reactions is introduced, with emphasis on its advantages and potential applications. Some open problems and future perspectives are outlined.

Agonist efficiency links binding and gating in a nicotinic receptor

Receptors signal by switching between resting (C) and active (O) shapes ('gating') under the influence of agonists. The receptor's maximum response depends on the difference in agonist binding energy, O minus C. In nicotinic receptors, efficiency (η) represents the fraction of agonist binding energy applied to a local rearrangement (an induced fit) that initiates gating. In this receptor, free energy changes in gating and binding can be interchanged by the conversion factor η. Efficiencies estimated from concentration-response curves (23 agonists, 53 mutations) sort into five discrete classes (%): 0.56 (17), 0.51(32), 0.45(13), 0.41(26), and 0.31(12), implying that there are 5 C versus O binding site structural pairs. Within each class efficacy and affinity are corelated linearly, but multiple classes hide this relationship. η unites agonist binding with receptor gating and calibrates one link in a chain of coupled domain rearrangements that comprises the allosteric transition of the protein.

Homology Modeling, de Novo Design of Ligands, and Molecular Docking Identify Potential Inhibitors of Leishmania donovani 24-Sterol Methyltransferase

The therapeutic challenges pertaining to leishmaniasis due to reported chemoresistance and toxicity necessitate the need to explore novel pathways to identify plausible inhibitory molecules. Leishmania donovani 24-sterol methyltransferase (LdSMT) is vital for the synthesis of ergosterols, the main constituents of Leishmania cellular membranes. So far, mammals have not been shown to possess SMT or ergosterols, making the pathway a prime candidate for drug discovery. The structural model of LdSMT was elucidated using homology modeling to identify potential novel 24-SMT inhibitors via virtual screening, scaffold hopping, and de-novo fragment-based design. Altogether, six potential novel inhibitors were identified with binding energies ranging from −7.0 to −8.4 kcal/mol with e-LEA3D using 22,26-azasterol and S1–S4 obtained from scaffold hopping via the ChEMBL, DrugBank, PubChem, ChemSpider, and ZINC15 databases. These ligands showed comparable binding energy to 22,26-azasterol (−7.6 kcal/mol), the main inhibitor of LdSMT. Moreover, all the compounds had plausible ligand efficiency-dependent lipophilicity (LELP) scores above 3. The binding mechanism identified Tyr92 to be critical for binding, and this was corroborated via molecular dynamics simulations and molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) calculations. The ligand A1 was predicted to possess antileishmanial properties with a probability of activity (Pa) of 0.362 and a probability of inactivity (Pi) of 0.066, while A5 and A6 possessed dermatological properties with Pa values of 0.205 and 0.249 and Pi values of 0.162 and 0.120, respectively. Structural similarity search via DrugBank identified vabicaserin, daledalin, zanapezil, imipramine, and cefradine with antileishmanial properties suggesting that the de-novo compounds could be explored as potential antileishmanial agents.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules

Finding low dimensional representation of data from long-timescale trajectories of biomolecular processes such as protein-folding or ligand-receptor binding is of fundamental importance and kinetic models such as Markov modeling have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and linear dynamical model in an end-to-end manner. VAMPNet is based on variational approach to Markov processes (VAMP) and relies on neural networks to learn the coarse-grained dynamics. In this contribution, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint which is used in the VAMPNet to generate a coarse-grained representation. This type of molecular representation results in a higher resolution and more interpretable Markov model than the standard VAMPNet enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Impact of crowded environments on binding between protein and single-stranded DNA

The concept of Molecular Crowding depicts the high density of diverse molecules present in the cellular interior. Here, we determine the impact of low molecular weight and larger molecules on binding capacity of single-stranded DNA (ssDNA) to the cold shock protein B (CspB). Whereas structural features of ssDNA-bound CspB are fully conserved in crowded environments as probed by high-resolution NMR spectroscopy, intrinsic fluorescence quenching experiments reveal subtle changes in equilibrium affinity. Kinetic stopped-flow data showed that DNA-to-protein association is significantly retarded independent of choice of the molecule that is added to the solution, but dissociation depends in a nontrivial way on its size and chemical characteristics. Thus, for this DNA-protein interaction, excluded volume effect does not play the dominant role but instead observed effects are dictated by the chemical properties of the crowder. We propose that surrounding molecules are capable of specific modification of the protein's hydration shell via soft interactions that, in turn, tune protein-ligand binding dynamics and affinity.

