Protein conformational plasticity and complex ligand-binding kinetics explored by atomistic simulations and Markov models

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

Efficient prediction and ranking of small molecule binders by their kinetic ( kon and koff) and thermodynamic ( Δ G) properties can be a valuable metric for drug lead optimization, as these quantities are often indicators of in vivo efficacy. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon's, koff's, and Δ G's. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, β-cyclodextrin, based on predicted kon's and koff's. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long time scale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and Δ G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish "best practices" for its future use.

Intriguing role of water in protein-ligand binding studied by neutron crystallography on trypsin complexes

Hydrogen bonds are key interactions determining protein-ligand binding affinity and therefore fundamental to any biological process. Unfortunately, explicit structural information about hydrogen positions and thus H-bonds in protein-ligand complexes is extremely rare and similarly the important role of water during binding remains poorly understood. Here, we report on neutron structures of trypsin determined at very high resolutions ≤1.5 Å in uncomplexed and inhibited state complemented by X-ray and thermodynamic data and computer simulations. Our structures show the precise geometry of H-bonds between protein and the inhibitors N-amidinopiperidine and benzamidine along with the dynamics of the residual solvation pattern. Prior to binding, the ligand-free binding pocket is occupied by water molecules characterized by a paucity of H-bonds and high mobility resulting in an imperfect hydration of the critical residue Asp189. This phenomenon likely constitutes a key factor fueling ligand binding via water displacement and helps improving our current view on water influencing protein-ligand recognition.

Single glucose molecule transport process revealed by force tracing and molecular dynamics simulations

Transporting individual molecules across cell membranes is a fundamental process in cellular metabolism. Although the crystal diffraction technique has greatly contributed to our understanding of the structures of the involved transporters, a description of the dynamic transport mechanism at the single-molecule level has been extremely elusive. In this study, we applied atomic force microscopy (AFM)-based force tracing to directly monitor the transport of a single molecule, d-glucose, across living cell membranes. Our results show that the force to transport a single molecule of d-glucose across cell membranes is 37 ± 9 pN, and the corresponding transport interval is approximately 20 ms, while the average speed is approximately 0.3 μm s^-1. Furthermore, our calculated force profile from molecular dynamics simulations showed quantitatively good agreement with the force tracing observation and revealed detailed information regarding the glucose transport path, indicating that two salt bridges, K38/E299 and K300/E426, play critical roles during glucose transport across glucose transporter 1 (GLUT1). This role was further verified using biological experiments that disrupted these two bridges and measured the uptake of glucose into the cells. Our approaches led to the first unambiguous description of the glucose transport process across cell membranes at the single-molecule level and demonstrated the biological importance of the two salt bridges for transporting glucose across GLUT1.

Predicting ligand binding affinity using on- and off-rates for the SAMPL6 SAMPLing challenge

Interest in ligand binding kinetics has been growing rapidly, as it is being discovered in more and more systems that ligand residence time is the crucial factor governing drug efficacy. Many enhanced sampling methods have been developed with the goal of predicting ligand binding rates ([Formula: see text]) and/or ligand unbinding rates ([Formula: see text]) through explicit simulation of ligand binding pathways, and these methods work by very different mechanisms. Although there is not yet a blind challenge for ligand binding kinetics, here we take advantage of experimental measurements and rigorously computed benchmarks to compare estimates of [Formula: see text] calculated as the ratio of two rates: [Formula: see text]. These rates were determined using a new enhanced sampling method based on the weighted ensemble framework that we call "REVO": Reweighting of Ensembles by Variance Optimization. This is a further development of the WExplore enhanced sampling method, in which trajectory cloning and merging steps are guided not by the definition of sampling regions, but by maximizing trajectory variance. Here we obtain estimates of [Formula: see text] and [Formula: see text] that are consistent across multiple simulations, with an average log10-scale standard deviation of 0.28 for on-rates and 0.56 for off-rates, which is well within an order of magnitude and far better than previously observed for previous applications of the WExplore algorithm. Our rank ordering of the three host-guest pairs agrees with the reference calculations, however our predicted [Formula: see text] values were systematically lower than the reference by an average of 4.2 kcal/mol. Using tree network visualizations of the trajectories in the REVO algorithm, and conformation space networks for each system, we analyze the results of our sampling, and hypothesize sources of discrepancy between our [Formula: see text] values and the reference. We also motivate the direct inclusion of [Formula: see text] and [Formula: see text] challenges in future iterations of SAMPL, to further develop the field of ligand binding kinetics prediction and modeling.

