Hybrid Methods for Macromolecular Modeling by Molecular Mechanics Simulations with Experimental Data

MDSPACE and MDTOMO Software for Extracting Continuous Conformational Landscapes from Datasets of Single Particle Images and Subtomograms Based on Molecular Dynamics Simulations: Latest Developments in ContinuousFlex Software Package

Cryo electron microscopy (cryo-EM) instrumentation allows obtaining 3D reconstruction of the structure of biomolecular complexes in vitro (purified complexes studied by single particle analysis) and in situ (complexes studied in cells by cryo electron tomography). Standard cryo-EM approaches allow high-resolution reconstruction of only a few conformational states of a molecular complex, as they rely on data classification into a given number of classes to increase the resolution of the reconstruction from the most populated classes while discarding all other classes. Such discrete classification approaches result in a partial picture of the full conformational variability of the complex, due to continuous conformational transitions with many, uncountable intermediate states. In this article, we present the software with a user-friendly graphical interface for running two recently introduced methods, namely, MDSPACE and MDTOMO, to obtain continuous conformational landscapes of biomolecules by analyzing in vitro and in situ cryo-EM data (single particle images and subtomograms) based on molecular dynamics simulations of an available atomic model of one of the conformations. The MDSPACE and MDTOMO software is part of the open-source ContinuousFlex software package (starting from version 3.4.2 of ContinuousFlex), which can be run as a plugin of the Scipion software package (version 3.1 and later), broadly used in the cryo-EM field.

A hybrid approach to study large conformational transitions of biomolecules from single particle XFEL diffraction data

X-ray free-electron laser (XFEL) is the latest generation of the X-ray source that could become an invaluable technique in structural biology. XFEL has ultrashort pulse duration, extreme peak brilliance, and high spatial coherence, which could enable the observation of the biological molecules in near nature state at room temperature without crystallization. However, for biological systems, due to their low diffraction power and complexity of sample delivery, experiments and data analysis are not straightforward, making it extremely challenging to reconstruct three-dimensional (3D) structures from single particle XFEL data. Given the current limitations to the amount and resolution of the data from such XFEL experiments, we propose a new hybrid approach for characterizing biomolecular conformational transitions by using a single 2D low-resolution XFEL diffraction pattern in combination with another known conformation. In our method, we represent the molecular structure with a coarse-grained model, the Gaussian mixture model, to describe large conformational transitions from low-resolution XFEL data. We obtain plausible 3D structural models that are consistent with the XFEL diffraction pattern by deforming an initial structural model to maximize the similarity between the target pattern and the simulated diffraction patterns from the candidate models. We tested the proposed algorithm on two biomolecules of different sizes with different complexities of conformational transitions, adenylate kinase, and elongation factor 2, using synthetic XFEL data. The results show that, with the proposed algorithm, we can successfully describe the conformational transitions by flexibly fitting the coarse-grained model of one conformation to become consistent with an XFEL diffraction pattern simulated from another conformation. In addition, we showed that the incident beam orientation has some effect on the accuracy of the 3D structure modeling and discussed the reasons for the inaccuracies for certain orientations. The proposed method could serve as an alternative approach for retrieving information on 3D conformational transitions from the XFEL diffraction patterns to interpret experimental data. Since the molecules are represented by Gaussian kernels and no atomic structure is needed in principle, such a method could also be used as a tool to seek initial models for 3D reconstruction algorithms.

Sampling of Protein Conformational Space Using Hybrid Simulations: A Critical Assessment of Recent Methods

Recent years have seen several hybrid simulation methods for exploring the conformational space of proteins and their complexes or assemblies. These methods often combine fast analytical approaches with computationally expensive full atomic molecular dynamics (MD) simulations with the goal of rapidly sampling large and cooperative conformational changes at full atomic resolution. We present here a systematic comparison of the utility and limits of four such hybrid methods that have been introduced in recent years: MD with excited normal modes (MDeNM), collective modes-driven MD (CoMD), and elastic network model (ENM)-based generation, clustering, and relaxation of conformations (ClustENM) as well as its updated version integrated with MD simulations (ClustENMD). We analyzed the predicted conformational spaces using each of these four hybrid methods, applied to four well-studied proteins, triosephosphate isomerase (TIM), 3-phosphoglycerate kinase (PGK), HIV-1 protease (PR) and HIV-1 reverse transcriptase (RT), which provide extensive ensembles of experimental structures for benchmarking and comparing the methods. We show that a rigorous multi-faceted comparison and multiple metrics are necessary to properly assess the differences between conformational ensembles and provide an optimal protocol for achieving good agreement with experimental data. While all four hybrid methods perform well in general, being especially useful as computationally efficient methods that retain atomic resolution, the systematic analysis of the same systems by these four hybrid methods highlights the strengths and limitations of the methods and provides guidance for parameters and protocols to be adopted in future studies.

