Computing ensembles of transitions from stable states: Dynamic importance sampling

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

Toward Convergence in Free Energy Calculations for Protein Conformational Changes: A Case Study on the Thin Gate of Mhp1 Transporter

It has been challenging to obtain reliable free energies for protein conformational changes from all-atom molecular dynamics simulations, despite the availability of many enhanced sampling techniques. To alleviate the difficulties associated with the enormous complexity of the conformational space, here we propose a few practical strategies for such calculations, including (1) a stringent method to examine convergence by comparing independent simulations starting from different initial coordinates, (2) adoption of multistep schemes in which the complete conformational change consists of multiple transition steps, each sampled using a distinct reaction coordinate, and (3) application of boundary restraints to simplify the conformational space. We demonstrate these strategies on the conformational changes between the outward-facing and outward-occluded states of the Mhp1 membrane transporter, obtaining the equilibrium thermodynamics of the relevant metastable states, the kinetic rates between these states, and the reactive trajectories that reveal the atomic details of spontaneous transitions. Our approaches thus promise convergent and reliable calculations to examine intuition-based hypotheses and to eventually elucidate the underlying molecular mechanisms of reversible conformational changes in complex protein systems.

Structural insight into the formation of lipoprotein-β-barrel complexes

The β-barrel assembly machinery (BAM) inserts outer membrane β-barrel proteins (OMPs) in the outer membrane of Gram-negative bacteria. In Enterobacteriacea, BAM also mediates export of the stress sensor lipoprotein RcsF to the cell surface by assembling RcsF-OMP complexes. Here, we report the crystal structure of the key BAM component BamA in complex with RcsF. BamA adopts an inward-open conformation, with the lateral gate to the membrane closed. RcsF is lodged deep inside the lumen of the BamA barrel, binding regions proposed to undergo an outward and lateral opening during OMP insertion. On the basis of our structural and biochemical data, we propose a push-and-pull model for RcsF export upon conformational cycling of BamA and provide a mechanistic explanation for how RcsF uses its interaction with BamA to detect envelope stress. Our data also suggest that the flux of incoming OMP substrates is involved in the control of BAM activity.

Large-Scale Conformational Changes and Protein Function: Breaking the in silico Barrier

Large-scale conformational changes are essential to link protein structures with their function at the cell and organism scale, but have been elusive both experimentally and computationally. Over the past few years developments in cryo-electron microscopy and crystallography techniques have started to reveal multiple snapshots of increasingly large and flexible systems, deemed impossible only short time ago. As structural information accumulates, theoretical methods become central to understand how different conformers interconvert to mediate biological function. Here we briefly survey current in silico methods to tackle large conformational changes, reviewing recent examples of cross-validation of experiments and computational predictions, which show how the integration of different scale simulations with biological information is already starting to break the barriers between the in silico, in vitro, and in vivo worlds, shedding new light onto complex biological problems inaccessible so far.

Perspectives towards antiviral drug discovery against Ebola virus

Ebola virus disease (EVD), caused by Ebola viruses, resulted in more than 11 500 deaths according to a recent 2018 WHO report. With mortality rates up to 90%, it is nowadays one of the most deadly infectious diseases. However, no Food and Drug Administration‐approved Ebola drugs or vaccines are available yet with the mainstay of therapy being supportive care. The high fatality rate and absence of effective treatment or vaccination make Ebola virus a category‐A biothreat pathogen. Fortunately, a series of investigational countermeasures have been developed to control and prevent this global threat. This review summarizes the recent therapeutic advances and ongoing research progress from research and development to clinical trials in the development of small‐molecule antiviral drugs, small‐interference RNA molecules, phosphorodiamidate morpholino oligomers, full‐length monoclonal antibodies, and vaccines. Moreover, difficulties are highlighted in the search for effective countermeasures against EVD with additional focus on the interplay between available in silico prediction methods and their evidenced potential in antiviral drug discovery.