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques.

Role of conformational dynamics in the evolution of novel enzyme function

The free energy landscape concept that describes enzymes as an ensemble of differently populated conformational sub-states in dynamic equilibrium is key for evaluating enzyme activity, enantioselectivity, and specificity. Mutations introduced in the enzyme sequence can alter the populations of the pre-existing conformational states, thus strongly modifying the enzyme ability to accommodate alternative substrates, revert its enantiopreferences, and even increase the activity for some residual promiscuous reactions. In this feature article, we present an overview of the current experimental and computational strategies to explore the conformational free energy landscape of enzymes. We provide a series of recent publications that highlight the key role of conformational dynamics for the enzyme evolution towards new functions and substrates, and provide some perspectives on how conformational dynamism should be considered in future computational enzyme design protocols.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Exploring Substrate Binding in the Extracellular Vestibule of MhsT by Atomistic Simulations and Markov Models

Neurotransmitter:sodium symporters (NSS) terminate neurotransmission through Na⁺-driven reuptake of cognate neurotransmitters. Crystallographically, whereas both substrates and inhibitors have been found to bind in the central binding (S1) site of NSS, inhibitors were found to bind to a second binding (S2) site in the extracellular vestibule (EV) of transporters for leucine (LeuT) and serotonin. On the basis of computational and experimental studies, we proposed that substrates bind to the S2 site of LeuT as well and that substrate binding to the S2 site is essential for Na⁺-coupled symport. Recent binding experiments show that substrate (l-Trp) binding in the S2 site of MhsT, another bacterial NSS, is also central to the allosteric transport mechanism. Here, we used extensive molecular dynamics simulations combined with Markov state model analysis to investigate the interaction of l-Trp with the EV of MhsT and identified potential binding poses of l-Trp as well as induced conformational changes in the EV. Our computational findings were validated by experimental mutagenesis studies and shed light on the ligand binding characteristics of the EV of NSS, which may facilitate development of allosteric ligands targeting NSS.

Estimation of Drug-Target Residence Times by τ-Random Acceleration Molecular Dynamics Simulations

Drug-target residence time (τ), one of the main determinants of drug efficacy, remains highly challenging to predict computationally and, therefore, is usually not considered in the early stages of drug design. Here, we present an efficient computational method, τ-random acceleration molecular dynamics (τRAMD), for the ranking of drug candidates by their residence time and obtaining insights into ligand-target dissociation mechanisms. We assessed τRAMD on a data set of 70 diverse drug-like ligands of the N-terminal domain of HSP90α, a pharmaceutically important target with a highly flexible binding site, obtaining computed relative residence times with an accuracy of about 2.3τ for 78% of the compounds and less than 2.0τ within congeneric series. Analysis of dissociation trajectories reveals features that affect ligand unbinding rates, including transient polar interactions and steric hindrance. These results suggest that τRAMD will be widely applicable as a computationally efficient aid to improving drug residence times during lead optimization.

Predicting the Conformational Variability of Abl Tyrosine Kinase using Molecular Dynamics Simulations and Markov State Models

Understanding protein conformational variability remains a challenge in drug discovery. The issue arises in protein kinases, whose multiple conformational states can affect the binding of small-molecule inhibitors. To overcome this challenge, we propose a comprehensive computational framework based on Markov state models (MSMs). Our framework integrates the information from explicit-solvent molecular dynamics simulations to accurately rank-order the accessible conformational variants of a target protein. We tested the methodology using Abl kinase with a reference and blind-test set. Only half of the Abl conformational variants discovered by our approach are present in the disclosed X-ray structures. The approach successfully identified a protein conformational state not previously observed in public structures but evident in a retrospective analysis of Lilly in-house structures: the X-ray structure of Abl with WHI-P154. Using a MSM-derived model, the free energy landscape and kinetic profile of Abl was analyzed in detail highlighting opportunities for targeting the unique metastable states.

