de Groot, B.

Seeliger, D.

English

de Groot, B. L.

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Prediction of protein flexibility from geometrical constraints

MPG.PuRe

A protein is a many-body system with 3N degrees of freedom(where N is the number of atoms in the molecule). In mostcases the greatest biological interest concerns only the low fre-quency motions, the so called "essential" degrees of freedom [1,2], which typically appear in timescales of nanoseconds tomicroseconds and play important roles in signalling, activationand enzyme function. Despite the rapid growth of computerpower these timescales are not accessible with current molecu-lar dynamic simulations systems. The CONCOORD systemattempts to alleviate this sampling problem by predicting pro-tein flexibility from geometrical constraints, thereby efficientlycrossing local barriers in the rugged potential energy landscape.The starting point is a 3D-structure of the protein. This struc-ture is analysed for interactions which are translated into a setof geometrical constraints, based on which an ensemble of newstructures is generated. The "essential" degrees of freedom canbe obtained by analysing the generated ensemble using princi-pal component analysis.GEOMETRICAL CONSTRAINTSThe 3-dimensional structure of a protein is determined by vari-ous interactions, such as covalent bonds, hydrogen bonds andthe hydrophobic effect. CONCOORD performs a careful analy-sis of the input structure and evaluates interactions. Figure 1shows a schematic diagram of interactions within a proteinstructure. The hydrogen bond framework (blue) and thehydrophobic core restrict the flexibility of the peptide chain(grey). Some regions of a protein structure are kept tightlytogether by a large number of interactions, whereas others, suchas loop regions, which often function as binding sites, displayPrediction of protein flexibilityfrom geometrical constraintsProtein function is in many cases coupled to molecularflexibility. However prediction of protein flexibilitywith molecular dynamics simulations is computation-ally demanding. The CONCOORD method provides anefficient way to predict the "essential" degrees of free-dom of a protein from a given 3-dimensional structure.by Daniel Seeliger and Dr Bert L. de GrootFigure 1. Geometrical constraints in staphylococcal nuclease(PDB 1ey4). Besides covalent connections, residues are connect-ed via hydrogen bonds (blue) and interactions in the hydropho-bic core (green). For clarity, amino acids are represented by theirCα-atom.Figure 2. A CONCOORD ensemble of staphylococcal nuclease,computed from PDB 1ey4.As published in BTi April/May 2006STRUCTURE DETERMINATIONenhanced flexibility. CONCOORD turns this information intogeometrical constraints with upper and lower bounds, depend-ing on the strength of the interaction, leading to a detailed atom-ic description of the protein comparable to a construction plan.STRUCTURE GENERATION AND ANALYSISIn a second step, CONCOORD uses the pre-defined constraintsto generate a structure ensemble. The CONCOORD kernel is aSHAKE - based algorithm that iteratively corrects distancesuntil the pre-defined constraints are fulfilled [3]. Starting fromrandom coordinates guarantees complete independencebetween subsequently generated structures. Usually, a set of afew hundred structures suffices for a converged coverage of theavailable conformational space. Thus, the method does not suf-fer from sampling problems inherent to other techniques suchas MD-simulations.Depending on the size of the protein and the chosen parame-ters, an ensemble of several hundred structures can be obtainedwithin a few hours or days. Figure 2 shows a CONCOORDensemble that is generated from the structure PDB 1ey4(staphylococcal nuclease). For comparison an NMR-ensembleof the same protein is shown in Figure 3. This shows that thereis a favourable agreement with the experimentally measuredflexibility. Highly ordered regions show little flexibility whereasthe large loop appears in different conformations.Structure ensembles are commonly analysed by principal com-ponent analysis (PCA). This is based on diagonalisation of thecovariance matrix of atomic fluctuations; it extracts the "essen-tial" degrees of freedom from an ensemble and allows a quanti-tative comparison of different ensembles along the majormodes of collective fluctuation.Figure 4 shows a comparisonof the CONCOORD ensemble and the NMR ensemble ofstaphylococcal nuclease. The PCA was carried out on theCONCOORD ensemble and both ensembles were projectedon the first three eigenvectors that correspond to the threelargest collective motions. The plot shows that the CONCO-ORD ensemble, started from the X-ray structure (red), sam-ples the complete conformational space that is accessible bythe NMR ensemble.APPLICATION TO LARGE SYSTEMSBecause of its computational efficiency, CONCOORD canbe routinely applied to extract functionally relevant modesof flexibility for molecular systems that are beyond the sizelimitations of other atomistic simulation techniques such asmolecular dynamics simulations. Application of the systemto the chaperonin GroEL-GroES complex that containsFigure 3. NMR ensemble of staphylococcal nuclease (PDB 1jor).Figure 4. Principal components analysis was carried out on theCONCOORD ensemble. The axes represent the three eigenvectorswith the largest eigenvalues and correspond to the main collectivemotions of the protein. Each dot represents a single structure. Thered dot represents the X-ray structure (1ey4) that was used asinput for CONCOORD. Blue dots represent CONCOORDstructures and the green dots belong to the NMR ensemble.STRUCTURE DETERMINATIONSTRUCTURE DETERMINATIONmore than 8000 amino acids revealed a novel form of cou-pling between intra-ring and inter-ring cooperativity [4].Each GroEL ring displays two main modes of collectivemotion: the main conformational transition upon bindingof the co-chaperonin GroES (coloured blue in Figure 5 ),and a secondary transition upon ATPbinding [Figure 5, upper right panel].CONCOORD simulations of a singleGroEL ring did not show any couplingbetween these modes, whereas simula-tions of the double ring system showeda strict correlation between the twomodes, thereby providing an explana-tion for how nucleotide binding is cou-pled to GroES affinity in the doublering, but not in a single ring.REFERENCES1. de Groot B L, van Aalten DMF, ScheekRM, Amadei A, Vriend G and BerendsenHJC. PROTEINS: Structure, Function andGenetics 1997; 29: 240-251.2. Amadei A, Linssen ABM and  BerendsenHJC, PROTEINS: Structure, Function andGenetics 1993; 17: 412-425.3. Ryckaert J-P, Cicotti G, Berendsen HJC. JComput Chem 1977; 23: 327-341.4. de Groot BL, Vriend G and BerendsenHJC. J MolBiol 1999; 286: 1241-1249.THE AUTHORSDaniel Seeliger, Dipl. Chem.Bert L. de Groot, Ph D.,Computational biomolecular dynamics group,Max-Planck-Institute for Biophysical Chemistry,D-37077 Göttingen,Germany.Figure 5. Asymmetric GroEL-GroES complex (left), together with CONCOORDsimulation results (right). The co-chaperonin GroES is shown in blue, the trans ring ofGroEL, bound to GroES, in red, and the cis-ring in green. A principal component analy-sis revealed two main structural transitions per GroEL ring, upon nucleotide binding(vertical axis in the right panels) and GroES binding (horizontal axis), respectively. Insimulations of the double ring, but not in a single ring, these modes were found to be cou-pled, suggesting a coupling between intra-ring and inter-ring cooperativity.

Prediction of protein flexibility from geometrical constraints.

http://hdl.handle.net/11858/00-001M-0000-0012-E8B9-5

Prediction of protein flexibility from geometrical constraints

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