Binding free energies in the SAMPL6 octa-acid host-guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10-20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4-5.2 kJ/mol and a correlation coefficient (R²) of 0.77-0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD = 3-8 kJ/mol and R² = 0.1-0.9), but the results were improved compared to previous studies of this system with similar methods.

re-TAMD: exploring interactions between H3 peptide and YEATS domain using enhanced sampling

BACKGROUND

Analysis of preferred binding regions of a ligand on a protein is important for detecting cryptic binding pockets and improving the ligand selectivity.

RESULT

The enhanced sampling approach TAMD has been adapted to allow a ligand to unbind from its native binding site and explore the protein surface. This so-called re-TAMD procedure was then used to explore the interaction between the N terminal peptide of histone H3 and the YEATS domain. Depending on the length of the peptide, several regions of the protein surface were explored. The peptide conformations sampled during the re-TAMD correspond to peptide free diffusion around the protein surface.

CONCLUSIONS

The re-TAMD approach permitted to get information on the relative influence of different regions of the N terminal peptide of H3 on the interaction between H3 and YEATS.

Conformational landscapes of membrane proteins delineated by enhanced sampling molecular dynamics simulations

The expansion of computational power, better parameterization of force fields, and the development of novel algorithms to enhance the sampling of the free energy landscapes of proteins have allowed molecular dynamics (MD) simulations to become an indispensable tool to understand the function of biomolecules. The temporal and spatial resolution of MD simulations allows for the study of a vast number of processes of interest. Here, we review the computational efforts to uncover the conformational free energy landscapes of a subset of membrane proteins: ion channels, transporters and G-protein coupled receptors. We focus on the various enhanced sampling techniques used to study these questions, how the conclusions come together to build a coherent picture, and the relationship between simulation outcomes and experimental observables.

Physical properties of the HIV-1 capsid from all-atom molecular dynamics simulations

Human immunodeficiency virus type 1 (HIV-1) infection is highly dependent on its capsid. The capsid is a large container, made of ∼1,300 proteins with altogether 4 million atoms. Although the capsid proteins are all identical, they nevertheless arrange themselves into a largely asymmetric structure made of hexamers and pentamers. The large number of degrees of freedom and lack of symmetry pose a challenge to studying the chemical details of the HIV capsid. Simulations of over 64 million atoms for over 1 μs allow us to conduct a comprehensive study of the chemical–physical properties of an empty HIV-1 capsid, including its electrostatics, vibrational and acoustic properties, and the effects of solvent (ions and water) on the capsid. The simulations reveal critical details about the capsid with implications to biological function.

The large and complex HIV-1 capsid modulates several molecular events during HIV-1’s infective cycle. Here the authors use all-atom molecular dynamic simulations to probe the biophysical properties of the genome-free HIV-1 capsid.

Molecular Modeling of the Catalytic Domain of CyaA Deepened the Knowledge of Its Functional Dynamics

Although CyaA has been studied for over three decades and revealed itself to be a very good prototype for developing various biotechnological applications, only a little is known about its functional dynamics and about the conformational landscape of this protein. Molecular dynamics simulations helped to clarify the view on these points in the following way. First, the model of interaction between AC and calmodulin (CaM) has evolved from an interaction centered on the surface between C-CaM hydrophobic patch and the α helix H of AC, to a more balanced view, in which the C-terminal tail of AC along with the C-CaM Calcium loops play an important role. This role has been confirmed by the reduction of the affinity of AC for calmodulin in the presence of R338, D360 and N347 mutations. In addition, enhanced sampling studies have permitted to propose a representation of the conformational space for the isolated AC. It remains to refine this representation using structural low resolution information measured on the inactive state of AC. Finally, due to a virtual screening study on another adenyl cyclase from Bacillus anthracis, weak inhibitors of AC have been discovered.

Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter

Protein conformational change is of central importance in molecular biology. Here we demonstrate a computational approach to characterize the transition between two metastable conformations in all-atom simulations. Our approach is based on the finite temperature string method, and the implementation is essentially a generalization of umbrella sampling simulations with Hamiltonian replica exchange. We represent the transition pathway by a curve in the conformational space, with the curve parameter taken as the reaction coordinate. Our approach can efficiently refine a transition pathway and compute a one-dimensional free energy as a function of the reaction coordinate. A diffusion model can then be used to calculate the forward and backward transition rates, the major kinetic quantities for the transition. We applied the approach on a local transition in the ligand-free Mhp1 transporter, between its outward-facing conformation and an intermediate conformation with the side chain of Phe305 flipped to the outside of the protein. Our simulations predict that the flipped-out position of this side chain has a free energy 6.5 kcal/mol higher than the original position in the crystal structure, and that the forward and backward transition rates are in the millisecond and submicrosecond time scales, respectively.