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

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

Dynamic Consequences of Mutation of Tryptophan 215 in Thrombin

Thrombin normally cleaves fibrinogen to promote coagulation; however, binding of thrombomodulin to thrombin switches the specificity of thrombin toward protein C, triggering the anticoagulation pathway. The W215A thrombin mutant was reported to have decreased activity toward fibrinogen without significant loss of activity toward protein C. To understand how mutation of Trp215 may alter thrombin specificity, hydrogen-deuterium exchange experiments (HDXMS), accelerated molecular dynamics (AMD) simulations, and activity assays were carried out to compare the dynamics of Trp215 mutants with those of wild type (WT) thrombin. Variation in NaCl concentration had no detectable effect on the sodium-binding (220s_CT) loop, but appeared to affect other surface loops. Trp215 mutants showed significant increases in amide exchange in the 170s_CT loop consistent with a loss of H-bonding in this loop identified by the AMD simulations. The W215A thrombin showed increased amide exchange in the 220s_CT loop and in the N-terminus of the heavy chain. The AMD simulations showed that a transient conformation of the W215A thrombin has a distorted catalytic triad. HDXMS experiments revealed that mutation of Phe227, which engages in a π-stacking interaction with Trp215, also caused significantly increased amide exchange in the 170s_CT loop. Activity assays showed that only the F227V mutant had wild type catalytic activity, whereas all other mutants showed markedly lower activity. Taken together, the results explain the reduced pro-coagulant activity of the W215A mutant and demonstrate the allosteric connection between Trp215, the sodium-binding loop, and the active site.

Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures

Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.

Ensemble Docking in Drug Discovery

Ensemble docking corresponds to the generation of an "ensemble" of drug target conformations in computational structure-based drug discovery, often obtained by using molecular dynamics simulation, that is used in docking candidate ligands. This approach is now well established in the field of early-stage drug discovery. This review gives a historical account of the development of ensemble docking and discusses some pertinent methodological advances in conformational sampling.

Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations

Unstructured proteins and peptides typically fold during binding to ligand proteins. A challenging problem is to identify the mechanism and kinetics of these binding-induced folding processes in experiments and atomistic simulations. In this Article, we present a detailed picture for the folding of the inhibitor peptide PMI into a helix during binding to the oncoprotein fragment ^25-109Mdm2 obtained from atomistic, explicit-water simulations and Markov state modeling. We find that binding-induced folding of PMI is highly parallel and can occur along a multitude of pathways. Some pathways are induced-fit-like with binding occurring prior to PMI helix formation, while other pathways are conformational-selection-like with binding after helix formation. On the majority of pathways, however, binding is intricately coupled to folding, without clear temporal ordering. A central feature of these pathways is PMI motion on the Mdm2 surface, along the binding groove of Mdm2 or over the rim of this groove. The native binding groove of Mdm2 thus appears as an asymmetric funnel for PMI binding. Overall, binding-induced folding of PMI does not fit into the classical picture of induced fit or conformational selection that implies a clear temporal ordering of binding and folding events. We argue that this holds in general for binding-induced folding processes because binding and folding events in these processes likely occur on similar time scales and do exhibit the time-scale separation required for temporal ordering.

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.

Dopamine D3 receptor antagonist reveals a cryptic pocket in aminergic GPCRs

The recent increase in the number of X-ray crystal structures of G-protein coupled receptors (GPCRs) has been enabling for structure-based drug design (SBDD) efforts. These structures have revealed that GPCRs are highly dynamic macromolecules whose function is dependent on their intrinsic flexibility. Unfortunately, the use of static structures to understand ligand binding can potentially be misleading, especially in systems with an inherently high degree of conformational flexibility. Here, we show that docking a set of dopamine D3 receptor compounds into the existing eticlopride-bound dopamine D3 receptor (D3R) X-ray crystal structure resulted in poses that were not consistent with results obtained from site-directed mutagenesis experiments. We overcame the limitations of static docking by using large-scale high-throughput molecular dynamics (MD) simulations and Markov state models (MSMs) to determine an alternative pose consistent with the mutation data. The new pose maintains critical interactions observed in the D3R/eticlopride X-ray crystal structure and suggests that a cryptic pocket forms due to the shift of a highly conserved residue, F^6.52. Our study highlights the importance of GPCR dynamics to understand ligand binding and provides new opportunities for drug discovery.

