Analysis Of Protein Dynamics Research Articles

Uncertainties in Markov State Models of Small Proteins.

Markov state models are widely used to describe and analyze protein dynamics based on molecular dynamics simulations, specifically to extract functionally relevant characteristic time scales and motions. Particularly for larger biomolecules such as proteins, however, insufficient sampling is a notorious concern and often the source of large uncertainties that are difficult to quantify. Furthermore, there are several other sources of uncertainty, such as choice of the number of Markov states and lag time, choice and parameters of dimension reduction preprocessing step, and uncertainty due to the limited number of observed transitions; the latter is often estimated via a Bayesian approach. Here, we quantified and ranked all of these uncertainties for four small globular test proteins. We found that the largest uncertainty is due to insufficient sampling and initially increases with the total trajectory length T up to a critical tipping point, after which it decreases as , thus providing guidelines for how much sampling is required for given accuracy. We also found that single long trajectories yielded better sampling accuracy than many shorter trajectories starting from the same structure. In comparison, the remaining sources of the above uncertainties are generally smaller by a factor of about 5, rendering them less of a concern but certainly not negligible. Importantly, the Bayes uncertainty, commonly used as the only uncertainty estimate, captures only a relatively small part of the true uncertainty, which is thus often drastically underestimated.

Analysis of Protein Folding Simulation with Moving Root Mean Square Deviation.

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

Analyzing protein dynamics from fluorescence intensity traces using unsupervised deep learning network

We propose an unsupervised deep learning network to analyze the dynamics of membrane proteins from the fluorescence intensity traces. This system was trained in an unsupervised manner with the raw experimental time traces and synthesized ones, so neither predefined state number nor pre-labelling were required. With the bidirectional Long Short-Term Memory (biLSTM) networks as the hidden layers, both the past and future context can be used fully to improve the prediction results and can even extract information from the noise distribution. The method was validated with the synthetic dataset and the experimental dataset of monomeric fluorophore Cy5, and then applied to extract the membrane protein interaction dynamics from experimental data successfully.

LARMD: integration of bioinformatic resources to profile ligand-driven protein dynamics with a case on the activation of estrogen receptor.

Protein dynamics is central to all biological processes, including signal transduction, cellular regulation and biological catalysis. Among them, in-depth exploration of ligand-driven protein dynamics contributes to an optimal understanding of protein function, which is particularly relevant to drug discovery. Hence, a wide range of computational tools have been designed to investigate the important dynamic information in proteins. However, performing and analyzing protein dynamics is still challenging due to the complicated operation steps, giving rise to great difficulty, especially for nonexperts. Moreover, there is a lack of web protocol to provide online facility to investigate and visualize ligand-driven protein dynamics. To this end, in this study, we integrated several bioinformatic tools to develop a protocol, named Ligand and Receptor Molecular Dynamics (LARMD, http://chemyang.ccnu.edu.cn/ccb/server/LARMD/ and http://agroda.gzu.edu.cn:9999/ccb/server/LARMD/), for profiling ligand-driven protein dynamics. To be specific, estrogen receptor (ER) was used as a case to reveal ERβ-selective mechanism, which plays a vital role in the treatment of inflammatory diseases and many types of cancers in clinical practice. Two different residues (Ile373/Met421 and Met336/Leu384) in the pocket of ERβ/ERα were the significant determinants for selectivity, especially Met336 of ERβ. The helix H8, helix H11 and H7-H8 loop influenced the migration of selective agonist (WAY-244). These computational results were consistent with the experimental results. Therefore, LARMD provides a user-friendly online protocol to study the dynamic property of protein and to design new ligand or site-directed mutagenesis.

Study of correlations between protein peptide plane dynamics and side chain dynamics.

Protein dynamics is pivotal to biological processes. However, experiments are very demanding and difficult to perform, and all-atom molecular dynamics simulations can still not provide all the answers. This motivates us to analyze protein dynamics in terms of different reduced coordinate representations. We then need to resolve how to reconstruct the full all-atom dynamics from its coarse grained approximation. Accordingly we scrutinize all-atom molecular dynamics trajectories in terms of crystallographic Protein Data Bank (PDB) structures, and inquire to what extent is it possible to predict the dynamics of side chain Cβ atoms in terms of the static properties of backbone Cα and O atoms. Here we find that simulated Cβ dynamics at near physiological conditions can be reconstructed with very high precision, using the knowledge of the crystallographic backbone Cα and O positions. The precision we can reach with our PDB-based Statistical Method reconstruction exceeds that of popular all-atom reconstruction methods such as Remo and Pulchra, and is fully comparable with the precision of the highly elaborate Scwrl4 all-atom reconstruction method that we have enhanced with the knowledge of the backbone Cα and O atom positions. We then conclude that in a dynamical protein that moves around at physiological conditions, the relative positions of its Cβ atoms with respect to the backbone Cα and O atoms, deviate very little from their relative positions in static crystallographic PDB structures. This proposes that the dynamics of a biologically active protein could remain subject to very similar, stringent stereochemical constraints that dictate the structure of a folded crystallographic protein. Thus, our results provide a strong impetus to the development of coarse grained techniques that are based on reduced coordinate representations.