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.

Kinetics and free energy of ligand dissociation using weighted ensemble milestoning

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

Markov State Model Analysis of Haloperidol Binding to the D3 Dopamine Receptor

We have developed Markov state models (MSMs) and hidden Markov models (HMMs) that describe the binding of haloperidol to the D₃ dopamine receptor. Haloperidol is an antipsychotic drug that binds with nanomolar affinity to the D₃ dopamine receptor, where it functions as an inverse agonist. The models were constructed using an adaptive sampling approach from 519 individual molecular dynamics simulations totaling 122 μs of simulated time and encompass the entire drug binding process. They reveal short-lived metastable bound states and two distinct long-lived bound conformations that cannot be separated in affinity using our current methodology. This work extends the use of MSMs and HMMs to study ligand binding, which thus far has been limited to simpler systems.

Dynamical matrix propagator scheme for large-scale proton dynamics simulations

We derive a matrix formalism for the simulation of long range proton dynamics for extended systems and timescales. On the basis of an ab initio molecular dynamics simulation, we construct a Markov chain, which allows us to store the entire proton dynamics in an M × M transition matrix (where M is the number of oxygen atoms). In this article, we start from common topology features of the hydrogen bond network of good proton conductors and utilize them as constituent constraints of our dynamic model. We present a thorough mathematical derivation of our approach and verify its uniqueness and correct asymptotic behavior. We propagate the proton distribution by means of transition matrices, which contain kinetic data from both ultra-short (sub-ps) and intermediate (ps) timescales. This concept allows us to keep the most relevant features from the microscopic level while effectively reaching larger time and length scales. We demonstrate the applicability of the transition matrices for the description of proton conduction trends in proton exchange membrane materials.

Combined Linear Interaction Energy and Alchemical Solvation Free-Energy Approach for Protein-Binding Affinity Computation

Calculating free energies of binding (ΔG_bind) between ligands and their target protein is of major interest to drug discovery and safety, yet it is still associated with several challenges and difficulties. Linear interaction energy (LIE) is an efficient in silico method for ΔG_bind computation. LIE models can be trained and used to directly calculate binding affinities from interaction energies involving ligands in the bound and unbound states only, and LIE can be combined with statistical weighting to calculate ΔG_bind for flexible proteins that may bind their ligands in multiple orientations. Here, we investigate if LIE predictions can be effectively improved by explicitly including the entropy of (de)solvation into our free-energy calculations. For that purpose, we combine LIE calculations for the protein-ligand-bound state with explicit free-energy perturbation to rigorously compute the unbound ligand's solvation free energy. We show that for 28 Cytochrome P450 2A6 (CYP2A6) ligands, coupling LIE with alchemical solvation free-energy calculation helps to improve obtained correlation between computed and reference (experimental) binding data.

Health Risk Assessment of Occupationally Pesticide-Exposed Population of Cancer Prone Area of Punjab

