Protein structure-structure alignment with discrete Fréchet distance

Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is well known that the Hausdorff distance is useful for matching two point sets, and that the Fréchet distance is a superior measure for matching two polygonal chains. The discrete Fréchet distance closely approximates the (continuous) Fréchet distance, and is a natural measure for the geometric similarity of the folded 3D structures of biomolecules such as proteins. In this paper, we present new algorithms for matching two polygonal chains in two dimensions to minimize their discrete Fréchet distance under translation and rotation, and an effective heuristic for matching two polygonal chains in three dimensions. We also describe our empirical results on the application of the discrete Fréchet distance to protein structure-structure alignment.     

Kalign – an accurate and fast multiple sequence alignment algorithm

Background  

The alignment of multiple protein sequences is a fundamental step in the analysis of biological data. It has traditionally been applied to analyzing protein families for conserved motifs, phylogeny, structural properties, and to improve sensitivity in homology searching. The availability of complete genome sequences has increased the demands on multiple sequence alignment (MSA) programs. Current MSA methods suffer from being either too inaccurate or too computationally expensive to be applied effectively in large-scale comparative genomics.     

Is multiple-sequence alignment required for accurate inference of phylogeny?

The process of inferring phylogenetic trees from molecular sequences almost always starts with a multiple alignment of these sequences but can also be based on methods that do not involve multiple sequence alignment. Very little is known about the accuracy with which such alignment-free methods recover the correct phylogeny or about the potential for increasing their accuracy. We conducted a large-scale comparison of ten alignment-free methods, among them one new approach that does not calculate distances and a faster variant of our pattern-based approach; all distance-based alignment-free methods are freely available from http://www.bioinformatics.org.au (as Python package decaf+py). We show that most methods exhibit a higher overall reconstruction accuracy in the presence of high among-site rate variation. Under all conditions that we considered, variants of the pattern-based approach were significantly better than the other alignment-free methods. The new pattern-based variant achieved a speed-up of an order of magnitude in the distance calculation step, accompanied by a small loss of tree reconstruction accuracy. A method of Bayesian inference from k-mers did not improve on classical alignment-free (and distance-based) methods but may still offer other advantages due to its Bayesian nature. We found the optimal word length k of word-based methods to be stable across various data sets, and we provide parameter ranges for two different alphabets. The influence of these alphabets was analyzed to reveal a trade-off in reconstruction accuracy between long and short branches. We have mapped the phylogenetic accuracy for many alignment-free methods, among them several recently introduced ones, and increased our understanding of their behavior in response to biologically important parameters. In all experiments, the pattern-based approach emerged as superior, at the expense of higher resource consumption. Nonetheless, no alignment-free method that we examined recovers the correct phylogeny as accurately as does an approach based on maximum-likelihood distance estimates of multiply aligned sequences.     

How well does the HoT score reflect sequence alignment accuracy?

Multiple sequence alignment is an essential tool in many areas of biological research, and the accuracy of an alignment can strongly affect the accuracy of a downstream application such as phylogenetic analysis, identification of functional motifs, or polymerase chain reaction primer design. The heads or tails (HoT) method (Landan G, Graur D. 2007. Heads or tails: a simple reliability check for multiple sequence alignments. Mol Biol Evol. 24:1380-1383.) assesses the consistency of an alignment by comparing the alignment of a set of sequences with the alignment of the same set of sequences written in reverse order. This study shows that HoT scores and the alignment accuracies are positively correlated, so alignments with higher HoT scores are preferable. However, HoT scores are overestimates of alignment accuracy in general, with the extent of overestimation depending on the method used for multiple sequence alignment.     

Where did the BLOSUM62 alignment score matrix come from?

Many sequence alignment programs use the BLOSUM62 score matrix to score pairs of aligned residues. Where did BLOSUM62 come from?     

The structural alignment between two proteins: is there a unique answer?

Structurally similar but sequentially unrelated proteins have been discovered and rediscovered by many researchers, using a variety of structure comparison tools. For several pairs of such proteins, existing structural alignments obtained from the literature, as well as alignments prepared using several different similarity criteria, are compared with each other. It is shown that, in general, they differ from each other, with differences increasing with diminishing sequence similarity. Differences are particularly strong between alignments optimizing global similarity measures, such as RMS deviation between C alpha atoms, and alignments focusing on more local features, such as packing or interaction pattern similarity. Simply speaking, by putting emphasis on different aspects of structure, different structural alignments show the unquestionable similarity in a different way. With differences between various alignments extending to a point where they can differ at all positions, analysis of structural similarities leads to contradictory results reported by groups using different alignment techniques. The problem of uniqueness and stability of structural alignments is further studied with the help of visualization of the suboptimal alignments. It is shown that alignments are often degenerate and whole families of alignments can be generated with almost the same score as the "optimal alignment." However, for some similarity criteria, specially those based on side-chain positions, rather than C alpha positions, alignments in some areas of the protein are unique. This opens the question of how and if the structural alignments can be used as "standards of truth" for protein comparison.     

