ADP_EM: fast exhaustive multi-resolution docking for high-throughput coverage

gEMfitter: a highly parallel FFT-based 3D density fitting tool with GPU texture memory acceleration

Fitting high resolution protein structures into low resolution cryo-electron microscopy (cryo-EM) density maps is an important technique for modeling the atomic structures of very large macromolecular assemblies. This article presents "gEMfitter", a highly parallel fast Fourier transform (FFT) EM density fitting program which can exploit the special hardware properties of modern graphics processor units (GPUs) to accelerate both the translational and rotational parts of the correlation search. In particular, by using the GPU's special texture memory hardware to rotate 3D voxel grids, the cost of rotating large 3D density maps is almost completely eliminated. Compared to performing 3D correlations on one core of a contemporary central processor unit (CPU), running gEMfitter on a modern GPU gives up to 26-fold speed-up. Furthermore, using our parallel processing framework, this speed-up increases linearly with the number of CPUs or GPUs used. Thus, it is now possible to use routinely more robust but more expensive 3D correlation techniques. When tested on low resolution experimental cryo-EM data for the GroEL-GroES complex, we demonstrate the satisfactory fitting results that may be achieved by using a locally normalised cross-correlation with a Laplacian pre-filter, while still being up to three orders of magnitude faster than the well-known COLORES program.

iMODFIT: efficient and robust flexible fitting based on vibrational analysis in internal coordinates

Here, we employed the collective motions extracted from Normal Mode Analysis (NMA) in internal coordinates (torsional space) for the flexible fitting of atomic-resolution structures into electron microscopy (EM) density maps. The proposed methodology was validated using a benchmark of simulated cases, highlighting its robustness over the full range of EM resolutions and even over coarse-grained representations. A systematic comparison with other methods further showcased the advantages of this proposed methodology, especially at medium to lower resolutions. Using this method, computational costs and potential overfitting problems are naturally reduced by constraining the search in low-frequency NMA space, where covalent geometry is implicitly maintained. This method also effectively captures the macromolecular changes of a representative set of experimental test cases. We believe that this novel approach will extend the currently available EM hybrid methods to the atomic-level interpretation of large conformational changes and their functional implications.

NONUNIFORM FOURIER TRANSFORMS FOR RIGID-BODY AND MULTI-DIMENSIONAL ROTATIONAL CORRELATIONS

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ³ that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transform to achieve a speedup either with respect to the sought translation or rotation. We present PFcorr, a new exhaustive solution, based on the non-equispaced SO(3) Fourier transform, to the rigid-body correlation problem; unlike previous solutions, ours achieves a combination of translational and rotational speedups without requiring equispaced grids. PFcorr can be straightforwardly applied to a variety of problems in protein structure prediction and refinement that involve correlations under rigid-body motions of the protein. Additionally, we show how it applies, along with an appropriate flexibility model, to analogs of the above problems in which the flexibility of the protein is relevant.

Computational methods for constructing protein structure models from 3D electron microscopy maps

Protein structure determination by cryo-electron microscopy (EM) has made significant progress in the past decades. Resolutions of EM maps have been improving as evidenced by recently reported structures that are solved at high resolutions close to 3Å. Computational methods play a key role in interpreting EM data. Among many computational procedures applied to an EM map to obtain protein structure information, in this article we focus on reviewing computational methods that model protein three-dimensional (3D) structures from a 3D EM density map that is constructed from two-dimensional (2D) maps. The computational methods we discuss range from de novo methods, which identify structural elements in an EM map, to structure fitting methods, where known high resolution structures are fit into a low-resolution EM map. A list of available computational tools is also provided.

ATTRACT-EM: a new method for the computational assembly of large molecular machines using cryo-EM maps

Many of the most important functions in the cell are carried out by proteins organized in large molecular machines. Cryo-electron microscopy (cryo-EM) is increasingly being used to obtain low resolution density maps of these large assemblies. A new method, ATTRACT-EM, for the computational assembly of molecular assemblies from their components has been developed. Based on concepts from the protein-protein docking field, it utilizes cryo-EM density maps to assemble molecular subunits at near atomic detail, starting from millions of initial subunit configurations. The search efficiency was further enhanced by recombining partial solutions, the inclusion of symmetry information, and refinement using a molecular force field. The approach was tested on the GroES-GroEL system, using an experimental cryo-EM map at 23.5 Å resolution, and on several smaller complexes. Inclusion of experimental information on the symmetry of the systems and the application of a new gradient vector matching algorithm allowed the efficient identification of docked assemblies in close agreement with experiment. Application to the GroES-GroEL complex resulted in a top ranked model with a deviation of 4.6 Å (and a 2.8 Å model within the top 10) from the GroES-GroEL crystal structure, a significant improvement over existing methods.

