Configurational Ensemble Research Articles

Cation Distribution and Anion Transport in the La3Ga5-xGe1+xO14+0.5x Langasite Structure.

Exploration of compositional disorder using conventional diffraction-based techniques is challenging for systems containing isoelectronic ions possessing similar coherent neutron scattering lengths. Here, we show that a multinuclear solid-state Nuclear Magnetic Resonance (NMR) approach provides compelling insight into the Ga3+/Ge4+ cation distribution and oxygen anion transport in a family of solid electrolytes with langasite structure and La3Ga5-xGe1+xO14+0.5x composition. Ultrahigh field 71Ga Magic Angle Spinning (MAS) NMR experiments acquired at 35.2 T offer striking resolution enhancement, thereby enabling clear detection of Ga sites in different coordination environments. Three-connected GaO4, four-connected GaO4 and GaO6 polyhedra are probed for the parent La3Ga5GeO14 structure, while one additional spectral feature corresponding to the key (Ga,Ge)2O8 structural unit which forms to accommodate the interstitial oxide ions is detected for the Ge4+-doped La3Ga3.5Ge2.5O14.75 phase. The complex spectral line shapes observed in the MAS NMR spectra are reproduced very accurately by the NMR parameters computed for a symmetry-adapted configurational ensemble that comprehensively models site disorder. This approach further reveals a Ga3+/Ge4+ distribution across all Ga/Ge sites that is controlled by a kinetically governed cation diffusion process. Variable temperature 17O MAS NMR experiments up to 700 °C importantly indicate that the presence of interstitial oxide ions triggers chemical exchange between all oxygen sites, thereby enabling atomic-scale understanding of the anion diffusion mechanism underpinning the transport properties of these materials.

Role of morphology in defect formation and photo-induced carrier instabilities in amorphous indium oxide

Ab initio molecular dynamics liquid-quench simulations and hybrid density functional calculations are performed to model the effects of room-temperature atomic fluctuations and photo-illumination on the structural and electronic properties of amorphous sub-stoichiometric In2O2.96. A large configurational ensemble is employed to reliably predict the distribution of localized defects as well as their response to the thermal and light activation. The results reveal that the illumination effects on the carrier concentration are greater in amorphous configurations with shorter In–O bond length and reduced polyhedral sharing as compared to the structures with a more uniform morphology. The obtained correlation between the photo-induced carrier density and the reduction in the number of fully coordinated In-atoms implies that metal oxides with a significant fraction of crystalline/amorphous interfaces would show a more pronounced response to illumination. Photo-excitation also produces In–O2–In defects that have not been previously found in sub-stoichiometric amorphous oxides; these defects are responsible for carrier instabilities due to overdoping.

ATRANET - Automated generation of transition networks for the structural characterization of intrinsically disordered proteins.

Intrinsically disordered proteins (IDPs) do not fold into a unique three-dimensional structure but sample different configurations of different probabilities that further change with the surrounding of the IDPs. The structural heterogeneity and dynamics of IDPs pose a challenge for the characterization of their structures by experimental techniques only. Molecular dynamics (MD) simulations provide a powerful complement to experimental approaches for that purpose. However, MD simulations on the micro- to millisecond timescale generate a lot of data of protein motions, necessitating advanced post-processing techniques to extract the relevant information. Here, we demonstrate how transition networks created from MD trajectories allow revealing the configurational ensemble and structural interconversions of IDPs, using the amyloid-β peptide as example. The construction of transition networks relies on molecular descriptors as input, and we show how the choice of descriptors influences the resulting transition network. The transition networks are generated with the open-source Python script ATRANET, and we explain the usage of ATRANET by providing a detailed workflow and exemplary analysis for amyloid-β, which can be easily generalized to other IDPs and even protein aggregation.

Modeling the Structure and Interactions of Intrinsically Disordered Peptides with Multiple Replica, Metadynamics-Based Sampling Methods and Force-Field Combinations.

