Flexible Biomolecules Research Articles

Time-Resolved Graphs of Polymorphic Cycles for H-Bonded Network Identification in Flexible Biomolecules.

A novel approach based on a coarse-grained representation of topological graphs is proposed for the automatic analysis of molecular dynamics (MD) trajectories of hydrogen-bonded (H-Bonded) flexible biomolecules. Herein, our approach models an H-Bonded biomolecule by its H-Bonded cycles and its graph of cycles in which the vertices and links represent the intersections between these cycles. We propose a methodology in which each identified conformer/isomer from the MD is represented by a well-chosen set of H-Bonded cycles called a minimum cycle basis. The key component is the "polycycles" that distinguish the cycles that play the same polymorphic role in the molecule from the ones that lead to an actual conformational change of the molecule. The relevance of our proposed method is evaluated on MD trajectories of gas-phase biomolecules, for which the covalent bonds are unchanged over time and only the hydrogen bonds change over time. The polygraphs and their time evolution are shown to reveal the dynamicity of the metastructure(s) of the H-Bonded biomolecules while providing polymorphic information on the cycles. Such information on the dynamics and changes in the H-bond network, as some cycles change identity while retaining the same role in the overall structure, is not easily captured at the atomic level of representation. Such information can instead be captured by polymorphic cycles.

Molecular Dynamics Simulation and Docking of MUC1 O-Glycopeptide.

Advances in computer performance and computational simulations allow increasing sophistication in applications in biological systems. Molecular dynamics (MD) simulations are especially suitable for studying conformation, dynamics, and interaction of flexible biomolecules such as free glycans and glycopeptides. Computer simulations are best performed when the scope and limitations in performance have been thoroughly assessed. Proper outputs are obtained only under suitable parameter settings, and results need to be properly validated. In this chapter, we will introduce an example of molecular dynamics simulations of MUC1 O-glycopeptide and its docking to anti-MUC1 antibody Fv fragment.

Liquid-Liquid Phase Separation Modifies the Dynamic Properties of Intrinsically Disordered Proteins.

Liquid-liquid phase separation of flexible biomolecules has been identified as a ubiquitous phenomenon underlying the formation of membraneless organelles that harbor a multitude of essential cellular processes. We use nuclear magnetic resonance (NMR) spectroscopy to compare the dynamic properties of an intrinsically disordered protein (measles virus NTAIL) in the dilute and dense phases at atomic resolution. By measuring 15N NMR relaxation at different magnetic field strengths, we are able to characterize the dynamics of the protein in dilute and crowded conditions and to compare the amplitude and timescale of the different motional modes to those present in the membraneless organelle. Although the local backbone conformational sampling appears to be largely retained, dynamics occurring on all detectable timescales, including librational, backbone dihedral angle dynamics and segmental, chainlike motions, are considerably slowed down. Their relative amplitudes are also drastically modified, with slower, chain-like motions dominating the dynamic profile. In order to provide additional mechanistic insight, we performed extensive molecular dynamics simulations of the protein under self-crowding conditions at concentrations comparable to those found in the dense liquid phase. Simulation broadly reproduces the impact of formation of the condensed phase on both the free energy landscape and the kinetic interconversion between states. In particular, the experimentally observed reduction in the amplitude of the fastest component of backbone dynamics correlates with higher levels of intermolecular contacts or entanglement observed in simulations, reducing the conformational space available to this mode under strongly self-crowding conditions.

Single-Image Super-Resolution Improvement of X-ray Single-Particle Diffraction Images Using a Convolutional Neural Network.

Femtosecond X-ray pulse lasers are promising probes for the elucidation of the multiconformational states of biomolecules because they enable snapshots of single biomolecules to be observed as coherent diffraction images. Multi-image processing using an X-ray free-electron laser has proven to be a successful structural analysis method for viruses. However, the performance of single-particle analysis (SPA) for flexible biomolecules with sizes ≤100 nm remains difficult. Owing to the multiconformational states of biomolecules and noisy character of diffraction images, diffraction image improvement by multi-image processing is often ineffective for such molecules. Herein, a single-image super-resolution (SR) model was constructed using an SR convolutional neural network (SRCNN). Data preparation was performed in silico to consider the actual observation situation with unknown molecular orientations and the fluctuation of molecular structure and incident X-ray intensity. It was demonstrated that the trained SRCNN model improved the single-particle diffraction image quality, corresponding to an observed image with an incident X-ray intensity (approximately three to seven times higher than the original X-ray intensity), while retaining the individuality of the diffraction images. The feasibility of SPA for flexible biomolecules with sizes ≤100 nm was dramatically increased by introducing the SRCNN improvement at the beginning of the various structural analysis schemes.