Macromolecular structure modeling from 3D EM using VolRover 2.0

We review tools for structure identification and model-based refinement from three-dimensional electron microscopy implemented in our in-house software package, VOLROVER 2.0. For viral density maps with icosahedral symmetry, we segment the capsid, polymeric, and monomeric subunits using techniques based on automatic symmetry detection and multidomain fast marching. For large biomolecules without symmetry information, we again use our multidomain fast-marching method with manual or fit-based multiseeding to segment meaningful substructures. In either case, we subject the resulting segmented subunit to secondary structure detection when the EM resolution is sufficiently high, and rigid-body structure fitting when the corresponding X-ray structure is available. Secondary structure elements are identified by three techniques: our earlier volume-based and boundary-based skeletonization methods as well as a new method, currently in development, based on solving the grassfire flow equation. For rigid-body fitting, we adapt our earlier fast Fourier-based correlation scheme F2Dock. Our reported segmentation, secondary structure elements identification, and rigid-body fitting techniques, implemented in VOLROVER 2.0 are applied to the PSB 2011 cryo-EM modeling challenge data, and our results are briefly compared to similar results submitted from other research groups. The comparisons show that our techniques are equally capable of segmenting relatively accurate subunits from a viral or protein assembly, and that high segmentation quality leads in turn to higher-quality results of secondary structure elements identification and correlation-based rigid-body fitting. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 709-731, 2012.

Comparison of Segger and other methods for segmentation and rigid-body docking of molecular components in cryo-EM density maps

Segmentation and docking are useful methods for the discovery of molecular components in electron cryo-microscopy (cryo-EM) density maps of macromolecular complexes. In this article, we describe the segmentation and docking methods implemented in Segger. For 11 targets posted in the 2010 cryo-EM challenge, we segmented the regions corresponding to individual molecular components using Segger. We then used the segmented regions to guide rigid-body docking of individual components. Docking results were evaluated by comparing the docked components with published structures, and by calculation of several scores, such as atom inclusion, density occupancy, and geometry clash. The accuracy of the component segmentation using Segger and other methods was assessed by comparing segmented regions with docked components.

Disease mutations in the ryanodine receptor central region: crystal structures of a phosphorylation hot spot domain

Ryanodine Receptors (RyRs) are huge Ca²⁺ release channels in the endoplasmic reticulum membrane and form targets for phosphorylation and disease mutations. We present crystal structures of a domain in three RyR isoforms, containing the Ser2843 (RyR1) and Ser2808/Ser2814 (RyR2) phosphorylation sites. The RyR1 domain is the target for 11 disease mutations. Several of these are clustered near the phosphorylation sites, suggesting that phosphorylation and disease mutations may affect the same interface. The L2867G mutation causes a drastic thermal destabilization and aggregation at room temperature. Crystal structures for other disease mutants show that they affect surface properties and intradomain salt bridges. In vitro phosphorylation experiments show that up to five residues in one long loop of RyR2 can be phosphorylated by PKA or CaMKII. Docking into cryo-electron microscopy maps suggests a putative location in the clamp region, implying that mutations and phosphorylation may affect the allosteric motions within this area.

High-throughput subtomogram alignment and classification by Fourier space constrained fast volumetric matching

Cryo-electron tomography allows the visualization of macromolecular complexes in their cellular environments in close-to-live conditions. The nominal resolution of subtomograms can be significantly increased when individual subtomograms of the same kind are aligned and averaged. A vital step for such a procedure are algorithms that speedup subtomogram alignment and improve its accuracy to allow reference-free subtomogram classifications. Such methods will facilitate automation of tomography analysis and overall high throughput in the data processing. Building on previous work, here we propose a fast rotational alignment method that uses the Fourier equivalent form of a popular constrained correlation measure that considers missing wedge corrections and density variances in the subtomograms. The fast rotational search is based on 3D volumetric matching, which improves the rotational alignment accuracy in particular for highly distorted subtomograms with low SNR and tilt angle ranges in comparison to fast rotational matching of projected 2D spherical images. We further integrate our fast rotational alignment method in a reference-free iterative subtomogram classification scheme, and propose a local feature enhancement strategy in the classification process. As a proof of principle, we can demonstrate that the automatic method can successfully classify a large number of experimental subtomograms without the need of a reference structure.

