Efficiency of 2D alignment methods

Cryo-EM image alignment based on nonuniform fast Fourier transform

Cryo-electron microscopy (cryo-EM) single-particle image analysis is a powerful technique to resolve structures of biomacromolecules, while the challenge is that the cryo-EM image is of a low signal-to-noise ratio. For both two-dimensional image analysis and three-dimensional density map analysis, image alignment is an important step to improve the precision of the image distance calculation. In this paper, we introduce a new algorithm for performing two-dimensional pairwise alignment for cryo-EM particle images, which is based on the Fourier transform and power spectrum analysis. Compared to the existing heuristic iterative alignment methods, our method utilizes the signal distribution and signal feature on images' power spectrum to directly compute the alignment parameters. It does not require iterative computations and is robust against the cryo-EM image noise. Both theoretical analysis and experimental results suggest that our power-spectrum-feature-based alignment method is highly computational-efficient and is capable of offering effective alignment results. This new alignment algorithm is publicly available at: www.csbio.sjtu.edu.cn/bioinf/EMAF/for academic use.

Chapter 7 - Electron Microscopy and Single Particle Analysis for Solving Three-Dimensional Structures of Macromolecules

Single particle reconstruction of membrane proteins: A tool for understanding the 3D structure of disease-related macromolecules

BackgroundMulti-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over O(N2), so that it is difficult to process a data set of a large number of genes N, such as in the case of whole genome microarray data.ResultsWe developed a new rapid metric MDS method with a low computational complexity, making metric MDS applicable for large data sets. Computer simulation showed that the new method of split-and-combine MDS (SC-MDS) is fast, accurate and efficient. Our empirical studies using microarray data on the yeast cell cycle showed that the performance of K-means in the reduced dimensional space is similar to or slightly better than that of K-means in the original space, but about three times faster to obtain the clustering results. Our clustering results using SC-MDS are more stable than those in the original space. Hence, the proposed SC-MDS is useful for analyzing whole genome data.ConclusionOur new method reduces the computational complexity from O(N3) to O(N) when the dimension of the feature space is far less than the number of genes N, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent high dimensional large data set in a low dimensional space not only efficiently but also effectively.

Application of template matching technique to particle detection in electron micrographs

Three-dimensional (3D) protein structures facilitate the understanding of their biological functions and provide valuable information for developing medicines. Single-particle analysis (SPA) from electron microscopy (EM) is a structure determination method suitable for macromolecules. To achieve a high resolution using combinations of several SPA software packages, 'workflow' optimization and comparative evaluation by scoring results are essential. Two-dimensional (2D) averaging is a key step for 3D reconstruction. The integrated convergence-evaluation oriented system (IC-EOS) proposed here provides an effective tool for customizing 2D averaging. This assesses the behavior and characteristics of workflows and evaluates the convergence of iteration steps without human intervention. We chose five base measurements for quantifying convergence: resolution, variance, similarity, shift-distance and rotation-angle. Curve fitting to history graphs scored their stability. We call this score 'fluctuation'. The number of particle images discarded from the library and the number of classification groups were examined to see their effects on optimization levels and fluctuation of measurements, allowing the IC-EOS to select the most appropriate workflow for the target. A case study using a bacterial sodium channel and a simulation study using GroEL showed that resolution of 2D averaging improved with relatively stricter particle selection. With fewer groups, resolutions of class averages improved, but similarities between class-averages and their constituent particle images degraded. Fluctuation was useful for selecting adequate conditions, even when achieved values alone were not conclusive. The vote method, using fluctuation, was robust against noise and enabled a decision without exhaustive search trials. Thus, the IC-EOS is a step toward full automation of SPA.

