Determination of the residue-specific 15N CSA tensor principal components using multiple alignment media

The individual components of the backbone ¹⁵N CSA tensor, σ₁₁, σ₂₂, σ₃₃, and the orientation of σ₁₁ relative to the NH bond described by the angle β have been determined for uniformly labeled ¹⁵N, ¹³C ubiquitin from partial alignment in phospholipid bicelles, Pf1 phage, and poly(ethylene glycol) by measuring the residue-specific residual dipolar couplings and chemical shift deviations. No strong correlation between any of the CSA tensor components is observed with any single structural feature. However, the experimentally determined tensor components agree with the previously determined average CSA principal components [Cornilescu and Bax (2000) J. Am. Chem. Soc. 122, 10143–10154]. Significant deviations from the averages coincide with residues in β-strand or extended regions, while α-helical residue tensor components cluster close to the average values.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Fitting experimental data to models that use morphological data from public databases

Ideally detailed neuron models should make use of morphological and electrophysiological data from the same cell. However, this rarely happens. Typically a modeler will choose a cell morphology from a public database, assign standard values for R _a, C _m, and other parameters and then do the modeling study. The assumption is that the model will produce results representative of what might be obtained experimentally. To test this assumption we developed models of CA1 hippocampal pyramidal neurons using 4 different morphologies obtained from 3 public databases. The multiple run fitter in NEURON was used to fit parameter values in each of the 4 morphological models to match experimental data recorded from 19 CA1 pyramidal cells. Fits with fixed standard parameter values produced results that were generally not representative of our experimental data. However, when parameter values were allowed to vary, excellent fits were obtained in almost all cases, but the fitted parameter values were very different among the 4 reconstructions and did not match standard values. The differences in fitted values can be explained by very different diameters, total lengths, membrane areas and volumes among the reconstructed cells, reflecting either cell heterogeneity or issues with the reconstruction data. The fitted values compensated for these differences to make the database cells and experimental cells more similar electrotonically. We conclude that models using fully reconstructed morphologies need to be calibrated with experimental data (even when morphological and electrophysiological data come from the same cell), model results should be generated with multiple reconstructions, morphological and experimental cells should come from the same strain of animal at the same age, and blind use of standard parameter values in models that use reconstruction data may not produce representative experimental results. Action Editor: Steve Redman     

Combining partial order alignment and progressive multiple sequence alignment increases alignment speed and scalability to very large alignment problems

MOTIVATION: Partial order alignment (POA) has been proposed as a new approach to multiple sequence alignment (MSA), which can be combined with existing methods such as progressive alignment. This is important for addressing problems both in the original version of POA (such as order sensitivity) and in standard progressive alignment programs (such as information loss in complex alignments, especially surrounding gap regions). RESULTS: We have developed a new Partial Order-Partial Order alignment algorithm that optimally aligns a pair of MSAs and which therefore can be applied directly to progressive alignment methods such as CLUSTAL. Using this algorithm, we show the combined Progressive POA alignment method yields results comparable with the best available MSA programs (CLUSTALW, DIALIGN2, T-COFFEE) but is far faster. For example, depending on the level of sequence similarity, aligning 1000 sequences, each 500 amino acids long, took 15 min (at 90% average identity) to 44 min (at 30% identity) on a standard PC. For large alignments, Progressive POA was 10-30 times faster than the fastest of the three previous methods (CLUSTALW). These data suggest that POA-based methods can scale to much larger alignment problems than possible for previous methods. AVAILABILITY: The POA source code is available at http://www.bioinformatics.ucla.edu/poa     

Fitting bent lines to data, with applications to allometry

Change-point models, in which a linear or non-linear relation is generalized by allowing it to change at a point not fixed in advance, are of growing importance in allometric and other types of modeling. Frequently, the change-point is picked "by eye" and separate regressions are run for each resultant subdomain. This procedure is deficient, however, for the following reasons: first, a repeatable and objective procedure for estimating the change-point has not been used; second, the subsequent analysis usually does not take into account the fact that the change-point is estimated from the data; and last, the usually desirable requirement of continuity at the change-point is ignored. This paper describes various methods for jointly estimating linear relations and the intervening change-point from the data. In the simplest case, with normal errors and a linear relation of one variable upon another, this amounts to fitting a "bent line" via least squares techniques. In addition, tests and graphical diagnostics for the presence of change-points are presented. An example is given where a change-point and slopes are estimated for the relation of running speed with size among land mammals. In the past, these data have been fit with a straight line or a parabola. It is shown here that superior fit and interpretability are achieved using a change-point model.     

