Modeling tricks and fitting techniques for multiresolution structures

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.

Building and refining protein models within cryo-electron microscopy density maps based on homology modeling and multiscale structure refinement

Automatic modeling methods using cryoelectron microscopy (cryoEM) density maps as constraints are promising approaches to building atomic models of individual proteins or protein domains. However, their application to large macromolecular assemblies has not been possible largely due to computational limitations inherent to such unsupervised methods. Here we describe a new method, EM-IMO (electron microscopy-iterative modular optimization), for building, modifying and refining local structures of protein models using cryoEM maps as a constraint. As a supervised refinement method, EM-IMO allows users to specify parameters derived from inspections so as to guide, and as a consequence, significantly speed up the refinement. An EM-IMO-based refinement protocol is first benchmarked on a data set of 50 homology models using simulated density maps. A multiscale refinement strategy that combines EM-IMO-based and molecular dynamics-based refinement is then applied to build backbone models for the seven conformers of the five capsid proteins in our near-atomic-resolution cryoEM map of the grass carp reovirus virion, a member of the Aquareovirus genus of the Reoviridae family. The refined models allow us to reconstruct a backbone model of the entire grass carp reovirus capsid and provide valuable functional insights that are described in the accompanying publication [Cheng, L., Zhu, J., Hui, W. H., Zhang, X., Honig, B., Fang, Q. & Zhou, Z. H. (2010). Backbone model of an aquareovirus virion by cryo-electron microscopy and bioinformatics. J. Mol. Biol. (this issue). doi:10.1016/j.jmb.2009.12.027.]. Our study demonstrates that the integrated use of homology modeling and a multiscale refinement protocol that combines supervised and automated structure refinement offers a practical strategy for building atomic models based on medium- to high-resolution cryoEM density maps.

Using Situs for the integration of multi-resolution structures

Situs is a modular and widely used software package for the integration of biophysical data across the spatial resolution scales. It has been developed over the last decade with a focus on bridging the resolution gap between atomic structures, coarse-grained models, and volumetric data from low-resolution biophysical origins, such as electron microscopy, tomography, or small-angle scattering. Structural models can be created and refined with various flexible and rigid body docking strategies. The software consists of multiple, stand-alone programs for the format conversion, analysis, visualization, manipulation, and assembly of 3D data sets. The programs have been ported to numerous platforms in both serial and shared memory parallel architectures and can be combined in various ways for specific modeling applications. The modular design facilitates the updating of individual programs and the development of novel application workflows. This review provides an overview of the Situs package as it exists today with an emphasis on functionality and workflows supported by version 2.5.

From electron microscopy maps to atomic structures using normal mode-based fitting

Electron microscopy (EM) has made possible to solve the structure of many proteins. However, the resolution of some of the EM maps is too low for interpretation at the atomic level, which is particularly important to describe function. We describe methods that combine low-resolution EM data with atomic structures for different conformations of the same protein in order to produce atomic models compatible with the EM map.We illustrate these methods with EM data from decavanadate-induced tubular crystals of a pseudo-phosphorylated intermediate of Ca-ATPase and the various atomic structures of other intermediates available in the Protein Data Bank (PDB). Determination of atomic structure permits not only to analyse protein-protein interactions in the crystals, but also to localize residues in the proximity of the crystallizing agent both within Ca-ATPase and between Ca-ATPase molecules.

Bend-twist-stretch model for coarse elastic network simulation of biomolecular motion

The empirical harmonic potential function of elastic network models (ENMs) is augmented by three- and four-body interactions as well as by a parameter-free connection rule. In the new bend-twist-stretch (BTS) model the complexity of the parametrization is shifted from the spatial level of detail to the potential function, enabling an arbitrary coarse graining of the network. Compared to distance cutoff-based Hookean springs, the approach yields a more stable parametrization of coarse-grained ENMs for biomolecular dynamics. Traditional ENMs give rise to unbounded zero-frequency vibrations when (pseudo)atoms are connected to fewer than three neighbors. A large cutoff is therefore chosen in an ENM (about twice the average nearest-neighbor distance), resulting in many false-positive connections that reduce the spatial detail that can be resolved. More importantly, the required three-neighbor connectedness also limits the coarse graining, i.e., the network must be dense, even in the case of low-resolution structures that exhibit few spatial features. The new BTS model achieves such coarse graining by extending the ENM potential to include three-and four-atom interactions (bending and twisting, respectively) in addition to the traditional two-atom stretching. Thus, the BTS model enables reliable modeling of any three-dimensional graph irrespective of the atom connectedness. The additional potential terms were parametrized using continuum elastic theory of elastic rods, and the distance cutoff was replaced by a competitive Hebb connection rule, setting all free parameters in the model. We validate the approach on a carbon-alpha representation of adenylate kinase and illustrate its use with electron microscopy maps of E. coli RNA polymerase, E. coli ribosome, and eukaryotic chaperonin containing T-complex polypeptide 1, which were difficult to model with traditional ENMs. For adenylate kinase, we find excellent reproduction (>90% overlap) of the ENM modes and B factors when BTS is applied to the carbon-alpha representation as well as to coarser descriptions. For the volumetric maps, coarse BTS yields similar motions (70%-90% overlap) to those obtained from significantly denser representations with ENM. Our Python-based algorithms of ENM and BTS implementations are freely available.

