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2.  Coarse-Grained Models Reveal Functional Dynamics - I. Elastic Network Models – Theories, Comparisons and Perspectives 
In this review, we summarize the progress on coarse-grained elastic network models (CG-ENMs) in the past decade. Theories were formulated to allow study of conformational dynamics in time/space frames of biological interest. Several highlighted models and their underlined hypotheses are introduced in physical depth. Important ENM offshoots, motivated to reproduce experimental data as well as to address the slow-mode-encoded configurational transitions, are also introduced. With the theoretical developments, computational cost is significantly reduced due to simplified potentials and coarse-grained schemes. Accumulating wealth of data suggest that ENMs agree equally well with experiment in describing equilibrium dynamics despite their distinct potentials and levels of coarse-graining. They however do differ in the slowest motional components that are essential to address large conformational changes of functional significance. The difference stems from the dissimilar curvatures of the harmonic energy wells described for each model. We also provide our views on the predictability of ‘open to close’ (open→close) transitions of biomolecules on the basis of conformational selection theory. Lastly, we address the limitations of the ENM formalism which are partially alleviated by the complementary CG-MD approach, to be introduced in the second paper of this two-part series.
PMCID: PMC2735964  PMID: 19812764
normal mode analysis; potential surface; low-frequency motions; GNM; NMR; X-ray; B-factors
3.  Global Dynamics of Proteins: Bridging Between Structure and Function 
Biomolecular systems possess unique, structure-encoded dynamic properties that underlie their biological functions. Recent studies indicate that these dynamic properties are determined to a large extent by the topology of native contacts. In recent years, elastic network models used in conjunction with normal mode analyses have proven to be useful for elucidating the collective dynamics intrinsically accessible under native state conditions, including in particular the global modes of motions that are robustly defined by the overall architecture. With increasing availability of structural data for well-studied proteins in different forms (liganded, complexed, or free), there is increasing evidence in support of the correspondence between functional changes in structures observed in experiments and the global motions predicted by these coarse-grained analyses. These observed correlations suggest that computational methods may be advantageously employed for assessing functional changes in structure and allosteric mechanisms intrinsically favored by the native fold.
doi:10.1146/annurev.biophys.093008.131258
PMCID: PMC2938190  PMID: 20192781
elastic network models; normal modes; principal component analysis; collective motions; allosteric changes in conformation; closed/open conformations
5.  Principal component analysis of native ensembles of biomolecular structures (PCA_NEST): insights into functional dynamics 
Bioinformatics  2009;25(5):606-614.
Motivation: To efficiently analyze the ‘native ensemble of conformations’ accessible to proteins near their folded state and to extract essential information from observed distributions of conformations, reliable mathematical methods and computational tools are needed.
Result: Examination of 24 pairs of structures determined by both NMR and X-ray reveals that the differences in the dynamics of the same protein resolved by the two techniques can be tracked to the most robust low frequency modes elucidated by principal component analysis (PCA) of NMR models. The active sites of enzymes are found to be highly constrained in these PCA modes. Furthermore, the residues predicted to be highly immobile are shown to be evolutionarily conserved, lending support to a PCA-based identification of potential functional sites. An online tool, PCA_NEST, is designed to derive the principal modes of conformational changes from structural ensembles resolved by experiments or generated by computations.
Availability: http://ignm.ccbb.pitt.edu/oPCA_Online.htm
Contact: lwy1@iam.u-tokyo.ac.jp
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btp023
PMCID: PMC2647834  PMID: 19147661
6.  Insights into Equilibrium Dynamics of Proteins from Comparison of NMR and X-Ray Data with Computational Predictions 
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.
doi:10.1016/j.str.2007.04.014
PMCID: PMC2760440  PMID: 17562320
7.  Coarse-Grained Models Reveal Functional Dynamics – II. Molecular Dynamics Simulation at the Coarse-Grained Level – Theories and Biological Applications 
Molecular dynamics (MD) simulation has remained the most indispensable tool in studying equilibrium/non-equilibrium conformational dynamics since its advent 30 years ago. With advances in spectroscopy accompanying solved biocomplexes in growing sizes, sampling their dynamics that occur at biologically interesting spatial/temporal scales becomes computationally intractable; this motivated the use of coarse-grained (CG) approaches. CG-MD models are used to study folding and conformational transitions in reduced resolution and can employ enlarged time steps due to the absence of some of the fastest motions in the system. The Boltzmann-Inversion technique, heavily used in parameterizing these models, provides a smoothed-out effective potential on which molecular conformation evolves at a faster pace thus stretching simulations into tens of microseconds. As a result, a complete catalytic cycle of HIV-1 protease or the assembly of lipid-protein mixtures could be investigated by CG-MD to gain biological insights. In this review, we survey the theories developed in recent years, which are categorized into Folding-based and Molecular-Mechanics-based. In addition, physical bases in the selection of CG beads/time-step, the choice of effective potentials, representation of solvent, and restoration of molecular representations back to their atomic details are systematically discussed.
PMCID: PMC2735960  PMID: 19812774
conformational transitions; molecular mechanics; Gō-model; Boltzmann-Inversion; simulation time-step
8.  Coupling between Catalytic Site and Collective Dynamics: A Requirement for Mechanochemical Activity of Enzymes 
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.
doi:10.1016/j.str.2005.03.015
PMCID: PMC1489920  PMID: 15939021
9.  iGNM: a database of protein functional motions based on Gaussian Network Model 
Bioinformatics (Oxford, England)  2005;21(13):2978-2987.
Motivation
The knowledge of protein structure is not sufficient for understanding and controlling its function. Function is a dynamic property. Although protein structural information has been rapidly accumulating in databases, little effort has been invested to date toward systematically characterizing protein dynamics. The recent success of analytical methods based on elastic network models, and in particular the Gaussian Network Model (GNM), permits us to perform a high-throughput analysis of the collective dynamics of proteins.
Results
We computed the GNM dynamics for 20 058 structures from the Protein Data Bank, and generated information on the equilibrium dynamics at the level of individual residues. The results are stored on a web-based system called i GNM and configured so as to permit the users to visualize or download the results through a standard web browser using a simple search engine. Static and animated images for describing the conformational mobility of proteins over a broad range of normal modes are accessible, along with an online calculation engine available for newly deposited structures. A case study of the dynamics of 20 non-homologous hydrolases is presented to illustrate the utility of the iGNM database for identifying key residues that control the cooperative motions and revealing the connection between collective dynamics and catalytic activity.
Availability
http://ignm.ccbb.pitt.edu/
doi:10.1093/bioinformatics/bti469
PMCID: PMC1752228  PMID: 15860562
10.  oGNM: online computation of structural dynamics using the Gaussian Network Model 
Nucleic Acids Research  2006;34(Web Server issue):W24-W31.
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 .
doi:10.1093/nar/gkl084
PMCID: PMC1538811  PMID: 16845002

Results 1-10 (10)