DNA replication is a key cellular process and is the basis for cell division. In order to understand replication initiation in mammalian cells, viral systems such as bovine papillomavirus (BPV) are used as simplified models of the process. BPV uses a single protein E1 to perform both DNA binding and unwinding functions essential for the initiation of replication (Figure A). Biochemical assays for a cell‐free replication initiation system has been established for BPV. To have a clearer understanding of a biological process at a molecular level, it is essential to determine the three‐dimensional (3D) arrangement and dynamics of molecules and how macromolecular machines are assembled. Electron microscopy (EM), single particle analysis and image processing have been used in this work to reveal the structures of the BPV E1 helicase domain (E1HD), full‐length E1 (E1FL), a single‐labelled E1FL‐replication fork DNA complex with monovalent tetrameric streptavidin (MTS) on the dsDNA of the fork and a double‐labelled E1FLwith MTS on the dsDNA and FAB on the ssDNA of the fork. The structure of BPV E1FL in complex with DNA was initially determined by EM both by applying 6‐fold symmetry and without applying any symmetry. EM demonstrated that the E1FL helicase forms a hexamer that has a diameter of 130Å and a height of 100Å, consistent with an overall mass of ~410 kDa. The oligomer has a central channel inside the molecule, with a variable diameter. E1FL is a single polypeptide chain, and the OBD domain can be fitted into the structure in two different ways. In one case the DNA binding site would be located on the inner surface and in the other case it would be on the outer surface of the complex. To determine the orientation of the OBD domain, a 12‐residue epitope sequence GGYPYDVPDYAG was inserted into the OBD domain after the residue 226. EM has demonstrated that the antibody was bound to the E1FL. That proves that the binding site for AB is located on the outer surface of E1FL (Figure B). The points of the entrance of dsDNA and exit of 5′ ssDNA were also determined in the complex of E1FL and DNA. Labelling with streptavidin was performed to reveal the position of the dsDNA, whereas ssDNA was labelled with DIG‐FAB to reveal the 5′ ssDNA position in an asymmetrical structure of the BPV E1 hexamer bound to a replication fork DNA substrate. Comparison of the 3D structures showed that dsDNA enters the molecule between the N‐terminus and ori DNA‐binding domain (OBD), and the 5′ ssDNA exits the molecule between the collar domain and OBD. The angle between the point of dsDNA entrance and 5′ ssDNA exit was ~170°. Prior to our research, the most accepted model of “steric exclusion” for dsDNA unwinding suggested that the active 3′ ssDNA strand is pulled through the helicase motor and dsDNA is wedged apart outside the protein assembly (Figure C). Our structural observations indicated that strand separation is taking place inside E1 in a chamber above the helicase domain and that the 5′ passive ssDNA strand leaves the assembly through a channel located on the opposite side to dsDNA entry. Therefore, our data suggest an alternative model for DNA unwinding by this general class of replication enzymes.

BackgroundSimilarity of sequences is a key mathematical notion for Classification and Phylogenetic studies in Biology. It is currently primarily handled using alignments. However, the alignment methods seem inadequate for post-genomic studies since they do not scale well with data set size and they seem to be confined only to genomic and proteomic sequences. Therefore, alignment-free similarity measures are actively pursued. Among those, USM (Universal Similarity Metric) has gained prominence. It is based on the deep theory of Kolmogorov Complexity and universality is its most novel striking feature. Since it can only be approximated via data compression, USM is a methodology rather than a formula quantifying the similarity of two strings. Three approximations of USM are available, namely UCD (Universal Compression Dissimilarity), NCD (Normalized Compression Dissimilarity) and CD (Compression Dissimilarity). Their applicability and robustness is tested on various data sets yielding a first massive quantitative estimate that the USM methodology and its approximations are of value. Despite the rich theory developed around USM, its experimental assessment has limitations: only a few data compressors have been tested in conjunction with USM and mostly at a qualitative level, no comparison among UCD, NCD and CD is available and no comparison of USM with existing methods, both based on alignments and not, seems to be available.ResultsWe experimentally test the USM methodology by using 25 compressors, all three of its known approximations and six data sets of relevance to Molecular Biology. This offers the first systematic and quantitative experimental assessment of this methodology, that naturally complements the many theoretical and the preliminary experimental results available. Moreover, we compare the USM methodology both with methods based on alignments and not. We may group our experiments into two sets. The first one, performed via ROC (Receiver Operating Curve) analysis, aims at assessing the intrinsic ability of the methodology to discriminate and classify biological sequences and structures. A second set of experiments aims at assessing how well two commonly available classification algorithms, UPGMA (Unweighted Pair Group Method with Arithmetic Mean) and NJ (Neighbor Joining), can use the methodology to perform their task, their performance being evaluated against gold standards and with the use of well known statistical indexes, i.e., the F-measure and the partition distance. Based on the experiments, several conclusions can be drawn and, from them, novel valuable guidelines for the use of USM on biological data. The main ones are reported next.ConclusionUCD and NCD are indistinguishable, i.e., they yield nearly the same values of the statistical indexes we have used, accross experiments and data sets, while CD is almost always worse than both. UPGMA seems to yield better classification results with respect to NJ, i.e., better values of the statistical indexes (10% difference or above), on a substantial fraction of experiments, compressors and USM approximation choices. The compression program PPMd, based on PPM (Prediction by Partial Matching), for generic data and Gencompress for DNA, are the best performers among the compression algorithms we have used, although the difference in performance, as measured by statistical indexes, between them and the other algorithms depends critically on the data set and may not be as large as expected. PPMd used with UCD or NCD and UPGMA, on sequence data is very close, although worse, in performance with the alignment methods (less than 2% difference on the F-measure). Yet, it scales well with data set size and it can work on data other than sequences. In summary, our quantitative analysis naturally complements the rich theory behind USM and supports the conclusion that the methodology is worth using because of its robustness, flexibility, scalability, and competitiveness with existing techniques. In particular, the methodology applies to all biological data in textual format. The software and data sets are available under the GNU GPL at the supplementary material web page.