Prediction and validation of protein intermediate states from structurally rich ensembles and coarse-grained simulations

Protein conformational changes are at the heart of cell functions, from signalling to ion transport. However, the transient nature of the intermediates along transition pathways hampers their experimental detection, making the underlying mechanisms elusive. Here we retrieve dynamic information on the actual transition routes from principal component analysis (PCA) of structurally-rich ensembles and, in combination with coarse-grained simulations, explore the conformational landscapes of five well-studied proteins. Modelling them as elastic networks in a hybrid elastic-network Brownian dynamics simulation (eBDIMS), we generate trajectories connecting stable end-states that spontaneously sample the crystallographic motions, predicting the structures of known intermediates along the paths. We also show that the explored non-linear routes can delimit the lowest energy passages between end-states sampled by atomistic molecular dynamics. The integrative methodology presented here provides a powerful framework to extract and expand dynamic pathway information from the Protein Data Bank, as well as to validate sampling methods in general.

Protein conformational changes are key to a wide range of cellular functions but remain difficult to access experimentally. Here the authors describe eBDIMS, a novel approach to predict intermediates observed in structural transition pathways from experimental ensembles.

Adaptive Multilevel Splitting Method for Molecular Dynamics Calculation of Benzamidine-Trypsin Dissociation Time

Adaptive multilevel splitting (AMS) is a rare event sampling method that requires minimal parameter tuning and allows unbiased sampling of transition pathways of a given rare event. Previous simulation studies have verified the efficiency and accuracy of AMS in the calculation of transition times for simple systems in both Monte Carlo and molecular dynamics (MD) simulations. Now, AMS is applied for the first time to an MD simulation of protein-ligand dissociation, representing a leap in complexity from the previous test cases. Of interest is the dissociation rate, which is typically too low to be accessible to conventional MD. The present study joins other recent efforts to develop advanced sampling techniques in MD to calculate dissociation rates, which are gaining importance in the pharmaceutical field as indicators of drug efficacy. The system investigated here, benzamidine bound to trypsin, is an example common to many of these efforts. The AMS estimate of the dissociation rate was found to be (2.6 ± 2.4) × 10(2) s(-1), which compares well with the experimental value.

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.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Many proteins are nanomachines that perform mechanical or chemical work by changing their three-dimensional shape and cycle between multiple conformational states. Computer simulations of such conformational transitions provide mechanistic insights into protein function but such simulations have been challenging. In particular, it is not clear how to quantitatively compare current simulation methods or to assess their accuracy. To that end, we present a general and flexible computational framework for quantifying transition paths—by measuring mutual geometric similarity—that, compared with existing approaches, requires minimal a-priori assumptions and can take advantage of full atomic detail alongside heuristic information derived from intuition. Using our Path Similarity Analysis (PSA) framework in parallel with several existing quantitative approaches, we examine transitions generated for a toy model of a transition and two biological systems, the enzyme adenylate kinase and diphtheria toxin. Our results show that PSA enables the quantitative comparison of different path sampling methods and aids the identification of potentially important atomistic motions by exploiting geometric information in transition paths. The method has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing macromolecular conformational transitions.