Molecular Modeling and Simulation Tools in the Development of Peptide-Based Biosensors for Mycotoxin Detection: Example of Ochratoxin

Mycotoxin contamination of food and feed is now ubiquitous. Exposures to mycotoxin via contact or ingestion can potentially induce adverse health outcomes. Affordable mycotoxin-monitoring systems are highly desired but are limited by (a) the reliance on technically challenging and costly molecular recognition by immuno-capture technologies; and (b) the lack of predictive tools for directing the optimization of alternative molecular recognition modalities. Our group has been exploring the development of ochratoxin detection and monitoring systems using the peptide NFO4 as the molecular recognition receptor in fluorescence, electrochemical and multimodal biosensors. Using ochratoxin as the model mycotoxin, we share our perspective on addressing the technical challenges involved in biosensor fabrication, namely: (a) peptide receptor design; and (b) performance evaluation. Subsequently, the scope and utility of molecular modeling and simulation (MMS) approaches to address the above challenges are described. Informed and enabled by phage display, the subsequent application of MMS approaches can rationally guide subsequent biomolecular engineering of peptide receptors, including bioconjugation and bioimmobilization approaches to be used in the fabrication of peptide biosensors. MMS approaches thus have the potential to reduce biosensor development cost, extend product life cycle, and facilitate multi-analyte detection of mycotoxins, each of which positively contributes to the overall affordability of mycotoxin biosensor monitoring systems.

Dynamic Docking: A Paradigm Shift in Computational Drug Discovery

Molecular docking is the methodology of choice for studying in silico protein-ligand binding and for prioritizing compounds to discover new lead candidates. Traditional docking simulations suffer from major limitations, mostly related to the static or semi-flexible treatment of ligands and targets. They also neglect solvation and entropic effects, which strongly limits their predictive power. During the last decade, methods based on full atomistic molecular dynamics (MD) have emerged as a valid alternative for simulating macromolecular complexes. In principle, compared to traditional docking, MD allows the full exploration of drug-target recognition and binding from both the mechanistic and energetic points of view (dynamic docking). Binding and unbinding kinetic constants can also be determined. While dynamic docking is still too computationally expensive to be routinely used in fast-paced drug discovery programs, the advent of faster computing architectures and advanced simulation methodologies are changing this scenario. It is feasible that dynamic docking will replace static docking approaches in the near future, leading to a major paradigm shift in in silico drug discovery. Against this background, we review the key achievements that have paved the way for this progress.

New approaches for computing ligand-receptor binding kinetics

The recent and growing evidence that the efficacy of a drug can be correlated to target binding kinetics has seeded the development of a multitude of novel methods aimed at computing rate constants for receptor-ligand binding processes, as well as gaining an understanding of the binding and unbinding pathways and the determinants of structure-kinetic relationships. These new approaches include various types of enhanced sampling molecular dynamics simulations and the combination of energy-based models with chemometric analysis. We assess these approaches in the light of the varying levels of complexity of protein-ligand binding processes.

Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations

Understanding and control of structures and rates involved in protein ligand binding are essential for drug design. Unfortunately, atomistic molecular dynamics (MD) simulations cannot directly sample the excessively long residence and rearrangement times of tightly binding complexes. Here we exploit the recently developed multi-ensemble Markov model framework to compute full protein-peptide kinetics of the oncoprotein fragment 25-109Mdm2 and the nano-molar inhibitor peptide PMI. Using this system, we report, for the first time, direct estimates of kinetics beyond the seconds timescale using simulations of an all-atom MD model, with high accuracy and precision. These results only require explicit simulations on the sub-milliseconds timescale and are tested against existing mutagenesis data and our own experimental measurements of the dissociation and association rates. The full kinetic model reveals an overall downhill but rugged binding funnel with multiple pathways. The overall strong binding arises from a variety of conformations with different hydrophobic contact surfaces that interconvert on the milliseconds timescale.

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.