Extracting time series matching a small-angle X-ray scattering profile from trajectories of molecular dynamics simulations

Solving structural ensembles of flexible biomolecules is a challenging research area. Here, we propose a method to obtain possible structural ensembles of a biomolecule based on small-angle X-ray scattering (SAXS) and molecular dynamics simulations. Our idea is to clip a time series that matches a SAXS profile from a simulation trajectory. To examine its practicability, we applied our idea to a multi-domain protein ER-60 and successfully extracted time series longer than 1 micro second from trajectories of coarse-grained molecular dynamics simulations. In the extracted time series, the domain conformation was distributed continuously and smoothly in a conformational space. Preferred domain conformations were also observed. Diversity among scattering curves calculated from each ER-60 structure was interpreted to reflect an open-close motion of the protein. Although our approach did not provide a unique solution for the structural ensemble of the biomolecule, each extracted time series can be an element of the real behavior of ER-60. Considering its low computational cost, our approach will play a key role to identify biomolecular dynamics by integrating SAXS, simulations, and other experiments.

Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides.

The application of machine learning to theoretical chemistry has made it possible to combine the accuracy of quantum chemical energetics with the thorough sampling of finite-temperature fluctuations. To reach this goal, a diverse set of methods has been proposed, ranging from simple linear models to kernel regression and highly nonlinear neural networks. Here we apply two widely different approaches to the same, challenging problem: the sampling of the conformational landscape of polypeptides at finite temperature. We develop a local kernel regression (LKR) coupled with a supervised sparsity method and compare it with a more established approach based on Behler-Parrinello type neural networks. In the context of the LKR, we discuss how the supervised selection of the reference pool of environments is crucial to achieve accurate potential energy surfaces at a competitive computational cost and leverage the locality of the model to infer which chemical environments are poorly described by the DFTB baseline. We then discuss the relative merits of the two frameworks and perform Hamiltonian-reservoir replica-exchange Monte Carlo sampling and metadynamics simulations, respectively, to demonstrate that both frameworks can achieve converged and transferable sampling of the conformational landscape of complex and flexible biomolecules with comparable accuracy and computational cost.

Interactions between Liquid Metal Droplets and Bacterial, Fungal, and Mammalian Cells

AbstractLiquid metals (LMs) have emerged as novel materials for biomedical applications. Here, the interactions taking place between cells and LMs are reported, presenting a unique opportunity to explore and understand the LM‐biological interface. Several high‐resolution imaging techniques are used to characterize the interaction between droplets of gallium LM and bacterial, fungal, and mammalian cells. Adhesive interactions between cells and LM droplets are observed, causing deformation of the LM droplet surface, resulting in surface wrinkling and in some cases, breakage of the native oxide layer present on the LM droplet surface. In many instances, the cell wall deforms to intimately contact the LM droplets. Single‐cell force spectroscopy is performed to quantify the adhesion forces between cells and LM and characterize the nature of the adhesion. It is proposed that the flexible nature of the cell enables multiple adhesion sites with the LM droplets, imparting tensile forces on the LM droplet surface, which results in surface wrinkling on the LM droplets due to their liquid nature. Molecular dynamics simulations also suggest that flexible biomolecules on the cell surface can disrupt the Ga2O3 layer formed at the LM droplet surface. This study reveals a unique biointerfacial interaction and provides insights into the mechanisms involved.

Structural and Vibrational Properties of Amino Acids from Composite Schemes and Double-Hybrid DFT: Hydrogen Bonding in Serine as a Test Case

The structures, relative stabilities, and vibrational wavenumbers of the two most stable conformers of serine, stabilized by the O-H···N, O-H···O═C and N-H···O-H intramolecular hydrogen bonds, have been evaluated by means of state-of-the-art composite schemes based on coupled-cluster (CC) theory. The so-called "cheap" composite approach (CCSD(T)/(CBS+CV)MP2) allowed determination of accurate equilibrium structures and harmonic vibrational wavenumbers, also pointing out significant corrections beyond the CCSD(T)/cc-pVTZ level. These accurate results stand as a reference for benchmarking selected hybrid and double-hybrid, dispersion-corrected DFT functionals. B2PLYP-D3 and DSDPBEP86 in conjunction with a triple-ζ basis set have been confirmed as effective methodologies for structural and spectroscopic studies of medium-sized flexible biomolecules, also showing intramolecular hydrogen bonding. These best performing double-hybrid functionals have been employed to simulate IR spectra by means of vibrational perturbation theory, also considering hybrid CC/DFT schemes. The best overall agreement with experiment, with mean absolute error of 8 cm-1, has been obtained by combining CCSD(T)/(CBS+CV)MP2 harmonic wavenumbers with B2PLYP-D3/maug-cc-pVTZ anharmonic corrections. Finally, a composite scheme entirely based on CCSD(T) calculations (CCSD(T)/CBS+CV) has been employed for energetics, further confirming that serine II is the most stable conformer, also when zero-point vibrational energy corrections are included.

