An Effective Computational Method Incorporating Multiple Secondary Structure Predictions in Topology Determination for Cryo-EM Images

A key idea in de novo modeling of a medium-resolution density image obtained from cryo-electron microscopy is to compute the optimal mapping between the secondary structure traces observed in the density image and those predicted on the protein sequence. When secondary structures are not determined precisely, either from the image or from the amino acid sequence of the protein, the computational problem becomes more complex. We present an efficient method that addresses the secondary structure placement problem in presence of multiple secondary structure predictions and computes the optimal mapping. We tested the method using 12 simulated images from alpha-proteins and two Cryo-EM images of α-β proteins. We observed that the rank of the true topologies is consistently improved by using multiple secondary structure predictions instead of a single prediction. The results show that the algorithm is robust and works well even when errors/ misses in the predicted secondary structures are present in the image or the sequence. The results also show that the algorithm is efficient and is able to handle proteins with as many as 33 helices

A Dynamic Programming Algorithm for Finding the Optimal Placement of a Secondary Structure Topology in Cryo-EM Data

The determination of secondary structure topology is a critical step in deriving the atomic structures from the protein density maps obtained from electron cryomicroscopy technique. This step often relies on matching the secondary structure traces detected from the protein density map to the secondary structure sequence segments predicted from the amino acid sequence. Due to inaccuracies in both sources of information, a pool of possible secondary structure positions needs to be sampled. One way to approach the problem is to first derive a small number of possible topologies using existing matching algorithms, and then find the optimal placement for each possible topology. We present a dynamic programming method of Θ(Nq2h) to find the optimal placement for a secondary structure topology. We show that our algorithm requires significantly less computational time than the brute force method that is in the order of Θ(qN h)

Tracing Beta Strands Using StrandTwister from Cryo-EM Density Maps at Medium Resolutions

Major secondary structure elements such as α helices and β sheets can be computationally detected from cryoelectron microscopy (cryo-EM) density maps with medium resolutions of 5–10 A˚ . However, a critical piece of information for modeling atomic structures is missing, because there are no tools to detect β strands from cryo-EM maps at medium resolutions. We propose a method, StrandTwister, to detect the traces of β strands through the analysis of twist, an intrinsic nature of a β sheet. StrandTwister has been tested using 100 β sheets simulated at 10 A˚ resolution and 39 β sheets computationally detected from cryo-EM density maps at 4.4–7.4 A˚ resolutions. Although experimentally derived cryoEMmaps contain errors, StrandTwister’s best detections over 39 cases were able to detect 81.87% of the β strands, with an overall 1.66 A˚ two-way distance between the detected and observed β traces. StrandTwister appears to detect the traces of β strands on major β sheets quite accurately, particularly at the central area of a β sheet

Comparing an Atomic Model or Structure to a Corresponding Cryo-Electron Microscopy Image at the Central Axis of a Helix

Three-dimensional density maps of biological specimens from cryo-electron microscopy (cryo-EM) can be interpreted in the form of atomic models that are modeled into the density, or they can be compared to known atomic structures. When the central axis of a helix is detectable in a cryo-EM density map, it is possible to quantify the agreement between this central axis and a central axis calculated from the atomic model or structure. We propose a novel arc-length association method to compare the two axes reliably. This method was applied to 79 helices in simulated density maps and six case studies using cryo-EM maps at 6.4-7.7 Å resolution. The arc-length association method is then compared to three existing measures that evaluate the separation of two helical axes: a two-way distance between point sets, the length difference between two axes, and the individual amino acid detection accuracy. The results show that our proposed method sensitively distinguishes lateral and longitudinal discrepancies between the two axes, which makes the method particularly suitable for the systematic investigation of cryo-EM map-model pairs

Estimating loop length from CryoEM images at medium resolutions

Background: De novo protein modeling approaches utilize 3-dimensional (3D) images derived from electron cryomicroscopy (CryoEM) experiments. The skeleton connecting two secondary structures such as α-helices represent the loop in the 3D image. The accuracy of the skeleton and of the detected secondary structures are critical in De novo modeling. It is important to measure the length along the skeleton accurately since the length can be used as a constraint in modeling the protein. Results: We have developed a novel computational geometric approach to derive a simplified curve in order to estimate the loop length along the skeleton. The method was tested using fifty simulated density images of helix-loop-helix segments of atomic structures and eighteen experimentally derived density data from Electron Microscopy Data Bank (EMDB). The test using simulated density maps shows that it is possible to estimate within 0.5 angstrom of the expected length for 48 of the 50 cases. The experiments, involving eighteen experimentally derived CryoEM images, show that twelve cases have error within 2 angstrom. Conclusions:The tests using both simulated and experimentally derived images show that it is possible for our proposed method to estimate the loop length along the skeleton if the secondary structure elements, such as α-helices, can be detected accurately, and there is a continuous skeleton linking the α-helices

Computational Development for Secondary Structure Detection From Three-Dimensional Images of Cryo-Electron Microscopy