MultiFit: a web server for fitting multiple protein structures into their electron microscopy density map

Advances in electron microscopy (EM) allow for structure determination of large biological assemblies at increasingly higher resolutions. A key step in this process is fitting multiple component structures into an EM-derived density map of their assembly. Here, we describe a web server for this task. The server takes as input a set of protein structures in the PDB format and an EM density map in the MRC format. The output is an ensemble of models ranked by their quality of fit to the density map. The models can be viewed online or downloaded from the website. The service is available at; http://salilab.org/multifit/ and http://bioinfo3d.cs.tau.ac.il/.

Flexible tethering of primase and DNA Pol α in the eukaryotic primosome

The Pol α/primase complex or primosome is the primase/polymerase complex that initiates nucleic acid synthesis during eukaryotic replication. Within the primosome, the primase synthesizes short RNA primers that undergo limited extension by Pol α. The resulting RNA–DNA primers are utilized by Pol δ and Pol ε for processive elongation on the lagging and leading strands, respectively. Despite its importance, the mechanism of RNA–DNA primer synthesis remains poorly understood. Here, we describe a structural model of the yeast primosome based on electron microscopy and functional studies. The 3D architecture of the primosome reveals an asymmetric, dumbbell-shaped particle. The catalytic centers of primase and Pol α reside in separate lobes of high relative mobility. The flexible tethering of the primosome lobes increases the efficiency of primer transfer between primase and Pol α. The physical organization of the primosome suggests that a concerted mechanism of primer hand-off between primase and Pol α would involve coordinated movements of the primosome lobes. The first three-dimensional map of the eukaryotic primosome at 25 Å resolution provides an essential structural template for understanding initiation of eukaryotic replication.

Three-dimensional cryoEM reconstruction of native LDL particles to 16Å resolution at physiological body temperature

Background

Low-density lipoprotein (LDL) particles, the major carriers of cholesterol in the human circulation, have a key role in cholesterol physiology and in the development of atherosclerosis. The most prominent structural components in LDL are the core-forming cholesteryl esters (CE) and the particle-encircling single copy of a huge, non-exchangeable protein, the apolipoprotein B-100 (apoB-100). The shape of native LDL particles and the conformation of native apoB-100 on the particles remain incompletely characterized at the physiological human body temperature (37°C).

Methodology/Principal Findings

To study native LDL particles, we applied cryo-electron microscopy to calculate 3D reconstructions of LDL particles in their hydrated state. Images of the particles vitrified at 6°C and 37°C resulted in reconstructions at ∼16 Å resolution at both temperatures. 3D variance map analysis revealed rigid and flexible domains of lipids and apoB-100 at both temperatures. The reconstructions showed less variability at 6°C than at 37°C, which reflected increased order of the core CE molecules, rather than decreased mobility of the apoB-100. Compact molecular packing of the core and order in a lipid-binding domain of apoB-100 were observed at 6°C, but not at 37°C. At 37°C we were able to highlight features in the LDL particles that are not clearly separable in 3D maps at 6°C. Segmentation of apoB-100 density, fitting of lipovitellin X-ray structure, and antibody mapping, jointly revealed the approximate locations of the individual domains of apoB-100 on the surface of native LDL particles.

Conclusions/Significance

Our study provides molecular background for further understanding of the link between structure and function of native LDL particles at physiological body temperature.

Exploring the spatial and temporal organization of a cell's proteome

To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.

Improved protein surface comparison and application to low-resolution protein structure data

Background

Recent advancements of experimental techniques for determining protein tertiary structures raise significant challenges for protein bioinformatics. With the number of known structures of unknown function expanding at a rapid pace, an urgent task is to provide reliable clues to their biological function on a large scale. Conventional approaches for structure comparison are not suitable for a real-time database search due to their slow speed. Moreover, a new challenge has arisen from recent techniques such as electron microscopy (EM), which provide low-resolution structure data. Previously, we have introduced a method for protein surface shape representation using the 3D Zernike descriptors (3DZDs). The 3DZD enables fast structure database searches, taking advantage of its rotation invariance and compact representation. The search results of protein surface represented with the 3DZD has showngood agreement with the existing structure classifications, but some discrepancies were also observed.