ArcRNAs and the formation of nuclear bodies.

Long noncoding RNAs (lncRNAs) have long been collectively and passively defined as transcripts that do not encode proteins. However, extensive functional studies performed over the last decade have enabled the classification of lncRNAs into multiple categories according to their functions and/or molecular properties. Architectual RNAs (arcRNAs) are a group of lncRNAs that serve as architectural components of submicron-scale cellular bodies or nonmembranous organelles, which are composed of specific sets of proteins and nucleic acids involved in particular molecular processes. In this review, we focus on arcRNAs that function in the nucleus, which provide a structural basis for the formation of nuclear bodies, nonmembranous organelles in the cell nucleus. We will summarize the current list of arcRNAs and proteins associated with classic and more recently discovered nuclear bodies and discuss general rules that govern the formation of nuclear bodies, emphasizing weak multivalent interactions mediated by innately flexible biomolecules.

Arginine multivalency stabilizes protein/RNA condensates.

Biomolecular condensates assembled through liquid-liquid phase separation (LLPS) of proteins and RNAs are currently recognized to play an important role in cellular organization. Their assembly depends on the formation of a network of transient, multivalent interactions between flexible scaffold biomolecules. Understanding how protein and RNA sequences determine these interactions and ultimately regulate the phase separation is an open key challenge. Recent in vitro studies have revealed that arginine and lysine residues, which are enriched in most cellular condensates, have markedly distinct propensities to drive the LLPS of protein/RNA mixtures. Here, we employ explicit-solvent atomistic molecular dynamics simulations to shed light on the microscopic origin of this difference by investigating mixtures of polyU oligonucleotides with either polyR/polyK peptides. In agreement with experiments, our simulations indicate that arginine has a higher affinity for polyU than lysine both in highly diluted conditions and in concentrated solutions with a biomolecular density comparable to cellular condensate. The analysis of intermolecular contacts suggests that this differential behavior is due to the propensity of arginine side chains to simultaneously form a higher number of specific interactions with oligonucleotides, including hydrogen bonds and stacking interactions. Our results provide a molecular description of how the multivalency of the guanidinium group enables the coordination of multiple RNA groups by a single arginine residue, thus ultimately stabilizing protein/RNA condensates.

Simplified time-dependent density functional theory (sTD-DFT) for molecular optical rotation.

Theoretical methods able to screen large sets (e.g., conformers) of possibly large compounds are needed in many typical quantum chemistry applications. For this purpose, we here extend the well-established simplified time-dependent density functional theory (sTD-DFT) method for the calculation of optical rotation. This new scheme is benchmarked against 42 compounds of the OR45 set as well as thirteen helicene derivatives and one bio-molecular system. The sTD-DFT method yields optical rotations in good quantitative agreement with experiment for compounds with a valence-dominated response, e.g., conjugated π-systems, at a small fraction of the computational cost compared to TD-DFT (1-3 orders of magnitude speed-up). For smaller molecules with a Rydberg state dominated response, the agreement between TD-DFT and the simplified version using standard hybrid functionals is somewhat worse but still reasonable for typical applications. Our new implementation in the stda code enables computations for systems with up to 1000 atoms, e.g., for studying flexible bio-molecules.

Coarse-Grained Diffraction Template Matching Model to Retrieve Multiconformational Models for Biomolecule Structures from Noisy Diffraction Patterns.

Biomolecular imaging using X-ray free-electron lasers (XFELs) has been successfully applied to serial femtosecond crystallography. However, the application of single-particle analysis for structure determination using XFELs with 100 nm or smaller biomolecules has two practical problems: the incomplete diffraction data sets for reconstructing 3D assembled structures and the heterogeneous conformational states of samples. A new diffraction template matching method is thus presented here to retrieve a plausible 3D structural model based on single noisy target diffraction patterns, assuming candidate structures. Two concepts are introduced here: prompt candidate diffraction, generated by enhanced sampled coarse-grain (CG) candidate structures, and efficient molecular orientation searching for matching based on Bayesian optimization. A CG model-based diffraction-matching protocol is proposed that achieves a 100-fold speed increase compared to exhaustive diffraction matching using an all-atom model. The conditions that enable multiconformational analysis were also investigated by simulated diffraction data for various conformational states of chromatin and ribosomes. The proposed method can enable multiconformational analysis, with a structural resolution of at least 20 Å for 270-800 Å flexible biomolecules, in experimental single-particle structure analyses that employ XFELs.

