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Willy Wriggers

Publications and source records attributed to Willy Wriggers.

At least 19 recordsLinked to original sources
PubMed2006

Limulus polyphemus hemocyanin: 10 A cryo-EM structure, sequence analysis, molecular modelling and rigid-body fitting reveal the interfaces between the eight hexamers.

The blue copper protein hemocyanin from the horseshoe crab Limulus polyphemus is among the largest respiratory proteins found in nature (3.5 MDa) and exhibits a highly cooperative oxygen binding. Its 48 subunits are arranged as eight hexamers (1x6mers) that form the native 8x6mer in a nested hierarchy of 2x6mers and 4x6mers. This quaternary structure is established by eight subunit types (termed I, IIA, II, IIIA, IIIB, IV, V, and VI), of which only type II has been sequenced. Crystal structures of the 1x6mer are available, but for the 8x6mer only a 40 A 3D reconstruction exists. Consequently, the structural parameters of the 8x6mer are not firmly established, and the molecular interfaces between the eight hexamers are still to be defined. This, however, is crucial for understanding how allosteric transitions are mediated between the different levels of hierarchy. Here, we show the 10 A structure (FSC(1/2-bit) criterion) of the oxygenated 8x6mer from cryo-electron microscopy (cryo-EM) and single-particle analysis. Moreover, we show its molecular model as obtained by DNA sequencing of subunits II, IIIA, IV and VI, and molecular modelling and rigid-body fitting of all subunit types. Remarkably, the latter enabled us to improve the resolution of the cryo-EM structure from 11 A to the final 10 A. The 10 A structure allows firm assessment of various structural parameters of the 8x6mer, the 4x6mer and the 2x6mer, and reveals a total of 46 inter-hexamer bridges. These group as 11 types of interface: four at the 2x6mer level (II-II, II-IV, V-VI, IV-VI), three form the 4x6mer (V-V, V-VI, VI-IIIB/IV/V), and four are required to assemble the 8x6mer (IIIA-IIIA, IIIA-IIIB, II-IV, IV-IV). The molecular model shows the amino acid residues involved, and reveals that several of the interfaces are intriguingly histidine-rich and likely to transfer allosteric signals between the different levels of the nested hierarchy.

Amino Acid Sequence↗
PubMed2006

Entropic folding pathway of human epidermal growth factor explored by disulfide scrambling and amplified collective motion simulations.

Epidermal growth factor (EGF) regulates cell proliferation and differentiation by binding to the EGF receptor (EGFR) extra-cellular domains. Human EGF is a small, single-chain protein comprising three distinct loops (A, B, and C), which are connected by three disulfide bridges (Cys6-Cys20, Cys14-Cys31, and Cys33-Cys42). These disulfide bridges are essential for structural stability and biological activity. EGF was extensively studied by disulfide scrambling, an experimental technique for the conformational entrapment of intermediate states, which allows us to study the folding pathway of proteins containing disulfide bonds. The experimental results showed that there is a major 2-disulfide intermediate (denoted EGF-II) and that the native disulfide bonding pattern is less prevalent in one of the mutants. In this article, we investigated for the first time the solution conformations of wild-type EGF, EGF-II, and the mutant S9C through extensive molecular dynamics (MD) simulations in water using both the standard MD technique and a recently developed amplified-collective-motion (ACM) sampling method. Compared to standard MD simulations, we achieved a much more enhanced sampling by the ACM simulations, and the structures were sufficiently relaxed to estimate configurational entropies. The simulation results suggest a predominantly entropic folding pathway governed by the disorder of three functional loop regions. Although EGF-II exhibits two native disulfide bonds (Cys14-Cys31 and Cys33- Cys42), its large configurational entropy inhibits a direct transition to the native structure in the folding process. When Ser9 is mutated into Cys, a non-native disulfide bridge Cys9- Cys20 is slightly more favorable than the native Cys6-Cys20 because a less constrained N-terminus affords larger entropy. Isomers that are functionally less active also exhibit a more localized dynamics of the functional loop regions, which may suggest a possible mechanism for the modulation of EGF activity.

Amino Acid Sequence↗
PubMed2006

Multi-resolution anchor-point registration of biomolecular assemblies and their components.