Molecular dynamics flexible fitting: a practical guide to combine cryo-electron microscopy and X-ray crystallography

Hybrid computational methods for combining structural data from different sources and resolutions are becoming an essential part of structural biology, especially as the field moves toward the study of large macromolecular assemblies. We have developed the molecular dynamics flexible fitting (MDFF) method for combining high-resolution atomic structures with cryo-electron microscopy (cryo-EM) maps, that results in atomic models representing the conformational state captured by cryo-EM. The method has been applied successfully to the ribosome, a ribonucleoprotein complex responsible for protein synthesis. MDFF involves a molecular dynamics simulation in which a guiding potential, based on the cryo-EM map, is added to the standard force field. Forces proportional to the gradient of the density map guide an atomic structure, available from X-ray crystallography, into high-density regions of a cryo-EM map. In this paper we describe the necessary steps to set up, run, and analyze MDFF simulations and the software packages that implement the corresponding functionalities.

FitEM2EM--tools for low resolution study of macromolecular assembly and dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top.

Three-dimensional reconstruction of tarantula myosin filaments suggests how phosphorylation may regulate myosin activity

Muscle contraction involves the interaction of the myosin heads of the thick filaments with actin subunits of the thin filaments. Relaxation occurs when this interaction is blocked by molecular switches on these filaments. In many muscles, myosin-linked regulation involves phosphorylation of the myosin regulatory light chains (RLCs). Electron microscopy of vertebrate smooth muscle myosin molecules (regulated by phosphorylation) has provided insight into the relaxed structure, revealing that myosin is switched off by intramolecular interactions between its two heads, the free head and the blocked head. Three-dimensional reconstruction of frozen-hydrated specimens revealed that this asymmetric head interaction is also present in native thick filaments of tarantula striated muscle. Our goal in this study was to elucidate the structural features of the tarantula filament involved in phosphorylation-based regulation. A new reconstruction revealed intra- and intermolecular myosin interactions in addition to those seen previously. To help interpret the interactions, we sequenced the tarantula RLC and fitted an atomic model of the myosin head that included the predicted RLC atomic structure and an S2 (subfragment 2) crystal structure to the reconstruction. The fitting suggests one intramolecular interaction, between the cardiomyopathy loop of the free head and its own S2, and two intermolecular interactions, between the cardiac loop of the free head and the essential light chain of the blocked head and between the Leu305-Gln327 interaction loop of the free head and the N-terminal fragment of the RLC of the blocked head. These interactions, added to those previously described, would help switch off the thick filament. Molecular dynamics simulations suggest how phosphorylation could increase the helical content of the RLC N-terminus, weakening these interactions, thus releasing both heads and activating the thick filament.

Computational approaches for automatic structural analysis of large biomolecular complexes

We present computational solutions to two problems of macromolecular structure interpretation from reconstructed three-dimensional electron microscopy (3D-EM) maps of large bio-molecular complexes at intermediate resolution (5A-15 A). The two problems addressed are: 1) 3D structural alignment (matching) between identified and segmented 3D maps of structure units (e.g. trimeric configuration of proteins), and 2) the secondary structure identification of a segmented protein 3D map (i.e.locations of alpha-helices, beta-sheets). For problem 1, we present an efficient algorithm to correlate spatially (and structurally) two 3D maps of structure units. Besides providing a similarity score between structure units, the algorithm yields an effective technique for resolution refinement of repeated structure units, by 3D alignment and averaging. For problem 2, we present an efficient algorithm to compute eigenvalues and link eigenvectors of a Gaussian convoluted structure tensor derived from the protein 3D Map, thereby identifying and locating secondary structural motifs of proteins. The efficiency and performance of our approach is demonstrated on several experimentally reconstructed 3D maps of virus capsid shells from single-particle cryo-electron microscopy (cryo-EM), as well as computationally simulated protein structure density 3D maps generated from protein model entries in the Protein Data Bank.