Multiscale Simulation of Receptor-Drug Association Kinetics: Application to Neuraminidase Inhibitors

A detailed understanding of the drug-receptor association process is of fundamental importance for drug design. Due to the long time scales of typical binding kinetics, the atomistic simulation of the ligand traveling from bulk solution into the binding site is still computationally challenging. In this work, we apply a multiscale approach of combined Molecular Dynamics (MD) and Brownian Dynamics (BD) simulations to investigate association pathway ensembles for the two prominent H1N1 neuraminidase inhibitors oseltamivir and zanamivir. Including knowledge of the approximate binding site location allows for the selective confinement of detailed but expensive MD simulations and application of less demanding BD simulations for the diffusion controlled part of the association pathway. We evaluate a binding criterion based on the residence time of the inhibitor in the binding pocket and compare it to geometric criteria that require prior knowledge about the binding mechanism. The method ranks the association rates of both inhibitors in qualitative agreement with experiment and yields reasonable absolute values depending, however, on the reaction criteria. The simulated association pathway ensembles reveal that, first, ligands are oriented in the electrostatic field of the receptor. Subsequently, a salt bridge is formed between the inhibitor's carboxyl group and neuraminidase residue Arg368, followed by adopting the native binding mode. Unexpectedly, despite oseltamivir's higher overall association rate, the rate into the intermediate salt-bridge state was found to be higher for zanamivir. The present methodology is intrinsically parallelizable and, although computationally demanding, allows systematic binding rate calculation on selected sets of potential drug molecules.

Biomolecular conformational changes and ligand binding: from kinetics to thermodynamics

The behaviour of biomolecular systems is governed by their thermodynamic and kinetic properties. It is thus important to be able to calculate, for example, both the affinity and rate of binding and dissociation of a protein-ligand complex, or the populations and exchange rates between distinct conformational states. Because these are typically rare events, calculating these properties from long molecular dynamics simulations remains extremely difficult. Instead, one often adopts a divide-and-conquer strategy in which equilibrium free-energy differences and the fastest state-to-state transition (e.g. ligand association or minor-to-major state conversion) are combined to estimate the slow rate (e.g. ligand dissociation) using a two-state assumption. Here we instead address these problems by using a previously developed method to calculate both the forward and backward rates directly from simulations. We then estimate the thermodynamics from the rates, and validate these values by independent means. We applied the approach to three systems of increasing complexity, including the association and dissociation of benzene to a fully buried cavity inside the L99A mutant variant of T4 lysozyme. In particular, we were able to determine both millisecond association and dissociation rates, and the affinity, of the protein-ligand system by directly observing dozens of rare events in atomic detail. Our approach both sheds light on the precision of methods for calculating kinetics and further provides a generally useful test for the internal consistency of kinetics and thermodynamics. We also expect our route to be useful for obtaining both the kinetics and thermodynamics at the same time in more challenging cases.

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.

Adaptive simulations, towards interactive protein-ligand modeling

Modeling the dynamic nature of protein-ligand binding with atomistic simulations is one of the main challenges in computational biophysics, with important implications in the drug design process. Although in the past few years hardware and software advances have significantly revamped the use of molecular simulations, we still lack a fast and accurate ab initio description of the binding mechanism in complex systems, available only for up-to-date techniques and requiring several hours or days of heavy computation. Such delay is one of the main limiting factors for a larger penetration of protein dynamics modeling in the pharmaceutical industry. Here we present a game-changing technology, opening up the way for fast reliable simulations of protein dynamics by combining an adaptive reinforcement learning procedure with Monte Carlo sampling in the frame of modern multi-core computational resources. We show remarkable performance in mapping the protein-ligand energy landscape, being able to reproduce the full binding mechanism in less than half an hour, or the active site induced fit in less than 5 minutes. We exemplify our method by studying diverse complex targets, including nuclear hormone receptors and GPCRs, demonstrating the potential of using the new adaptive technique in screening and lead optimization studies.