Intrinsically disordered proteins play a key role in many biological processes, including the formation of biomolecular condensates within cells. A detailed characterization of their configurational ensemble and structure–function paradigm is crucial for understanding their biological activity and for exploiting them as building blocks in material sciences. In this work, we incorporate bias-exchange metadynamics and parallel-tempering well-tempered metadynamics with CHARMM36m and CHARMM22* to explore the structural and thermodynamic characteristics of a short archetypal disordered sequence derived from a DEAD-box protein. The conformational landscapes emerging from our simulations are largely congruent across methods and force fields. Nevertheless, differences in fine details emerge from varying combinations of force-fields and sampling methods. For this protein, our analysis identifies features that help to explain the low propensity of this sequence to undergo self-association in vitro, which are common to all force-field/sampling method combinations. Overall, our work demonstrates the importance of using multiple force-field and sampling method combinations for accurate structural and thermodynamic information in the study of disordered proteins.

Ensemble Switching Unveils a Kinetic Rheostat Mechanism of the Eukaryotic Thiamine Pyrophosphate Riboswitch.

Thiamine pyrophosphate (TPP) riboswitches regulate thiamine metabolism by inhibiting the translation of enzymes essential to thiamine synthesis pathways upon binding to thiamine pyrophosphate in cells across all domains of life. Recent work on the Arabidopsis thaliana TPP riboswitch suggests a multistep TPP binding process involving multiple riboswitch configurational ensembles and Mg2+ dependence underlies the mechanism of TPP recognition and subsequent transition to the expression-inhibiting state of the aptamer domain followed by changes in the expression platform. However, details of the relationship between TPP riboswitch conformational changes and interactions with TPP and Mg2+ in the aptamer domain constituting this mechanism are unknown. Therefore, we integrated single-molecule multiparameter fluorescence and force spectroscopy with atomistic molecular dynamics simulations and found that conformational transitions within the aptamer domain's sensor helices associated with TPP and Mg2+ ligand binding occurred between at least five different ensembles on timescales ranging from µs to ms. These dynamics are orders of magnitude faster than the 10 sec-timescale folding kinetics associated with expression-state switching in the switch helix. Together, our results show that a TPP and Mg2+ dependent mechanism determines dynamic configurational state ensemble switching of the aptamer domain's sensor helices that regulate the switch helix's stability, which ultimately may lead to the expression-inhibiting state of the riboswitch. Additionally, we propose that two pathways exist for ligand recognition and that this mechanism underlies a kinetic rheostat-like behavior of the Arabidopsis thaliana TPP riboswitch.

Inferring functional units in ion channel pores via relative entropy

Coarse-grained protein models approximate the first-principle physical potentials. Among those modeling approaches, the relative entropy framework yields promising and physically sound results, in which a mapping from the target protein structure and dynamics to a model is defined and subsequently adjusted by an entropy minimization of the model parameters. Minimization of the relative entropy is equivalent to maximization of the likelihood of reproduction of (configurational ensemble) observations by the model. In this study, we extend the relative entropy minimization procedure beyond parameter fitting by a second optimization level, which identifies the optimal mapping to a (dimension-reduced) topology. We consider anisotropic network models of a diverse set of ion channels and assess our findings by comparison to experimental results.

Deciphering High-Order Structural Correlations within Fluxional Molecules from Classical and Quantum Configurational Entropy.