An atomic scale interpretation facilitates the assignment of functional properties to 3D reconstructions of macromolecular assemblies in electron microscopy (EM). Such a high-resolution interpretation is typically achieved by docking the known atomic structures of components into the volumetric EM maps. Docking locations are often determined by maximizing the cross-correlation coefficient of the two objects in a slow, exhaustive search. If time is of essence, such as in related visualization and image processing fields, the matching of data is accelerated by incorporating feature points that form a compact description of 3D objects. The complexity reduction afforded by the feature point representation enables a near-instantaneous matching. We show that such reduced matching can also deliver robust and accurate results in the presence of noise or artifacts. We therefore propose a novel multi-resolution registration technique employing feature-based shape descriptions of the volumetric and structural data. The pattern-matching algorithm carries out a hierarchical alignment of the point sets generated by vector quantization. The search-space complexity is reduced by an integrated tree-pruning technique, which permits the detection of subunits in large macromolecular assemblies in real-time. The efficiency and accuracy of the novel algorithm are validated on a standard test system of homo-oligomeric assemblies.

Algorithms↗
PubMed2006

Local feature analysis: a statistical theory for reproducible essential dynamics of large macromolecules.

Multivariate statistical methods are widely used to extract functional collective motions from macromolecular molecular dynamics (MD) simulations. In principal component analysis (PCA), a covariance matrix of positional fluctuations is diagonalized to obtain orthogonal eigenvectors and corresponding eigenvalues. The first few eigenvectors usually correspond to collective modes that approximate the functional motions in the protein. However, PCA representations are globally coherent by definition and, for a large biomolecular system, do not converge on the time scales accessible to MD. Also, the forced orthogonalization of modes leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. Here, we describe for the first time the application of local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low dimensional, and like PCA provide a reduced basis set for collective motions, but they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows. Also, the intrinsic dynamics of local domains is more extensively sampled than that of globally coherent PCA modes.

Bacteriophage T4↗
PubMed2005

Fast rotational matching of single-particle images.

The presence of noise and absence of contrast in electron micrographs lead to a reduced resolution of the final 3D reconstruction, due to the inherent limitations of single-particle image alignment. The fast rotational matching (FRM) algorithm was introduced recently for an accurate alignment of 2D images under such challenging conditions. Here, we implemented this algorithm for the first time in a standard 3D reconstruction package used in electron microscopy. This allowed us to carry out exhaustive tests of the robustness and reliability in iterative orientation determination, classification, and 3D reconstruction on simulated and experimental image data. A classification test on GroEL chaperonin images demonstrates that FRM assigns up to 13% more images to their correct reference orientation, compared to the classical self-correlation function method. Moreover, at sub-nanometer resolution, GroEL and rice dwarf virus reconstructions exhibit a remarkable resolution gain of 10-20% that is attributed to the novel image alignment kernel.

Algorithms↗
PubMed2005

Control of protein functional dynamics by peptide linkers.

Control of structural flexibility is essential for the proper functioning of a large number of proteins and multiprotein complexes. At the residue level, such flexibility occurs due to local relaxation of peptide bond angles whose cumulative effect may result in large changes in the secondary, tertiary or quaternary structures of protein molecules. Such flexibility, and its absence, most often depends on the nature of interdomain linkages formed by oligopeptides. Both flexible and relatively rigid peptide linkers are found in many multidomain proteins. Linkers are thought to control favorable and unfavorable interactions between adjacent domains by means of variable softness furnished by their primary sequence. Large-scale structural heterogeneity of multidomain proteins and their complexes, facilitated by soft peptide linkers, is now seen as the norm rather than the exception. Biophysical discoveries as well as computational algorithms and databases have reshaped our understanding of the often spectacular biomolecular dynamics enabled by soft linkers. Absence of such motion, as in so-called molecular rulers, also has desirable functional effects in protein architecture. We review here the historic discovery and current understanding of the nature of domains and their linkers from a structural, computational, and biophysical point of view. A number of emerging applications, based on the current understanding of the structural properties of peptides, are presented in the context of domain fusion of synthetic multifunctional chimeric proteins.

Amino Acid Sequence↗
PubMed2004

Conformations of variably linked chimeric proteins evaluated by synchrotron X-ray small-angle scattering.