Recognition of protein allosteric states and residues: Machine learning approaches.

Allostery is a process by which proteins transmit the effect of perturbation at one site to a distal functional site upon certain perturbation. As an intrinsically global effect of protein dynamics, it is difficult to associate protein allostery with individual residues, hindering effective selection of key residues for mutagenesis studies. The machine learning models including decision tree (DT) and artificial neural network (ANN) models were applied to develop classification model for a cell signaling allosteric protein with two states showing extremely similar tertiary structures in both crystallographic structures and molecular dynamics simulations. Both DT and ANN models were developed with 75% and 80% of predicting accuracy, respectively. Good agreement between machine learning models and previous experimental as well as computational studies of the same protein validates this approach as an alternative way to analyze protein dynamics simulations and allostery. In addition, the difference of distributions of key features in two allosteric states also underlies the population shift hypothesis of dynamics-driven allostery model. © 2018 Wiley Periodicals, Inc.

Time-Resolved Measurement of the ATP-Dependent Motion of the Group II Chaperonin by Diffracted Electron Tracking.

Previously, we demonstrated the ATP-dependent dynamics of a group II chaperonin at the single-molecule level by diffracted X-ray tracking (DXT). The disadvantage of DXT is that it requires a strong X-ray source and also perfect gold nano-crystals. To resolve this problem, we developed diffracted electron tracking (DET). Electron beams have scattering cross-sections that are approximately 1000 times larger than those of X-rays. Thus, DET enables us to perform super-accurate measurements of the time-resolved 3D motion of proteins labeled with commercially available gold nanorods using a scanning electron microscope. In this study, we compared DXT and DET using the group II chaperonin from Methanococcus maripaludis (MmCpn) as a model protein. In DET, the samples are prepared in an environmental cell (EC). To reduce the electron beam-induced protein damage, we immobilized MmCpn on the bottom of the EC to expose gold nanorods close to the carbon thin film. The sample setup worked well, and the motions of gold nanorods were clearly traced. Compared with the results of DXT, the mobility in DET was significantly higher, which is probably due to the difference in the method for immobilization. In DET, MmCpn was immobilized on a film of triacetyl cellulose. Whereas proteins are directly attached on the surface of solid support in DXT. Therefore, MmCpn could move relatively freely in DET. DET will be a state-of-the-art technology for analyzing protein dynamics.

A Comparison of Collective Coordinates for Analyzing Protein Dynamics

The internal dynamics of a protein is commonly analyzed by examining the fluctuations along the protein's alpha-carbons. However, a vast majority of an N-residue protein's internal dynamics can be described successfully using less than the complete (3N-6)-dimensional space spanned by the protein's internal fluctuations. This dimensionality reduction is achieved by transforming from the lab-frame coordinates to a set of judiciously-selected collective coordinates. A common technique, called principal component analysis (PCA), is to select the collective coordinates along which the variance of the original (3N-6)-dimensional coordinates is maximized. These statistically-independent, collective coordinates are termed principal modes (PMs) and are ordered in terms of descending variance, with the first PM possessing the maximum variance. However, these PMs contain no inherent information regarding the timescale over which the motion described by the PM occurs. We present an alternative set of independent, collective coordinates generated using the Langevin Equation for Protein Dynamics (LE4PD), a method for analyzing the internal fluctuations of proteins along its alpha-carbon backbone. The LE4PD accounts for the presence of hydrodynamic interactions between each residue and barriers on each mode's free-energy surface. In contrast to PMs, the LE4PD normal modes are ordered by timescales instead of variance; thus, the first normal mode from the LE4PD describes longest timescale internal motion. The fluctuations predicted by the corresponding PMs and LE4PD normal modes are in good agreement without including hydrodynamics or barriers in the LE4PD, but inclusion of these phenomena have a significant impact on the location and magnitude of the predicted fluctuations along the protein's backbone. The results suggest the LE4PD is an effective method for describing the internal fluctuations of proteins along collective coordinates, and the inclusion of hydrodynamic interactions and free-energy barriers significantly alters the fluctuations predicted along each normal mode.