Results

The three new surface representations of backbone atoms, originally devised all-atom-surface representation, and the combination of all-atom surface with the backbone representation are examined. All representations are encoded with the 3DZD. Also, we have investigated the applicability of the 3DZD for searching protein EM density maps of varying resolutions. The surface representations are evaluated on structure retrieval using two existing classifications, SCOP and the CE-based classification.

Conclusions

Overall, the 3DZDs representing backbone atoms show better retrieval performance than the original all-atom surface representation. The performance further improved when the two representations are combined. Moreover, we observed that the 3DZD is also powerful in comparing low-resolution structures obtained by electron microscopy.

Using Sculptor and Situs for simultaneous assembly of atomic components into low-resolution shapes

We describe an integrated software system called Sculptor that combines visualization capabilities with molecular modeling algorithms for the analysis of multi-scale data sets. Sculptor features extensive special purpose visualization techniques that are based on modern GPU programming and are capable of representing complex molecular assemblies in real-time. The integration of graphics and modeling offers several advantages. The user interface not only eases the usually steep learning curve of pure algorithmic techniques, but it also permits instant analysis and post-processing of results, as well as the integration of results from external software. Here, we implemented an interactive peak-selection strategy that enables the user to explore a preliminary score landscape generated by the colors tool of Situs. The interactive placement of components, one at a time, is advantageous for low-resolution or ambiguously shaped maps, which are sometimes difficult to interpret by the fully automatic peak selection of colors. For the subsequent refinement of the preliminary models resulting from both interactive and automatic peak selection, we have implemented a novel simultaneous multi-body docking in Sculptor and Situs that softly enforces shape complementarities between components using the normalization of the cross-correlation coefficient. The proposed techniques are freely available in Situs version 2.6 and Sculptor version 2.0.

A fast mathematical programming procedure for simultaneous fitting of assembly components into cryoEM density maps

MOTIVATION

Single-particle cryo electron microscopy (cryoEM) typically produces density maps of macromolecular assemblies at intermediate to low resolution (approximately 5-30 A). By fitting high-resolution structures of assembly components into these maps, pseudo-atomic models can be obtained. Optimizing the quality-of-fit of all components simultaneously is challenging due to the large search space that makes the exhaustive search over all possible component configurations computationally unfeasible.

RESULTS

We developed an efficient mathematical programming algorithm that simultaneously fits all component structures into an assembly density map. The fitting is formulated as a point set matching problem involving several point sets that represent component and assembly densities at a reduced complexity level. In contrast to other point matching algorithms, our algorithm is able to match multiple point sets simultaneously and not only based on their geometrical equivalence, but also based on the similarity of the density in the immediate point neighborhood. In addition, we present an efficient refinement method based on the Iterative Closest Point registration algorithm. The integer quadratic programming method generates an assembly configuration in a few seconds. This efficiency allows the generation of an ensemble of candidate solutions that can be assessed by an independent scoring function. We benchmarked the method using simulated density maps of 11 protein assemblies at 20 A, and an experimental cryoEM map at 23.5 A resolution. Our method was able to generate assembly structures with root-mean-square errors <6.5 A, which have been further reduced to <1.8 A by the local refinement procedure.

AVAILABILITY

The program is available upon request as a Matlab code package.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics Online.

Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions

A structural characterization of multi-component cellular assemblies is essential to explain the mechanisms governing biological function. Macromolecular architectures may be revealed by integrating information collected from various biophysical sources - for instance, by interpreting low-resolution electron cryomicroscopy reconstructions in relation to the crystal structures of the constituent fragments. A simultaneous registration of multiple components is beneficial when building atomic models as it introduces additional spatial constraints to facilitate the native placement inside the map. The high-dimensional nature of such a search problem prevents the exhaustive exploration of all possible solutions. Here we introduce a novel method based on genetic algorithms, for the efficient exploration of the multi-body registration search space. The classic scheme of a genetic algorithm was enhanced with new genetic operations, tabu search and parallel computing strategies and validated on a benchmark of synthetic and experimental cryo-EM datasets. Even at a low level of detail, for example 35-40 A, the technique successfully registered multiple component biomolecules, measuring accuracies within one order of magnitude of the nominal resolutions of the maps. The algorithm was implemented using the Sculptor molecular modeling framework, which also provides a user-friendly graphical interface and enables an instantaneous, visual exploration of intermediate solutions.