Full-length Escherichia coli SecA dimerizes in a closed conformation in solution as determined by cryo-electron microscopy

SecA is an obligatory component of the Escherichia coli general secretion pathway. However, the oligomeric structure of SecA and SecA conformational changes during translocation processes are still unclear. Here we obtained the three-dimensional structure of E. coli wild-type full-length SecA in solution by single particle cryo-electron microscopy and determined its oligomeric organization. In this structure, SecA occurs as a dimer in which the two protomers are arranged in an antiparallel mode, with a novel electrostatic interface, and both protomers are in closed conformation. The system developed here may provide a promising technique for studying dynamic structural changes in SecA.

Biomolecular pleiomorphism probed by spatial interpolation of coarse models

In low resolution structures of biological assemblies one can often observe conformational deviations that require a flexible rearrangement of structural domains fitted at the atomic level. We are evaluating interpolation methods for the flexible alignment of atomic models based on coarse models. Spatial interpolation is well established in image-processing and visualization to describe the overall deformation or warping of an object or an image. Combined with a coarse representation of the biological system by feature vectors, such methods can provide a flexible approximation of the molecular structure. We have compared three well-known interpolation techniques and evaluated the results by comparing them with constrained molecular dynamics. One method, inverse distance weighting interpolation, consistently produced models that were nearly indistinguishable on the alpha carbon level from the molecular dynamics results. The method is simple to apply and enables flexing of structures by non-expert modelers. This is useful for the basic interpretation of volumetric data in biological applications such as electron microscopy. The method can be used as a general interpretation tool for sparsely sampled motions derived from coarse models.

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.

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.

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.

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution

Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.

A structural model reveals energy transduction in dynein

Intracellular active transport is driven by ATP-hydrolyzing motor proteins that move along cytoskeletal filaments. In particular, the microtubule-associated dynein motor is involved in the transport of organelles and vesicles, the maintenance of the Golgi, and mitosis. However, unlike kinesin and myosin, the mechanism by which dynein converts chemical energy into mechanical force remains largely a mystery, due primarily to the lack of a high-resolution molecular structure. Using homology modeling and normal mode analysis, we propose a complete atomic structure and a mechanism for force generation by the motor protein dynein. In agreement with very recent electron microscopy (EM) reconstructions showing dynein as a ring-shaped heptamer, our model consists of six ATPases of the AAA (ATPases associated with various cellular activities) superfamily and a C-terminal domain, which is experimentally known to control motor function. Our model shows a coiled coil spanning the diameter of the motor that accounts for previously unidentified structures in EM studies and provides a potential mechanism for long-range communication between the AAA domains. Furthermore, normal mode analysis reveals that the subunits of the motor that contain the nucleotide binding sites exhibit minimal movement, whereas the rest of the motor is very mobile. Our analysis suggests the likely domain rearrangements of the motor unit that generate its power stroke. This study provides insights into the structure and function of dynein that can guide further experimental investigations into energy transduction in dynein.

Nanostructures of APOBEC3G support a hierarchical assembly model of high molecular mass ribonucleoprotein particles from dimeric subunits

Human APOBEC3G (hA3G) is a cytidine deaminase that restricts human immunodeficiency virus (HIV)-1 infection in a vif (the virion infectivity factor from HIV)-dependent manner. hA3G from HIV-permissive activated CD4+ T-cells exists as an inactive, high molecular mass (HMM) complex that can be transformed in vitro into an active, low molecular mass (LMM) variant comparable with that of HIV-non-permissive CD4+ T-cells. Here we present low resolution structures of hA3G in HMM and LMM forms determined by small angle x-ray scattering and advanced shape reconstruction methods. The results show that LMM particles have an extended shape, dissimilar to known cytidine deaminases, featuring novel tail-to-tail dimerization. Shape analysis of LMM and HMM structures revealed how symmetric association of dimers could lead to minimal HMM variants. These observations imply that the disruption of cellular HMM particles may require regulation of protein-RNA, as well as protein-protein interactions, which has implications for therapeutic development.

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.