Determination of Protein Structural Ensembles by Hybrid-Resolution SAXS Restrained Molecular Dynamics.

Small-angle X-ray scattering (SAXS) experiments provide low-resolution but valuable information about the dynamics of biomolecular systems, which could be ideally integrated into molecular dynamics (MD) simulations to accurately determine conformational ensembles of flexible proteins. The applicability of this strategy is hampered by the high computational cost required to calculate scattering intensities from three-dimensional structures. We previously presented a hybrid resolution method that makes atomistic SAXS-restrained MD simulation feasible by adopting a coarse-grained approach to efficiently back-calculate scattering intensities; here, we extend this technique, applying it in the framework of metainference with the aim to investigate the dynamical behavior of flexible biomolecules. The efficacy of the method is assessed on the K63-diubiquitin, showing that the inclusion of SAXS restraints is effective in generating a reliable conformational ensemble, improving the agreement with independent experimental data.

Structural Analyses of Intrinsically Disordered Proteins by Small-Angle X-Ray Scattering.

Small-angle X-ray scattering (SAXS) is a low-resolution method for the structural characterization of biological macromolecules in solution. Information about the overall structural features provided by SAXS is highly complementary to X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy, and cryo-electron microscopy, which are high-resolution methods. SAXS not only provides the shape, oligomeric state, and quaternary structure of folded proteins and protein complexes but also allows for quantitative analysis of flexible biomolecules. In this chapter, the most relevant SAXS procedures for structural characterization of flexible macromolecules, including intrinsically disordered proteins (IDPs), are presented. The sample requirements for SAXS experiments on protein solutions and the sequence of steps in data collection and processing are described. The use of the advanced data analysis tools to quantitatively characterize flexible proteins is presented in detail. Typical experimental issues and potential problems encountered during SAXS data measurements and analyses are discussed.

A Unified Description of Intrinsically Disordered Protein Dynamics under Physiological Conditions Using NMR Spectroscopy.

Intrinsically disordered proteins (IDPs) are flexible biomolecules whose essential functions are defined by their dynamic nature. Nuclear magnetic resonance (NMR) spectroscopy is ideally suited to the investigation of this behavior at atomic resolution. NMR relaxation is increasingly used to detect conformational dynamics in free and bound forms of IDPs under conditions approaching physiological, although a general framework providing a quantitative interpretation of these exquisitely sensitive probes as a function of experimental conditions is still lacking. Here, measuring an extensive set of relaxation rates sampling multiple-time-scale dynamics over a broad range of crowding conditions, we develop and test an integrated analytical description that accurately portrays the motion of IDPs as a function of the intrinsic properties of the crowded molecular environment. In particular we observe a strong dependence of both short-range and long-range motional time scales of the protein on the friction of the solvent. This tight coupling between the dynamic behavior of the IDP and its environment allows us to develop analytical expressions for protein motions and NMR relaxation properties that can be accurately applied over a vast range of experimental conditions. This unified dynamic description provides new insight into the physical behavior of IDPs, extending our ability to quantitatively investigate their conformational dynamics under complex environmental conditions, and accurately predicting relaxation rates reporting on motions on time scales up to tens of nanoseconds, both in vitro and in cellulo.

Efficient Ensemble Refinement by Reweighting.

Ensemble refinement produces structural ensembles of flexible and dynamic biomolecules by integrating experimental data and molecular simulations. Here we present two efficient numerical methods to solve the computationally challenging maximum-entropy problem arising from a Bayesian formulation of ensemble refinement. Recasting the resulting constrained weight optimization problem into an unconstrained form enables the use of gradient-based algorithms. In two complementary formulations that differ in their dimensionality, we optimize either the log-weights directly or the generalized forces appearing in the explicit analytical form of the solution. We first demonstrate the robustness, accuracy, and efficiency of the two methods using synthetic data. We then use NMR J-couplings to reweight an all-atom molecular dynamics simulation ensemble of the disordered peptide Ala-5 simulated with the AMBER99SB*-ildn-q force field. After reweighting, we find a consistent increase in the population of the polyproline-II conformations and a decrease of α-helical-like conformations. Ensemble refinement makes it possible to infer detailed structural models for biomolecules exhibiting significant dynamics, such as intrinsically disordered proteins, by combining input from experiment and simulation in a balanced manner.