RNA global alignment in the joint sequence–structure space using elastic shape analysis

The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence–structure–function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence–structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.     

Studies on the rules of β-strand alignment in a protein β-sheet structure

To further disclose the underlying mechanisms of protein β-sheet formation, studies were made on the rules of β-strands alignment forming β-sheet structure using statistical and machine learning approaches. Firstly, statistical analysis was performed on the sum of β-strands between each β-strand pairs in protein sequences. The results showed a propensity of near-neighbor pairing (or called “first come first pair”) in the β-strand pairs. Secondly, based on the same dataset, the pairwise cross-combinations of real β-strand pairs and four pseudo-β-strand contained pairs were classified by support vector machine (SVM). A novel feature extracting approach was designed for classification using the average amino acid pairing encoding matrix (APEM). Analytical results of the classification indicated that a segment of β-strand had the ability to distinguish β-strands from segments of α-helix and coil. However, the result also showed that a β-strand was not strongly conserved to choose its real partner from all the alternative β-strand partners, which was corresponding with the ordination results of the statistical analysis each other. Thus, the rules of “first come first pair” propensity and the non-conservative ability to choose real partner, were possible important factors affecting the β-strands alignment forming β-sheet structures.     

Do alignment thresholds define a critical boundary in long-range detection facilitation with co-linear lines?

Thresholds for line contrast detection (experiment 2) were measured with a two-alternative temporal forced-choice procedure as a function of the spatial position of a vertical target line with regard to two co-linear context lines. The different spatial positions of the target line corresponded to values near the position discrimination threshold (experiment 1) reflecting the just detectable lateral offset, or non-co-linearity, between the context lines which were vertically separated by about 100 minutes of visual arc. Target and context lines were vertically separated by about 30 minutes of arc, had equal contrast polarity in one case, and opposite contrast polarity in the other. Strong line contrast detection facilitation is found at perceptually co-linear target locations. This facilitation decreases noticeably at a horizontal target offset that corresponds to the alignment threshold measured with the context lines. The effects are independent of the relative contrast polarity of target and context and, as shown in a third experiment, also independent of both the relative length or number of lines, and the magnitude of their absolute co-axial separation. This independence seems to hold, provided individual line length and co-axial distance between lines are larger than what appears to be the lower limit of the long-range spatial domain for orientation or contour integration (i.e. 20 minutes of arc), as determined by previous studies. The findings reported here suggest that alignment thresholds are likely to define a critical lateral boundary in long-range detection facilitation with co-linear lines. They support models of contour integration based on interactions between neural mechanisms that integrate local signals of contrast, orientation, and relative position or end-to-end alignment. Such mechanisms may help to explain the formation of representations of virtual contours and object contours in human perception.     

4SALE – A tool for synchronous RNA sequence and secondary structure alignment and editing

Background  

In sequence analysis the multiple alignment builds the fundament of all proceeding analyses. Errors in an alignment could strongly influence all succeeding analyses and therefore could lead to wrong predictions. Hand-crafted and hand-improved alignments are necessary and meanwhile good common practice. For RNA sequences often the primary sequence as well as a secondary structure consensus is well known, e.g., the cloverleaf structure of the t-RNA. Recently, some alignment editors are proposed that are able to include and model both kinds of information. However, with the advent of a large amount of reliable RNA sequences together with their solved secondary structures (available from e.g. the ITS2 Database), we are faced with the problem to handle sequences and their associated secondary structures synchronously.     

Reconstitution and alignment by a magnetic field of a β-barrel membrane protein in bicelles

A protocol is described for the reconstitution of a transmembrane β-barrel protein domain, tOmpA, into lipid bicelles. tOmpA is the largest protein to be reconstituted in bicelles to date. Its insertion does not prevent bicelles from orienting with their plane either parallel or perpendicular to the magnetic field, depending on the absence or presence of paramagnetic ions. In the latter case, tOmpA is shown to align with the axis of the β-barrel parallel to the magnetic field, i.e. perpendicular to the plane of the bilayer, an orientation conforming to that in natural membranes and favourable to structural studies by solid-state NMR. Reconstitution into bicelles may offer an interesting approach for structural studies of membrane proteins in a medium resembling a biological membrane, using either NMR or other biophysical techniques. Our data suggest that alignment in the magnetic field of membrane proteins included into bicelles may be facilitated if the protein is folded as a β-barrel structure.     

