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An assessment of the equilibrium dynamics of biomolecular systems, and in particular their most cooperative fluctuations accessible under native state conditions, is a first step towards understanding molecular mechanisms relevant to biological function. We present a web-based system, oGNM that enables users to calculate online the shape and dispersion of normal modes of motion for proteins, oligonucleotides and their complexes, or associated biological units, using the Gaussian Network Model (GNM). Computations with the new engine are 5–6 orders of magnitude faster than those using conventional normal mode analyses. Two cases studies illustrate the utility of oGNM. The first shows that the thermal fluctuations predicted for 1250 non-homologous proteins correlate well with X-ray crystallographic data over a broad range [7.3–15 Å] of inter-residue interaction cutoff distances and the correlations improve with increasing observation temperatures. The second study, focused on 64 oligonucleotides and oligonucleotide–protein complexes, shows that good agreement with experiments is achieved by representing each nucleotide by three GNM nodes (as opposed to one-node-per-residue in proteins) along with uniform interaction ranges for all components of the complexes. These results open the way to a rapid assessment of the dynamics of DNA/RNA-containing complexes. The server can be accessed at .

A detailed analysis of high-resolution structural data and computationally predicted dynamics was carried out for a designed sugar binding protein. The mean-square-deviations in the positions of residues derived from Nuclear Magnetic Resonance (NMR) models, and those inferred from X-ray crystallographic B-factors for two different crystal forms were compared with the predictions based on the Gaussian Network Model (GNM), and the results from molecular dynamics (MD) simulations. GNM systematically yielded a higher correlation than MD, with experimental data, suggesting that the lack of atomistic details in the coarse-grained GNM is more than compensated for by the mathematically exact evaluation of fluctuations using the native contacts topology. Evidence is provided that particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments. Interestingly, the information conveyed by X-ray crystallography becomes more consistent with NMR models and computational predictions when ensembles of X-ray models are considered. Less precise (broadly distributed) ensembles indeed appear to describe the accessible conformational space under native state conditions better than B-factors. Our results highlight the importance of utilizing multiple conformations obtained by alternative experimental methods, and analyzing results from both coarse-grained models and atomic simulations, for accurate assessment of motions accessible to proteins under native state conditions.

SUMMARY

For a representative set of 64 nonhomologous proteins, each containing a structure solved by NMR and X-ray crystallography, we analyzed the variations in atomic coordinates between NMR models, the temperature (B) factors measured by X-ray crystallography, and the fluctuation dynamics predicted by the Gaussian network model (GNM). The NMR and X-ray data exhibited a correlation of 0.49. The GNM results, on the other hand, yielded a correlation of 0.59 with X-ray data and a distinctively better correlation (0.75) with NMR data. The higher correlation between GNM and NMR data, compared to that between GNM and X-ray B factors, is shown to arise from the differences in the spectrum of modes accessible in solution and in the crystal environment. Mainly, large-amplitude motions sampled in solution are restricted, if not inaccessible, in the crystalline environment of X-rays. Combined GNM and NMR analysis emerges as a useful tool for assessing protein dynamics.

The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new Gaussian network model, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified, and others to become less feasible. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.

We consider a recently suggested “equation of state” for natively folded proteins, and verify its validity for a set of about 5800 proteins. The equation is based on a fractal viewpoint of proteins, on a generalization of the Landau-Peierls instability, and on a marginal stability criterion. The latter allows for coexistence of stability and flexibility of proteins, which is required for their proper function. The equation of state relates the protein fractal dimension , its spectral dimension , and the number of amino acids N. Using structural data from the protein data bank (PDB) and the Gaussian network model (GNM), we compute and for the entire set and demonstrate that the equation of state is well obeyed. Addressing the fractal properties and making use of the equation of state may help to engineer biologically inspired catalysts.

Background

In the last decade, various coarse-grained elastic network models have been developed to study the large-scale motions of proteins and protein complexes where computer simulations using detailed all-atom models are not feasible. Among these models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) have been widely used. Both models have strengths and limitations. GNM can predict the relative magnitudes of protein fluctuations well, but due to its isotropy assumption, it can not be applied to predict the directions of the fluctuations. In contrast, ANM adds the ability to do the latter, but loses a significant amount of precision in the prediction of the magnitudes.