A new level of architectural complexity in the human pyruvate dehydrogenase complex

Mammalian pyruvate dehydrogenase multienzyme complex (PDC) is a key metabolic assembly comprising a 60-meric pentagonal dodecahedral E2 (dihydrolipoamide acetyltransferase) core attached to which are 30 pyruvate decarboxylase E1 heterotetramers and 6 dihydrolipoamide dehydrogenase E3 homodimers at maximal occupancy. Stable E3 integration is mediated by an accessory E3-binding protein (E3BP) located on each of the 12 E2 icosahedral faces. Here, we present evidence for a novel subunit organization in which E3 and E3BP form subcomplexes with a 1:2 stoichiometry implying the existence of a network of E3 "cross-bridges" linking pairs of E3BPs across the surface of the E2 core assembly. We have also determined a low resolution structure for a truncated E3BP/E3 subcomplex using small angle x-ray scattering showing one of the E3BP lipoyl domains docked into the E3 active site. This new level of architectural complexity in mammalian PDC contrasts with the recently published crystal structure of human E3 complexed with its cognate subunit binding domain and provides important new insights into subunit organization, its catalytic mechanism and regulation by the intrinsic PDC kinase.

Combining electron microscopy and comparative protein structure modeling

Recently, advances have been made in methods and applications that integrate electron microscopy density maps and comparative modeling to produce atomic structures of macromolecular assemblies. Electron microscopy can benefit from comparative modeling through the fitting of comparative models into electron microscopy density maps. Also, comparative modeling can benefit from electron microscopy through the use of intermediate-resolution density maps in fold recognition, template selection and sequence-structure alignment.

Introduction to 3D reconstruction of macromolecules using single particle electron microscopy

Single-particle electron microscopy has now reached maturity, becoming a commonly used method in the examination of macromolecular structure. Using a small amount of purified protein, isolated molecules are observed under the electron microscope and the data collected can be averaged into a 3D reconstruction. Single-particle electron microscopy is an appropriate tool for the analysis of proteins that can only be obtained in modest quantities, like many of the large complexes currently of interest in biomedicine. Whilst the use of electron microscopy expands, new methods are being developed and improved to deal with further challenges, such as reaching higher resolutions and the combination of information at different levels of structural detail. More importantly, present methodology is still not robust enough when studying certain tricky proteins like those displaying extensive conformational flexibility and a great deal of user expertise is required, posing a threat to the consistency of the final structure. This mini review describes a brief outline of the methods currently used in the 3D analysis of macromolecules using single-particle electron microscopy, intended for those first approaching this field. A summary of methods, techniques, software, and some recent work is presented. The spectacular improvements to the technique in recent years, its advantages and limitations compared to other structural methods, and its future developments are discussed.

Combining X-ray crystallography and electron microscopy

The combination of cryo-electron microscopy to study large biological assemblies at low resolution with crystallography to determine near atomic structures of assembly fragments is quickly expanding the horizon of structural biology. This technique can be used to advantage in the study of large structures that cannot be crystallized, to follow dynamic processes, and to “purify” samples by visual selection of particles. Factors affecting the quality of cryo-electron microscopy maps and limits of accuracy in fitting known structural fragments are discussed.

Fitting of high-resolution structures into electron microscopy reconstruction images

Dynamic macromolecular assemblies, such as ribosomes, viruses, and muscle protein complexes, are often more amenable to visualization by electron microscopy than by high-resolution X-ray crystallography or NMR. When high-resolution structures of component structures are available, it is possible to build an atomic model that gives information about the molecular interactions at greater detail than the experimental resolution, due to constraints of modeling placed upon the interpretation. There are now several competing computational methods to search systematically for orientations and positions of components that match the experimental image density, and continuing developments will be reviewed. Attention is now also moving toward the related task of optimization, with flexible and/or multifragment models and sometimes with stereochemically restrained refinement methods. This paper will review the various approaches and describe advances in the authors' methods and applications of real-space refinement.

Conformational changes of p97 during nucleotide hydrolysis determined by small-angle X-Ray scattering

Valosin-containing protein (VCP)/p97 is an AAA family ATPase that has been implicated in the removal of misfolded proteins from the endoplasmic reticulum and in membrane fusion. p97 forms a homohexamer whose protomers consist of an N-terminal (N) domain responsible for binding to effector proteins, followed by two AAA ATPase domains, D1 and D2. Small-angle X-ray scattering (SAXS) measurements of p97 in the presence of AMP-PNP (ATP state), ADP-AlF(x) (hydrolysis transition state), ADP, or no nucleotide reveal major changes in the positions of the N domains with respect to the hexameric ring during the ATP hydrolysis cycle. Nucleotide binding and hydrolysis experiments indicate that D2 inhibits nucleotide exchange by D1. The data suggest that the conversion of the chemical energy of ATP hydrolysis into mechanical work on substrates involves transmission of conformational changes generated by D2 through D1 to move N.