Quantitative analysis of cryo-EM density map segmentation by watershed and scale-space filtering, and fitting of structures by alignment to regions

Cryo-electron microscopy produces 3D density maps of molecular machines, which consist of various molecular components such as proteins and RNA. Segmentation of individual components in such maps is a challenging task, and is mostly accomplished interactively. We present an approach based on the immersive watershed method and grouping of the resulting regions using progressively smoothed maps. The method requires only three parameters: the segmentation threshold, a smoothing step size, and the number of smoothing steps. We first apply the method to maps generated from molecular structures and use a quantitative metric to measure the segmentation accuracy. The method does not attain perfect accuracy, however it produces single or small groups of regions that roughly match individual proteins or subunits. We also present two methods for fitting of structures into density maps, based on aligning the structures with single regions or small groups of regions. The first method aligns centers and principal axes, whereas the second aligns centers and then rotates the structure to find the best fit. We describe both interactive and automated ways of using these two methods. Finally, we show segmentation and fitting results for several experimentally-obtained density maps.

Electron microscopy of Xrcc4 and the DNA ligase IV-Xrcc4 DNA repair complex

The DNA ligase IV-Xrcc4 complex is responsible for the ligation of broken DNA ends in the non-homologous end-joining (NHEJ) pathway of DNA double strand break repair in mammals. Mutations in DNA ligase IV (Lig4) lead to immunodeficiency and radiosensitivity in humans. Only partial structural information for Lig4 and Xrcc4 is available, while the structure of the full-length proteins and their arrangement within the Lig4-Xrcc4 complex is unknown. The C-terminal domain of Xrcc4, whose structure has not been solved, contains phosphorylation sites for DNA-PKcs and is phylogenetically conserved, indicative of a regulatory role in NHEJ. Here, we have purified full length Xrcc4 and the Lig4-Xrcc4 complex, and analysed their structure by single-particle electron microscopy. The three-dimensional structure of Xrcc4 at a resolution of approximately 37A reveals that the C-terminus of Xrcc4 forms a dimeric globular domain connected to the N-terminus by a coiled-coil. The N- and C-terminal domains of Xrcc4 locate at opposite ends of an elongated molecule. The electron microscopy images of the Lig4-Xrcc4 complex were examined by two-dimensional image processing and a double-labelling strategy, identifying the site of the C-terminus of Xrcc4 and the catalytic core of Lig4 within the complex. The catalytic domains of Lig4 were found to be in the vicinity of the N-terminus of Xrcc4. We provide a first sight of the structural organization of the Lig4-Xrcc4 complex, which suggests that the BRCT domains could provide the link of the ligase to Xrcc4 while permitting some movements of the catalytic domains of Lig4. This arrangement may facilitate the ligation of diverse configurations of damaged DNA.

FRODOCK: a new approach for fast rotational protein-protein docking

MOTIVATION

Prediction of protein-protein complexes from the coordinates of their unbound components usually starts by generating many potential predictions from a rigid-body 6D search followed by a second stage that aims to refine such predictions. Here, we present and evaluate a new method to effectively address the complexity and sampling requirements of the initial exhaustive search. In this approach we combine the projection of the interaction terms into 3D grid-based potentials with the efficiency of spherical harmonics approximations to accelerate the search. The binding energy upon complex formation is approximated as a correlation function composed of van der Waals, electrostatics and desolvation potential terms. The interaction-energy minima are identified by a novel, fast and exhaustive rotational docking search combined with a simple translational scanning. Results obtained on standard protein-protein benchmarks demonstrate its general applicability and robustness. The accuracy is comparable to that of existing state-of-the-art initial exhaustive rigid-body docking tools, but achieving superior efficiency. Moreover, a parallel version of the method performs the docking search in just a few minutes, opening new application opportunities in the current 'omics' world.

AVAILABILITY

http://sbg.cib.csic.es/Software/FRODOCK/

Plasmid replication initiator RepB forms a hexamer reminiscent of ring helicases and has mobile nuclease domains

RepB initiates plasmid rolling-circle replication by binding to a triple 11-bp direct repeat (bind locus) and cleaving the DNA at a specific distant site located in a hairpin loop within the nic locus of the origin. The structure of native full-length RepB reveals a hexameric ring molecule, where each protomer has two domains. The origin-binding and catalytic domains show a three-layer alpha-beta-alpha sandwich fold. The active site is positioned at one of the faces of the beta-sheet and coordinates a Mn2+ ion at short distance from the essential nucleophilic Y99. The oligomerization domains (ODs), each consisting of four alpha-helices, together define a compact ring with a central channel, a feature found in ring helicases. The toroidal arrangement of RepB suggests that, similar to ring helicases, it encircles one of the DNA strands during replication to confer processivity to the replisome complex. The catalytic domains appear to be highly mobile with respect to ODs. This mobility may account for the adaptation of the protein to two distinct DNA recognition sites.