We employ the kth nearest-neighbor estimator of configurational entropy in order to decode within a parameter-free numerical approach the complex high-order structural correlations in fluxional molecules going much beyond the usual linear, bivariate correlations. This generic entropy-based scheme for determining many-body correlations is applied to the complex configurational ensemble of protonated acetylene, a prototype for fluxional molecules featuring large-amplitude motion. After revealing the importance of high-order correlations beyond the simple two-coordinate picture for this molecule, we analyze in detail the evolution of the relevant correlations with temperature as well as the impact of nuclear quantum effects down to the ultralow temperature regime of 1 K. We find that quantum delocalization and zero-point vibrations significantly reduce all correlations in protonated acetylene in the deep quantum regime. Even at low temperatures up to about 100 K, most correlations are essentially absent in the quantum case and only gain importance at higher temperatures. In the high temperature regime, beyond roughly 800 K, the increasing thermal fluctuations are found to exert a destructive effect on the presence of correlations. At intermediate temperatures of approximately 100-800 K, a quantum-to-classical cross-over regime is found where classical mechanics starts to correctly describe trends in the correlations whereas it even qualitatively fails below 100 K. Finally, a classical description of the nuclei provides correlations that are in quantitative agreement with the quantum ones only at temperatures exceeding 1000 K. This data-intensive analysis has been made possible due to recent developments of machine learning techniques based on high-dimensional neural network potential energy surfaces in full dimensionality that allow us to exhaustively sample both the classical and quantum ensemble of protonated acetylene at essentially converged coupled cluster accuracy from 1 to more than 1000 K. The presented non-parametric analysis of correlations beyond usual linear two-coordinate terms is transferable to other system classes. The technique is also expected to complement and guide the analysis of experimental measurements, in particular multidimensional vibrational spectroscopy, by revealing the complex coupling between various degrees of freedom.

Generation of the Configurational Ensemble of an Intrinsically Disordered Protein

A major challenge in biology is characterizing the structural flexibility of intrinsically disordered proteins (IDPs). Ensemble‐averaged experimental data do not provide the underlying protein structures. Here, we performed independently small‐angle neutron and X‐ray scattering experiments and unbiased molecular dynamics simulations to probe the solution structure of an IDP. We report that enhancing the sampling of the simulations can generate an ensemble of IDP structures in quantitative agreement with scattering and NMR, without the need for biasing the simulation or reweighting the results. The demonstration of established simulation technology that produces accurate physical models of flexible biosystems may pave the way to relating conformational flexibility to biological function.Support or Funding InformationThis work is supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, and by project ERKP300 funded by the Office of Biological & Environmental Research in the Department of Energy Office of Science.Configurational ensemble of c‐Src kinaseFigure 1

Ensemble-Based Modeling of the NMR Spectra of Solid Solutions: Cation Disorder in Y2(Sn,Ti)2O7.

The sensitivity of NMR to the local environment, without the need for any long-range order, makes it an ideal tool for the characterization of disordered materials. Computational prediction of NMR parameters can be of considerable help in the interpretation and assignment of NMR spectra of solids, but the statistical representation of all possible chemical environments for a solid solution is challenging. Here, we illustrate the use of a symmetry-adapted configurational ensemble in the simulation of NMR spectra, in combination with solid-state NMR experiments. We show that for interpretation of the complex and overlapped lineshapes that are typically observed, it is important to go beyond a single-configuration representation or a simple enumeration of local environments. The ensemble method leads to excellent agreement between simulated and experimental spectra for Y2(Sn,Ti)2O7 pyrochlore ceramics, where the overlap of signals from different local environments prevents a simple decomposition of the experimental spectral lineshapes. The inclusion of a Boltzmann weighting confirms that the best agreement with experiment is obtained at higher temperatures, in the limit of full disorder. We also show that to improve agreement with experiment, in particular at low dopant concentrations, larger supercells are needed, which might require alternative simulation approaches as the complexity of the system increases. It is clear that ensemble-based modeling approaches in conjunction with NMR spectroscopy offer great potential for understanding configurational disorder, ultimately aiding the future design of functional materials.

Generation of the configurational ensemble of an intrinsically disordered protein from unbiased molecular dynamics simulation

Intrinsically disordered proteins (IDPs) are abundant in eukaryotic proteomes, play a major role in cell signaling, and are associated with human diseases. To understand IDP function it is critical to determine their configurational ensemble, i.e., the collection of 3-dimensional structures they adopt, and this remains an immense challenge in structural biology. Attempts to determine this ensemble computationally have been hitherto hampered by the necessity of reweighting molecular dynamics (MD) results or biasing simulation in order to match ensemble-averaged experimental observables, operations that reduce the precision of the generated model because different structural ensembles may yield the same experimental observable. Here, by employing enhanced sampling MD we reproduce the experimental small-angle neutron and X-ray scattering profiles and the NMR chemical shifts of the disordered N terminal (SH4UD) of c-Src kinase without reweighting or constraining the simulations. The unbiased simulation results reveal a weakly funneled and rugged free energy landscape of SH4UD, which gives rise to a heterogeneous ensemble of structures that cannot be described by simple polymer theory. SH4UD adopts transient helices, which are found away from known phosphorylation sites and could play a key role in the stabilization of structural regions necessary for phosphorylation. Our findings indicate that adequately sampled molecular simulations can be performed to provide accurate physical models of flexible biosystems, thus rationalizing their biological function.