Into the Dynamics of a Supramolecular Polymer at Submolecular Resolution

To rationally design supramolecular polymers capable of self-healing or reconfiguring their structure in a dynamically controlled way, it is imperative to gain access into the intrinsic dynamics of the supramolecular polymer (dynamic exchange of monomers) while maintaining a high-resolution description of the monomer structure. But this is prohibitively difficult at experimental level. Here we show atomistic, coarse-grained modelling combined with advanced simulation approaches to characterize the molecular mechanisms and relative kinetics of monomer exchange in structural variants of a synthetic supramolecular polymer in different conditions. We can capture differences in supramolecular dynamics consistent with the experimental observations, revealing that monomer exchange in and out the fibres originates from the defects present in their supramolecular structure. At the same time, the submolecular resolution of this approach offers a molecular-level insight into the dynamics of these bioinspired materials, and a flexible tool to obtain structure-dynamics relationships for a variety of polymeric assemblies.Accessing the dynamics of soft self-assembled materials at high resolution is very difficult. Here the authors show atomistic and coarse-grained modelling combined with enhanced sampling to characterize the molecular mechanisms and kinetics of monomer exchange in synthetic supramolecular polymers.

Combining experimental and simulation data of molecular processes via augmented Markov models

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few [Formula: see text], which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

Intrinsic dynamics study identifies two amino acids of TIMP-1 critical for its LRP-1-mediated endocytosis in neurons

The tissue inhibitor of metalloproteinases-1 (TIMP-1) exerts inhibitory activity against matrix metalloproteinases and cytokine-like effects. We previously showed that TIMP-1 reduces neurite outgrowth in mouse cortical neurons and that this cytokine-like effect depends on TIMP-1 endocytosis mediated by the low-density lipoprotein receptor-related protein-1 (LRP-1). To gain insight into the interaction between TIMP-1 and LRP-1, we considered conformational changes that occur when a ligand binds to its receptor. TIMP-1 conformational changes have been studied using biomolecular simulations, and our results provide evidence for a hinge region that is critical for the protein movement between the N- and C-terminal TIMP-1 domains. In silico mutants have been proposed on residues F12 and K47, which are located in the hinge region. Biological analyses of these mutants show that F12A or K47A mutation does not alter MMP inhibitory activity but impairs the effect of TIMP-1 on neurite outgrowth. Interestingly, these mutants bind to LRP-1 but are not endocytosed. We conclude that the intrinsic dynamics of TIMP-1 are not involved in its binding to LRP-1 but rather in the initiation of endocytosis and associated biological effects.

Multiple Ligand Unbinding Pathways and Ligand-Induced Destabilization Revealed by WExplore

We report simulations of full ligand exit pathways for the trypsin-benzamidine system, generated using the sampling technique WExplore. WExplore is able to observe millisecond-scale unbinding events using many nanosecond-scale trajectories that are run without introducing biasing forces. The algorithm generates rare events by dividing the coordinate space into regions, on-the-fly, and balancing computational effort between regions through cloning and merging steps, as in the weighted ensemble method. The averaged exit flux yields a ligand exit rate of 180 μs, which is within an order of magnitude of the experimental value. We obtain broad sampling of ligand exit pathways, and visualize our findings using conformation space networks. The analysis shows three distinct exit channels, two of which are formed through large, rare motions of the loop regions in trypsin. This broad set of ligand-bound poses is then used to investigate general properties of ligand binding: we observe both a direct stabilizing effect of ligand-protein interactions and an indirect destabilizing effect on intraprotein interactions that is induced by the ligand. Significantly, the crystallographic binding poses are distinguished not only because their ligands induce large stabilizing effects, but also because they induce relatively low indirect destabilizations.

Computational and Experimental Evaluation of Designed β-Cap Hairpins Using Molecular Simulations and Kinetic Network Models

Molecular simulation has been used to model the detailed folding properties of peptides, yet prospective computational peptide design by such approaches remains challenging and nontrivial. To test the accuracy of simulation-based hairpin design, we characterized the folding properties of a series of so-called β-cap hairpin peptides designed to mimic a conserved hairpin of LapD, a bacterial intracellular signaling protein, both experimentally by NMR spectroscopy and computationally by implicit-solvent replica-exchange molecular dynamics using three different AMBER force fields (ff96, ff99sb-ildn, and ff99sb-ildn-NMR). A unique challenge presented by these designs is the presence of both a terminal Trp-Trp capping motif and a conserved GWxQ motif in the hairpin turn required for binding to LapG. Consistent with previous studies, we found AMBER ff96 to be the most accurate when used with the OBC GBSA implicit solvent model, despite its known bias toward β-sheet conformations when used in explicit-solvent simulations. To gain microscopic insight into the folding landscape of the hairpin designs, we additionally performed parallel simulations on the Folding@home distributed computing platform using AMBER ff99sb-ildn-NMR with TIP3P explicit solvent. Markov state models (MSMs) built from trajectory data reveal a number of non-native interactions between Trp and other amino acid side chains, creating potential problems in achieving well-folded hairpin structures in solution.