3D architecture of DNA Pol alpha reveals the functional core of multi-subunit replicative polymerases

Eukaryotic DNA replication requires the coordinated activity of the multi-subunit DNA polymerases: Pol alpha, Pol delta and Pol epsilon. The conserved catalytic and regulatory B subunits associate in a constitutive heterodimer that represents the functional core of all three replicative polymerases. Here, we combine X-ray crystallography and electron microscopy (EM) to describe subunit interaction and 3D architecture of heterodimeric yeast Pol alpha. The crystal structure of the C-terminal domain (CTD) of the catalytic subunit bound to the B subunit illustrates a conserved mechanism of accessory factor recruitment by replicative polymerases. The EM reconstructions of Pol alpha reveal a bilobal shape with separate catalytic and regulatory modules. Docking of the B-CTD complex in the EM reconstruction shows that the B subunit is tethered to the polymerase domain through a structured but flexible linker. Our combined findings provide a structural template for the common functional architecture of the three major replicative DNA polymerases.

3D structure of the C3bB complex provides insights into the activation and regulation of the complement alternative pathway convertase

Generation of the alternative pathway C3-convertase, the central amplification enzyme of the complement cascade, initiates by the binding of factor B (fB) to C3b to form the proconvertase, C3bB. C3bB is subsequently cleaved by factor D (fD) at a single site in fB, producing Ba and Bb fragments. Ba dissociates from the complex, while Bb remains bound to C3b, forming the active alternative pathway convertase, C3bBb. Using single-particle electron microscopy we have determined the 3-dimensional structures of the C3bB and the C3bBb complexes at approximately 27A resolution. The C3bB structure shows that fB undergoes a dramatic conformational change upon binding to C3b. However, the C3b-bound fB structure was easily interpreted after independently fitting the atomic structures of the isolated Bb and Ba fragments. Interestingly, the divalent cation-binding site in the von Willebrand type A domain in Bb faces the C345C domain of C3b, whereas the serine-protease domain of Bb points outwards. The structure also shows that the Ba fragment interacts with C3b separately from Bb at the level of the alpha'NT and CUB domains. Within this conformation, the long and flexible linker between Bb and Ba is likely exposed and accessible for cleavage by fD to form the active convertase, C3bBb. The architecture of the C3bB and C3bBb complexes reveals that C3b could promote cleavage and activation of fB by actively displacing the Ba domain from the von Willebrand type A domain in free fB. These structures provide a structural basis to understand fundamental aspects of the activation and regulation of the alternative pathway C3-convertase.

Architecture of the pontin/reptin complex, essential in the assembly of several macromolecular complexes

Pontin and reptin belong to the AAA+ family, and they are essential for the structural integrity and catalytic activity of several chromatin remodeling complexes. They are also indispensable for the assembly of several ribonucleoprotein complexes, including telomerase. Here, we propose a structural model of the yeast pontin/reptin complex based on a cryo-electron microscopy reconstruction at 13 A. Pontin/reptin hetero-dodecamers were purified from in vivo assembled complexes forming a double ring. Two rings interact through flexible domains projecting from each hexamer, constituting an atypical asymmetric form of oligomerization. These flexible domains and the AAA+ cores reveal significant conformational changes when compared with the crystal structure of human pontin that generate enlarged channels. This structure of endogenously assembled pontin/reptin complexes is different than previously described structures, suggesting that pontin and reptin could acquire distinct structural states to regulate their broad functions as molecular motors and scaffolds for nucleic acids and proteins.