Simulating and analysing configurational landscapes of protein-protein contact formation.

Interacting proteins can form aggregates and protein-protein interfaces with multiple patterns and different stabilities. Using molecular simulation one would like to understand the formation of these aggregates and which of the observed states are relevant for protein function and recognition. To characterize the complex configurational ensemble of protein aggregates, one needs a quantitative measure for the similarity of structures. We present well-suited descriptors that capture the essential features of non-covalent protein contact formation and domain motion. This set of collective variables is used with a nonlinear multi-dimensional scaling-based dimensionality reduction technique to obtain a low-dimensional representation of the configurational landscape of two ubiquitin proteins from coarse-grained simulations. We show that this two-dimensional representation is a powerful basis to identify meaningful states in the ensemble of aggregated structures and to calculate distributions and free energy landscapes for different sets of simulations. By using a measure to quantitatively compare free energy landscapes we can show how the introduction of a covalent bond between two ubiquitin proteins at different positions alters the configurational states of these dimers.

Building maps in collective variable space.

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables (CVs). The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work, we discuss how auxiliary variables can be mapped in CV space. We show that maps of auxiliary variables allow one to analyze both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyze the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.

A "Tug of War" Maintains a Dynamic Protein-Membrane Complex: Molecular Dynamics Simulations of C-Raf RBD-CRD Bound to K-Ras4B at an Anionic Membrane.

Association of Raf kinase with activated Ras triggers downstream signaling cascades toward regulating transcription in the cells’ nucleus. Dysregulation of Ras–Raf signaling stimulates cancers. We investigate the C-Raf RBD and CRD regions when bound to oncogenic K-Ras4B at the membrane. All-atom molecular dynamics simulations suggest that the membrane plays an integral role in regulating the configurational ensemble of the complex. Remarkably, the complex samples a few states dynamically, reflecting a competition between C-Raf CRD- and K-Ras4B- membrane interactions. This competition arises because the interaction between the RBD and K-Ras is strong while the linker between the RBD and CRD is short. Such a mechanism maintains a modest binding for the overall complex at the membrane and is expected to facilitate fast signaling processes. Competition of protein–membrane contacts is likely a common mechanism for other multiprotein complexes, if not multidomain proteins at membranes.

Emergence of order in self-assembly of the intrinsically disordered biomineralisation peptide n16N

We present the results of an aggregation study on the intrinsically disordered biomineralisation peptide n16N, which selects the aragonite polymorph of calcium carbonate and is expected to have aggregation-dependent structure and function. The peptide is a sub-sequence of the in vivo protein n16, with putative framework and polymorph selection roles in the nacre layer of pearl oyster (Pinctada fucata). Employing the intermediate-resolution coarse-grained protein model PLUM*, which has previously been validated with respect to n16N, we simulate assemblies of these peptide units for system sizes inaccessible to atomistic models. We use extensive conformational sampling to show that the configurational ensemble explored by n16N aggregates contains a significant proportion of ordered -structure, within which arrangement of monomers is consistent with a previous hypothesis on functionally distinct subdomains of n16N. We also study an n16N mutant which fails to aggregate in experimental studies and obtain very similar behaviour, the consequences of which are discussed.