Temperature Accelerated Molecular Dynamics with Soft-Ratcheting Criterion Orients Enhanced Sampling by Low-Resolution Information

Many proteins exhibit an equilibrium between multiple conformations, some of them being characterized only by low-resolution information. Visiting all conformations is a demanding task for computational techniques performing enhanced but unfocused exploration of collective variable (CV) space. Otherwise, pulling a structure toward a target condition biases the exploration in a way difficult to assess. To address this problem, we introduce here the soft-ratcheting temperature-accelerated molecular dynamics (sr-TAMD), where the exploration of CV space by TAMD is coupled to a soft-ratcheting algorithm that filters the evolving CV values according to a predefined criterion. Any low resolution or even qualitative information can be used to orient the exploration. We validate this technique by exploring the conformational space of the inactive state of the catalytic domain of the adenyl cyclase AC from Bordetella pertussis. The domain AC gets activated by association with calmodulin (CaM), and the available crystal structure shows that in the complex the protein has an elongated shape. High-resolution data are not available for the inactive, CaM-free protein state, but hydrodynamic measurements have shown that the inactive AC displays a more globular conformation. Here, using as CVs several geometric centers, we use sr-TAMD to enhance CV space sampling while filtering for CV values that correspond to centers moving close to each other, and we thus rapidly visit regions of conformational space that correspond to globular structures. The set of conformations sampled using sr-TAMD provides the most extensive description of the inactive state of AC up to now, consistent with available experimental information.

Molecular dynamics simulations of the bacterial UraA H+-uracil symporter in lipid bilayers reveal a closed state and a selective interaction with cardiolipin

The Escherichia coli UraA H⁺-uracil symporter is a member of the nucleobase/ascorbate transporter (NAT) family of proteins, and is responsible for the proton-driven uptake of uracil. Multiscale molecular dynamics simulations of the UraA symporter in phospholipid bilayers consisting of: 1) 1-palmitoyl 2-oleoyl-phosphatidylcholine (POPC); 2) 1-palmitoyl 2-oleoyl-phosphatidylethanolamine (POPE); and 3) a mixture of 75% POPE, 20% 1-palmitoyl 2-oleoyl-phosphatidylglycerol (POPG); and 5% 1-palmitoyl 2-oleoyl-diphosphatidylglycerol/cardiolipin (CL) to mimic the lipid composition of the bacterial inner membrane, were performed using the MARTINI coarse-grained force field to self-assemble lipids around the crystal structure of this membrane transport protein, followed by atomistic simulations. The overall fold of the protein in lipid bilayers remained similar to the crystal structure in detergent on the timescale of our simulations. Simulations were performed in the absence of uracil, and resulted in a closed state of the transporter, due to relative movement of the gate and core domains. Anionic lipids, including POPG and especially CL, were found to associate with UraA, involving interactions between specific basic residues in loop regions and phosphate oxygens of the CL head group. In particular, three CL binding sites were identified on UraA: two in the inner leaflet and a single site in the outer leaflet. Mutation of basic residues in the binding sites resulted in the loss of CL binding in the simulations. CL may play a role as a “proton trap” that channels protons to and from this transporter within CL-enriched areas of the inner bacterial membrane.

Symporters are proteins that are responsible for the co-transport of ions and small molecule solutes across cell membranes. UraA is an example of a symporter, and is responsible for the proton-driven uptake of uracil in bacteria like E. coli. Despite its importance as a member of a large family of nucleobase/ascorbate transporters (NAT) and the existence of structural and functional data, the mechanism by which UraA transports uracil across the bacterial membrane, and in particular the role of its diverse and complex lipid environment in the transport mechanism, remains elusive. In this study, we have used a multiscale computational methodology to examine the dynamics of UraA and to elucidate its interactions with lipids that resemble its native environment in the bacterial inner membrane. Our results demonstrate that negatively-charged lipids in the membrane (phosphatidylglycerol and cardiolipin) associate preferentially with UraA and may play a role in its function. Additionally, our simulations resulted in a closed state of UraA, a likely intermediate in the transport mechanism that may not be readily accessible by experimental methods.

Computing ensembles of transitions with molecular dynamics simulations

A molecular understanding of conformational change is important for connecting structure and function. Without the ability to sample on the meaningful large-scale conformational changes, the ability to infer biological function and to understand the effect of mutations and changes in environment is not possible. Our Dynamic Importance Sampling method (DIMS), part of the CHARMM simulation package, is a method that enables sampling over ensembles of transition intermediates. This chapter outlines the context for the method and the usage within the program.

