Local refinement: an attempt to correct for shrinkage and distortion in electron tomography

A critical problem in electron tomography is the deformation of the specimen due to radiation, or "shrinkage," which interferes with image alignment and thereby limits resolution. Here, we describe a general strategy for refining preliminary reconstructions which allows the damage due to the shrinkage of plastic-embedded thin sectioned specimens (50-80 nm) to be corrected. The basic steps of the strategy involve: (a) the partition of the preliminary reconstruction into sub-volumes; (b) the extraction of corresponding sub-areas for each sub-volume from the micrographs of the tilt series; (c) the re-projection of each sub-volume according to the orientation parameters; and (d) the refinement of these parameters by correlating each sub-area to the corresponding computed projection. We tested the strategy by refining chemical synapses reconstructed from series imaged with conical, double and single tilt geometries. The results gathered with local refinement were evaluated by visually inspecting the structure of biological membranes in the maps. In an effort to quantify these improvements, we studied the refined maps using correlation criteria and mapped the corrections applied to the orientation parameters in each sub-volume of the reconstruction. Simulation experiments complemented the data gathered by correlation analysis. Based on these criteria, we concluded that local refinement significantly improves the overall quality of the reconstructions of chemical synapses calculated from series imaged with conical and double tilt geometries.     

Top-down approach in protein RDC data analysis: <Emphasis Type="Italic">de novo</Emphasis> estimation of the alignment tensor

In solution NMR spectroscopy the residual dipolar coupling (RDC) is invaluable in improving both the precision and accuracy of NMR structures during their structural refinement. The RDC also provides a potential to determine protein structure de novo. These procedures are only effective when an accurate estimate of the alignment tensor has already been made. Here we present a top–down approach, starting from the secondary structure elements and finishing at the residue level, for RDC data analysis in order to obtain a better estimate of the alignment tensor. Using only the RDCs from N–H bonds of residues in α-helices and CA–CO bonds in β-strands, we are able to determine the offset and the approximate amplitude of the RDC modulation-curve for each secondary structure element, which are subsequently used as targets for global minimization. The alignment order parameters and the orientation of the major principal axis of individual helix or strand, with respect to the alignment frame, can be determined in each of the eight quadrants of a sphere. The following minimization against RDC of all residues within the helix or strand segment can be carried out with fixed alignment order parameters to improve the accuracy of the orientation. For a helical protein Bax, the three components A _xx , A _yy and A _zz , of the alignment order can be determined with this method in average to within 2.3% deviation from the values calculated with the available atomic coordinates. Similarly for β-sheet protein Ubiquitin they agree in average to within 8.5%. The larger discrepancy in β-strand parameters comes from both the diversity of the β-sheet structure and the lower precision of CA–CO RDCs. This top-down approach is a robust method for alignment tensor estimation and also holds a promise for providing a protein topological fold using limited sets of RDCs.     

Comparison of two alignment techniques within a single complex data set: POY versus Clustal

Sensitivity analyses can be performed with respect to different methodologies, differential analytical parameters or models within a single methodology, or alignment parameters. The latter investigations are particularly relevant when divergence and/or the size of molecular data sets make alignment of sequences difficult. Sensitivity analyses are often performed for analyses incorporating Direct Optimization (via POY), either to select optimal alignment parameters or to investigate the stability of topology across parameter sets. Such investigations are rarely, if ever, performed for Clustal alignments as some manual adjustments are nearly always incorporated in the final alignment. Exploration of the performance of both POY and Clustal for a large insect data set incorporating three genes (18S, 28S, H3) and morphology reveals that the performance of POY, as measured by and ILD metric, is predictable across the landscape topology with minimal incongruence when all parameters are treated equally. In contrast, Clustal alignment followed by parsimony analysis yields a landscape with less overall variance, but less predictable behaviour across the parameter topology. © The Willi Hennig Society 2005.     

A novel acetabular alignment guide for THR using selective anatomic landmarks on the pelvis

This paper presents a novel approach for acetabular alignment during the implant of a prosthetic hip joint in a natural pelvis. The alignment instrument uses selective anatomic bony landmarks on the pelvis, which are accessible in surgery, to guide the placement of the acetabular component in the appropriate orientation. A closed form solution, involving both a forward and reverse analysis, is presented to relate the parameters of the device with the abduction and anteversion angles. Using mathematical models, this device should allow the surgeon to place the acetabular component with an orientation between 10.9 degrees and 19.1 degrees anteversion and 35.7 degrees and 44.3 degrees abduction with 95% confidence in a male/left specimen for the commonly accepted target of 15 degrees anteversion and 40 degrees abduction. This device is currently being used successfully by one of the authors in THR surgery.     

