Ognm: Online Computation of Structural Dynamics Using the Gaussian Network Model Lee-Wei Yang1, A
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W24–W31 Nucleic Acids Research, 2006, Vol. 34, Web Server issue doi:10.1093/nar/gkl084 oGNM: online computation of structural dynamics using the Gaussian Network Model Lee-Wei Yang1, A. J. Rader1, Xiong Liu1,2, Cristopher Jon Jursa2, Shann Ching Chen1, Hassan A. Karimi2 and Ivet Bahar1,* 1Department of Computational Biology, School of Medicine and 2Department of Information Science and Telecommunications, School of Information Science, University of Pittsburgh, Pittsburgh, PA 15213, USA Received December 14, 2005; Revised January 25, 2006; Accepted March 6, 2006 ABSTRACT INTRODUCTION An assessment of the equilibrium dynamics of An emerging view in structural and molecular biology is biomolecular systems, and in particular their most that the conformational mechanisms involved in biomolecular functions are determined by the intrinsic dynamics of cooperativefluctuationsaccessibleundernativestate biomolecules, and the intrinsic dynamics are, in turn, defined conditions, is a first step towards understanding by the overall structural architecture (1). A better understand- molecular mechanisms relevant to biological func- ing of structural dynamics that underlie important biological tion. We present a web-based system, oGNM that functions has been gained in recent years by modeling enables users to calculate online the shape and biomolecular systems as biomachines. Elastic network (EN) dispersion of normal modes of motion for proteins, models and simplified normal mode analyses (NMA), have oligonucleotides and their complexes, or associated proven particularly useful to this aim, as recently reviewed biological units, using the Gaussian Network Model (2,3). Recently, we have constructed a database (DB) of (GNM). Computations with the new engine are 5–6 protein motions, iGNM (4), by using such an EN model, orders of magnitude faster than those using conven- the Gaussian Network Model (GNM) (5,6). The dynamics tional normal mode analyses. Two cases studies of 20 058 structures that were accessible in the Protein Data Bank (PDB) (7) in the fall of 2003 have been collected in the illustrate the utility of oGNM. The first shows that the iGNM DB. The present study builds on this work to introduce thermal fluctuations predicted for 1250 non-homologous an on-line calculation server, oGNM, for examining the proteins correlate well with X-ray crystallographic essential dynamics of the complete set of over 34 000 PDB data over a broad range [7.3–15 A˚ ] of inter-residue structures, as well as that of user-modified and unreleased interaction cutoff distances and the correlations structures or models. improve with increasing observation temperatures. Results from the NMAs of proteins can currently be The second study, focused on 64 oligonucleotides obtained from a number of online sources. The most detailed and oligonucleotide–protein complexes, shows that NMA is performed at the atomic level by the Molecular Vibra- good agreement with experiments is achieved by tions Evaluation Server (MoViES; http://ang.cz3.nus.edu.sg/ representing each nucleotide by three GNM nodes cgi-bin/prog/norm.pl (8). MoViES calculates the normal (as opposed to one-node-per-residue in proteins) modes and thermal vibrations for relatively small structures (<4000 heavy atoms), sending the results via email after seven along with uniform interaction ranges for all compo- days. The database of macromolecular movements (MolMovDB; nents of the complexes. These results open the way to http://molmovdb.org/) features a web submission interface for a rapid assessment of the dynamics of DNA/ calculating the five lowest frequency modes (9). WEBnm@ RNA-containing complexes. The server can be (http://www.bioinfo.no/tools/normalmodes) (10) calculates the accessed at http://ignm.ccbb.pitt.edu/GNM_Online_ slowest fourteen modes and associated deformation Calculation.htm. energies. Both systems employ the same Molecular Modeling *To whom correspondence should be addressed. Tel: +1 412 648 3333; Fax: +1 412 648 3163; Email: [email protected] Present addresses: A.J. Rader, Department of Physics, Indiana University-Purdue University Indianapolis, USA Shann Ching Chen, Department of Biomedical Engineering, Carnegie Mellon University, USA The authors wish it to be known that, in their opinion, the first two authors should be regarded as joint First Authors Ó The Author 2006. Published by Oxford University Press. All rights reserved. The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact [email protected] Nucleic Acids Research, 2006, Vol. 34, Web Server issue W25 Toolkit (MMTK) package (11) that adopts a residue-level EN (24) and functional motions (2,3,25). Clearly there is a great representation. Although both provide the option of generating deal of dynamical information/patterns encoded in biomolecu- and downloading movies of these modes, they are restricted lar structures that can be efficiently extracted using the oGNM. to the analysis of single domain or single chain proteins, respectively. Online calculations for larger structures can be accomplished by elNe´mo (http://igs-server.cnrs-mrs.fr/ MATERIALS AND METHODS elnemo/index.html) (12). elNe´mo uses an alternative engine based upon the Rotation Translation Block (RTB) method (13) The Gaussian Network Model (GNM) which collapses consecutive residues into rigid blocks, each The biomolecular structure is modeled as a network of N nodes representing the nodes in a low resolution EN model. This identified by the a-carbon atoms of proteins and other selected server requires minutes, hours or longer to calculate the 100 atoms of nucleotides (see below). Drawing on the statistical slowest modes for large structures. Our oGNM server provides mechanical theory of polymer networks (26), the fluctuations online calculation of normal modes at the residue-level within of each node are assumed to be isotropic and Gaussian. The a few minutes regardless of biomolecular size. topology of the network is recorded in a N · N Kirchhoff While a large number of studies have tested and verified the matrix, G, where the off-diagonal elements are À1 if the nodes applicability of EN models to proteins, the optimal model are within a cutoff distance, rc, and zero otherwise (5,6). The and parameters for representing nucleotides remains to be diagonal elements represent the coordination number of each established (14). Two major issues in the application of EN residue. Assigning a uniform spring constant, g, to all contacts, models to biomolecules are the choice of the particular atoms the cross-correlations between the fluctuations DRi and DRj of for defining the nodes, and the cutoff distance (rc) of inter- residues i and j are evaluated as actions that define the connectors/springs between the nodes, which are carefully considered in building GNM. In an initial À1 o hDRi · DRji¼ð3kBT/gÞ½G ij 1 application of the GNM that accurately described the change in the fluctuation behavior of tRNAs nucleotides between where kB is the Boltzmann constant, T is the absolute À1 th the free- and synthetase-bound-forms (15), a single-node- temperature and [G ]ij is the ij element of the inverse of per-nucleotide, at the phosphorous atom, was used to model G (5,6). Setting j ¼ i in Equation 1, we obtain the mean-square 2 free tRNA, while two-nodes per nucleotide, identified by the (ms) fluctuations of residue i, h(DRi) i, which may be directly atoms P and O40, were used for tRNA complexed with compared to the corresponding X-ray crystallographic B-factor 2 2 synthetase. Because the distance between the P-atoms of base Bi ¼ (8p /3) h(DRi) i reported in the PDB, thus providing a pair forming nucleotides on adjacent strands varies from 13 to quantitative measure of correlation between computations and 16 s, a larger cutoff value, rp, was adopted compared to that experimental data. GNM yields the distribution of residue a (rc ¼ 7 s) commonly used for amino acid nodes (C -atoms). fluctuations; the absolute sizes are found by normalizing the exp Coarse-graining of nucleotides were found to adequately uncover results with respect to experimental B-factors (Bi ), which the global motions for translation (16,17) and replication permits us to determine g for a given choice of rc. machineries (18). The latter study adopted a three-node- The equilibrium dynamics of the structure results from the per-nucleotide model, using the P-, C2- (base) and C40- superposition of N À 1 nonzero modes found by the eigenvalue (sugar) atoms with the cutoff distances, rp and rc, set to the decomposition of G. The elements of the kth eigenvector, uk, same value. Given that the average mass of a nucleotide is describe the displacements of the residues along the kth mode approximately three times that of an amino acid, such a model coordinate, and the kth eigenvalue, lk, scales with the fre- may reflect a more consistent EN representation for the entire quency of the kth mode, where 1 < k < N À 1. The contribution network. of the kth mode to the ms fluctuations of residue i is The oGNM server offers three major advantages: (i) it is not limited to relatively small structures, or single domains; (ii) it 2 3kBT 1 T ½ðDRiÞ k ¼ ukuk 2 returns the results within seconds, i.e. its computational speed g lk ii is significantly faster compared to existing servers that may where (u u T) designates the ith diagonal element of the require minutes, hours or days to obtain the normal modes; k k ii matrix enclosed in parenthesis.