ProteinAC: a frequency domain technique for analyzing protein dynamics

It is widely believed that the interactions of proteins with ligands and other proteins are determined by their dynamic characteristics as opposed to only static, time-invariant processes. We propose a novel computational technique, called ProteinAC (PAC), that can be used to analyze small scale functional protein motions as well as interactions with ligands directly in the frequency domain. PAC was inspired by a frequency domain analysis technique that is widely used in electronic circuit design, and can be applied to both coarse-grained and all-atom models. It can be considered as a generalization of previously proposed static perturbation-response methods, where the frequency of the perturbation becomes the key. We discuss the precise relationship of PAC to static perturbation-response schemes. We show that the frequency of the perturbation may be an important factor in protein dynamics. Perturbations at different frequencies may result in completely different response behavior while magnitude and direction are kept constant. Furthermore, we introduce several novel frequency dependent metrics that can be computed via PAC in order to characterize response behavior. We present results for the ferric binding protein that demonstrate the potential utility of the proposed techniques.

An optimal distance cutoff for contact-based Protein Structure Networks using side-chain centers of mass

Proteins are highly dynamic entities attaining a myriad of different conformations. Protein side chains change their states during dynamics, causing clashes that are propagated at distal sites. A convenient formalism to analyze protein dynamics is based on network theory using Protein Structure Networks (PSNs). Despite their broad applicability, few efforts have been devoted to benchmarking PSN methods and to provide the community with best practices. In many applications, it is convenient to use the centers of mass of the side chains as nodes. It becomes thus critical to evaluate the minimal distance cutoff between the centers of mass which will provide stable network properties. Moreover, when the PSN is derived from a structural ensemble collected by molecular dynamics (MD), the impact of the MD force field has to be evaluated. We selected a dataset of proteins with different fold and size and assessed the two fundamental properties of the PSN, i.e. hubs and connected components. We identified an optimal cutoff of 5 Å that is robust to changes in the force field and the proteins. Our study builds solid foundations for the harmonization and standardization of the PSN approach.

Ward Clustering Improves Cross-Validated Markov State Models of Protein Folding.

Markov state models (MSMs) are a powerful framework for analyzing protein dynamics. MSMs require the decomposition of conformation space into states via clustering, which can be cross-validated when a prediction method is available for the clustering method. We present an algorithm for predicting cluster assignments of new data points with Ward's minimum variance method. We then show that clustering with Ward's method produces better or equivalent cross-validated MSMs for protein folding than other clustering algorithms.

Comparative proteomics analyses of intraspecific differences in the response of Stipa purpurea to drought

Stipa purpurea is widely distributed along a large precipitation gradient on the Tibetan Plateau. This implies that S. purpurea from different populations may have different responses to drought stress. To explore this we compared the morphological and physiological changes of S. purpurea seedlings cultivated from seeds from Gar County and Nagqu County after 7 and 14 days of drought stress and subsequent re-watering. The results showed that S. purpurea plants from the more arid Gar area were more tolerant to drought stress than that from Nagqu. To investigate the potential mechanisms underlying this difference, we used iTRAQ quantitative proteomics technology to analyze protein dynamics in S. purpurea samples treated with 7 days of drought stress and subsequent re-watering. The results indicated that, during the process of drought and re-watering treatments, there were differentially expressed proteins in either or both S. purpurea populations. These differential proteins were divided into 24 functional categories that were mainly associated with stress response, the antioxidant system, photosynthesis, carbohydrate metabolism, and post-translational modifications. According to these results, we concluded that the molecular basis of stronger drought resistance likely lies in the specific up-regulation or higher expression of many proteins involved in stress response, the antioxidant system, post-translational modification and osmotic regulation in S. purpurea from Gar County compared with that from Nagqu. This study improves our understanding of the intraspecific differences in drought resistance within S. purpurea populations, which helps to understand the distribution of S. purpurea along the moisture gradient, as well as the effect of climate change on this species.