Assessing the Accuracy of Two Enhanced Sampling Methods Using EGFR Kinase Transition Pathways: The Influence of Collective Variable Choice

Structurally elucidating transition pathways between protein conformations gives deep mechanistic insight into protein behavior but is typically difficult. Unbiased molecular dynamics (MD) simulations provide one solution, but their computational expense is often prohibitive, motivating the development of enhanced sampling methods that accelerate conformational changes in a given direction, embodied in a collective variable. The accuracy of such methods is unclear for complex protein transitions, because obtaining unbiased MD data for comparison is difficult. Here, we use long-time scale, unbiased MD simulations of epidermal growth factor receptor kinase deactivation as a complex biological test case for two widely used methods-steered molecular dynamics (SMD) and the string method. We found that common collective variable choices, based on the root-mean-square deviation (RMSD) of the entire protein, prevented the methods from producing accurate paths, even in SMD simulations on the time scale of the unbiased transition. Using collective variables based on the RMSD of the region of the protein known to be important for the conformational change, however, enabled both methods to provide a more accurate description of the pathway in a fraction of the simulation time required to observe the unbiased transition.

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

Flexible gates generate occluded intermediates in the transport cycle of LacY

The major facilitator superfamily (MFS) transporter lactose permease (LacY) alternates between cytoplasmic and periplasmic open conformations to co-transport a sugar molecule together with a proton across the plasma membrane. Indirect experimental evidence suggested the existence of an occluded transition intermediate of LacY, which would prevent leaking of the proton gradient. As no experimental structure is known, the conformational transition is not fully understood in atomic detail. We simulated transition events from a cytoplasmic open conformation to a periplasmic open conformation with the dynamic importance sampling molecular dynamics method and observed occluded intermediates. Analysis of water permeation pathways and the electrostatic free-energy landscape of a solvated proton indicated that the occluded state contains a solvated central cavity inaccessible from either side of the membrane. We propose a pair of geometric order parameters that capture the state of the pathway through the MFS transporters as shown by a survey of available crystal structures and models. We present a model for the occluded state of apo-LacY, which is similar to the occluded crystal structures of the MFS transporters EmrD, PepT_So, NarU, PiPT and XylE. Our simulations are consistent with experimental double electron spin–spin distance measurements that have been interpreted to show occluded conformations. During the simulations, a salt bridge that has been postulated to be involved in driving the conformational transition formed. Our results argue against a simple rigid-body domain motion as implied by a strict “rocker-switch mechanism” and instead hint at an intricate coupling between two flexible gates.

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The transport mechanism of LacY is hypothesized to involve an intermediate “occluded” state.

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Such a state is observed in computer simulations of the conformational transitions.

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Simulation data are validated with experimental double electron–electron spin resonance measurements.

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The structural gating elements of LacY are identified.

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Occluded LacY is similar to known occluded structures of homologous proteins.

Toward an understanding of agonist binding to human Orexin-1 and Orexin-2 receptors with G-protein-coupled receptor modeling and site-directed mutagenesis

The class A G-protein-coupled receptors (GPCRs) Orexin-1 (OX1) and Orexin-2 (OX2) are located predominantly in the brain and are linked to a range of different physiological functions, including the control of feeding, energy metabolism, modulation of neuro-endocrine function, and regulation of the sleep-wake cycle. The natural agonists for OX1 and OX2 are two neuropeptides, Orexin-A and Orexin-B, which have activity at both receptors. Site-directed mutagenesis (SDM) has been reported on both the receptors and the peptides and has provided important insight into key features responsible for agonist activity. However, the structural interpretation of how these data are linked together is still lacking. In this work, we produced and used SDM data, homology modeling followed by MD simulation, and ensemble-flexible docking to generate binding poses of the Orexin peptides in the OX receptors to rationalize the SDM data. We also developed a protein pairwise similarity comparing method (ProS) and a GPCR-likeness assessment score (GLAS) to explore the structural data generated within a molecular dynamics simulation and to help distinguish between different GPCR substates. The results demonstrate how these newly developed methods of structural assessment for GPCRs can be used to provide a working model of neuropeptide-Orexin receptor interaction.