The alarming health issues especially the unusually high number of cancer cases in agriculture community of Bathinda district of Punjab (India) is a serious concern. There is limited knowledge about the role of gene-environment interactions in oncogenesis prevalent in this area. The aim of this study was to evaluate the association of oxidative stress with CYP1A2, CYP2B6, CYP2C9, CYP3A4, and PON1 genetic variation in the pesticide-exposed (occupationally) population of Bathinda district of Punjab (India). This study demonstrated significantly elevated relative risk (RR) of lower antioxidant defense mechanism (Glutathione, Catalase, Superoxide Dismutase, Glutathione peroxidases, and Glutathione Reductase) in occupationally pesticide-exposed group (n = 120) as compared with unexposed group (n = 84) from Bathinda district of Punjab (India). Our data shows pesticide exposure to be a major risk factor leading to increased oxidative stress inside the body. Gas chromatographic analysis revealed the residues of organophosphates (chlorpyriphos, dichlorvos, ethoprophos) and herbicides (atrazine, butachlor, alachlor, metolachlor) in the blood samples of the exposed population. In vitro results showed a dose dependent decrease in cell viability following treatment of pesticides detected in blood samples in hPBMCs and A549 cell line. Genetic variation analysis revealed missense mutations in CYP2B6 (2 mutations), CY3A4 (1 mutation), and CYP2C9 (2 mutations). The observed mutations have been predicted to cause structural and conformation change in protein structure which could result in altered stability. In first of its kind of study, our data reveal oxidative stress and pesticide residue accumulation inside the body to be the major reasons for health concerns in Bathinda district.

Structural dynamics behind variants in pyrazinamidase and pyrazinamide resistance

Pyrazinamide (PZA) is an important component of first-line anti-tuberculosis (anti-TB) drugs. The anti-TB agent is activated into an active form, pyrazinoic acid (POA), by Mycobacterium tuberculosis (MTB) pncA gene encoding pyrazinamidase (PZase). The major cause of PZA-resistance has been associated with mutations in the pncA gene. We have detected several novel mutations including V131F, Q141P, R154T, A170P, and V180F (GeneBank Accession No. MH461111) in the pncA gene of PZA-resistant isolates during PZA drug susceptibility testing followed by pncA gene sequencing. Here, we investigated molecular mechanism of PZA-resistance by comparing the results of experimental and molecular dynamics. The mutants (MTs) and wild type (WT) PZase structures in apo and complex with PZA were subjected to molecular dynamic simulations (MD) at the 40 ns. Multiple factors, including root mean square deviations (RMSD), binding pocket, total energy, dynamic cross correlation, and root mean square fluctuations (RMSF) of MTs and WT were compared. The MTs attained a high deviation and fluctuation compared to WT. Binding pocket volumes of the MTs, were found, lower than the WT, and the docking scores were high than WT while shape complementarity scores were lower than that of the WT. Residual motion in MTs are seemed to be dominant in anti-correlated motion. Mutations at locations, V131F, Q141P, R154T, A170P, and V180F, might be involved in the structural changes, possibly affecting the catalytic property of PZase to convert PZA into POA. Our study provides useful information that will enhance the understanding for better management of TB. AbbreviationsDSTdrug susceptibility testingΔelecelectrostatic energyLJLowenstein-Jensen mediumMGITmycobacterium growth indicator tubesMTsmutantsMDmolecular dynamic simulationsMTBMycobacterium tuberculosisNALC-NaOHN-acetyl-l-cysteine-sodium hydroxideNIHNational Institutes of HealthNPTamount of substance (N), pressure (P) temperature (T)NVTmoles (N), volume (V) temperature (T)PZasepyrazinamidaseΔpspolar solvation energyPTRLProvincial Tuberculosis Reference LaboratoryRMSDroot mean square deviationsRMSFroot mean square fluctuationsΔSASAsolvent accessible surface area energyTBtuberculosisGTotaltotal binding free energyΔvdWVan der Waals energyWTwild typeCommunicated by Ramaswamy H. Sarma.

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.

Homology models of mouse and rat estrogen receptor-α ligand-binding domain created by in silico mutagenesis of a human template: molecular docking with 17ß-estradiol, diethylstilbestrol, and paraben analogs