Fitting numerical solutions of differential equations to experimental data: a case study and some general remarks

A simple and efficient algorithm for least-squares estimation of the parameters of a numerically solved diffusion model is presented. The algorithm has been specially developed for the analysis of data obtained by vitreous fluorophotometry (a method in clinical eye research), but it has several straightforward generalizations which are also outlined in the paper.     

Discovering large conserved functional components in global network alignment by graph matching

Background

Aligning protein-protein interaction (PPI) networks is very important to discover the functionally conserved sub-structures between different species. In recent years, the global PPI network alignment problem has been extensively studied aiming at finding the one-to-one alignment with the maximum matching score. However, finding large conserved components remains challenging due to its NP-hardness.

Results

We propose a new graph matching method GMAlign for global PPI network alignment. It first selects some pairs of important proteins as seeds, followed by a gradual expansion to obtain an initial matching, and then it refines the current result to obtain an optimal alignment result iteratively based on the vertex cover. We compare GMAlign with the state-of-the-art methods on the PPI network pairs obtained from the largest BioGRID dataset and validate its performance. The results show that our algorithm can produce larger size of alignment, and can find bigger and denser common connected subgraphs as well for the first time. Meanwhile, GMAlign can achieve high quality biological results, as measured by functional consistency and semantic similarity of the Gene Ontology terms. Moreover, we also show that GMAlign can achieve better results which are structurally and biologically meaningful in the detection of large conserved biological pathways between species.

Conclusions

GMAlign is a novel global network alignment tool to discover large conserved functional components between PPI networks. It also has many potential biological applications such as conserved pathway and protein complex discovery across species. The GMAlign software and datasets are avaialbile at https://github.com/yzlwhu/GMAlign.

     

Constrained multiple sequence alignment tool development and its application to RNase family alignment

In this paper, we design a heuristic algorithm of computing a constrained multiple sequence alignment (CMSA for short) for guaranteeing that the generated alignment satisfies the user-specified constraints that some particular residues should be aligned together. If the number of residues needed to be aligned together is a constant alpha, then the time-complexity of our CMSA algorithm for aligning K sequences is O(alphaKn(4)), where n is the maximum of the lengths of sequences. In addition, we have built up such a CMSA software system and made several experiments on the RNase sequences, which mainly function in catalyzing the degradation of RNA molecules. The resulting alignments illustrate the practicability of our method.     

Optimal alignment between groups of sequences and its application to multiple sequence alignment

Four algorithms, A–D, were developed to align two groupsof biological sequences. Algorithm A is equivalent to the conventionaldynamic programming method widely used for aligning ordinarysequences, whereas algorithms B – D are designed to evaluatethe cost for a deletion/insertion more accurately when internalgaps are present in either or both groups of sequences. Rigorousoptimization of the ‘sum of pairs’ (SP) score isachieved by algorithm D, whose average performance is closeto O(MNL²) where M and N are numbers of sequences included inthe two groups and L is the mean length of the sequences. AlgorithmB uses some app mximations to cope with profile-based operations,whereas algorithm C is a simpler variant of algorithm D. Thesegroup-to-group alignment algorithms were applied to multiplesequence alignment with two iterative strategies: a progressivemethod based on a given binary tree and a randomized grouping-realignmentmethod. The advantages and disadvantages of the four algorithmsare discussed on the basis of the results of exatninations ofseveral protein families.     

Fitting Regression Models to Ordinal Data

This paper deals with the analysis of ordinal data by means of a threshold model. Maximum likelihood estimation is discussed and two examples are used to illustrate the methods.     

A word-oriented approach to alignment validation

MOTIVATION: Multiple sequence alignment at the level of whole proteomes requires a high degree of automation, precluding the use of traditional validation methods such as manual curation. Since evolutionary models are too general to describe the history of each residue in a protein family, there is no single algorithm/model combination that can yield a biologically or evolutionarily optimal alignment. We propose a 'shotgun' strategy where many different algorithms are used to align the same family, and the best of these alignments is then chosen with a reliable objective function. We present WOOF, a novel 'word-oriented' objective function that relies on the identification and scoring of conserved amino acid patterns (words) between pairs of sequences. RESULTS: Tests on a subset of reference protein alignments from BAliBASE showed that WOOF tended to rank the (manually curated) reference alignment highest among 1060 alternative (automatically generated) alignments for a majority of protein families. Among the automated alignments, there was a strong positive relationship between the WOOF score and similarity to the reference alignment. The speed of WOOF and its independence from explicit considerations of three-dimensional structure make it an excellent tool for analyzing large numbers of protein families. AVAILABILITY: On request from the authors.     