Retrovirus envelope protein complex structure in situ studied by cryo-electron tomography

We used cryo-electron tomography in conjunction with single-particle averaging techniques to study the structures of frozen-hydrated envelope glycoprotein (Env) complexes on intact Moloney murine leukemia retrovirus particles. Cryo-electron tomography allows 3D imaging of viruses in toto at a resolution sufficient to locate individual macromolecules, and local averaging of abundant complexes substantially improves the resolution. The averaging of repetitive features in electron tomograms is hampered by a low signal-to-noise ratio and anisotropic resolution, which results from the "missing-wedge" effect. We developed an iterative 3D averaging algorithm that compensates for this effect and used it to determine the trimeric structure of Env to a resolution of 2.7 nm, at which individual domains can be resolved. Strikingly, the 3D reconstruction is shaped like a tripod in which the trimer penetrates the membrane at three distinct locations approximately 4.5 nm apart from one another. The Env reconstruction allows tentative docking of the x-ray crystal structure of the receptor-binding domain. This study thus provides 3D structural information regarding the prefusion conformation of an intact unstained retrovirus surface protein.

Structural characterization of components of protein assemblies by comparative modeling and electron cryo-microscopy

We explore structural characterization of protein assemblies by a combination of electron cryo-microscopy (cryoEM) and comparative protein structure modeling. Specifically, our method finds an optimal atomic model of a given assembly subunit and its position within an assembly by fitting alternative comparative models into a cryoEM map. The alternative models are calculated by MODELLER [J. Mol. Biol. 234 (1993) 313] from different sequence alignments between the modeled protein and its template structures. The fitting of these models into a cryoEM density map is performed either by FOLDHUNTER [J. Mol. Biol. 308 (2001) 1033] or by a new density fitting module of MODELLER (Mod-EM). Identification of the most accurate model is based on the correlation between the model accuracy and the quality of fit into the cryoEM density map. To quantify this correlation, we created a benchmark consisting of eight proteins of different structural folds with corresponding density maps simulated at five resolutions from 5 to 15 angstroms, with three noise levels each. Each of the proteins in the set was modeled based on 300 different alignments to their remotely related templates (12-32% sequence identity), spanning the range from entirely inaccurate to essentially accurate alignments. The benchmark revealed that one of the most accurate models can usually be identified by the quality of its fit into the cryoEM density map, even for noisy maps at 15 angstroms resolution. Therefore, a cryoEM density map can be helpful in improving the accuracy of a comparative model. Moreover, a pseudo-atomic model of a component in an assembly may be built better with comparative models of the native subunit sequences than with experimentally determined structures of their homologs.

Electron microscopy studies on DNA recognition by DNA-PK

Advances in transmission electron microscopy coupled to increasingly powerful biocomputing techniques are opening enormous possibilities to understand the structure and function of complex biological processes performed by large multi-protein assemblies. This is an exciting time for electron microscopists because we can combine our efforts with X-ray crystallographers and NMR spectroscopists to reach the prospect of studying the structure and dynamics of the so-called 'molecular machines'. One of these fascinating systems is the macromolecular complex formed around double-stranded DNA breaks (DSBs). Non-homologous end-joining (NHEJ) is the main DSBs repair pathway in mammalian cells, where a collection of proteins interact to rejoin two broken DNA ends. During NHEJ, DNA-dependent protein kinase (DNA-PK) binds damaged DNA with high affinity and acts as the main scaffold for other repair factors. Several studies have made use of the electron microscope to reveal the three-dimensional architecture of DNA-PK and the structural basis for the recognition of damaged DNA and the activation of DNA-PK's kinase activity.

Normal mode-based fitting of atomic structure into electron density maps: application to sarcoplasmic reticulum Ca-ATPase

A method for the flexible docking of high-resolution atomic structures into lower resolution densities derived from electron microscopy is presented. The atomic structure is deformed by an iterative process using combinations of normal modes to obtain the best fit of the electron microscopical density. The quality of the computed structures has been evaluated by several techniques borrowed from crystallography. Two atomic structures of the SERCA1 Ca-ATPase corresponding to different conformations were used as a starting point to fit the electron density corresponding to a different conformation. The fitted models have been compared to published models obtained by rigid domain docking, and their relation to the known crystallographic structures are explored by normal mode analysis. We find that only a few number of modes contribute significantly to the transition. The associated motions involve almost exclusively rotation and translation of the cytoplasmic domains as well as displacement of cytoplasmic loops. We suggest that the movements of the cytoplasmic domains are driven by the conformational change that occurs between nonphosphorylated and phosphorylated intermediate, the latter being mimicked by the presence of vanadate at the phosphorylation site in the electron microscopy structure.