Exploration of conformational transition pathways from coarse-grained simulations

MOTIVATION

A new algorithm to trace conformational transitions in proteins is presented. The method uses discrete molecular dynamics as engine to sample protein conformational space. A multiple minima Go-like potential energy function is used in combination with several enhancing sampling strategies, such as metadynamics, Maxwell Demon molecular dynamics and essential dynamics. The method, which shows an unprecedented computational efficiency, is able to trace a wide range of known experimental transitions. Contrary to simpler methods our strategy does not introduce distortions in the chemical structure of the protein and is able to reproduce well complex non-linear conformational transitions. The method, called GOdMD, can easily introduce additional restraints to the transition (presence of ligand, known intermediate, known maintained contacts, …) and is freely distributed to the community through the Spanish National Bioinformatics Institute (http://mmb.irbbarcelona.org/GOdMD).

AVAILABILITY

Freely available on the web at http://mmb.irbbarcelona.org/GOdMD.

Molecular dynamics simulations of transitions for ECD epidermal growth factor receptors show key differences between human and drosophila forms of the receptors

Recent X-ray structural work on the Drosophila epidermal growth factor receptor (EFGR) has suggested an asymmetric dimer that rationalizes binding affinity measurements that go back decades (Alvarado et al., Cell 2010;142:568-579; Dawson et al., Structure 2007;15:942-954; Lemmon et al., Embo J 1997;16:281-294; Mattoon et al., Proc Natl Acad Sci USA 2004;101:923-928; Mayawala et al., Febs Lett 2005;579:3043-3047; Ozcan et al., Proc Natl Acad Sci USA 2006;103:5735-5740). This type of asymmetric structure has not been seen for the human EGF receptor family and it may or may not be important for function in that realm. We hypothesize that conformational changes in the Drosophila system have been optimized for the transition, whereas the barrier for the same transition is much higher in the human forms. To address our hypothesis we perform dynamic importance sampling (DIMS) (Perilla et al., J Comput Chem 2010;32:196-209) for barrier crossing transitions in both Drosophila and human EFGRs. For each set of transitions, we work from the hypothesis, based on results from the AdK system, that salt-bridge pairs making and breaking connections are central to the conformational change. To evaluate the effectiveness of the salt-bridges as drivers for the conformational change, we use the effective transfer entropy based on stable state MD calculations (Kamberaj and Der Vaart, Biophys J 2009;97:1747-1755) to define a reduced subset of degrees of freedom that seem to be important for driving the transition (Perilla and Woolf, J Chem Phys 2012;136:164101). Our results suggest that salt-bridge making and breaking is not the dominant factor in driving the symmetric to asymmetric transition, but that instead it is a result of more concerted and correlated functional motions within a subset of the dimer structures. Furthermore, the analysis suggests that the set of residues involved in the transitions from the Drosophila relative to the human forms differs and that this difference in substate distributions relates to why the asymmetric form may be more common to Drosophila than to the human forms. We close with a discussion about the residues that may be changed in the human and the Drosophila forms to potentially shift the kinetics of the symmetric to asymmetric transition.

Coarse-grained simulations of transitions in the E2-to-E1 conformations for Ca ATPase (SERCA) show entropy-enthalpy compensation

SERCA is a membrane transport protein that has been extensively studied. There are a large number of highly resolved X-ray structures and several hundred mutations that have been characterized functionally. Despite this, the molecular details of the catalytic cycle, a cycle that includes large conformational changes, is not fully understood. In this computational study, we provide molecular dynamics descriptions of conformational changes during the E2→E1 transitions. The motivating point for these calculations was a series of insertion mutants in the A-M3 linker region that led to significant shifts in measured rates between the E2 and E1 states, as shown by experimental characterization. Using coarse-grained dynamic importance sampling within the context of a population shift framework, we sample on the intermediates along the transition pathway to address the mechanism for the conformational changes and the effects of the insertion mutations on the kinetics of the transition. The calculations define an approximation for the relative changes in entropy and enthalpy along the transition. These are found to be important for understanding the experimentally observed differences in rates. In particular, the interactions between cytoplasmic domains, water interactions, and the shifts in protein degrees of freedom with the insertion mutations show mutual compensation for the E2→E1 transitions in wild-type and mutant systems.