Goal: Over the decades, there have been improvements in the sequence alignment algorithm, with significant advances in various aspects such as complexity and accuracy. However, human-defined algorithms have an explicit limitation in view of developmental completeness. This paper introduces a novel local alignment method to obtain optimal sequence alignment based on reinforcement learning. Methods: There is a DQNalign algorithm that learns and performs sequence alignment through deep reinforcement learning. This paper proposes a DQN x-drop algorithm that performs local alignment without human intervention by combining the x-drop algorithm with this DQNalign algorithm. The proposed algorithm performs local alignment by repeatedly observing the subsequences and selecting the next alignment direction until the x-drop algorithm terminates the DQNalign algorithm. This proposed algorithm has an advantage in view of linear computational complexity compared to conventional local alignment algorithms. Results: This paper compares alignment performance (coverage and identity) and complexity for a fair comparison between the proposed DQN x-drop algorithm and the conventional greedy x-drop algorithm. Firstly, we prove the proposed algorithm's superiority by comparing the two algorithms’ computational complexity through numerical analysis. After that, we tested the alignment performance actual HEV and E.coli sequence datasets. The proposed method shows the comparable identity and coverage performance to the conventional alignment method while having linear complexity for the n}{}X parameter. Conclusions: Through this study, it was possible to confirm the possibility of a new local alignment algorithm that minimizes computational complexity without human intervention.

BAli-Phy, a popular Bayesian method that co-estimates multiple sequence alignments and phylogenetic trees, is a rigorous statistical method, but due to its computational requirements, it has generally been limited to relatively small datasets (at most about 100 sequences). Here, we repurpose BAli-Phy as a 'phylogeny-aware' alignment method: we estimate the phylogeny from the input of unaligned sequences, and then use that as a fixed tree within BAli-Phy. We show that this approach achieves high accuracy, greatly superior to Prank, the current most popular phylogeny-aware alignment method, and is even more accurate than MAFFT, one of the top performing alignment methods in common use. Furthermore, this approach can be used to align very large datasets (up to 1000 sequences in this study). See https://doi.org/10.13012/B2IDB-7863273_V1 for datasets used in this study. Supplementary data are available at Bioinformatics online.

A long-sought goal in structural biology has been the imaging of membrane proteins in their membrane environments. This goal has been achieved with electron crystallography in those special cases where a protein forms highly ordered arrays in lipid bilayers. It has also been achieved by NMR methods in proteins up to 50 kilodaltons (kDa) in size, although milligram quantities of protein and isotopic labelling are required. For structural analysis of large soluble proteins in microgram quantities, an increasingly powerful method that does not require crystallization is single-particle reconstruction from electron microscopy of cryogenically cooled samples (electron cryomicroscopy (cryo-EM)). Here we report the first single-particle cryo-EM study of a membrane protein, the human large-conductance calcium- and voltage-activated potassium channel (BK), in a lipid environment. The new method is called random spherically constrained (RSC) single-particle reconstruction. BK channels, members of the six-transmembrane-segment (6TM) ion channel family, were reconstituted at low density into lipid vesicles (liposomes), and their function was verified by a potassium flux assay. Vesicles were also frozen in vitreous ice and imaged in an electron microscope. From images of 8,400 individual protein particles, a three-dimensional (3D) reconstruction of the BK channel and its membrane environment was obtained at a resolution of 1.7-2.0 nm. Not requiring the formation of crystals, the RSC approach promises to be useful in the structural study of many other membrane proteins as well.