Complete protein-protein association kinetics in atomic detail revealed by molecular dynamics simulations and Markov modelling

Protein-protein association is fundamental to many life processes. However, a microscopic model describing the structures and kinetics during association and dissociation is lacking on account of the long lifetimes of associated states, which have prevented efficient sampling by direct molecular dynamics (MD) simulations. Here we demonstrate protein-protein association and dissociation in atomistic resolution for the ribonuclease barnase and its inhibitor barstar by combining adaptive high-throughput MD simulations and hidden Markov modelling. The model reveals experimentally consistent intermediate structures, energetics and kinetics on timescales from microseconds to hours. A variety of flexibly attached intermediates and misbound states funnel down to a transition state and a native basin consisting of the loosely bound near-native state and the tightly bound crystallographic state. These results offer a deeper level of insight into macromolecular recognition and our approach opens the door for understanding and manipulating a wide range of macromolecular association processes.

Exploring the Dynamics of Propeller Loops in Human Telomeric DNA Quadruplexes Using Atomistic Simulations

We have carried out a series of extended unbiased molecular dynamics (MD) simulations (up to 10 μs long, ∼162 μs in total) complemented by replica-exchange with the collective variable tempering (RECT) approach for several human telomeric DNA G-quadruplex (GQ) topologies with TTA propeller loops. We used different AMBER DNA force-field variants and also processed simulations by Markov State Model (MSM) analysis. The slow conformational transitions in the propeller loops took place on a scale of a few μs, emphasizing the need for long simulations in studies of GQ dynamics. The propeller loops sampled similar ensembles for all GQ topologies and for all force-field dihedral-potential variants. The outcomes of standard and RECT simulations were consistent and captured similar spectrum of loop conformations. However, the most common crystallographic loop conformation was very unstable with all force-field versions. Although the loss of canonical γ-trans state of the first propeller loop nucleotide could be related to the indispensable bsc0 α/γ dihedral potential, even supporting this particular dihedral by a bias was insufficient to populate the experimentally dominant loop conformation. In conclusion, while our simulations were capable of providing a reasonable albeit not converged sampling of the TTA propeller loop conformational space, the force-field description still remained far from satisfactory.

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.

SEEKR: Simulation Enabled Estimation of Kinetic Rates, A Computational Tool to Estimate Molecular Kinetics and Its Application to Trypsin-Benzamidine Binding

We present the Simulation Enabled Estimation of Kinetic Rates (SEEKR) package, a suite of open-source scripts and tools designed to enable researchers to perform multiscale computation of the kinetics of molecular binding, unbinding, and transport using a combination of molecular dynamics, Brownian dynamics, and milestoning theory. To demonstrate its utility, we compute the kon, koff, and ΔGbind for the protein trypsin with its noncovalent binder, benzamidine, and examine the kinetics and other results generated in the context of the new software, and compare our findings to previous studies performed on the same system. We compute a kon estimate of (2.1 ± 0.3) × 107 M-1 s-1, a koff estimate of 83 ± 14 s-1, and a ΔGbind of -7.4 ± 0.1 kcal·mol-1, all of which compare closely to the experimentally measured values of 2.9 × 107 M-1 s-1, 600 ± 300 s-1, and -6.71 ± 0.05 kcal·mol-1, respectively.

Kinetics for Drug Discovery: an industry-driven effort to target drug residence time

A considerable number of approved drugs show non-equilibrium binding characteristics, emphasizing the potential role of drug residence times for in vivo efficacy. Therefore, a detailed understanding of the kinetics of association and dissociation of a target-ligand complex might provide crucial insight into the molecular mechanism-of-action of a compound. This deeper understanding will help to improve decision making in drug discovery, thus leading to a better selection of interesting compounds to be profiled further. In this review, we highlight the contributions of the Kinetics for Drug Discovery (K4DD) Consortium, which targets major open questions related to binding kinetics in an industry-driven public-private partnership.