Conformational states of Zika virus non-structural protein 3 determined by molecular dynamics simulations with small-angle X-Ray scattering data

Zika virus (ZIKV) has become a great public health emergency. Its non-structural protein 3 (NS3) is a key enzyme in viral replication and has been considered as a potential therapeutic target. A conformational characterization of ZIKV NS3 is critical for a comprehensive understanding of its molecular interactions and functions. However, the high conformational flexibility of solution NS3 obstacles the structural characterization of NS3 solely from the experimental observable that averages over its heterogeneous conformations. Here, we employed replica exchange with solute tempering (REST) method to simulate the di-domain protein ZIKV NS3. Three independent MD simulations identified a conserved conformational ensemble of NS3, consisting of a major conformational state and several minor states from compact to loose conformations. The major state agrees well with the scattering profile from small-angle X-ray scattering (SAXS) experiments. Moreover, the simulated ensemble is supported by a direct data-fitting result that requires both short- and long-range structural contacts to recover the experimental data. We discussed the interplay between simulation and experiment in ensemble construction of flexible biomolecules and shed light on the physically derived conformational ensembles.

Competing Dispersive Interactions: From Small Energy Differences to Large Structural Effects in Methyl Jasmonate and Zingerone.

Modern structural studies of biologically relevant molecules require an exhaustive interplay between experiment and theory. In this work, we present two examples where a poor choice of the theoretical method led to a misinterpretation of experimental results. We do that by performing a rotational spectroscopy study on two large and flexible biomolecules: methyl jasmonate and zingerone. The results show the enormous potential of rotational spectroscopy as a benchmark to evaluate the performance of theoretical methods.

Conformational ensembles of RNA oligonucleotides from integrating NMR and molecular simulations.

RNA molecules are key players in numerous cellular processes and are characterized by a complex relationship between structure, dynamics, and function. Despite their apparent simplicity, RNA oligonucleotides are very flexible molecules, and understanding their internal dynamics is particularly challenging using experimental data alone. We show how to reconstruct the conformational ensemble of four RNA tetranucleotides by combining atomistic molecular dynamics simulations with nuclear magnetic resonance spectroscopy data. The goal is achieved by reweighting simulations using a maximum entropy/Bayesian approach. In this way, we overcome problems of current simulation methods, as well as in interpreting ensemble- and time-averaged experimental data. We determine the populations of different conformational states by considering several nuclear magnetic resonance parameters and point toward properties that are not captured by state-of-the-art molecular force fields. Although our approach is applied on a set of model systems, it is fully general and may be used to study the conformational dynamics of flexible biomolecules and to detect inaccuracies in molecular dynamics force fields.

Covalent dye attachment influences the dynamics and conformational properties of flexible peptides.

Fluorescence spectroscopy techniques like Förster resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) have become important tools for the in vitro and in vivo investigation of conformational dynamics in biomolecules. These methods rely on the distance-dependent quenching of the fluorescence signal of a donor fluorophore either by a fluorescent acceptor fluorophore (FRET) or a non-fluorescent quencher, as used in FCS with photoinduced electron transfer (PET). The attachment of fluorophores to the molecule of interest can potentially alter the molecular properties and may affect the relevant conformational states and dynamics especially of flexible biomolecules like intrinsically disordered proteins (IDP). Using the intrinsically disordered S-peptide as a model system, we investigate the impact of terminal fluorescence labeling on the molecular properties. We perform extensive molecular dynamics simulations on the labeled and unlabeled peptide and compare the results with in vitro PET-FCS measurements. Experimental and simulated timescales of end-to-end fluctuations were found in excellent agreement. Comparison between simulations with and without labels reveal that the π-stacking interaction between the fluorophore labels traps the conformation of S-peptide in a single dominant state, while the unlabeled peptide undergoes continuous conformational rearrangements. Furthermore, we find that the open to closed transition rate of S-peptide is decreased by at least one order of magnitude by the fluorophore attachment. Our approach combining experimental and in silico methods provides a benchmark for the simulations and reveals the significant effect that fluorescence labeling can have on the conformational dynamics of small biomolecules, at least for inherently flexible short peptides. The presented protocol is not only useful for comparing PET-FCS experiments with simulation results but provides a strategy to minimize the influence on molecular properties when chosing labeling positions for fluorescence experiments.