Zero field resonance and spin alignment of the triplet state of chloroplasts at 2°K

Microwave induced transitions in zero magnetic field have been observed in the photoinduced triplet of chloroplasts treated with dithionite by monitoring changes in the intensity of the 735 nm fluorescence band at 2°K. Similar results were obtained with chloroplasts treated with hydroxylamine plus 3-(3,4-dichlorophenyl)-1,1-dimethylurea and preillumination. The zero field parameters are $\text{D = 0.02794 ± 0.00007}\text{cm}{}^{\mathrm{?1}}$, $\text{E = 0.00382 ± 0.00007}\text{cm}{}^{\mathrm{?1}}$, i.e. equal to those of monomeric chlorophyll $\text{a}$ to within the experimental error. The photoinduced triplet appears to be linked to Photosystem II. This indicates that the low temperature 735 nm fluorescence band of chloroplasts is at least partly due to Photosystem II.     

Conformational dynamics and alignment properties of loop lanthanide-binding-tags (LBTs) studied in interleukin-1β

Encodable lanthanide binding tags (LBTs) have become an attractive tool in modern structural biology as they can be expressed as fusion proteins of targets of choice. Previously, we have demonstrated the feasibility of inserting encodable LBTs into loop positions of interleukin-1β (Barthelmes et al. in J Am Chem Soc 133:808–819, 2011). Here, we investigate the differences in fast dynamics of selected loop-LBT interleukin-1β constructs by measuring ¹⁵N nuclear spin relaxation experiments. We show that the loop-LBT does not significantly alter the dynamic motions of the host protein in the sub-τ_c-timescale and that the loop-LBT adopts a rigid conformation with significantly reduced dynamics compared to the terminally attached encodable LBT leading to increased paramagnetic alignment strength. We further analyze residual dipolar couplings (RDCs) obtained by loop-LBTs and additional liquid crystalline media to assess the applicability of the loop-LBT approach for RDC-based methods to determine structure and dynamics of proteins, including supra-τc dynamics. Using orthogonalized linear combinations (OLCs) of RDCs and Saupe matrices, we show that the combined use of encodable LBTs and external alignment media yields up to five linear independent alignments.     

Domain cooperativity in multidomain proteins: what can we learn from molecular alignment in anisotropic media?

Many proteins have modular design with multiple globular domains connected via flexible linkers. As a simple model of such system, we study a tandem construct consisting of two identical SH3 domains and a variable-length Gly/Ser linker. When the linker is short, this construct represents a dumbbell-shaped molecule with limited amount of domain-domain mobility. Due to its elongated shape, this molecule efficiently aligns in steric alignment media. As the length of the linker increases, the two domains become effectively uncoupled and begin to behave as independent entities. Consequently, their degree of alignment drops, approaching that found in the (near-spherical) isolated SH3 domains. To model the dependence of alignment parameters on the length of the interdomain linker, we have generated in silico a series of conformational ensembles representing SH3 tandems with different linker length. These ensembles were subsequently used as input for alignment prediction software PALES. The predicted alignment tensors were compared with the results of experimental measurements using a series of tandem-SH3 samples in PEG/hexanol alignment media. This comparison broadly confirmed the expected trends. At the same time, it has been found that the isolated SH3 domain aligns much stronger than expected. This finding can be attributed to complex morphology of the PEG/hexanol media and/or to weak site-specific interactions between the protein and the media. In the latter case, there are strong indications that electrostatic interactions may play a role. The fact that PEG/hexanol does not behave as a simple steric media should serve as a caution for studies that use PALES as a quantitative prediction tool (especially for disordered proteins). Further progress in this area depends on our ability to accurately model the anisotropic media and its site-specific interactions with protein molecules. Once this ability is improved, it should be possible to use the alignment parameters as a measure of domain-domain cooperativity, thus identifying the situations where two domains transiently interact with each other or become coupled through a partially structured linker.     

Are special read alignment strategies necessary and cost-effective when handling sequencing reads from patient-derived tumor xenografts?