An effortless procedure to align the local frame of an inertial measurement unit to the local frame of another motion capture system

Inertial measurement units (IMUs) offer great opportunities to analyze segmental and joints kinematics. When combined with another motion capture system (MCS), for example, to validate new IMU-based applications or to develop mixed systems, it is necessary to align the local frame of the IMU sensors to the local frame of the MCS. Currently, all alignment methods use landmarks on the IMU's casing. Therefore, they can only be used with well-documented IMUs and they are prone to error when the IMU's casing is small. This study proposes an effortless procedure to align the local frame of any IMU to the local frame of any other MCS able to measure the orientation of its local frame. The general concept of this method is to derive the gyroscopic angles for both devices during an alignment movement, and then to use an optimization algorithm to calculate the alignment matrix between both local frames. The alignment movement consists of rotations around three more or less orthogonal axes and it can easily be performed by hands. To test the alignment procedure, an IMU and a magnetic marker were attached to a plate, and 20 alignment movements were recorded. The maximum errors of alignment (accuracy±precision) were 1.02°±0.32° and simulations showed that the method was robust against noise that typically affect IMUs. In conclusion, this study describes an efficient alignment procedure that is quick and easy to perform, and that does not require any alignment device or any knowledge about the IMU casing.     

All-atom molecular dynamics simulations using orientational constraints from anisotropic NMR samples

Orientational constraints obtained from solid state NMR experiments on anisotropic samples are used here in molecular dynamics (MD) simulations for determining the structure and dynamics of several different membrane-bound molecules. The new MD technique is based on the inclusion of orientation dependent pseudo-forces in the COSMOS-NMR force field. These forces drive molecular rotations and re-orientations in the simulation, such that the motional time-averages of the tensorial NMR properties approach the experimentally measured parameters. The orientational-constraint-driven MD simulations are universally applicable to all NMR interaction tensors, such as chemical shifts, dipolar couplings and quadrupolar interactions. The strategy does not depend on the initial choice of coordinates, and is in principle suitable for any flexible molecule. To test the method on three systems of increasing complexity, we used as constraints some deuterium quadrupolar couplings from the literature on pyrene, cholesterol and an antimicrobial peptide embedded in oriented lipid bilayers. The MD simulations were able to reproduce the NMR parameters within experimental error. The alignment of the three membrane-bound molecules and some aspects of their conformation were thus derived from the NMR data, in good agreement with previous analyses. Furthermore, the new approach yielded for the first time the distribution of segmental orientations with respect to the membrane and the order parameter tensors of all three systems.     

Markov random field based automatic image alignment for electron tomography

We present a method for automatic full-precision alignment of the images in a tomographic tilt series. Full-precision automatic alignment of cryo electron microscopy images has remained a difficult challenge to date, due to the limited electron dose and low image contrast. These facts lead to poor signal to noise ratio (SNR) in the images, which causes automatic feature trackers to generate errors, even with high contrast gold particles as fiducial features. To enable fully automatic alignment for full-precision reconstructions, we frame the problem probabilistically as finding the most likely particle tracks given a set of noisy images, using contextual information to make the solution more robust to the noise in each image. To solve this maximum likelihood problem, we use Markov Random Fields (MRF) to establish the correspondence of features in alignment and robust optimization for projection model estimation. The resulting algorithm, called Robust Alignment and Projection Estimation for Tomographic Reconstruction, or RAPTOR, has not needed any manual intervention for the difficult datasets we have tried, and has provided sub-pixel alignment that is as good as the manual approach by an expert user. We are able to automatically map complete and partial marker trajectories and thus obtain highly accurate image alignment. Our method has been applied to challenging cryo electron tomographic datasets with low SNR from intact bacterial cells, as well as several plastic section and X-ray datasets.     

Multiple sequence alignment with hierarchical clustering.

An algorithm is presented for the multiple alignment of sequences, either proteins or nucleic acids, that is both accurate and easy to use on microcomputers. The approach is based on the conventional dynamic-programming method of pairwise alignment. Initially, a hierarchical clustering of the sequences is performed using the matrix of the pairwise alignment scores. The closest sequences are aligned creating groups of aligned sequences. Then close groups are aligned until all sequences are aligned in one group. The pairwise alignments included in the multiple alignment form a new matrix that is used to produce a hierarchical clustering. If it is different from the first one, iteration of the process can be performed. The method is illustrated by an example: a global alignment of 39 sequences of cytochrome c.     

