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.     

Combining electron microscopic with x-ray crystallographic structures

Analgorithm has been developed for placing three-dimensional atomic structures into appropriately scaled cryoelectron microscopy maps. The first stage in this process is to conduct a three-dimensional angular search in which the center of gravity of an X-ray crystallographically determined structure is placed on a selected position in the cryoelectron microscopy map. The quality of the fit is measured by the sum of the density at each atomic position. The second stage is to refine the three angles and three translational parameters for the best (usually 25 to 100) fits. Useful criteria for this refinement include the sum of densities at atomic sites, the lack of atoms in negative or low density, the absence of atomic clashes between symmetry-related positions of the atomic structure, and the distances between identifiable features in the map and their positions on the fitted atomic structure. These refinements generally lead to a convergence of the originally chosen, top scoring fits to just a few (about 3 to 8) acceptable possibilities. Usually, the best remaining fit is clearly superior to any of the others.     

Modeling shape and topology of low-resolution density maps of biological macromolecules

In the present work we develop an efficient way of representing the geometry and topology of volumetric datasets of biological structures from medium to low resolution, aiming at storing and querying them in a database framework. We make use of a new vector quantization algorithm to select the points within the macromolecule that best approximate the probability density function of the original volume data. Connectivity among points is obtained with the use of the alpha shapes theory. This novel data representation has a number of interesting characteristics, such as 1) it allows us to automatically segment and quantify a number of important structural features from low-resolution maps, such as cavities and channels, opening the possibility of querying large collections of maps on the basis of these quantitative structural features; 2) it provides a compact representation in terms of size; 3) it contains a subset of three-dimensional points that optimally quantify the densities of medium resolution data; and 4) a general model of the geometry and topology of the macromolecule (as opposite to a spatially unrelated bunch of voxels) is easily obtained by the use of the alpha shapes theory.     

Map2mod--a server for evaluation of crystallographic models and their agreement with electron density maps

Here we report on recent developments of the map2mod server. It has been designed for validation of protein models created by X-ray data interpretation. It can also be used during the refinement process since it is able to indicate problem regions in the model. Apart from evaluation of model quality, it has an option to remove atoms of side chains, which are not consistent with the maps as well as improperly placed water molecules. There are two additional options: checking the B-factors of atoms in the provided model and comparison of R and R(free) values obtained as the result of refinement with the averages characteristic for the data resolution shell.     

Deriving topology and sequence alignment for the helix skeleton in low-resolution protein density maps

Cryoelectron microscopy (cryoEM) is an experimental technique to determine the three-dimensional (3D) structure of large protein complexes. Currently, this technique is able to generate protein density maps at 6-9 A resolution, at which the skeleton of the structure (which is composed of alpha-helices and beta-sheets) can be visualized. As a step towards predicting the entire backbone of the protein from the protein density map, we developed a method to predict the topology and sequence alignment for the skeleton helices. Our method combines the geometrical information of the skeleton helices with the Rosetta ab initio structure prediction method to derive a consensus topology and sequence alignment for the skeleton helices. We tested the method with 60 proteins. For 45 proteins, the majority of the skeleton helices were assigned a correct topology from one of our top ten predictions. The offsets of the alignment for most of the assigned helices were within +/-2 amino acids in the sequence. We also analyzed the use of the skeleton helices as a clustering tool for the decoy structures generated by Rosetta. Our comparison suggests that the topology clustering is a better method than a general overlap clustering method to enrich the ranking of decoys, particularly when the decoy pool is small.     