We constructed chimeric proteins that consist of two green fluorescent protein variants, EBFP and EGFP, connected by flexible linkers, (GGGGS)n (n = 3 approximately 4), and helical linkers, (EAAAK)n (n = 2 approximately 5). The conformations of the chimeric proteins with the various linkers were evaluated using small-angle X-ray scattering (SAXS). The SAXS experiments showed that introducing the short helical linkers (n = 2 approximately 3) causes multimerization, while the longer linkers (n = 4 approximately 5) solvate monomeric chimeric proteins. With the moderate-length linkers (n = 4), the observed radius of gyration (R(g)) and maximum dimension (D(max)) were 38.8 A and 120 A with the flexible linker, and 40.2 A and 130 A with the helical linker, respectively. The chimeric protein with the helical linker assumed a more elongated conformation as compared to that with the flexible linker. When the length of the helical linker increased (n = 5), R(g) and D(max) increased to 43.2 A and 140 A, respectively. These results suggest that the longer helix effectively separates the two domains of the chimeric protein. Considering the connectivity of the backbone peptide of the protein, the helical linker seems to connect the two domains diagonally. Surprisingly, the chimeric proteins with the flexible linker exhibited an elongated conformation, rather than the most compact side-by-side conformation expected from the fluorescence resonance energy transfer (FRET) analysis. Furthermore, the SAXS analyses suggest that destabilization of the short helical linker causes multimerization of the chimeric proteins. Information about the global conformation of the chimeric protein is thus be necessary for optimization of the linker design.

Fluorescence Resonance Energy Transfer↗
PubMed2003

Structure and function of the transcription elongation factor GreB bound to bacterial RNA polymerase.

Bacterial GreA and GreB promote transcription elongation by stimulating an endogenous, endonucleolytic transcript cleavage activity of the RNA polymerase. The structure of Escherichia coli core RNA polymerase bound to GreB was determined by cryo-electron microscopy and image processing of helical crystals to a nominal resolution of 15 A, allowing fitting of high-resolution RNA polymerase and GreB structures. In the resulting model, the GreB N-terminal coiled-coil domain extends 45 A through a channel directly to the RNA polymerase active site. The model leads to detailed insights into the mechanism of Gre factor activity that explains a wide range of experimental observations and points to a key role for conserved acidic residues at the tip of the Gre factor coiled coil in modifying the RNA polymerase active site to catalyze the cleavage reaction. Mutational studies confirm that these positions are critical for Gre factor function.

Bacterial Proteins↗
PubMed2003

Fast rotational matching of rigid bodies by fast Fourier transform acceleration of five degrees of freedom.

The 'fast rotational matching' method (an approach to find the three rotational degrees of freedom in matching problems using just one three-dimensional FFT) is extended to the full six-dimensional (rotation and translation) matching scenario between two three-dimensional objects. By recasting this problem into a formulation involving five angles and just one translational parameter, it was possible to accelerate, by means of fast Fourier transforms, five of the six degrees of freedom of the problem. This method was successfully applied to the docking of atomic structures of components into three-dimensional low-resolution density maps. Timing comparisons performed with our method and with 'fast translational matching' (the standard way to accelerate the translational parameters utilizing fast Fourier transforms) demonstrates that the performance gain can reach several orders of magnitude, especially for large map sizes. This gain can be particularly advantageous for spherical- and toroidal-shaped maps, since the scanning range of the translational parameter would be significantly constrained in these cases. The method can also be harnessed to the complementary surface (or 'exterior docking') problem and to pattern recognition in image processing.

Fourier Analysis↗
PubMed2003

Like-charge attraction between polyelectrolytes induced by counterion charge density waves.

Electrostatics in aqueous media is commonly understood in terms of screened Coulomb interactions, where like-charged objects, such as polyelectrolytes, always repel. These intuitive expectations are based on mean field theories, such as the Poisson-Boltzmann formalism, which are routinely used in colloid science and computational biology [Israelachvili, J. (1992) Intermolecular and Surface Forces (Academic, London), 2nd ed.]. Like-charge attractions, however, have been observed in a variety of systems [Gelbart, W. M., Bruinsma, R. F., Pincus, P. A. & Parsegian, V. A. (2000) Phys. Today 53, 38-44]. Intense theoretical scrutiny over the last 30 years suggests that counterions play a central role, but no consensus exists for the precise mechanism. We have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well defined biological polyelectrolyte) by using synchrotron x-ray diffraction and discovered an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actin's helical symmetry; rather, the counterions organize into "frozen" ripples parallel to the actin filaments and form 1D charge density waves. Moreover, this 1D counterion charge density wave couples to twist distortions of the oppositely charged actin filaments. This general cooperative molecular mechanism is analogous to the formation of polarons in ionic solids and mediates attractions by facilitating a "zipper-like" charge alignment between the counterions and the polyelectrolyte charge distribution. We believe these results can fundamentally impinge on our general understanding of electrostatics in aqueous media and are relevant to a wide range of colloidal and biomedical processes.

Actins↗
PubMed2003

Mega-Dalton biomolecular motion captured from electron microscopy reconstructions.