State-dependent sequential allostery exhibited by chaperonin TRiC/CCT revealed by network analysis of Cryo-EM maps

The eukaryotic chaperonin TRiC/CCT plays a major role in assisting the folding of many proteins through an ATP-driven allosteric cycle. Recent structures elucidated by cryo-electron microscopy provide a broad view of the conformations visited at various stages of the chaperonin cycle, including a sequential activation of its subunits in response to nucleotide binding. But we lack a thorough mechanistic understanding of the structure-based dynamics and communication properties that underlie the TRiC/CCT machinery. In this study, we present a computational methodology based on elastic network models adapted to cryo-EM density maps to gain a deeper understanding of the structure-encoded allosteric dynamics of this hexadecameric machine. We have analysed several structures of the chaperonin resolved in different states toward mapping its conformational landscape. Our study indicates that the overall architecture intrinsically favours cooperative movements that comply with the structural variabilities observed in experiments. Furthermore, the individual subunits CCT1-CCT8 exhibit state-dependent sequential events at different states of the allosteric cycle. For example, in the ATP-bound state, subunits CCT5 and CCT4 selectively initiate the lid closure motions favoured by the overall architecture; whereas in the apo form of the heteromer, the subunit CCT7 exhibits the highest predisposition to structural change. The changes then propagate through parallel fluxes of allosteric signals to neighbours on both rings. The predicted state-dependent mechanisms of sequential activation provide new insights into TRiC/CCT intra- and inter-ring signal transduction events.

Multiagent Consensus Equilibrium in Molecular Structure Determination

Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.

Towards gaining sight of multiscale events: utilizing network models and normal modes in hybrid methods

With the explosion of normal mode analyses (NMAs) based on elastic network models (ENMs) in the last decade, and the proven precision of MD simulations for visualizing interactions at atomic scale, many hybrid methods have been proposed in recent years. These aim at exploiting the best of both worlds: the atomic precision of MD that often fall short of exploring time and length scales of biological interest, and the capability of ENM-NMA to predict the cooperative and often functional rearrangements of large structures and assemblies, albeit at low resolution. We present an overview of recent progress in the field with examples of successful applications highlighting the utility of such hybrid methods and pointing to emerging future directions guided by advances in experimental characterization of biomolecular systems structure and dynamics.

Modeling Conformationally Flexible Proteins With X-ray Scattering and Molecular Simulations

Proteins and protein complexes with high conformational flexibility participate in a wide range of biological processes. These processes include genome maintenance, gene expression, signal transduction, cell cycle regulation, and many others. Gaining a structural understanding of conformationally flexible proteins and protein complexes is arguably the greatest problem facing structural biologists today. Over the last decade, some progress has been made toward understanding the conformational flexibility of such systems using hybrid approaches. One particularly fruitful strategy has been the combination of small-angle X-ray scattering (SAXS) and molecular simulations. In this article, we provide a brief overview of SAXS and molecular simulations and then discuss two general approaches for combining SAXS data and molecular simulations: minimal ensemble approaches and full ensemble approaches. In minimal ensemble approaches, one selects a minimal ensemble of structures from the simulations that best fit the SAXS data. In full ensemble approaches, one validates a full ensemble of structures from the simulations using SAXS data. We argue that full ensemble models are more realistic than minimal ensemble searches models and that full ensemble approaches should be used wherever possible.

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Conformationally flexible proteins are a major challenge for structural biologists.

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Flexible proteins can be examined by combining molecular simulations and SAXS.

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Minimal ensemble searches are a common way of combining simulations and SAXS.

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Full ensemble methods use SAXS to validate simulations without curve fitting.

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Full ensemble models are more realistic than minimal ensemble searches models.