Combined probabilistic and principal component analysis approach for multivariate sensitivity evaluation and application to implanted patellofemoral mechanics

Many aspects of biomechanics are variable in nature, including patient geometry, joint mechanics, implant alignment and clinical outcomes. Probabilistic methods have been applied in computational models to predict distributions of performance given uncertain or variable parameters. Sensitivity analysis is commonly used in conjunction with probabilistic methods to identify the parameters that most significantly affect the performance outcome; however, it does not consider coupled relationships for multiple output measures. Principal component analysis (PCA) has been applied to characterize common modes of variation in shape and kinematics. In this study, a novel, combined probabilistic and PCA approach was developed to characterize relationships between multiple input parameters and output measures. To demonstrate the benefits of the approach, it was applied to implanted patellofemoral (PF) mechanics to characterize relationships between femoral and patellar component alignment and loading and the resulting joint mechanics. Prior studies assessing PF sensitivity have performed individual perturbation of alignment parameters. However, the probabilistic and PCA approach enabled a more holistic evaluation of sensitivity, including identification of combinations of alignment parameters that most significantly contributed to kinematic and contact mechanics outcomes throughout the flexion cycle, and the predictive capability to estimate joint mechanics based on alignment conditions without requiring additional analysis. The approach showed comparable results for Monte Carlo sampling with 500 trials and the more efficient Latin Hypercube sampling with 50 trials. The probabilistic and PCA approach has broad applicability to biomechanical analysis and can provide insight into the interdependencies between implant design, alignment and the resulting mechanics.     

A performance comparison of data and memory allocation strategies for sequence aligners on NUMA architectures

Over the last several years, many sequence alignment tools have appeared and become popular for the fast evolution of next generation sequencing technologies. Obviously, researchers that use such tools are interested in getting maximum performance when they execute them in modern infrastructures. Today’s NUMA (Non-uniform memory access) architectures present major challenges in getting such applications to achieve good scalability as more processors/cores are used. The memory system in NUMA systems shows a high complexity and may be the main cause for the loss of an application’s performance. The existence of several memory banks in NUMA systems implies a logical increase in latency associated with the accesses of a given processor to a remote bank. This phenomenon is usually attenuated by the application of strategies that tend to increase the locality of memory accesses. However, NUMA systems may also suffer from contention problems that can occur when concurrent accesses are concentrated on a reduced number of banks. Sequence alignment tools use large data structures to contain reference genomes to which all reads are aligned. Therefore, these tools are very sensitive to performance problems related to the memory system. The main goal of this study is to explore the trade-offs between data locality and data dispersion in NUMA systems. We have performed experiments with several popular sequence alignment tools on two widely available NUMA systems to assess the performance of different memory allocation policies and data partitioning strategies. We find that there is not one method that is best in all cases. However, we conclude that memory interleaving is the memory allocation strategy that provides the best performance when a large number of processors and memory banks are used. In the case of data partitioning, the best results are usually obtained when the number of partitions used is greater, sometimes combined with an interleave policy.     

Diffusion anisotropy in collagen gels and tumors: the effect of fiber network orientation

The interstitial matrix is comprised of cross-linked collagen fibers, generally arranged in nonisotropic orientations. Spatial alignment of matrix components within the tissue can affect diffusion patterns of drugs. In this study, we developed a methodology for the calculation of diffusion coefficients of macromolecules and nanoparticles in collagenous tissues. The tissues are modeled as three-dimensional, stochastic, fiber networks with varying degrees of alignment. We employed a random walk approach to simulate diffusion and a Stokesian dynamics method to account for hydrodynamic hindrance. We performed our analysis for four different structures ranging from nearly isotropic to perfectly aligned. We showed that the overall diffusion coefficient is not affected by the orientation of the network. However, structural anisotropy results in diffusion anisotropy, which becomes more significant with increase in the degree of alignment, the size of the diffusing particle, and the fiber volume fraction. To test our model predictions we performed diffusion measurements in reconstituted collagen gels and tumor xenografts. We measured fiber alignment and diffusion with second harmonic generation and multiphoton fluorescent recovery after photobleaching techniques, respectively. The results showed for the first time in tumors that the structure and orientation of collagen fibers in the extracellular space leads to diffusion anisotropy.     

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.     