The coherent signal averaging process requires an accurate estimation of the fiducial point in all beats to be averaged. The temporal cross-correlation between the detected beat and a template beat is the typical alignment method used with high-resolution ECG (HRECG) records. However, this technique does not produce a precise fiducial mark in records with high noise levels. In this study, we propose a new alignment method based on the multi-scale cross-correlation between the wavelet transforms of the template and the detected beat, respectively. The wavelet and temporal methods were tested for several simulated records corrupted with white noise and electromyographic (EMG) noise of different RMS levels. The results indicate that wavelet alignment method produces a lower trigger jitter than the temporal method in all tests. We conclude that the proposed alignment method can be used in records with high noise levels, like those found in Holter HRECG systems.

Electron microscopy and X-ray crystallography are revealing the structure of photosystem II. Electron crystallography has yielded a 3D structure at sufficient resolution to identify subunit positioning and transmembrane organization of the reaction-centre core complex of spinach. Single-particle analyses are providing 3D structures of photosystem II-light-harvesting complex II supercomplexes that can be used to incorporate high-resolution structural data emerging from electron and X-ray crystallography. The positions of the chlorins and metal centres within photosystem II are now available. It can be concluded that photosystem II is a dimeric complex with the transmembrane helices of CP47/D2 proteins related to those of the CP43/D1 proteins by a twofold axis within each monomer. Further, both electron microscopy and X-ray analyses show that P(680) is not a 'special pair' and that cytochrome b559 is located on the D2 side of the reaction centres some distance from P(680). However, although comparison of the electron microscopy and X-ray models for spinach and Synechococcus elongatus show considerable similarities, there seem to be differences in the number and positioning of some small subunits.

Highly accurate estimation of phylogenetic trees for large data sets is difficult, in part because multiple sequence alignments must be accurate for phylogeny estimation methods to be accurate. Coestimation of alignments and trees has been attempted but currently only SATé estimates reasonably accurate trees and alignments for large data sets in practical time frames (Liu K., Raghavan S., Nelesen S., Linder C.R., Warnow T. 2009b. Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science. 324:1561-1564). Here, we present a modification to the original SATé algorithm that improves upon SATé (which we now call SATé-I) in terms of speed and of phylogenetic and alignment accuracy. SATé-II uses a different divide-and-conquer strategy than SATé-I and so produces smaller more closely related subsets than SATé-I; as a result, SATé-II produces more accurate alignments and trees, can analyze larger data sets, and runs more efficiently than SATé-I. Generally, SATé is a metamethod that takes an existing multiple sequence alignment method as an input parameter and boosts the quality of that alignment method. SATé-II-boosted alignment methods are significantly more accurate than their unboosted versions, and trees based upon these improved alignments are more accurate than trees based upon the original alignments. Because SATé-I used maximum likelihood (ML) methods that treat gaps as missing data to estimate trees and because we found a correlation between the quality of tree/alignment pairs and ML scores, we explored the degree to which SATé's performance depends on using ML with gaps treated as missing data to determine the best tree/alignment pair. We present two lines of evidence that using ML with gaps treated as missing data to optimize the alignment and tree produces very poor results. First, we show that the optimization problem where a set of unaligned DNA sequences is given and the output is the tree and alignment of those sequences that maximize likelihood under the Jukes-Cantor model is uninformative in the worst possible sense. For all inputs, all trees optimize the likelihood score. Second, we show that a greedy heuristic that uses GTR+Gamma ML to optimize the alignment and the tree can produce very poor alignments and trees. Therefore, the excellent performance of SATé-II and SATé-I is not because ML is used as an optimization criterion for choosing the best tree/alignment pair but rather due to the particular divide-and-conquer realignment techniques employed.