Results

In this article, we develop a single model, called generalized spring tensor model (STeM), that is able to predict well both the magnitudes and the directions of the fluctuations. Specifically, STeM performs equally well in B-factor predictions as GNM and has the ability to predict the directions of fluctuations as ANM. This is achieved by employing a physically more realistic potential, the Gō-like potential. The potential, which is more sophisticated than that of either GNM or ANM, though adds complexity to the derivation process of the Hessian matrix (which fortunately has been done once for all and the MATLAB code is freely available electronically at http://www.cs.iastate.edu/~gsong/STeM), causes virtually no performance slowdown.

Conclusions

Derived from a physically more realistic potential, STeM proves to be a natural solution in which advantages that used to exist in two separate models, namely GNM and ANM, are achieved in one single model. It thus lightens the burden to work with two separate models and to relate the modes of GNM with those of ANM at times. By examining the contributions of different interaction terms in the Gō potential to the fluctuation dynamics, STeM reveals, (i) a physical explanation for why the distance-dependent, inverse distance square (i.e., ) spring constants perform better than the uniform ones, and (ii), the importance of three-body and four-body interactions to properly modeling protein dynamics.

HIV-1 integrase (IN) is an important target in the development of drugs against the AIDS virus. Drug design based on the structure of IN was markedly hampered due to the lack of three-dimensional structure information of HIV-1 IN-viral DNA complex. The prototype foamy virus (PFV) IN has a highly functional and structural homology with HIV-1 IN. Recently, the X-ray crystal complex structure of PFV IN with its cognate viral DNA has been obtained. In this study, both Gaussian network model (GNM) and anisotropy network model (ANM) have been applied to comparatively investigate the motion modes of PFV DNA-free and DNA-bound IN. The results show that the motion mode of PFV IN has only a slight change after binding with DNA. The motion of this enzyme is in favor of association with DNA, and the binding ability is determined by its intrinsic structural topology. Molecular docking experiments were performed to gain the binding modes of a series of diketo acid (DKA) inhibitors with PFV IN obtained from ANM, from which the dependability of PFV IN-DNA used in the drug screen for strand transfer (ST) inhibitors was confirmed. It is also found that the functional groups of keto-enol, bis-diketo, tetrazole and azido play a key role in aiding the recognition of viral DNA, and thus finally increase the inhibition capability for the corresponding DKA inhibitor. Our study provides some theoretical information and helps to design anti-AIDS drug based on the structure of IN.

HIV infection is initiated by binding of the viral glycoprotein gp120, to the cellular receptor CD4. Upon CD4 binding, gp120 undergoes conformational change, permitting binding to the chemokine receptor. Crystal structures of gp120 ternary complex reveal the CD4 bound conformation of gp120. We report here the application of Gaussian Network Model (GNM) to the crystal structures of gp120 bound to CD4 or CD4 mimic and 17b, to study the collective motions of the gp120 core and determine the communication propensities of the residue network. The GNM fluctuation profiles identify residues in the inner domain and outer domain that may facilitate conformational change or stability, respectively. Communication propensities delineate a residue network that is topologically suited for signal propagation from the Phe43 cavity throughout the gp120 outer domain. . These results provide a new context for interpreting gp120 core envelope structure-function relationships.

Summary

Growing evidence supports the view that enzymatic activity results from a subtle interplay between chemical kinetics and molecular motions. A systematic analysis is performed here to delineate the type and level of coupling between catalysis and conformational mechanics. The dynamics of a set of 98 enzymes representative of different EC classes are analyzed with the Gaussian network model (GNM) and compared with experimental data. In more than 70% of the examined enzymes, the global hinge centers predicted by the GNM are found to be colocalized with the catalytic sites experimentally identified. Low translational mobility (<7%) is observed for the catalytic residues, consistent with the fine-tuned design of enzymes to achieve precise mechanochemical activities. Ligand binding sites, while closely neighboring catalytic sites, enjoy a moderate flexibility to accommodate the ligand binding. These findings could serve as additionalcriteria for assessing drug binding residues and could lessen the computational burden of substrate docking searches.

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP5A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of 15N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg+2*ATP + AMP → Mg+2*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time τ⊥ and low order parameters, and fast (picoseconds) motions with correlation time τ|| and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP5A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, τ|| and τ⊥ are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time τ⊥, is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.