Electron cryo-microscopy (cryo-EM) as a cutting edge technology has carved a niche for itself in the study of large-scale protein complex. Although the protein backbone of complexes cannot be derived directly from the medium resolution (5-10 Å) of amino acids from three-dimensional (3D) density images, secondary structure elements (SSEs) such as alpha-helices and beta-sheets can still be detected. The accuracy of SSE detection from the volumetric protein density images is critical for ab initio backbone structure derivation in cryo-EM. So far it is challenging to detect the SSEs automatically and accurately from the density images at these resolutions. This dissertation presents four computational methods - SSEtracer, SSElearner, StrandTwister and StrandRoller for solving this critical problem. An effective approach, SSEtracer, is presented to automatically identify helices and β- sheets from the cryo-EM three-dimensional maps at medium resolutions. A simple mathematical model is introduced to represent the β-sheet density. The mathematical model can be used for β-strand detection from medium resolution density maps. A machine learning approach, SSElearner, has also been developed to automatically identify helices and β-sheets by using the knowledge from existing volumetric maps in the Electron Microscopy Data Bank (EMDB). The approach has been tested using simulated density maps and experimental cryo-EM maps of EMDB. The results of SSElearner suggest that it is effective to use one cryo-EM map for learning in order to detect the SSE in another cryo-EM map of similar quality. Major secondary structure elements such as a-helices and β-sheets can be computationally detected from cryo-EM density maps with medium resolutions of 5-10Å. However, a critical piece of information for modeling atomic structures is missing, since there are no tools to detect β-strands from cryo-EM maps at medium resolutions. A new method, StrandTwister, has been proposed to detect the traces of β-strands through the analysis of twist, an intrinsic nature of β-sheet. StrandTwister has been tested using 100 β-sheets simulated at 10Å resolution and 39 β-sheets computationally detected from cryoEM density maps at 4.4-7.4Å resolutions. StrandTwister appears to detect the traces of β-strands on major β-sheets quite accurately, particularly at the central area of a β-sheet. β-barrel is a structure feature that is formed by multiple β-strands in a barrel shape. There is no existing method to derive the β-strands from the 3D image of β-barrel. A new method, StrandRoller, has been proposed to generate small sets of possible β-traces from the density images at medium resolutions of 5-10Å. The results of StrandRoller suggest that it is possible to derive a small set of possible β-traces from the β-barrel cryo-EM image at medium resolutions even when it is not possible to visualize the separation of β-strands

Estimating Loop Length from CryoEM Images at Medium Resolutions

Background: De novo protein modeling approaches utilize 3-dimensional (3D) images derived from electron cryomicroscopy (CryoEM) experiments. The skeleton connecting two secondary structures such as α-helices represent the loop in the 3D image. The accuracy of the skeleton and of the detected secondary structures are critical in De novo modeling. It is important to measure the length along the skeleton accurately since the length can be used as a constraint in modeling the protein. Results: We have developed a novel computational geometric approach to derive a simplified curve in order to estimate the loop length along the skeleton. The method was tested using fifty simulated density images of helix-loop-helix segments of atomic structures and eighteen experimentally derived density data from Electron Microscopy Data Bank (EMDB). The test using simulated density maps shows that it is possible to estimate within 0.5 angstrom of the expected length for 48 of the 50 cases. The experiments, involving eighteen experimentally derived CryoEM images, show that twelve cases have error within 2 angstrom. Conclusions:The tests using both simulated and experimentally derived images show that it is possible for our proposed method to estimate the loop length along the skeleton if the secondary structure elements, such as α-helices, can be detected accurately, and there is a continuous skeleton linking the α-helices

Modeling Beta-Traces for Beta-Barrels from Cryo-EM Density Maps

Cryo-electron microscopy (cryo-EM) has produced density maps of various resolutions. Although ά-helices can be detected from density maps at 5-8 angstrom resolutions, β-strands are challenging to detect at such density maps due to close-spacing of β-strands. The variety of shapes of β-sheets adds the complexity of β-strands detection from density maps. We propose a new approach to model traces of β-strands for β-barrel density regions that are extracted from cryo-EM density maps. In the test containing eight β-barrels extracted from experimental cryo-EM density maps at 5.5 angstrom-8.25 angstrom resolution, StrandRoller detected about 74.26% of the amino acids in the β-strands with an overall 2.05 angstrom 2-way distance between the detected β-traces and the observed ones, if the best of the fifteen detection cases is considered

Of bits and bugs

Pur-α is a nucleic acid-binding protein involved in cell cycle control, transcription, and neuronal function. Initially no prediction of the three-dimensional structure of Pur-α was possible. However, recently we solved the X-ray structure of Pur-α from the fruitfly Drosophila melanogaster and showed that it contains a so-called PUR domain. Here we explain how we exploited bioinformatics tools in combination with X-ray structure determination of a bacterial homolog to obtain diffracting crystals and the high-resolution structure of Drosophila Pur-α. First, we used sensitive methods for remote-homology detection to find three repetitive regions in Pur-α. We realized that our lack of understanding how these repeats interact to form a globular domain was a major problem for crystallization and structure determination. With our information on the repeat motifs we then identified a distant bacterial homolog that contains only one repeat. We determined the bacterial crystal structure and found that two of the repeats interact to form a globular domain. Based on this bacterial structure, we calculated a computational model of the eukaryotic protein. The model allowed us to design a crystallizable fragment and to determine the structure of Drosophila Pur-α. Key for success was the fact that single repeats of the bacterial protein self-assembled into a globular domain, instructing us on the number and boundaries of repeats to be included for crystallization trials with the eukaryotic protein. This study demonstrates that the simpler structural domain arrangement of a distant prokaryotic protein can guide the design of eukaryotic crystallization constructs. Since many eukaryotic proteins contain multiple repeats or repeating domains, this approach might be instructive for structural studies of a range of proteins