Multiple alignment by aligning alignments

MOTIVATION: Multiple sequence alignment is a fundamental task in bioinformatics. Current tools typically form an initial alignment by merging subalignments, and then polish this alignment by repeated splitting and merging of subalignments to obtain an improved final alignment. In general this form-and-polish strategy consists of several stages, and a profusion of methods have been tried at every stage. We carefully investigate: (1) how to utilize a new algorithm for aligning alignments that optimally solves the common subproblem of merging subalignments, and (2) what is the best choice of method for each stage to obtain the highest quality alignment. RESULTS: We study six stages in the form-and-polish strategy for multiple alignment: parameter choice, distance estimation, merge-tree construction, sequence-pair weighting, alignment merging, and polishing. For each stage, we consider novel approaches as well as standard ones. Interestingly, the greatest gains in alignment quality come from (i) estimating distances by a new approach using normalized alignment costs, and (ii) polishing by a new approach using 3-cuts. Experiments with a parameter-value oracle suggest large gains in quality may be possible through an input-dependent choice of alignment parameters, and we present a promising approach for building such an oracle. Combining the best approaches to each stage yields a new tool we call Opal that on benchmark alignments matches the quality of the top tools, without employing alignment consistency or hydrophobic gap penalties. AVAILABILITY: Opal, a multiple alignment tool that implements the best methods in our study, is freely available at http://opal.cs.arizona.edu.     

An approach to the synthesis and attachment of scillabiose to steroids

Hellebrin and transvaalin are two naturally occurring saponins with biological activity. In the present paper, we describe a high yielding route to the synthesis and coupling of their shared glycone, scillabiose, to a model steroid. A convergent coupling strategy utilizing a scillabiose-based glycosyl donor was devised for the glycosylation. This convergent approach is appealing due to its high efficiency and simple deprotection procedure and may find further use in total synthesis of naturally occurring saponins and related compounds sharing the same glycone. Due to the widespread occurrence of this glycone in nature, the complete NMR spectroscopic characterization of all compounds prepared herein is provided as reference material. In addition, glycosylations were performed with the monosaccharide constituents of scillabiose, thereby providing a limited series of glycosylated steroids for potential future evaluation of the effects of the glycone on the overall biological activity.     

A strategy for the rapid multiple alignment of protein sequences. Confidence levels from tertiary structure comparisons

An algorithm is presented for the multiple alignment of protein sequences that is both accurate and rapid computationally. The approach is based on the conventional dynamic-programming method of pairwise alignment. Initially, two sequences are aligned, then the third sequence is aligned against the alignment of both sequences one and two. Similarly, the fourth sequence is aligned against one, two and three. This is repeated until all sequences have been aligned. Iteration is then performed to yield a final alignment. The accuracy of sequence alignment is evaluated from alignment of the secondary structures in a family of proteins. For the globins, the multiple alignment was on average 99% accurate compared to 90% for pairwise comparison of sequences. For the alignment of immunoglobulin constant and variable domains, the use of many sequences yielded an alignment of 63% average accuracy compared to 41% average for individual variable/constant alignments. The multiple alignment algorithm yields an assignment of disulphide connectivity in mammalian serotransferrin that is consistent with crystallographic data, whereas pairwise alignments give an alternative assignment.     

A quantile method for sizing optical maps.

Optical mapping is an integrated system for the analysis of single DNA molecules. It constructs restriction maps (noted as "optical map" ) from individual DNA molecules presented on surfaces after they are imaged by fluorescence microscopy. Because restriction digestion and fluorochrome staining are performed after molecules are mounted, resulting restriction fragments retain their order. Maps of fragment sizes and order are constructed by image processing techniques employing integrated fluorescence intensity measurements. Such analysis, in place of molecular length measurements, obviates need for uniformly elongated molecules, but requires samples containing small fluorescent reference molecules for accurate sizing. Although robust in practice, elimination of internal reference molecules would reduce errors and extend single molecule analysis to other platforms. In this paper, we introduce a new approach that does not use reference molecules for direct estimation of restriction fragment sizes, by the exploitation of the quantiles associated with their expected distribution. We show that this approach is comparable to the current reference-based method as evaluated by map alignment techniques in terms of the rate of placement of optical maps to published sequence.     