Current etching routes to process large graphene sheets into nanoscale graphene so as to open up a bandgap tend to produce structures with rough and disordered edges. This leads to detrimental electron scattering and reduces carrier mobility. In this work, we present a novel yet simple direct-growth strategy to yield graphene nanomesh (GNM) on a patterned Cu foil via nanosphere lithography. Raman spectroscopy and TEM characterizations show that the as-grown GNM has significantly smoother edges than post-growth etched GNM. More importantly, the transistors based on as-grown GNM with neck widths of 65-75 nm have a near 3-fold higher mobility than those derived from etched GNM with the similar neck widths.

The conformational dynamics data bank (CDDB, http://www.cdyn.org) is a database that aims to provide comprehensive results on the conformational dynamics of high molecular weight proteins and protein assemblies. Analysis is performed using a recently introduced coarse-grained computational approach that is applied to the majority of structures present in the electron microscopy data bank (EMDB). Results include equilibrium thermal fluctuations and elastic strain energy distributions that identify rigid versus flexible protein domains generally, as well as those associated with specific functional transitions, and correlations in molecular motions that identify molecular regions that are highly coupled dynamically, with implications for allosteric mechanisms. A practical web-based search interface enables users to easily collect conformational dynamics data in various formats. The data bank is maintained and updated automatically to include conformational dynamics results for new structural entries as they become available in the EMDB. The CDDB complements static structural information to facilitate the investigation and interpretation of the biological function of proteins and protein assemblies essential to cell function.

For the binding of peptides to wild-type HIV-1 and BIV TAR RNA and to mutants with bulges of various sizes, changes in the DeltaDelta G values of binding were determined from experimental K d values. The corresponding entropies of these bulges are estimated by enumerating all possible RNA bulge conformations on a lattice and then applying the Boltzmann relationship. Independent calculations of entropies from fluctuations are also carried out using the Gaussian network model (GNM) recently introduced for analyzing folded structures. Strong correlations are seen between the changes in free energy determined for binding and the two different unbound entropy calculations. The fact that the calculated entropy increase with larger bulge size is correlated with the enhanced experimental binding free energy is unusual. This system exhibits a dependence on the entropy of the unbound form that is opposite to usual binding models. Instead of a large initial entropy being unfavorable since it would be reduced upon binding, here the larger entropies actually favor binding. Several interpretations are possible: (i) the higher conformational freedom implies a higher competence for binding with a minimal strain, by suitable selection amongst the set of already accessible conformations; (ii) larger bulge entropies enhance the probability of the specific favorable conformation of the bound state; (iii) the increased freedom of the larger bulges contri-butes more to the bound state than to the unbound state; (iv) indirectly the large entropy of the bound state might have an unfavorable effect on the solvent structure. Nonetheless, this unusual effect is interesting.

The ALADYN web server aligns pairs of protein structures by comparing their internal dynamics and detecting regions that sustain similar large-scale movements. The latter often accompany functional conformational changes in proteins and enzymes. The ALADYN dynamics-based alignment can therefore highlight functionally-oriented correspondences that could be more elusive to sequence- or structure-based comparisons. The ALADYN server takes the structure files of the two proteins as input. The optimal relative positioning of the molecules is found by maximizing the similarity of the pattern of structural fluctuations which are calculated via an elastic network model. The resulting alignment is presented via an interactive graphical Java applet and is accompanied by a number of quantitative indicators and downloadable data files. The ALADYN web server is freely accessible at the http://aladyn.escience-lab.org address.

Background

Protein motions play an essential role in catalysis and protein-ligand interactions, but are difficult to observe directly. A substantial fraction of protein motions involve hinge bending. For these proteins, the accurate identification of flexible hinges connecting rigid domains would provide significant insight into motion. Programs such as GNM and FIRST have made global flexibility predictions available at low computational cost, but are not designed specifically for finding hinge points.

Results

Here we present the novel FlexOracle hinge prediction approach based on the ideas that energetic interactions are stronger within structural domains than between them, and that fragments generated by cleaving the protein at the hinge site are independently stable. We implement this as a tool within the Database of Macromolecular Motions, MolMovDB.org. For a given structure, we generate pairs of fragments based on scanning all possible cleavage points on the protein chain, compute the energy of the fragments compared with the undivided protein, and predict hinges where this quantity is minimal. We present three specific implementations of this approach. In the first, we consider only pairs of fragments generated by cutting at a single location on the protein chain and then use a standard molecular mechanics force field to calculate the enthalpies of the two fragments. In the second, we generate fragments in the same way but instead compute their free energies using a knowledge based force field. In the third, we generate fragment pairs by cutting at two points on the protein chain and then calculate their free energies.