Crystal structures exist for human, but not rodent, estrogen receptor-α ligand-binding domain (ERα-LBD). Consequently, rodent studies involving binding of compounds to ERα-LBD are limited in their molecular-level interpretation and extrapolation to humans. Because the sequences of rodent and human ERα-LBDs are > 95% identical, we expected their 3D structures and ligand binding to be highly similar. To test this hypothesis, we used the human ERα-LBD structure (PDB 3UUD) as a template to produce rat and mouse homology models. Employing the rodent models and human structure, we generated docking poses of 23 Group A ligands (17ß-estradiol, diethylstilbestrol, and 21 paraben analogs) in AutoDock Vina for interspecies comparisons. Ligand RMSDs (Å) (median, 95% CI) were 0.49 (0.21-1.82) (human-mouse) and 1.19 (0.22-1.82) (human-rat), well below the 2.0-2.5 Å range for equivalent docking poses. Numbers of interspecies ligand-receptor residue contacts were highly similar, with Sorensen Sc (%) = 96.8 (90.0-100) (human-mouse) and 97.7 (89.5-100) (human-rat). Likewise, numbers of interspecies ligand-receptor residue contacts were highly correlated: Pearson r = 0.913 (human-mouse) and 0.925 (human-rat). Numbers of interspecies ligand-receptor atom contacts were even more tightly correlated: r = 0.979 (human-mouse) and 0.986 (human-rat). Pyramid plots of numbers of ligand-receptor atom contacts by residue exhibited high interspecies symmetry and had Spearman r s = 0.977 (human-mouse) and 0.966 (human-rat). Group B ligands included 15 ring-substituted parabens recently shown experimentally to exhibit decreased binding to human ERα and to exert increased antimicrobial activity. Ligand efficiencies calculated from docking ligands into human ERα-LBD were well correlated with those derived from published experimental data (Pearson partial r p = 0.894 and 0.918; Groups A and B, respectively). Overall, the results indicate that our constructed rodent ERα-LBDs interact with ligands in like manner to the human receptor, thus providing a high level of confidence in extrapolations of rodent to human ligand-receptor interactions.

Tuning the chain length of new pyrene derivatives for site-selective photocleavage of avidin

Rational design of photoreagents with systematic modifications of their structures can provide valuable information for a better understanding of the protein photocleavage mechanism by these reagents. Variation of the length of the linker connecting the photoactive moiety with the protein anchoring-group allowed us to investigate the control of the protein photocleavage site. A series of new photochemical reagents (PMA-1A, PMA-2A and PMA-3A) with increasing chain lengths is examined in the current study. Using avidin as a model system, we examined the interaction of these probes by UV-Vis, fluorescence spectroscopic methods, photocleavage and computational docking studies. Hypochromism of the absorption spectrum was observed for the binding of these new photochemical reagents with estimated binding constants (K_b) of 6.2 × 10⁵, 6.7 × 10⁵ and 4.6 × 10⁵ M^-1, respectively. No significant changes of Stern-Volmer quenching constant (K_sv) with Co(NH₃)₆Cl₃ has been noted and the data indicated that the probes bind near the surface of the protein with sufficient exposure to the solvent. Photoexcitation of the probe-avidin complex, in the presence of Co(NH₃)₆Cl₃, resulted in protein fragmentation, and the cleavage yield decreased with the increase in the linker length, and paralleled with the observed K_sv values. Amino acid sequencing of the photofragments indicated that avidin is cleaved between Thr77 and Val78, as a major cleavage site for all the three photoreagents. This site is proximate to the biotin binding site on avidin, and molecular docking studies indicated that the H-bonding interactions between the polar end-group of the photoreagents and hydrophilic amino acids of avidin were important in positioning the reagent on the protein. The major cleavage site, at residues 77-78, was within 5 Å of the pyrenyl moiety of the probe, and hence, molecular tuning of the linker provided a simple approach to position the photoreagent along the potential photocleavage site.

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.

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.

Exploration of gated ligand binding recognizes an allosteric site for blocking FABP4-protein interaction

Fatty acid binding protein 4 (FABP4), reversibly binding to fatty acids and other lipids with high affinities, is a potential target for treatment of cancers. The binding site of FABP4 is buried in an interior cavity and thereby ligand binding/unbinding is coupled with opening/closing of FABP4. It is a difficult task both experimentally and computationally to illuminate the entry or exit pathway, especially with the conformational gating. In this report we combine extensive computer simulations, clustering analysis, and the Markov state model to investigate the binding mechanism of FABP4 and troglitazone. Our simulations capture spontaneous binding and unbinding events as well as the conformational transition of FABP4 between the open and closed states. An allosteric binding site on the protein surface is recognized for the development of novel FABP4 inhibitors. The binding affinity is calculated and compared with the experimental value. The kinetic analysis suggests that ligand residence on the protein surface may delay the binding process. Overall, our results provide a comprehensive picture of ligand diffusion on the protein surface, ligand migration into the buried cavity, and the conformational change of FABP4 at an atomic level.