The role of domain: domain interactions versus domain: water interactions in the coarse-grained simulations of the E1P to E2P transitions in Ca-ATPase (SERCA)

SERCA is an important model system for understanding the molecular details of conformational change in membrane transport systems. This reflects the large number of solved X-ray structures and the equally large database of mutations that have been assayed. In this computational study, we provide a molecular dynamics description of the conformational changes during the E1P → E2P transitions. This set of states further changes with insertion mutants in the A-M3 linker region. These mutants were experimentally shown to lead to significant shifts in rates between the E1P → E2P states. Using the population shift framework and dynamic importance sampling method along with coarse-grained representations of the protein, lipid, and water, we suggest why these changes are found. The calculations sample on intermediates and suggest that changes in interactions, individual helix interactions, and water behavior are key elements in the molecular compositions that underlie shifts in kinetics. In particular, as the insertion length grows, it attracts more water and disrupts domain interactions, creating changes as well at the sites of key helix interactions between the A-Domain and the P-Domain. This provides a conceptual picture that aids understanding of the experimental results.

Towards the prediction of order parameters from molecular dynamics simulations in proteins

A molecular understanding of how protein function is related to protein structure requires an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy barriers and within a complex energy landscape. This makes it very difficult to reliably connect, for example by all-atom molecular dynamics calculations, the states, their energies, and the pathways between them. A major issue needed to improve sampling on the intermediate states is an order parameter--a reduced descriptor for the major subset of degrees of freedom--that can be used to aid sampling for the large conformational change. We present a method to combine information from molecular dynamics using non-linear time series and dimensionality reduction, in order to quantitatively determine an order parameter connecting two large-scale conformationally distinct protein states. This new method suggests an implementation for molecular dynamics calculations that may be used to enhance sampling of intermediate states.

Exploration of multi-state conformational dynamics and underlying global functional landscape of maltose binding protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.

A central goal of biology is to understand the function of the organism and its constituent parts at each of its scales of complexity. Function at the molecular level is often realized by changes in conformation. Unfortunately, experimental explorations of global motions critical for functional conformational changes are still challenging. In the present work, we developed a coarse grained triple-well structure-based model to explore the underlying functional landscape of maltose-binding protein (MBP). By quantitative flux analysis, we uncover the underlying mechanism by which the major induced fit and minor population shift pathways co-exist. Though we have previously lent credence to the assertion that dynamical equilibrium between open and minor closed conformations exist for all the free PBPs, the generality of this rule is still a matter of open debate. We found that the hinge flexibility is favorable to population shift mechanism. This finding provides a theoretical explanation of the mechanism discrepancies in PBP protein family. We also simulated the folding dynamics using this functional multi-basin model which successfully reproduced earlier protein melting experiment. This represents an exciting opportunity to characterize the interplay between folding and function, which is a long-standing question in the community. The theoretical approach employed in this study is general and can be applied to other systems.

Cooperative nature of gating transitions in K(+) channels as seen from dynamic importance sampling calculations

The growing dataset of K(+) channel x-ray structures provides an excellent opportunity to begin a detailed molecular understanding of voltage-dependent gating. These structures, while differing in sequence, represent either a stable open or closed state. However, an understanding of the molecular details of gating will require models for the transitions and experimentally testable predictions for the gating transition. To explore these ideas, we apply dynamic importance sampling to a set of homology models for the molecular conformations of K(+) channels for four different sets of sequences and eight different states. In our results, we highlight the importance of particular residues upstream from the Pro-Val-Pro (PVP) region to the gating transition. This supports growing evidence that the PVP region is important for influencing the flexibility of the S6 helix and thus the opening of the gating domain. The results further suggest how gating on the molecular level depends on intra-subunit motions to influence the cooperative behavior of all four subunits of the K(+) channel. We hypothesize that the gating process occurs in steps: first sidechain movement, then inter-S5-S6 subunit motions, and lastly the large-scale domain rearrangements.