Experimental charge density from electron microscopic maps

The charge density (CD) distribution of an atom is the difference per unit volume between the positive charge of its nucleus and the distribution of the negative charges carried by the electrons that are associated with it. The CDs of the atoms in macromolecules are responsible for their electrostatic potential (ESP) distributions, which can now be visualized using cryo‐electron microscopy at high resolution. CD maps can be recovered from experimental ESP density maps using the negative Laplacian operation. CD maps are easier to interpret than ESP maps because they are less sensitive to long‐range electrostatic effects. An ESP‐to‐CD conversion involves multiplication of amplitudes of structure factors as Fourier transforms of these maps in reciprocal space by 1/d², where d is the resolution of reflections. In principle, it should be possible to determine the charges carried by the individual atoms in macromolecules by comparing experimental CD maps with experimental ESP maps.     

Situs: A package for docking crystal structures into low-resolution maps from electron microscopy

Three-dimensional image reconstructions of large-scale protein aggregates are routinely determined by electron microscopy (EM). We combine low-resolution EM data with high-resolution structures of proteins determined by x-ray crystallography. A set of visualization and analysis procedures, termed the Situs package, has been developed to provide an efficient and robust method for the localization of protein subunits in low-resolution data. Topology-representing neural networks are employed to vector-quantize and to correlate features within the structural data sets. Microtubules decorated with kinesin-related ncd motors are used as model aggregates to demonstrate the utility of this package of routines. The precision of the docking has allowed for the extraction of unique conformations of the macromolecules and is limited only by the reliability of the underlying structural data.     

Edged watershed segmentation: A semi-interactive algorithm for segmentation of low-resolution maps from electron cryomicroscopy

Electron cryomicroscopy (cryo-EM) allows for the structural analysis of large protein complexes that may be difficult to study by other means. Frequently, maps of complexes from cryo-EM are obtained at resolutions between 10 and 25 Å. To aid in the interpretation of these medium- to low-resolution maps, they may be subdivided into three-dimensional segments representing subunits or subcomplexes. This division is often accomplished using a manual segmentation approach. While extremely useful, manual segmentation is subjective. We have developed a novel semi-interactive segmentation algorithm that can incorporate prior knowledge of subunit composition or structure without biasing the boundaries between subunits or subcomplexes. This algorithm has been characterized with experimental and simulated cryo-EM density maps at resolutions between 10 and 25 Å.     

Fast fitting to low resolution density maps: elucidating large-scale motions of the ribosome

Determining the conformational rearrangements of large macromolecules is challenging experimentally and computationally. Case in point is the ribosome; it has been observed by high-resolution crystallography in several states, but many others are known only from low-resolution methods including cryo-electron microscopy. Combining these data into dynamical trajectories that may aid understanding of its largest-scale conformational changes has so far remained out of reach of computational methods. Most existing methods either model all atoms explicitly, resulting in often prohibitive cost, or use approximations that lose interesting structural and dynamical detail. In this work, I introduce Internal Coordinate Flexible Fitting, which uses full atomic forces and flexibility in limited regions of a model, capturing extensive conformational rearrangements at low cost. I use it to turn multiple low-resolution density maps, crystallographic structures and biochemical information into unified all-atoms trajectories of ribosomal translocation. Internal Coordinate Flexible Fitting is three orders of magnitude faster than the most comparable existing method.     

Using enhanced sampling and structural restraints to refine atomic structures into low-resolution electron microscopy maps

For a variety of problems in structural biology, low-resolution maps generated by electron microscopy imaging are often interpreted with the help of various flexible-fitting computational algorithms. In this work, we systematically analyze the quality of final models of various proteins obtained via molecular dynamics flexible fitting (MDFF) by varying the map-resolution, strength of structural restraints, and the steering forces. We find that MDFF can be extended to understand conformational changes in lower-resolution maps if larger structural restraints and lower steering forces are used to prevent overfitting. We further show that the capabilities of MDFF can be extended by combining it with an enhanced conformational sampling method, temperature-accelerated molecular dynamics (TAMD). Specifically, either TAMD can be used to generate better starting configurations for MDFF fitting or TAMD-assisted MDFF (TAMDFF) can be performed to accelerate conformational search in atomistic simulations.     