Kinetics of O2 Entry and Exit in Monomeric Sarcosine Oxidase via Markovian Milestoning Molecular Dynamics

The flavoenzyme monomeric sarcosine oxidase (MSOX) catalyzes a complex set of reactions currently lacking a consensus mechanism. A key question that arises in weighing competing mechanistic models of MSOX function is to what extent ingress of O2 from the solvent (and its egress after an unsuccessful oxidation attempt) limits the overall catalytic rate. To address this question, we have applied to the MSOX/O2 system the relatively new simulation method of Markovian milestoning molecular dynamics simulations, which, as we recently showed [ Yu et al. J. Am. Chem. Soc. 2015 , 137 , 3041 ], accurately predicted the entry and exit kinetics of CO in myoglobin. We show that the mechanism of O2 entry and exit, in terms of which possible solvent-to-active-site channels contribute to the flow of O2, is sensitive to the presence of the substrate-mimicking competitive inhibitor 2-furoate in the substrate site. The second-order O2 entry rate constants were computed to be 8.1 × 10(6) and 3.1 × 10(6) M(-1) s(-1) for bound and apo MSOX, respectively, both of which moderately exceed the experimentally determined second-order rate constant of (2.83 ± 0.07) × 10(5) M(-1) s(-1) for flavin oxidation by O2 in MSOX. This suggests that the rate of flavin oxidation by O2 is likely not strongly limited by diffusion from the solvent to the active site. The first-order exit rate constants were computed to be 10(7) s(-1) and 7.2 × 10(6) s(-1) for the apo and bound states, respectively. The predicted faster entry and slower exit of O2 for the bound state indicate a longer residence time within MSOX, increasing the likelihood of collisions with the flavin isoalloxazine ring, a step required for reduction of molecular O2 and subsequent reoxidation of the flavin. This is also indirectly supported by previous experimental evidence favoring the so-called modified ping-pong mechanism, the distinguishing feature of which is an intermediate complex involving O2, the flavin, and the oxidized substrate simultaneously in the cavity. These findings demonstrate the utility of the Markovian milestoning approach in contributing new understanding of complicated enyzmatic function.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Insights into Protein-Ligand Interactions: Mechanisms, Models, and Methods

Molecular recognition, which is the process of biological macromolecules interacting with each other or various small molecules with a high specificity and affinity to form a specific complex, constitutes the basis of all processes in living organisms. Proteins, an important class of biological macromolecules, realize their functions through binding to themselves or other molecules. A detailed understanding of the protein–ligand interactions is therefore central to understanding biology at the molecular level. Moreover, knowledge of the mechanisms responsible for the protein-ligand recognition and binding will also facilitate the discovery, design, and development of drugs. In the present review, first, the physicochemical mechanisms underlying protein–ligand binding, including the binding kinetics, thermodynamic concepts and relationships, and binding driving forces, are introduced and rationalized. Next, three currently existing protein-ligand binding models—the “lock-and-key”, “induced fit”, and “conformational selection”—are described and their underlying thermodynamic mechanisms are discussed. Finally, the methods available for investigating protein–ligand binding affinity, including experimental and theoretical/computational approaches, are introduced, and their advantages, disadvantages, and challenges are discussed.

Elucidating dominant pathways of the nano-particle self-assembly process

Self-assembly processes play a key role in the fabrication of functional nano-structures with wide application in drug delivery and micro-reactors.

PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models

Markov (state) models (MSMs) and related models of molecular kinetics have recently received a surge of interest as they can systematically reconcile simulation data from either a few long or many short simulations and allow us to analyze the essential metastable structures, thermodynamics, and kinetics of the molecular system under investigation. However, the estimation, validation, and analysis of such models is far from trivial and involves sophisticated and often numerically sensitive methods. In this work we present the open-source Python package PyEMMA ( http://pyemma.org ) that provides accurate and efficient algorithms for kinetic model construction. PyEMMA can read all common molecular dynamics data formats, helps in the selection of input features, provides easy access to dimension reduction algorithms such as principal component analysis (PCA) and time-lagged independent component analysis (TICA) and clustering algorithms such as k-means, and contains estimators for MSMs, hidden Markov models, and several other models. Systematic model validation and error calculation methods are provided. PyEMMA offers a wealth of analysis functions such that the user can conveniently compute molecular observables of interest. We have derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system. Plotting functions to produce a manuscript-ready presentation of the results are available. In this work, we demonstrate the features of the software and show new methodological concepts and results produced by PyEMMA.

Computational design of a time-dependent histone deacetylase 2 selective inhibitor

Development of isoform-selective histone deacetylase (HDAC) inhibitors is of great biological and medical interest. Among 11 zinc-dependent HDAC isoforms, it is particularly challenging to achieve isoform inhibition selectivity between HDAC1 and HDAC2 due to their very high structural similarities. In this work, by developing and applying a novel de novo reaction-mechanism-based inhibitor design strategy to exploit the reactivity difference, we have discovered the first HDAC2-selective inhibitor, β-hydroxymethyl chalcone. Our bioassay experiments show that this new compound has a unique time-dependent selective inhibition on HDAC2, leading to about 20-fold isoform-selectivity against HDAC1. Furthermore, our ab initio QM/MM molecular dynamics simulations, a state-of-the-art approach to study reactions in biological systems, have elucidated how the β-hydroxymethyl chalcone can achieve the distinct time-dependent inhibition toward HDAC2.

Automatic state partitioning for multibody systems (APM): an efficient algorithm for constructing Markov state models to elucidate conformational dynamics of multibody systems

The conformational dynamics of multibody systems plays crucial roles in many important problems. Markov state models (MSMs) are powerful kinetic network models that can predict long-time-scale dynamics using many short molecular dynamics simulations. Although MSMs have been successfully applied to conformational changes of individual proteins, the analysis of multibody systems is still a challenge because of the complexity of the dynamics that occur on a mixture of drastically different time scales. In this work, we have developed a new algorithm, automatic state partitioning for multibody systems (APM), for constructing MSMs to elucidate the conformational dynamics of multibody systems. The APM algorithm effectively addresses different time scales in the multibody systems by directly incorporating dynamics into geometric clustering when identifying the metastable conformational states. We have applied the APM algorithm to a 2D potential that can mimic a protein-ligand binding system and the aggregation of two hydrophobic particles in water and have shown that it can yield tremendous enhancements in the computational efficiency of MSM construction and the accuracy of the models.

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

Protein-ligand recognition plays key roles in many biological processes. One of the most fascinating questions about protein-ligand recognition is to understand its underlying mechanism, which often results from a combination of induced fit and conformational selection. In this study, we have developed a three-pronged approach of Markov State Models, Molecular Dynamics simulations, and flux analysis to determine the contribution of each model. Using this approach, we have quantified the recognition mechanism of the choline binding protein (ChoX) to be ∼90% conformational selection dominant under experimental conditions. This is achieved by recovering all the necessary parameters for the flux analysis in combination with available experimental data. Our results also suggest that ChoX has several metastable conformational states, of which an apo-closed state is dominant, consistent with previous experimental findings. Our methodology holds great potential to be widely applied to understand recognition mechanisms underlining many fundamental biological processes.