Biasing the Sampling of Local States to Drive the Exploration of Global Conformations in Proteins

IntroductionConformational changes associated with protein function often occur at timescales inaccessible to unbiased Molecular Dynamics (MD) simulations, consequently different approaches have been developed to accelerate their sampling. Here we investigate how the knowledge of backbone conformations preferentially adopted by protein fragments, as contained in pre-calculated libraries known as Structural Alphabets (SA)[1], can be used to explore the landscape of global protein conformations in MD simulations.MethodsSAs were successfully used to analyze protein dynamics after simulation[2,3]. Here we define a novel SA-based Collective Variable (CVSA) to bias the sampling of backbone conformations of protein fragments towards experimentally preferred local states[4].ResultsWe find that: a) Enhancing the sampling of native local states allows recovery of global folded states, both in Metadynamics and in Steered MD, when the local states are encoded by strings of SA letters derived from the native structures. b) Global folded states are still recovered when the information on the native local states is reduced by using a low-resolution SA, where the original letters are clustered into macrostates. The macrostates provide the approximate shape of the fragments, while sampling with the atomistic force field allows the structure to adopt the native conformation of the specific amino acid sequence. c) SA strings derived from collections of structural motifs can be effectively used to sample alternative conformations of pre-selected regions. These findings have potential impact on a wide range of applications, from protein model refinement to folding and design.

Protein flexibility in the light of structural alphabets.

Protein structures are valuable tools to understand protein function. Nonetheless, proteins are often considered as rigid macromolecules while their structures exhibit specific flexibility, which is essential to complete their functions. Analyses of protein structures and dynamics are often performed with a simplified three-state description, i.e., the classical secondary structures. More precise and complete description of protein backbone conformation can be obtained using libraries of small protein fragments that are able to approximate every part of protein structures. These libraries, called structural alphabets (SAs), have been widely used in structure analysis field, from definition of ligand binding sites to superimposition of protein structures. SAs are also well suited to analyze the dynamics of protein structures. Here, we review innovative approaches that investigate protein flexibility based on SAs description. Coupled to various sources of experimental data (e.g., B-factor) and computational methodology (e.g., Molecular Dynamic simulation), SAs turn out to be powerful tools to analyze protein dynamics, e.g., to examine allosteric mechanisms in large set of structures in complexes, to identify order/disorder transition. SAs were also shown to be quite efficient to predict protein flexibility from amino-acid sequence. Finally, in this review, we exemplify the interest of SAs for studying flexibility with different cases of proteins implicated in pathologies and diseases.

Resolving Isotopic Fine Structure to Detect and Quantify Natural Abundance- and Hydrogen/Deuterium Exchange-Derived Isotopomers

Hydrogen/deuterium exchange (HDX) mass spectrometry (MS) is used for analyzing protein dynamics, protein folding/unfolding, and molecular interactions. Until this study, HDX MS experiments employed mass spectral resolving powers that afforded only one peak per nominal mass in a given peptide's isotope distribution, and HDX MS data analysis methods were developed accordingly. A level of complexity that is inherent to HDX MS remained unaddressed, namely, various combinations of natural abundance heavy isotopes and exchanged deuterium shared the same nominal mass and overlapped at previous resolving powers. For example, an A + 2 peak is comprised of (among other isotopomers) a two-(2)H-exchanged/zero-(13)C isotopomer, a one-(2)H-exchanged/one-(13)C isotopomer, and a zero-(2)H-exchanged/two-(13)C isotopomer. Notably, such isotopomers differ slightly in mass as a result of the ∼3 mDa mass defect between (2)H and (13)C atoms. Previous HDX MS methods did not resolve these isotopomers, requiring a natural-abundance-only (before HDX or "time zero") spectrum and data processing to remove its contribution. It is demonstrated here that high-resolution mass spectrometry can be used to detect isotopic fine structure, such as in the A + 2 profile example above, deconvolving the isotopomer species resulting from deuterium incorporation. Resolving isotopic fine structure during HDX MS therefore permits direct monitoring of HDX, which can be calculated as the sum of the fractional peak magnitudes of the deuterium-exchanged isotopomers. This obviates both the need for a time zero spectrum as well as data processing to account for natural abundance heavy isotopes, saving instrument and analysis time.