Distance-restrained docking of rifampicin and rifamycin SV to RNA polymerase using systematic FRET measurements: developing benchmarks of model quality and reliability

We are developing distance-restrained docking strategies for modeling macromolecular complexes that combine available high-resolution structures of the components and intercomponent distance restraints derived from systematic fluorescence resonance energy transfer (FRET) measurements. In this article, we consider the problem of docking small-molecule ligands within macromolecular complexes. Using simulated FRET data, we have generated a series of benchmarks that permit estimation of model accuracy based on the quantity and quality of FRET-derived distance restraints, including the number, random error, systematic error, distance distribution, and radial distribution of FRET-derived distance restraints. We find that expected model accuracy is 10 A or better for models based on: i), > or =20 restraints with up to 15% random error and no systematic error, or ii), > or =20 restraints with up to 15% random error, up to 10% systematic error, and a symmetric radial distribution of restraints. Model accuracies can be improved to 5 A or better by increasing the number of restraints to > or =40 and/or by optimizing the distance distribution of restraints. Using experimental FRET data, we have defined the positions of the binding sites within bacterial RNA polymerase of the small-molecule inhibitors rifampicin (Rif) and rifamycin SV (Rif SV). The inferred binding sites for Rif and Rif SV were located with accuracies of, respectively, 7 and 10 A relative to the crystallographically defined binding site for Rif. These accuracies agree with expectations from the benchmark simulations and suffice to indicate that the binding sites for Rif and Rif SV are located within the RNA polymerase active-center cleft, overlapping the binding site for the RNA-DNA hybrid.

Methods for generating high-resolution structural models from electron microscope tomography data

Reconstructed volumes generated by tilt-image electron-microscope tomography offer the best spatial resolution currently available for studying cell structures in situ. Analysis is often accomplished by creating surface models that delineate grayscale contrast boundaries. Here, we introduce a specialized and convenient sequence of segmentation operations for making such models that greatly improves their reliability and spatial resolution as compared to current approaches, providing a basis for making accurate measurements. To assess the reliability of the surface models, we introduce a spatial uncertainty measurement based on grayscale gradient scale length. The model generation and measurement methods are validated by applying them to synthetic data, and their utility is demonstrated by using them to characterize macromolecular architecture of active zone material at the frog's neuromuscular junction.

Analysis of functional motions in Brownian molecular machines with an efficient block normal mode approach: myosin-II and Ca2+ -ATPase

The structural flexibilities of two molecular machines, myosin and Ca(2+)-ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improved implementation of the block normal mode (BNM) approach. The BNM results clearly illustrated that the large-scale conformational transitions implicated in the functional cycles of the two motor systems can be largely captured with a small number of low-frequency normal modes. Therefore, the results support the idea that structural flexibility is an essential part of the construction principle of molecular motors through evolution. Such a feature is expected to be more prevalent in motor proteins than in simpler systems (e.g., signal transduction proteins) because in the former, large-scale conformational transitions often have to occur before the chemical events (e.g., ATP hydrolysis in myosin and ATP binding/phosphorylation in Ca(2+)-ATPase). This highlights the importance of Brownian motions associated with the protein domains that are involved in the functional transitions; in this sense, Brownian molecular machines is an appropriate description of molecular motors, although the normal mode results do not address the origin of the ratchet effect. The results also suggest that it might be more appropriate to describe functional transitions in some molecular motors as intrinsic elastic motions modulating local structural changes in the active site, which in turn gets stabilized by the subsequent chemical events, in contrast with the conventional idea of local changes somehow getting amplified into larger-scale motions. In the case of myosin, for example, we favor the idea that Brownian motions associated with the flexible converter propagates to the Switch I/II region, where the salt-bridge formation gets stabilized by ATP hydrolysis, in contrast with the textbook notion that ATP hydrolysis drives the converter motion. Another useful aspect of the BNM results is that selected low-frequency normal modes have been identified to form a set of collective coordinates that can be used to characterize the progress of a significant fraction of large-scale conformational transitions. Therefore, the present normal mode analysis has provided a stepping-stone toward more elaborate microscopic simulations for addressing critical issues in free energy conversions in molecular machines, such as the coupling and the causal relationship between collective motions and essential local changes at the catalytic active site where ATP hydrolysis occurs.