Markov state models of biomolecular conformational dynamics

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

Quantitative comparison of alternative methods for coarse-graining biological networks

Markov models and master equations are a powerful means of modeling dynamic processes like protein conformational changes. However, these models are often difficult to understand because of the enormous number of components and connections between them. Therefore, a variety of methods have been developed to facilitate understanding by coarse-graining these complex models. Here, we employ Bayesian model comparison to determine which of these coarse-graining methods provides the models that are most faithful to the original set of states. We find that the Bayesian agglomerative clustering engine and the hierarchical Nyström expansion graph (HNEG) typically provide the best performance. Surprisingly, the original Perron cluster cluster analysis (PCCA) method often provides the next best results, outperforming the newer PCCA+ method and the most probable paths algorithm. We also show that the differences between the models are qualitatively significant, rather than being minor shifts in the boundaries between states. The performance of the methods correlates well with the entropy of the resulting coarse-grainings, suggesting that finding states with more similar populations (i.e., avoiding low population states that may just be noise) gives better results.

Crystal structure of the Mycobacterium tuberculosis phosphate binding protein PstS3

Mycobacterium tuberculosis evades host immune responses by colonizing macrophages. Intraphagosomal M. tuberculosis is exposed to environmental stresses such as reactive oxygen and nitrogen intermediates as well as acid shock and inorganic phosphate (Pi) depletion. Experimental evidence suggests that expression levels of mycobacterial protein PstS3 (Rv0928) are significantly increased when M. tuberculosis bacilli are exposed to Pi starvation. Hence, PstS3 may be important for survival of Mtb in conditions where there is limited supply of Pi. We report here the structure of PstS3 from M. tuberculosis at 2.3-Å resolution. The protein presents a structure typical for ABC phosphate transfer receptors. Comparison with its cognate receptor PstS1 showed a different pattern distribution of surface charges in proximity to the Pi recognition site, suggesting complementary roles of the two proteins in Pi uptake.

Kinetic characterization of fragment binding in AmpC β-lactamase by high-throughput molecular simulations

Small molecules used in fragment-based drug discovery form multiple, promiscuous binding complexes difficult to capture experimentally. Here, we identify such binding poses and their associated energetics and kinetics using molecular dynamics simulations on AmpC β-lactamase. Only one of the crystallographic binding poses was found to be thermodynamically favorable; however, the ligand shows several binding poses within the pocket. This study demonstrates free-binding molecular simulations in the context of fragment-to-lead development and its potential application in drug design.

Monte Carlo Free Ligand Diffusion with Markov State Model Analysis and Absolute Binding Free Energy Calculations

Obtaining absolute binding free energies from unbiased ligand diffusion has attracted a significant amount of attention due to its implications in drug design. Several studies have used special purpose computers and software to achieve microsecond molecular dynamics which, combined with a Markov state model analysis, are capable of providing absolute binding free energies. We have recently developed a Monte Carlo based technique, PELE, capable of performing a dynamical exploration of the protein-ligand energy landscape including free ligand diffusion into the active site, at a fraction of the computational cost of molecular dynamics techniques. We demonstrate here the capabilities of our Monte Carlo technique in obtaining absolute binding free energies for a series of benzamidine like inhibitors into trypsin. Our results are in good agreement with experimental data and other molecular dynamics simulations, indicating that PELE can be a useful tool for quick estimates of binding free energies and mechanisms.

Hierarchical Nyström methods for constructing Markov state models for conformational dynamics

Markov state models (MSMs) have become a popular approach for investigating the conformational dynamics of proteins and other biomolecules. MSMs are typically built from numerous molecular dynamics simulations by dividing the sampled configurations into a large number of microstates based on geometric criteria. The resulting microstate model can then be coarse-grained into a more understandable macrostate model by lumping together rapidly mixing microstates into larger, metastable aggregates. However, finite sampling often results in the creation of many poorly sampled microstates. During coarse-graining, these states are mistakenly identified as being kinetically important because transitions to/from them appear to be slow. In this paper, we propose a formalism based on an algebraic principle for matrix approximation, i.e., the Nyström method, to deal with such poorly sampled microstates. Our scheme builds a hierarchy of microstates from high to low populations and progressively applies spectral clustering on sets of microstates within each level of the hierarchy. It helps spectral clustering identify metastable aggregates with highly populated microstates rather than being distracted by lowly populated states. We demonstrate the ability of this algorithm to discover the major metastable states on two model systems, the alanine dipeptide and trpzip2 peptide.