A Computational Investigation on the Connection between Dynamics Properties of Ribosomal Proteins and Ribosome Assembly

Assembly of the ribosome from its protein and RNA constituents has been studied extensively over the past 50 years, and experimental evidence suggests that prokaryotic ribosomal proteins undergo conformational changes during assembly. However, to date, no studies have attempted to elucidate these conformational changes. The present work utilizes computational methods to analyze protein dynamics and to investigate the linkage between dynamics and binding of these proteins during the assembly of the ribosome. Ribosomal proteins are known to be positively charged and we find the percentage of positive residues in r-proteins to be about twice that of the average protein: Lys+Arg is 18.7% for E. coli and 21.2% for T. thermophilus. Also, positive residues constitute a large proportion of RNA contacting residues: 39% for E. coli and 46% for T. thermophilus. This affirms the known importance of charge-charge interactions in the assembly of the ribosome. We studied the dynamics of three primary proteins from E. coli and T. thermophilus 30S subunits that bind early in the assembly (S15, S17, and S20) with atomic molecular dynamic simulations, followed by a study of all r-proteins using elastic network models. Molecular dynamics simulations show that solvent-exposed proteins (S15 and S17) tend to adopt more stable solution conformations than an RNA-embedded protein (S20). We also find protein residues that contact the 16S rRNA are generally more mobile in comparison with the other residues. This is because there is a larger proportion of contacting residues located in flexible loop regions. By the use of elastic network models, which are computationally more efficient, we show that this trend holds for most of the 30S r-proteins.

A femto-injection technique for dynamic analysis of protein function in living embryonic stem cells

The potential of a femto-injection technique for use in analyzing protein dynamics in embryonic stem (ES) cells was investigated. First, we showed that fluorescent proteins could be injected in a quantitative fashion into individual mouse ES cells. Second, we demonstrated that the technique could identify functional differences between proteins by analyzing the effect of a nuclear localization signal on the behavior of glutathione S-transferase conjugated to green fluorescent protein. The analysis showed a clear difference in the distribution of the protein when the nuclear localization signal was present. Our results confirm that the non-destructive, quantitative and time controllable aspects of the technique provide considerable advantages for the analysis of protein behavior in living ES cells. To the best of our knowledge, this is the first report of the successful introduction of proteins into living ES cells by an injection technique.

Linkage Between Dynamics and Assembly of Ribosomal Proteins

Assembly of the ribosome from its protein and RNA constituents has been studied extensively over the past 50 years, and experimental evidence suggests that prokaryotic ribosomal proteins undergo conformational changes during assembly. However, to date, no studies have attempted to elucidate these conformational changes. The present work utilizes computational methods to analyze protein dynamics and to investigate the linkage between dynamics and binding of these proteins played during the assembly of the ribosome. We studied the dynamics of three primary proteins from E. coli and T. thermophilus 30S subunits (S15, S17, and S20) with atomic molecular dynamic simulations, followed by a study of all r-proteins using elastic network models. We find that r-proteins contain a higher than average percentage of positive residues (Lys + Arg is 18.7% for E. coli and 21.2% for T. thermophilus). Also, positive residues constitute a large proportion of RNA contacting residues (39% for E. coli and 46% for T. thermophilus). This indicates the importance of charge-charge interactions in the assembly of the ribosome. Molecular Dynamics simulations show that solvent-exposed proteins (S15 and S17) tend to adopt more stable solution conformations than an RNA-embedded protein (S20). We also find protein residues that contact the 16S rRNA are generally more mobile in comparison with the other residues. This is because there is a larger proportion of contacting residues located in flexible loop regions. Using elastic network models, which are computationally more efficient, we show that this trend holds for most of the 30S r-proteins.

Fitting evolutionary process of influenza a virus nucleoproteins using analytical solution of system of differential equations

Very recently we explored the possibility of using differential equations to describe the evolution of proteins. In this study we used the amino-acid pair predictability to quantify 1709 nucleoproteins of influenza A viruses isolated from 1918 to 2008 to represent their evolutionary process, thereafter we used the analytical solution of system of differential equations to fit the evolution of the nucleoprotein family. The results showed that the analytical solution could fit the nucleoprotein evolution and the obtained parameters were useful for timing of future mutations. Our approach provided a way to quantitatively analyze protein dynamics and evolution.

Towards the Structural Characterization of Intrinsically Disordered Proteins by SAXS and MD Simulation

Dynamical structures of intrinsically disordered proteins (IDPs) and multi-domain proteins that include large ID regions between the domains are unable to be determined by such conventional methods as X-ray crystallography and electron microscopy. Small-angle X-ray scattering (SAXS) is suitable to determine low-resolution structures of proteins and protein complexes in solution, but the structural data on protein dynamics are averaged over the structural ensemble in protein solution. To overcome this problem, we have developed a novel method, named MD-SAXS, of the combined use of SAXS and molecular dynamics (MD) simulation to analyze protein dynamics in solution of multi-subunit protein complexes and multi-domain proteins toward the structural characterization of IDPs. Here we show validity of the method through the structural characterization of restriction Endonuclease EcoO109I.