Conclusion

Quantitative results demonstrate our method's ability to predict known hinges from the Database of Macromolecular Motions.

WebFEATURE (http://feature.stanford.edu/webfeature/) is a web-accessible structural analysis tool that allows users to scan query structures for functional sites in both proteins and nucleic acids. WebFEATURE is the public interface to the scanning algorithm of the FEATURE package, a supervised learning algorithm for creating and identifying 3D, physicochemical motifs in molecular structures. Given an input structure or Protein Data Bank identifier (PDB ID), and a statistical model of a functional site, WebFEATURE will return rank-scored ‘hits’ in 3D space that identify regions in the structure where similar distributions of physicochemical properties occur relative to the site model. Users can visualize and interactively manipulate scored hits and the query structure in web browsers that support the Chime plug-in. Alternatively, results can be downloaded and visualized through other freely available molecular modeling tools, like RasMol, PyMOL and Chimera. A major application of WebFEATURE is in rapid annotation of function to structures in the context of structural genomics.

The Metalloprotein Database and Browser (MDB; http://metallo.scripps.edu) at The Scripps Research Institute is a web-accessible resource for metalloprotein research. It offers the scientific community quantitative information on geometrical parameters of metal-binding sites in protein structures available from the Protein Data Bank (PDB). The MDB also offers analytical tools for the examination of trends or patterns in the indexed metal-binding sites. A user can perform interactive searches, metal-site structure visualization (via a Java applet), and analysis of the quantitative data by accessing the MDB through a web browser without requiring an external application or platform-dependent plugin. The MDB also has a non-interactive interface with which other web sites and network-aware applications can seamlessly incorporate data or statistical analysis results from metal-binding sites. The information contained in the MDB is periodically updated with automated algorithms that find and index metal sites from new protein structures released by the PDB.

Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models.

Author Summary

In recent years, there has been a surge in the number of studies using network models for understanding biomolecular systems dynamics. Essentially, two different groups of studies have been performed, driven by two different communities. The first is based on molecular biophysics and statistical mechanical concepts. Normal mode analyses using elastic network models lie in this group. The second is based on information theory and spectral graph methods. The present study demonstrates for the first time that signal transduction events directly depend on the fluctuation dynamics of the biomolecular systems, thus establishing the bridge between the (newly proposed) information-theoretic and the (well-established) physically inspired approaches. We have applied the new approach to five different enzymes. Functionally active residues are shown to possess enhanced communication propensities. Furthermore, secondary structural elements emerge as efficient mediators of communication. These results provide us with important insights for protein design and mechanisms of allostery.

PRTAD is a dedicated database and structural bioinformatics system for protein analysis and modeling. The database is developed to host and analyze the statistical data for protein residue level “virtual” bond and torsion angles obtained from their distributions in databases of known protein structures such as in the PDB Data Bank. PRTAD is capable of generating, caching, and displaying the statistical distributions of the angles of various types. The collected information can be used to extract geometric restraints or define statistical potentials for protein structure determination. PRTAD is supported with a friendly designed web interface so that users can easily specify the angle types, and retrieve, visualize, or download the distributions of the angles as they desire. The database PRTAD is freely accessible at http://www.math.iastate.edu/prtad.

Protein–protein interaction networks are currently visualized by software generated interaction webs based upon static experimental data. Current state is limited to static, mostly non-compartmental network and non time resolved protein interactions. A satisfactory mathematical foundation for particle interactions within a viscous liquid state (situation within the cytoplasm) does not exist nor do current computer programs enable building dynamic interaction networks for time resolved interactions. Building mathematical foundation for intracellular protein interactions can be achieved in two increments (a) trigger and capture the dynamic molecular changes for a select subset of proteins using several model systems and high throughput time resolved proteomics and, (b) use this information to build the mathematical foundation and computational algorithm for a compartmentalized and dynamic protein interaction network. Such a foundation is expected to provide benefit in at least two spheres: (a) understanding physiology enabling explanation of phenomenon such as incomplete penetrance in genetic disorders and (b) enabling several fold increase in biopharmaceutical production using impure starting materials.