Free energy landscape for the binding process of Huperzine A to acetylcholinesterase

Drug-target residence time (t = 1/k(off), where k(off) is the dissociation rate constant) has become an important index in discovering better- or best-in-class drugs. However, little effort has been dedicated to developing computational methods that can accurately predict this kinetic parameter or related parameters, k(off) and activation free energy of dissociation (ΔG(off)≠). In this paper, energy landscape theory that has been developed to understand protein folding and function is extended to develop a generally applicable computational framework that is able to construct a complete ligand-target binding free energy landscape. This enables both the binding affinity and the binding kinetics to be accurately estimated. We applied this method to simulate the binding event of the anti-Alzheimer's disease drug (-)-Huperzine A to its target acetylcholinesterase (AChE). The computational results are in excellent agreement with our concurrent experimental measurements. All of the predicted values of binding free energy and activation free energies of association and dissociation deviate from the experimental data only by less than 1 kcal/mol. The method also provides atomic resolution information for the (-)-Huperzine A binding pathway, which may be useful in designing more potent AChE inhibitors. We expect this methodology to be widely applicable to drug discovery and development.

Kinetics of ligand-receptor interaction reveals an induced-fit mode of binding in a cyclic nucleotide-activated protein

Many receptors and ion channels are activated by ligands. One key question concerns the binding mechanism. Does the ligand induce conformational changes in the protein via the induced-fit mechanism? Or does the protein preexist as an ensemble of conformers and the ligand selects the most complementary one, via the conformational selection mechanism? Here, we study ligand binding of a tetrameric cyclic nucleotide-gated channel from Mesorhizobium loti and of its monomeric binding domain (CNBD) using rapid mixing, mutagenesis, and structure-based computational biology. Association rate constants of ∼10(7) M(-1) s(-1) are compatible with diffusion-limited binding. Ligand binding to the full-length CNG channel and the isolated CNBD differ, revealing allosteric control of the CNBD by the effector domain. Finally, mutagenesis of allosteric residues affects only the dissociation rate constant, suggesting that binding follows the induced-fit mechanism. This study illustrates the strength of combining mutational, kinetic, and computational approaches to unravel important mechanistic features of ligand binding.

Modulation of a ligand's energy landscape and kinetics by the chemical environment

Understanding how the chemical environment modulates the predominant conformations and kinetics of flexible molecules is a core interest of biochemistry and a prerequisite for the rational design of synthetic catalysts. This study combines molecular dynamics simulation and Markov state models (MSMs) to a systematic computational strategy for investigating the effect of the chemical environment of a molecule on its conformations and kinetics. MSMs allow quantities to be computed that are otherwise difficult to access, such as the metastable sets, their free energies, and the relaxation time scales related to the rare transitions between metastable states. Additionally, MSMs are useful to identify observables that may act as sensors for the conformational or binding state of the molecule, thus guiding the design of experiments. In the present study, the conformation dynamics of UDP-GlcNAc are studied in vacuum, water, water + Mg(2+), and in the protein UDP-GlcNAc 2-epimerase. It is found that addition of Mg(2+) significantly affects the conformational stability, thermodynamics, and kinetics of UDP-GlcNAc. In particular, the slowest structural process, puckering of the GlcNAc sugar, depends on the overall conformation of UDP-GlcNAc and may thus act as a sensor of whether Mg(2+) is bound or not. Interestingly, transferring the molecule from vacuum to water makes the protein-binding conformations UDP-GlcNAc first accessible, while adding Mg(2+) further stabilizes them by specifically associating to binding-competent conformations. While Mg(2+) is not cocrystallized in the UDP-GlcNAc 2-epimerase complex, the selectively stabilized Mg(2+)/UDP-GlcNAc complex may be a template for the bound state, and Mg(2+) may accompany the binding-competent ligand conformation to the binding pocket. This serves as a possible explanation of the enhanced epimerization rate in the presence of Mg(2+). This role of Mg(2+) has previously not been described and opens the question whether "binding co-factors" may be a concept of general relevance for protein-ligand binding.