The vibrational analysis of elastic models suggests that the essential motions of large biomolecular assemblies can be captured efficiently at an intermediate scale without requiring knowledge of the atomic structure. While prior work has established a theoretical foundation for this analysis, we demonstrate here on experimental electron microscopy maps that vibrational modes indeed describe functionally relevant movements of macromolecular machines. The clamp closure in bacterial RNA polymerase, the ratcheting of 30S and 50S subunits of the ribosome, and the dynamic flexibility of chaperonin CCT are extracted directly from single electron microscopy structures at 15-27 A resolution. The striking agreement of the presented results with experimentally observed motions suggests that the motion of the large scale machinery in the cell is surprisingly independent of detailed atomic interactions and can be quite reasonably described as a motion of elastic bodies.

Chaperonin Containing TCP-1↗
PubMed2002

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory.

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.

Adenylate Kinase↗
PubMed2002

Fast rotational matching.

A computationally efficient method is presented - 'fast rotational matching' or FRM - that significantly accelerates the search of the three rotational degrees of freedom (DOF) in biomolecular matching problems. This method uses a suitable parametrization of the three-dimensional rotation group along with spherical harmonics, which allows efficient computation of the Fourier Transform of the rotational correlation function. Previous methods have used Fourier techniques only for two of the rotational DOFs, leaving the remaining angle to be determined by an exhaustive search. Here for the first time a formulation is presented that makes it possible to Fourier transform all three rotational DOFs, resulting in notable improvements in speed. Applications to the docking of atomic structures into electron-microscopy maps and the molecular-replacement problem in X-ray crystallography are considered.

Crystallography, X-Ray↗
PubMed2002

Regulation of yeast actin behavior by interaction of charged residues across the interdomain cleft.

His(73) participates in the regulation of the nucleotide binding cleft conformation in yeast actin. Earlier molecular dynamics studies suggested that Asp(184) interacts with His(73) thereby stabilizing a "closed-cleft" G-actin. However, beta-actin in the open-cleft state shows a closer interaction of His(73) with Asp(179) than with Asp(184). We have thus assessed the relative importance of Asp(184) and Asp(179) on yeast actin stability and function. Neutral substitutions at 184 or 179 alone had little adverse effect on the monomer and polymerization behavior of actin. Arg or His at 184 in H73E actin partially rescued the monomeric properties of H73E actin, as demonstrated by near-normal thermostability and wild-type (WT)-like protease digestion patterns. ATP exchange was still considerably faster than with WT-actin although slower than that of H73E alone. However, polymerization of H73E/D184R and H73E/D184H is worse than with H73E alone. Conversely, D179R rescued all monomeric properties of H73E to near WT values and largely restored polymerization rate and filament thermostability. These results and new simulations of G-actin in the "open" state underscore the importance of the His(73)-Asp(179) interaction and suggest that the open and not the closed state of yeast actin may be favored in the absence of the methyl group of His(73).

Actins↗
PubMed2002

Multi-resolution contour-based fitting of macromolecular structures.

A novel contour-based matching criterion is presented for the quantitative docking of high-resolution structures of components into low-resolution maps of macromolecular complexes. The proposed Laplacian filter is combined with a six-dimensional search using fast Fourier transforms to rapidly scan the rigid-body degrees of freedom of a probe molecule relative to a fixed target density map. A comparison of the docking performance with the standard cross-correlation criterion demonstrates that contour matching with the Laplacian filter significantly extends the viable resolution range of correlation-based fitting to resolutions as low as 30 A. The gain in docking precision at medium to low resolution (15-30 A) is critical for image reconstructions from electron microscopy (EM). The new algorithm enables for the first time the reliable docking of smaller molecular components into EM densities of large biomolecular assemblies at such low resolutions. As an example of the practical effectiveness of contour-based fitting, a new pseudo-atomic model of a microtubule was constructed from a 20 A resolution EM map and from atomic structures of alpha and beta tubulin subunits.

Algorithms↗
PubMed2002

Conformational flexibility of bacterial RNA polymerase.

The structure of Escherichia coli core RNA polymerase (RNAP) was determined by cryo-electron microscopy and image processing of helical crystals to a nominal resolution of 15 A. Because of the high sequence conservation between the core RNAP subunits, we were able to interpret the E. coli structure in relation to the high-resolution x-ray structure of Thermus aquaticus core RNAP. A very large conformational change of the T. aquaticus RNAP x-ray structure, corresponding to opening of the main DNA/RNA channel by nearly 25 A, was required to fit the E. coli map. This finding reveals, at least partially, the range of conformational flexibility of the RNAP, which is likely to have functional implications for the initiation of transcription, where the DNA template must be loaded into the channel.

Crystallization↗
PubMedDate not supplied

2D fast rotational matching for image processing of biophysical data.

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.

Algorithms↗