Multiple subunit fitting into a low-resolution density map of a macromolecular complex using a gaussian mixture model

Recently, electron microscopy measurement of single particles has enabled us to reconstruct a low-resolution 3D density map of large biomolecular complexes. If structures of the complex subunits can be solved by x-ray crystallography at atomic resolution, fitting these models into the 3D density map can generate an atomic resolution model of the entire large complex. The fitting of multiple subunits, however, generally requires large computational costs; therefore, development of an efficient algorithm is required. We developed a fast fitting program, “gmfit”, which employs a Gaussian mixture model (GMM) to represent approximated shapes of the 3D density map and the atomic models. A GMM is a distribution function composed by adding together several 3D Gaussian density functions. Because our model analytically provides an integral of a product of two distribution functions, it enables us to quickly calculate the fitness of the density map and the atomic models. Using the integral, two types of potential energy function are introduced: the attraction potential energy between a 3D density map and each subunit, and the repulsion potential energy between subunits. The restraint energy for symmetry is also employed to build symmetrical origomeric complexes. To find the optimal configuration of subunits, we randomly generated initial configurations of subunit models, and performed a steepest-descent method using forces and torques of the three potential energies. Comparison between an original density map and its GMM showed that the required number of Gaussian distribution functions for a given accuracy depended on both resolution and molecular size. We then performed test fitting calculations for simulated low-resolution density maps of atomic models of homodimer, trimer, and hexamer, using different search parameters. The results indicated that our method was able to rebuild atomic models of a complex even for maps of 30 Å resolution if sufficient numbers (eight or more) of Gaussian distribution functions were employed for each subunit, and the symmetric restraints were assigned for complexes with more than three subunits. As a more realistic test, we tried to build an atomic model of the GroEL/ES complex by fitting 21-subunit atomic models into the 3D density map obtained by cryoelectron microscopy using the C7 symmetric restraints. A model with low root mean-square deviations (14.7 Å) was obtained as the lowest-energy model, showing that our fitting method was reasonably accurate. Inclusion of other restraints from biological and biochemical experiments could further enhance the accuracy.

Structure of Epac2 in complex with a cyclic AMP analogue and RAP1B

Epac proteins are activated by binding of the second messenger cAMP and then act as guanine nucleotide exchange factors for Rap proteins. The Epac proteins are involved in the regulation of cell adhesion and insulin secretion. Here we have determined the structure of Epac2 in complex with a cAMP analogue (Sp-cAMPS) and RAP1B by X-ray crystallography and single particle electron microscopy. The structure represents the cAMP activated state of the Epac2 protein with the RAP1B protein trapped in the course of the exchange reaction. Comparison with the inactive conformation reveals that cAMP binding causes conformational changes that allow the cyclic nucleotide binding domain to swing from a position blocking the Rap binding site towards a docking site at the Ras exchange motif domain.

Accelerating and focusing protein-protein docking correlations using multi-dimensional rotational FFT generating functions

MOTIVATION

Predicting how proteins interact at the molecular level is a computationally intensive task. Many protein docking algorithms begin by using fast Fourier transform (FFT) correlation techniques to find putative rigid body docking orientations. Most such approaches use 3D Cartesian grids and are therefore limited to computing three dimensional (3D) translational correlations. However, translational FFTs can speed up the calculation in only three of the six rigid body degrees of freedom, and they cannot easily incorporate prior knowledge about a complex to focus and hence further accelerate the calculation. Furthemore, several groups have developed multi-term interaction potentials and others use multi-copy approaches to simulate protein flexibility, which both add to the computational cost of FFT-based docking algorithms. Hence there is a need to develop more powerful and more versatile FFT docking techniques.

RESULTS

This article presents a closed-form 6D spherical polar Fourier correlation expression from which arbitrary multi-dimensional multi-property multi-resolution FFT correlations may be generated. The approach is demonstrated by calculating 1D, 3D and 5D rotational correlations of 3D shape and electrostatic expansions up to polynomial order L=30 on a 2 GB personal computer. As expected, 3D correlations are found to be considerably faster than 1D correlations but, surprisingly, 5D correlations are often slower than 3D correlations. Nonetheless, we show that 5D correlations will be advantageous when calculating multi-term knowledge-based interaction potentials. When docking the 84 complexes of the Protein Docking Benchmark, blind 3D shape plus electrostatic correlations take around 30 minutes on a contemporary personal computer and find acceptable solutions within the top 20 in 16 cases. Applying a simple angular constraint to focus the calculation around the receptor binding site produces acceptable solutions within the top 20 in 28 cases. Further constraining the search to the ligand binding site gives up to 48 solutions within the top 20, with calculation times of just a few minutes per complex. Hence the approach described provides a practical and fast tool for rigid body protein-protein docking, especially when prior knowledge about one or both binding sites is available.