Background

Patient-derived tumor xenografts in mice are widely used in cancer research and have become important in developing personalized therapies. When these xenografts are subject to DNA sequencing, the samples could contain various amounts of mouse DNA. It has been unclear how the mouse reads would affect data analyses. We conducted comprehensive simulations to compare three alignment strategies at different mutation rates, read lengths, sequencing error rates, human-mouse mixing ratios and sequenced regions. We also sequenced a nasopharyngeal carcinoma xenograft and a cell line to test how the strategies work on real data.

Results

We found the "filtering" and "combined reference" strategies performed better than aligning reads directly to human reference in terms of alignment and variant calling accuracies. The combined reference strategy was particularly good at reducing false negative variants calls without significantly increasing the false positive rate. In some scenarios the performance gain of these two special handling strategies was too small for special handling to be cost-effective, but it was found crucial when false non-synonymous SNVs should be minimized, especially in exome sequencing.

Conclusions

Our study systematically analyzes the effects of mouse contamination in the sequencing data of human-in-mouse xenografts. Our findings provide information for designing data analysis pipelines for these data.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-1172) contains supplementary material, which is available to authorized users.     

Using ESTs for phylogenomics: Can one accurately infer a phylogenetic tree from a gappy alignment?

Background

Specialised leaf-eating is almost universally regarded as the ancestral state of all ruminants, yet little evidence can be cited in support of this assumption, apart from the fact that all early ruminants had low crowned cheek teeth. Instead, recent years have seen the emergence evidence contradicting the conventional view that low tooth crowns always indicate leaf-eating and high tooth crowns grass-eating.

Results

Here we report the results of two independent palaeodietary reconstructions for one of the earliest deer, Procervulus ginsburgi from the Early Miocene of Spain, suggesting that despite having lower tooth crowns than any living ruminant, this species included a significant proportion of grass in its diet.

Conclusion

The phylogenetic distribution of feeding styles strongly supports that leaf-grass mixed feeding was the original feeding style of deer, and that later dietary specialization on leaves or grass occurred independently in several lineages. Evidence for other ruminant clades suggests that facultative mixed feeding may in fact have been the primitive dietary state of the Ruminantia, which would have been morphologically expressed only under specific environmental factors.     

Cattle on pastures do align along the North–South axis, but the alignment depends on herd density

Alignment is a spontaneous behavioral preference of particular body orientation that may be seen in various vertebrate or invertebrate taxa. Animals often optimize their positions according to diverse directional environmental factors such as wind, stream, slope, sun radiation, etc. Magnetic alignment represents the simplest directional response to the geomagnetic field and a growing body of evidence of animals aligning their body positions according to geomagnetic lines whether at rest or during feedings is accumulating. Recently, with the aid of Google Earth application, evidence of prevailing North–South (N–S) body orientation of cattle on pastures was published (Begall et al. PNAS 105:13451–13455, 2008; Burda et al. PNAS 106:5708–5713, 2009). Nonetheless, a subsequent study from a different laboratory did not confirm this phenomenon (Hert et al. J Comp Physiol A 197:677–682, 2011). The aim of our study was to enlarge the pool of independently gained data on this remarkable animal behavior. By satellite snapshots analysis and using blinded protocol we scored positions of 2,235 individuals in 74 herds. Our results are in line with the original findings of prevailing N–S orientation of grazing cattle. In addition, we found that mutual distances between individual animals within herds (herd density) affect their N–S preference—a new phenomenon giving some insight into biological significance of alignment.     

The α-helix alignment of proteins in water solution toward a high-frequency electromagnetic field: A FTIR spectroscopy study

The aim of this article was to study the effects of mobile phone electromagnetic waves at 1750 MHz on the Amide I and Amide II vibration bands of some proteins in bidistilled water solution by means of Fourier transform infrared (FTIR) spectroscopy and Fourier self-deconvolution (FSD) analysis. The proteins that were used for the experiment were hemoglobin, myoglobin, bovine serum albumin and lysozyme.

The exposure system consisted of microwaves emitted by an operational mobile phone at the frequency at 1750 MHz at the average power density of 1 W/m². Exposed and control samples were analyzed using FTIR spectroscopy and FSD analysis. The main result was that Amide I band of the proteins that were used increased significantly (p < 0.05) after 4 h of exposure to MWs, whereas Amide II band did not change significantly. This result can be explained assuming that the α-helix structure of the proteins aligned itself with the direction of the electromagnetic field due to the alignment of C = O stretching and N ? H bending ligands that are oriented along with the α-helix axis that give rise to the Amide I mode.