Optimizing read mapping to reference genomes to determine composition and species prevalence in microbial communities

The Human Microbiome Project (HMP) aims to characterize the microbial communities of 18 body sites from healthy individuals. To accomplish this, the HMP generated two types of shotgun data: reference shotgun sequences isolated from different anatomical sites on the human body and shotgun metagenomic sequences from the microbial communities of each site. The alignment strategy for characterizing these metagenomic communities using available reference sequence is important to the success of HMP data analysis. Six next-generation aligners were used to align a community of known composition against a database comprising reference organisms known to be present in that community. All aligners report nearly complete genome coverage (>97%) for strains with over 6X depth of coverage, however they differ in speed, memory requirement and ease of use issues such as database size limitations and supported mapping strategies. The selected aligner was tested across a range of parameters to maximize sensitivity while maintaining a low false positive rate. We found that constraining alignment length had more impact on sensitivity than does constraining similarity in all cases tested. However, when reference species were replaced with phylogenetic neighbors, similarity begins to play a larger role in detection. We also show that choosing the top hit randomly when multiple, equally strong mappings are available increases overall sensitivity at the expense of taxonomic resolution. The results of this study identified a strategy that was used to map over 3 tera-bases of microbial sequence against a database of more than 5,000 reference genomes in just over a month.     

Identification of correct regions in protein models using structural, alignment, and consensus information

In this study we present two methods to predict the local quality of a protein model: ProQres and ProQprof. ProQres is based on structural features that can be calculated from a model, while ProQprof uses alignment information and can only be used if the model is created from an alignment. In addition, we also propose a simple approach based on local consensus, Pcons-local. We show that all these methods perform better than state-of-the-art methodologies and that, when applicable, the consensus approach is by far the best approach to predict local structure quality. It was also found that ProQprof performed better than other methods for models based on distant relationships, while ProQres performed best for models based on closer relationship, i.e., a model has to be reasonably good to make a structural evaluation useful. Finally, we show that a combination of ProQprof and ProQres (ProQlocal) performed better than any other nonconsensus method for both high- and low-quality models. Additional information and Web servers are available at: http://www.sbc.su.se/~bjorn/ProQ/.     

A non-directed approach to the differential analysis of multiple LC–MS-derived metabolic profiles

An essential element of any strategy for non-targeted metabolomics analysis of complex biological extracts is the capacity to perform comparisons between large numbers of samples. As the most widely used technologies are all based on mass spectrometry (e.g. GCMS, LCMS), this entails that we must be able to compare reliably and (semi)automatically large series of chromatographic mass spectra from which compositional differences are to be extracted in a statistically justifiable manner. In this paper we describe a novel approach for the extraction of relevant information from multiple full-scan metabolic profiles derived from LC–MS analyses. Specifically-designed software has made it possible to combine all mass peaks on the basis of retention time and m/z values only, without prior identification, to produce a data matrix output which can then be used for multivariate statistical analysis. To demonstrate the capacity of this approach, aqueous methanol extracts from potato tuber tissues of eight contrasting genotypes, harvested at two developmental stages have been used. Our results showed that it is possible to discover reproducibly discriminatory mass peaks related both to the genetic origin of the material as well as the developmental stage at which it was harvested. In addition the limitations of the approach are explored by a careful evaluation of the alignment quality.     

Determining rigid body transformation parameters from ill-conditioned spatial marker co-ordinates

The three-dimensional location of a body-fixed axis system is described by position and orientation parameters that can be calculated knowing local and global coordinates of three or more body-fixed markers. However, marker distribution can become ill-conditioned when marker placement is symmetrical with respect to the mean of the markers. As symmetry and ill-conditioning increases, random errors in marker locations can affect the stability of orientation parameters as a result of the mathematical approach adopted. The present study investigates the methods of Veldpaus et al. [1988; Journal of Biomechanics 21, 45], Challis [1995; Biomechanics 28, 733] and Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] for obtaining segment orientation parameters when segment markers ranged from well-defined to highly ill-conditioned depending on the symmetry of segment markers. A novel fourth approach is also presented that enabled comparisons of the root mean square error of reconstructed marker coordinates to verify that an optimal solution was obtained. No single method produced optimal results for all axis orientation parameters when reconstructing movement trials. The best performed was the method of Veldpaus et al. [1988; Journal of Biomechanics 21, 45] based on consistent results and ease of implementation. The fourth approach presented provided a reliable method in all but the highly ill-conditioned markers, however implementation was computationally difficult. The method of Challis [1995; Biomechanics 28, 733] was only suited to well-conditioned marker sets which avoided markers lying in a single plane with symmetries in marker distribution relative to the mean. The method of Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] produced, at best, orientation parameters that approximated the results obtained by least squares methods.