Multiscale enhanced sampling for protein systems: An extension via adiabatic separation

Multiscale enhanced sampling (MSES) calculates the configurational ensemble of all-atom (MM) protein systems with the help of coupling to a coarse-grained (CG) model. Here, for further improvement of the sampling efficiency, the approximation of adiabatic separation was introduced to the original MSES, by adopting a high CG temperature limit. An application to the folding of chignolin in explicit solvent demonstrated that the MSES formula based on adiabatic separation correctly sampled the canonical ensemble with excellent efficiency and robustness against the parameter selection, and thus MSES successfully achieved the scalability for applications to large protein systems.

On the use of a weak-coupling thermostat in replica-exchange molecular dynamics simulations.

In a molecular dynamics (MD) simulation, various thermostat algorithms, including Langevin dynamics (LD), Nosé-Hoover (NH), and weak-coupling (WC) thermostats, can be used to keep the simulation temperature constant. A canonical ensemble is generated by the use of LD and NH, while the nature of the ensemble produced by WC has not yet been identified. A few years ago, it was shown that when using a WC thermostat with particular values of the temperature coupling time for liquid water at ambient temperature and pressure, the distribution of the potential energy is less wide than the canonical one. This led to an artifact in temperature replica-exchange molecular dynamics (T-REMD) simulations in which the potential energy distributions appear not to be equal to the ones of standard MD simulations. In this paper, we re-investigate this problem. We show that this artifact is probably due to the ensemble generated by WC being incompatible with the T-REMD replica-exchange criterion, which assumes a canonical configurational ensemble. We also show, however, that this artifact can be reduced or even eliminated by particular choices of the temperature coupling time of WC and the replica-exchange time period of T-REMD, i.e., when the temperature coupling time is chosen very close to the MD time step or when the exchange time period is chosen large enough. An attempt to develop a T-REMD replica-exchange criterion which is likely to be more compatible with the WC configurational ensemble is reported. Furthermore, an exchange criterion which is compatible with a microcanonical ensemble is used in total energy REMD simulations.

Spatial analysis and quantification of the thermodynamic driving forces in protein-ligand binding: binding site variability.

The thermodynamic driving forces behind small molecule-protein binding are still not well-understood, including the variability of those forces associated with different types of ligands in different binding pockets. To better understand these phenomena we calculate spatially resolved thermodynamic contributions of the different molecular degrees of freedom for the binding of propane and methanol to multiple pockets on the proteins Factor Xa and p38 MAP kinase. Binding thermodynamics are computed using a statistical thermodynamics based end-point method applied on a canonical ensemble comprising the protein-ligand complexes and the corresponding free states in an explicit solvent environment. Energetic and entropic contributions of water and ligand degrees of freedom computed from the configurational ensemble provide an unprecedented level of detail into the mechanisms of binding. Direct protein-ligand interaction energies play a significant role in both nonpolar and polar binding, which is comparable to water reorganization energy. Loss of interactions with water upon binding strongly compensates these contributions leading to relatively small binding enthalpies. For both solutes, the entropy of water reorganization is found to favor binding in agreement with the classical view of the "hydrophobic effect". Depending on the specifics of the binding pocket, both energy-entropy compensation and reinforcement mechanisms are observed. It is notable to have the ability to visualize the spatial distribution of the thermodynamic contributions to binding at atomic resolution showing significant differences in the thermodynamic contributions of water to the binding of propane versus methanol.

Molecular dynamics simulation of configurational ensembles compatible with experimental FRET efficiency data through a restraint on instantaneous FRET efficiencies.

Förster resonance energy transfer (FRET) measurements are widely used to investigate (bio)molecular interactions or/and association. FRET efficiencies, the primary data obtained from this method, give, in combination with the common assumption of isotropic chromophore orientation, detailed insight into the lengthscale of molecular phenomena. This study illustrates the application of a FRET efficiency restraint during classical atomistic molecular dynamics simulations of a mutant mastoparan X peptide in either water or 7 M aqueous urea. The restraint forces acting on the donor and acceptor chromophores ensure that the sampled peptide configurational ensemble satisfies the experimental primary data by modifying interchromophore separation and chromophore transition dipole moment orientations. By means of a conformational cluster analysis, it is seen that indeed different configurational ensembles may be sampled without and with application of the restraint. In particular, while the FRET efficiency and interchromophore distances monitored in an unrestrained simulation may differ from the experimentally-determined values, they can be brought in agreement with experimental data through usage of the FRET efficiency restraining potential. Furthermore, the present results suggest that the assumption of isotropic chromophore orientation is not always justified. The FRET efficiency restraint allows the generation of configurational ensembles that may not be accessible with unrestrained simulations, and thereby supports a meaningful interpretation of experimental FRET results in terms of the underlying molecular degrees of freedom. Thus, it offers an additional tool to connect the realms of computer and wet-lab experimentation.