Computational exploration of structural information from cryo-electron tomograms

Cryo-electron tomography aims to act as an interface between in vivo cell imaging and techniques achieving atomic resolution. This attempt to bridge the resolution gap is facilitated by recent software and hardware advances. Information provided by atomically resolved macromolecules and molecular interaction data need to be put into a common framework in order to create a hybrid multidimensional cellular image. A major partner in this enterprise is the development of regularization and pattern recognition techniques, which try to identify macromolecular complexes as a function of their structural signature in cryo-electron tomograms of living cells.

Fast Fitting of Atomic Structures to Low-resolution Electron Density Maps by Surface Overlap Maximization

The complexities of X-ray crystallography and NMR spectroscopy for large protein complexes, and the comparative ease of approaches such as electron microscopy mean that low-resolution structures are often available long before their atomic resolution equivalents. To help bridge this gap in knowledge, we present 3SOM: an approach for finding the best fit of atomic resolution structures into lower-resolution density maps through surface overlap maximization. High-resolution templates (i.e. partial structures or models for multi-subunit complexes) and targets (lower-resolution maps) are initially represented as iso-surfaces. The latter are used first in a fast search for transformations that superimpose a significant portion of the target surface onto the template surface, which is quantified as surface overlap. The vast search space is reduced by considering key vectors that capture local surface information. The set of transformations with the highest surface overlap scores are then re-ranked by using more sophisticated scores including cross-correlation. We give a number of examples to illustrate the efficiency of the method and its restrictions. For targets for which partial complexes are available, the speed and performance of the method make it an attractive complement to existing methods, as many different hypotheses can be tested quickly on a single processor.

Combination of scoring functions improves discrimination in protein-protein docking

Two structure-based potentials are used for both filtering (i.e., selecting a subset of conformations generated by rigid-body docking), and rescoring and ranking the selected conformations. ACP (atomic contact potential) is an atom-level extension of the Miyazawa-Jernigan potential parameterized on protein structures, whereas RPScore (residue pair potential score) is a residue-level potential, based on interactions in protein-protein complexes. These potentials are combined with other energy terms and applied to 13 sets of protein decoys, as well as to the results of docking 10 pairs of unbound proteins. For both potentials, the ability to discriminate between near-native and non-native docked structures is substantially improved by refining the structures and by adding a van der Waals energy term. It is observed that ACP and RPScore complement each other in a number of ways (e.g., although RPScore yields more hits than ACP, mainly as a result of its better performance for charged complexes, ACP usually ranks the near-native complexes better). As a general solution to the protein-docking problem, we have found that the best discrimination strategies combine either an RPScore filter with an ACP-based scoring function, or an ACP-based filter with an RPScore-based scoring function. Thus, ACP and RPScore capture complementary structural information, and combining them in a multistage postprocessing protocol provides substantially better discrimination than the use of the same potential for both filtering and ranking the docked conformations.

Interactive fitting augmented by force-feedback and virtual reality

The synthesis of low-resolution electron microscopy data with high-resolution molecular structures has become a common routine in the modeling of biomolecular assemblies. In contrast to algorithmic "black box" solutions, the interactive "fitting by eye" takes advantage of an expert's structural or biochemical knowledge and can be used with very noisy experimental data. In the solution proposed in this paper, we support the expert user in an interactive fitting session by haptic rendering and virtual reality. The quantitative and tactile feedback facilitates and objectifies the otherwise unrestrained modeling. We introduce a highly accurate reduced representation of the gradient of the cross-correlation coefficient that sustains force updates for haptic rendering at sufficiently high refresh rates.

Three-dimensional structure of bacteriophage T4 baseplate

The baseplate of bacteriophage T4 is a multiprotein molecular machine that controls host cell recognition, attachment, tail sheath contraction and viral DNA ejection. We report here the three-dimensional structure of the baseplate-tail tube complex determined to a resolution of 12 A by cryoelectron microscopy. The baseplate has a six-fold symmetric, dome-like structure approximately 520 A in diameter and approximately 270 A long, assembled around a central hub. A 940 A-long and 96 A-diameter tail tube, coaxial with the hub, is connected to the top of the baseplate. At the center of the dome is a needle-like structure that was previously identified as a cell puncturing device. We have identified the locations of six proteins with known atomic structures, and established the position and shape of several other baseplate proteins. The baseplate structure suggests a mechanism of baseplate triggering and structural transition during the initial stages of T4 infection.

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.