Automated segmentation of molecular subunits in electron cryomicroscopy density maps

Electron cryomicroscopy (cryoEM) is capable of imaging large macromolecular machines composed of multiple components. However, it is currently only possible to achieve moderate resolution at which it may be possible to computationally extract the individual components in the machine. In this work, we present application details of an automated method for detecting and segmenting the components of a large machine in an experimentally determined density map. This method is applicable to object with and without symmetry and takes advantage of global and local symmetry axes if present. We have applied this segmentation algorithm to several cryoEM data sets already deposited in EMDB with various complexities, symmetries and resolutions and validated the results using manually segmented density and available structures of the components in the PDB. As such, automated segmentation could become a useful tool for the analysis of the ever-increasing number of structures of macromolecular machines derived from cryoEM.     

An x-ray crystallographic study of hemerythrin.

The non-heme iron protein, hemerythrin, has been crystallized from Themiste dyscritum. The crystals belong to the tetragonal space group P4 with unit cell dimensions $\text{a = b = 86.5}\text{A}\text{̊}\text{, c = 80.6}\text{A}\text{̊}$. A 2-fold molecular axis is suggested, implying that the asymmetric unit contains four subunits each with a molecular weight of 12,600.     

Application of the automated interpretation of electron density maps to Bence-Jones protein Rhe

The automated system for interpreting electron density maps of proteins has been applied to a newly calculated map of Bence-Jones protein Rhe. In order to test the methods and criteria incorporated in the program system, interpretation of Rhe was performed independently of the interpretation by Wang et al. (1974, 1975a,b²), who have used classical Richards box techniques. The automated system produced a single polypeptide chain which accounts for the whole molecule. Much of the secondary structure is detected and atomic co-ordinates are built for most of the main-chain atoms. The results indicate that the program system is able to interpret and build provisional main-chain co-ordinates for an electron density map of reasonable quality.     

Fitting low-resolution cryo-EM maps of proteins using constrained geometric simulations

Recent experimental advances in producing density maps from cryo-electron microscopy (cryo-EM) have challenged theorists to develop improved techniques to provide structural models that are consistent with the data and that preserve all the local stereochemistry associated with the biomolecule. We develop a new technique that maintains the local geometry and chemistry at each stage of the fitting procedure. A geometric simulation is used to drive the structure from some appropriate starting point (a nearby experimental structure or a modeled structure) toward the experimental density, via a set of small incremental motions. Structural motifs such as α-helices can be held rigid during the fitting procedure as the starting structure is brought into alignment with the experimental density. After validating this procedure on simulated data for adenylate kinase and lactoferrin, we show how cryo-EM data for two different GroEL structures can be fit using a starting x-ray crystal structure. We show that by incorporating the correct local stereochemistry in the modeling, structures can be obtained with effective resolution that is significantly higher than might be expected from the nominal cryo-EM resolution.     

A probabilistic approach to protein backbone tracing in electron density maps

One particularly time-consuming step in protein crystallography is interpreting the electron density map; that is, fitting a complete molecular model of the protein into a 3D image of the protein produced by the crystallographic process. In poor-quality electron density maps, the interpretation may require a significant amount of a crystallographer's time. Our work investigates automating the time-consuming initial backbone trace in poor-quality density maps. We describe ACMI (Automatic Crystallographic Map Interpreter), which uses a probabilistic model known as a Markov field to represent the protein. Residues of the protein are modeled as nodes in a graph, while edges model pairwise structural interactions. Modeling the protein in this manner allows the model to be flexible, considering an almost infinite number of possible conformations, while rejecting any that are physically impossible. Using an efficient algorithm for approximate inference--belief propagation--allows the most probable trace of the protein's backbone through the density map to be determined. We test ACMI on a set of ten protein density maps (at 2.5 to 4.0 A resolution), and compare our results to alternative approaches. At these resolutions, ACMI offers a more accurate backbone trace than current approaches.