Damped-dynamics flexible fitting

In fitting atomic structures into EM maps, it often happens that the map corresponds to a different conformation of the structure. We have developed a new methodology to handle these situations that preserves the covalent geometry of the structure and allows the modeling of large deformations. The first goal is achieved by working in generalized coordinates (positional and internal coordinates), and the second by avoiding harmonic potentials. Instead, we use dampers (shock absorbers) between every pair of atoms, combined with a force field that attracts the atomic structure toward incompletely occupied regions of the EM map. The trajectory obtained by integrating the resulting equations of motion converges to a conformation that, in our validation cases, was very close to the target atomic structure. Compared to current methods, our approach is more efficient and robust against wrong solutions and to overfitting, and does not require user intervention or subjective decisions. Applications to the computation of transition pathways between known conformers, homology and loop modeling, as well as protein docking, are also discussed.

Integrating diverse data for structure determination of macromolecular assemblies

To understand the cell, we need to determine the macromolecular assembly structures, which may consist of tens to hundreds of components. First, we review the varied experimental data that characterize the assemblies at several levels of resolution. We then describe computational methods for generating the structures using these data. To maximize completeness, resolution, accuracy, precision, and efficiency of the structure determination, a computational approach is required that uses spatial information from a variety of experimental methods. We propose such an approach, defined by its three main components: a hierarchical representation of the assembly, a scoring function consisting of spatial restraints derived from experimental data, and an optimization method that generates structures consistent with the data. This approach is illustrated by determining the configuration of the 456 proteins in the nuclear pore complex (NPC) from baker's yeast. With these tools, we are poised to integrate structural information gathered at multiple levels of the biological hierarchy--from atoms to cells--into a common framework.

3D structure of Syk kinase determined by single-particle electron microscopy

The cytoplasmic Syk kinase plays key roles in immune responses and comprises two N-terminal regulatory Src homology 2 (SH2) domains followed by a catalytic region. Atomic structures of these domains have only been solved in isolation. To gain insights into the three-dimensional structure of full-length Syk, we have used single-particle electron microscopy. Syk acquires a closed conformation resembling the inhibited structure of Zap-70, another member of the Syk family. Such configuration suggests an inhibition of the N-terminal domains on its catalytic activity. The phosphotyrosine binding pockets of both SH2 domains are not occluded and they could interact with other phosphoproteins.

Structure of TOR and its complex with KOG1

The target of rapamycin (TOR) is a large (281 kDa) conserved Ser/Thr protein kinase that functions as a central controller of cell growth. TOR assembles into two distinct multiprotein complexes: TORC1 and TORC2. A defining feature of TORC1 is the interaction of TOR with KOG1 (Raptor in mammals) and its sensitivity to a rapamycin-FKBP12 complex. Here, we have reconstructed in three dimensions the 25 A resolution structures of endogenous budding yeast TOR1 and a TOR-KOG1 complex, using electron microscopy. TOR features distinctive N-terminal HEAT repeats that form a curved tubular-shaped domain that associates with the C-terminal WD40 repeat domain of KOG1. The N terminus of KOG1 is in proximity to the TOR kinase domain, likely functioning to bring substrates into the vicinity of the catalytic region. A model is proposed for the molecular architecture of the TOR-KOG1 complex explaining its sensitivity to rapamycin.

Three-dimensional model for the isolated recombinant influenza virus polymerase heterotrimer

The genome of influenza A virus is organized into eight ribonucleoprotein complexes (RNPs), each containing one RNA polymerase complex. This RNA polymerase has also been found non-associated to RNPs and is possibly involved in distinct functions in the infection cycle. We have expressed the virus RNA polymerase complex by co-tranfection of the PB1, PB2 and PA genes in mammalian cells and the heterotrimer was purified by the TAP tag procedure. Its 3D structure was determined by electron microscopy and single-particle image processing. The model obtained resembles the structure previously reported for the polymerase complex associated to viral RNPs but appears to be in a more open conformation. Detailed model comparison indicated that specific areas of the complex show important conformational changes as compared to the structure for the RNP-associated polymerase, particularly in regions known to interact with the adjacent NP monomers in the RNP. Also, the PB2 subunit seems to undergo a substantial displacement as a result of the association of the polymerase to RNPs. The structural model presented suggests that a core conformation of the polymerase in solution exists but the interaction with other partners, such as proteins or RNA, will trigger distinct conformational changes to activate new functional properties.