A Complete Configurational Ensemble Approach to Expand Lsd1/Corest Druggability

Lysine specific demethylase-1 (LSD1/KDM1A) in complex with the corepressor protein CoREST is a promising target for epigenetic drugs yet no therapeutics targeting LSD1/CoREST are currently available. Extended molecular dynamics (MD) simulations have indicated that LSD1/CoREST nanoscale clamp dynamics are regulated by substrate binding and highlighted key hinge points of this large-scale motion as well as the relevance of local residue dynamics. Prompted by the urgent need for new molecular probes and inhibitors to understand LSD1/CoREST interactions with small-molecules, peptides, protein partners, and chromatin, we undertake here a complete configurational ensemble approach to expand LSD1/CoREST druggability. The independent algorithms FTMap and SiteMap and a newly developed Druggable Site Visualizer (DSV) software tool were used to predict and inspect favorable binding sites on an ensemble of structures generated by MD simulation. We found that three hinge points revealed by MD simulations are new potential targets for the discovery of molecular probes to block association of LSD1/CoREST with chromatin or protein partners. A fourth region was also predicted from simulated configurational ensembles and was experimentally validated to have strong binding propensity for a small peptide. This prediction would be prevented when using only the X-ray structures available (including the X-ray structure bound to the same peptide), which underscores the relevance of protein conformational dynamics in protein interactions. A fifth region was also highlighted corresponding to a small pocket on the AOD domain. This study sets the basis for future virtual screening campaigns targeting the five novel regions reported herein and for the design of LSD1/CoREST mutants to probe LSD1/CoREST binding with chromatin and various protein partners. The newly developed computational methods are being further validated on various protein receptors and have shown promising preliminary results.

Expanding the Druggable Space of the LSD1/CoREST Epigenetic Target: New Potential Binding Regions for Drug-Like Molecules, Peptides, Protein Partners, and Chromatin

Lysine specific demethylase-1 (LSD1/KDM1A) in complex with its corepressor protein CoREST is a promising target for epigenetic drugs. No therapeutic that targets LSD1/CoREST, however, has been reported to date. Recently, extended molecular dynamics (MD) simulations indicated that LSD1/CoREST nanoscale clamp dynamics is regulated by substrate binding and highlighted key hinge points of this large-scale motion as well as the relevance of local residue dynamics. Prompted by the urgent need for new molecular probes and inhibitors to understand LSD1/CoREST interactions with small-molecules, peptides, protein partners, and chromatin, we undertake here a configurational ensemble approach to expand LSD1/CoREST druggability. The independent algorithms FTMap and SiteMap and our newly developed Druggable Site Visualizer (DSV) software tool were used to predict and inspect favorable binding sites. We find that the hinge points revealed by MD simulations at the SANT2/Tower interface, at the SWIRM/AOD interface, and at the AOD/Tower interface are new targets for the discovery of molecular probes to block association of LSD1/CoREST with chromatin or protein partners. A fourth region was also predicted from simulated configurational ensembles and was experimentally validated to have strong binding propensity. The observation that this prediction would be prevented when using only the X-ray structures available (including the X-ray structure bound to the same peptide) underscores the relevance of protein dynamics in protein interactions. A fifth region was highlighted corresponding to a small pocket on the AOD domain. This study sets the basis for future virtual screening campaigns targeting the five novel regions reported herein and for the design of LSD1/CoREST mutants to probe LSD1/CoREST binding with chromatin and various protein partners.