Protein–protein interaction networks are currently visualized by software generated interaction webs based upon static experimental data. Current state is limited to static, mostly non-compartmental network and non time resolved protein interactions. A satisfactory mathematical foundation for particle interactions within a viscous liquid state (situation within the cytoplasm) does not exist nor do current computer programs enable building dynamic interaction networks for time resolved interactions. Building mathematical foundation for intracellular protein interactions can be achieved in two increments (a) trigger and capture the dynamic molecular changes for a select subset of proteins using several model systems and high throughput time resolved proteomics and, (b) use this information to build the mathematical foundation and computational algorithm for a compartmentalized and dynamic protein interaction network. Such a foundation is expected to provide benefit in at least two spheres: (a) understanding physiology enabling explanation of phenomenon such as incomplete penetrance in genetic disorders and (b) enabling several fold increase in biopharmaceutical production using impure starting materials.

N-Browse is a graphical network browser for the visualization and navigation of heterogeneous molecular interaction data. N-Browse runs as a Java applet in a Web browser, providing highly dynamic and interactive on-demand access to network data available from a remote server. The N-Browse interface is easy to use and accommodates multiple types of functional linkages with associated information, allowing the exploration of many layers of functional information simultaneously. Although created for applications in biology, N-Browse uses a generic database schema that can be adapted to network representations in any knowledge domain. The N-Browse client-server package is freely available for distribution, providing a convenient way for data producers and providers to distribute and offer interactive visualization of network-based data.

The DBAli tools use a comprehensive set of structural alignments in the DBAli database to leverage the structural information deposited in the Protein Data Bank (PDB). These tools include (i) the DBAlit program that allows users to input the 3D coordinates of a protein structure for comparison by MAMMOTH against all chains in the PDB; (ii) the AnnoLite and AnnoLyze programs that annotate a target structure based on its stored relationships to other structures; (iii) the ModClus program that clusters structures by sequence and structure similarities; (iv) the ModDom program that identifies domains as recurrent structural fragments and (v) an implementation of the COMPARER method in the SALIGN command in MODELLER that creates a multiple structure alignment for a set of related protein structures. Thus, the DBAli tools, which are freely accessible via the World Wide Web at http://salilab.org/DBAli/, allow users to mine the protein structure space by establishing relationships between protein structures and their functions.

The University of California Santa Cruz (UCSC) Genome Browser Database is an up to date source for genome sequence data integrated with a large collection of related annotations. The database is optimized to support fast interactive performance with the web-based UCSC Genome Browser, a tool built on top of the database for rapid visualization and querying of the data at many levels. The annotations for a given genome are displayed in the browser as a series of tracks aligned with the genomic sequence. Sequence data and annotations may also be viewed in a text-based tabular format or downloaded as tab-delimited flat files. The Genome Browser Database, browsing tools and downloadable data files can all be found on the UCSC Genome Bioinformatics website (http://genome.ucsc.edu), which also contains links to documentation and related technical information.

Background

Protein secondary structure prediction method based on probabilistic models such as hidden Markov model (HMM) appeals to many because it provides meaningful information relevant to sequence-structure relationship. However, at present, the prediction accuracy of pure HMM-type methods is much lower than that of machine learning-based methods such as neural networks (NN) or support vector machines (SVM).

Results

In this paper, we report a new method of probabilistic nature for protein secondary structure prediction, based on dynamic Bayesian networks (DBN). The new method models the PSI-BLAST profile of a protein sequence using a multivariate Gaussian distribution, and simultaneously takes into account the dependency between the profile and secondary structure and the dependency between profiles of neighboring residues. In addition, a segment length distribution is introduced for each secondary structure state. Tests show that the DBN method has made a significant improvement in the accuracy compared to other pure HMM-type methods. Further improvement is achieved by combining the DBN with an NN, a method called DBNN, which shows better Q3 accuracy than many popular methods and is competitive to the current state-of-the-arts. The most interesting feature of DBN/DBNN is that a significant improvement in the prediction accuracy is achieved when combined with other methods by a simple consensus.

Conclusion

The DBN method using a Gaussian distribution for the PSI-BLAST profile and a high-ordered dependency between profiles of neighboring residues produces significantly better prediction accuracy than other HMM-type probabilistic methods. Owing to their different nature, the DBN and NN combine to form a more accurate method DBNN. Future improvement may be achieved by combining DBNN with a method of SVM type.