In silico protein recombination: enhancing template and sequence alignment selection for comparative protein modelling

Comparative modelling of proteins is a predictive technique to build an atomic model for a given amino acid sequence, on the basis of the structures of other proteins (templates) that have been determined experimentally. Critical problems arise in this procedure: selecting the correct templates, aligning the query sequence with them and building the non-conserved surface loops. In this work, we apply a genetic algorithm, with crossover and mutation, as a new tool to overcome the first two. In silico protein recombination proves to be an effective way to exploit the variability of templates and sequence alignments to produce populations of optimized models by artificial selection. Despite some limitations, the procedure is shown to be robust to alignment errors, while simplifying the task of selecting templates, making it a good candidate for automatic building of reliable protein models.

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.

A core-weighted fitting method for docking atomic structures into low-resolution maps: application to cryo-electron microscopy

Cryo-electron microscopy of "single particles" is a powerful method to analyze structures of large macromolecular assemblies that are not amenable to investigation by traditional X-ray crystallographic methods. A key step in these studies is to obtain atomic interpretations of multiprotein complexes by fitting atomic structures of individual components into maps obtained from electron microscopic data. Here, we report the use of a "core-weighting" method, combined with a grid-threading Monte Carlo (GTMC) approach for this purpose. The "core" of an individual structure is defined to represent the part where the density distribution is least likely to be altered by other components that comprise the macromolecular assembly of interest. The performance of the method has been evaluated by its ability to determine the correct fit of (i) the alpha-chain of the T-cell receptor variable domain into a simulated map of the alphabeta complex at resolutions between 5 and 40 A, and (ii) the E2 catalytic domain of the pyruvate dehydrogenase into an experimentally determined map, at 14 A resolution, of the icosahedral complex formed by 60 copies of this enzyme. Using the X-ray structures of the two test cases as references, we demonstrate that, in contrast to more traditional methods, the combination of the core-weighting method and the grid-threading Monte Carlo approach can identify the correct fit reliably and rapidly from the low-resolution maps that are typical of structures determined with the use of single-particle electron microscopy.

Placement of the structural proteins in Sindbis virus

The structure of the lipid-enveloped Sindbis virus has been determined by fitting atomic resolution crystallographic structures of component proteins into an 11-A resolution cryoelectron microscopy map. The virus has T=4 quasisymmetry elements that are accurately maintained between the external glycoproteins, the transmembrane helical region, and the internal nucleocapsid core. The crystal structure of the E1 glycoprotein was fitted into the cryoelectron microscopy density, in part by using the known carbohydrate positions as restraints. A difference map showed that the E2 glycoprotein was shaped similarly to E1, suggesting a possible common evolutionary origin for these two glycoproteins. The structure shows that the E2 glycoprotein would have to move away from the center of the trimeric spike in order to expose enough viral membrane surface to permit fusion with the cellular membrane during the initial stages of host infection. The well-resolved E1-E2 transmembrane regions form alpha-helical coiled coils that were consistent with T=4 symmetry. The known structure of the capsid protein was fitted into the density corresponding to the nucleocapsid, revising the structure published earlier.

Activation of the nicotinic acetylcholine receptor involves a switch in conformation of the alpha subunits

The nicotinic acetylcholine (ACh) receptor belongs to a superfamily of synaptic ion channels that open in response to the binding of chemical transmitters. Their mechanism of activation is not known in detail, but a time-resolved electron microscopic study of the muscle-type ACh receptor had suggested that a local disturbance in the ligand-binding region and consequent rotations in the ligand-binding alpha subunits, connecting to the transmembrane portion, are involved. A more precise interpretation of this structural change is given here, based on comparison of the extracellular domain of the ACh receptor with an ACh-binding protein (AChBP) to which a putative agonist is bound. We find that, to a good approximation, there are two alternative extended conformations of the ACh receptor subunits, one characteristic of either alpha subunit before activation, and the other characteristic of all three non-alpha subunits and the protomer of AChBP. Substitution in the three-dimensional maps of alpha by non-alpha subunits mimics the changes seen on activation, suggesting that the structures of the alpha subunits are modified initially by their interactions with neighbouring subunits and switch to the non-alpha form when ACh binds. This structural change, which entails 15-16 degrees rotations of the inner pore-facing parts of the alpha subunits, most likely acts as the trigger that opens the gate in the membrane-spanning pore.

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.

Deriving folds of macromolecular complexes through electron cryomicroscopy and bioinformatics approaches

Intermediate-resolution (7-9A) structures of large macromolecular complexes can be obtained by electron cryomicroscopy. This structural information, combined with bioinformatics data for the individual protein components or domains, can lead to a fold model for the entire complex. Such approaches have been demonstrated with the 6.8 A structure of the rice dwarf virus to derive models for the major capsid shell proteins.