Fitting Circles and Spheres to Coordinate Measuring Machine Data

This work addresses the problem of enclosing given data points between two concentric circles (spheres) of minimum distance whose associated annulus measures the out-of-roundness (OOR) tolerance. The problem arises in analyzing coordinate measuring machine (CMM) data taken against circular (spherical) features of manufactured parts. It also can be interpreted as the “geometric” Chebychev problem of fitting a circle (sphere) to data so as to minimize the maximum distance deviation. A related formulation, the “algebraic” Chebychev formula, determines the equation of a circle (sphere) to minimize the maximum violation of the equation by the data points. In this paper, we describe a linear-programming approach for the algebraic Chebychev formula that determines reference circles (spheres) and related annuluses whose widths are very close to the widths of the true geometric Chebychev annuluses. We also compare the algebraic Chebychev formula against the popular algebraic least-squares solutions for various data sets. In most of these examples, the algebraic and geometric Chebychev solutions coincide, which appears to be the case for most real applications. Such solutions yield concentric circles whose separation is less than that of the corresponding least-squares solution. It is suggested that the linear-programming approach be considered as an alternate solution method for determining OOR annuluses for CMM data sets.     

Influence of the fluctuations of the alignment tensor on the analysis of the structure and dynamics of proteins using residual dipolar couplings

It has been suggested that the fluctuations of the alignment tensor can affect the results of procedures for characterizing the structure and the dynamics of proteins using residual dipolar couplings. We show here that the very significant fluctuations of the steric alignment tensor caused by the dynamics of proteins can be safely ignored when they do not correlate with those of the bond vectors. A detailed analysis of these correlations in the protein ubiquitin reveals that their effects are negligible for the analysis of backbone motions within secondary structure elements, but also that they may be significant in turns, loops and side chains, especially for bond vectors that have small residual dipolar couplings. Our results suggest that methods that explicitly consider the motions of the alignment tensor will be needed to study the large-scale structural fluctuations that take place on the millisecond timescale, which are often important for the biological function of proteins, from residual dipolar coupling measurements.     

Fitting probability distributions to animal movement trajectories: using artificial neural networks to link distance, resources, and memory

Animal movement paths are often thought of as a confluence of behavioral processes and landscape patterns. Yet it has proven difficult to develop frameworks for analyzing animal movement that can test these interactions. Here we describe a novel method for fitting movement models to data that can incorporate diverse aspects of landscapes and behavior. Using data from five elk (Cervus canadensis) reintroduced to central Ontario, we employed artificial neural networks to estimate movement probability kernels as functions of three landscape-behavioral processes. These consisted of measures of the animals' response to the physical spatial structure of the landscape, the spatial variability in resources, and memory of previously visited locations. The results support the view that animal movement results from interactions among elements of landscape structure and behavior, motivating context-dependent movement probabilities, rather than from successive realizations of static distributions, as some traditional models of movement and resource selection assume. Flexible, nonlinear models may thus prove useful in understanding the mechanisms controlling animal movement patterns.     

Membrane instability induced by purified myelin components. Its possible relevance to experimental allergic encephalomyelitis

The fusogenic properties of purified myelin components in a system employing chicken erythrocytes were studied. Sulphatides, myelin basic protein and the apoprotein of Folch-Lees proteolipid were capable of individually inducing membrane fusion in the presence of Ca²⁺. By contrast, cerebrosides or a mixture of sulphatides and myelin basic protein (molar ratio 19 : 1) did not show such effect. The fusogenic ability of sulphatide was correlated to its behaviour in mixed monolayers with phospholipids at the air-water interface. Mixed films of sulphatides with phosphatidylcholine or sphingomyelin but not with phosphatidylethanolamine showed reductions of molecular packing and surface potential similar to those found for other fusogenic compounds. The effects of myelin components described could be of importance in the membrane instability and vesicular disruption of myelin occurring in demyelinative disorders.     

Dielectric energy of orientation in dead and living cells of Schizosaccharomyces pombe. Fitting of experimental results to a theoretical model.

Using the experimental data obtained with killed cells of Schizosaccharomyces pombe (1), we have formulated a theoretical model that is able to predict cell orientation for microorganisms with ellipsoidal or cylindrical shapes as a function of the frequency of the electric field and of the conductivity of the external medium. In this model, comparison of the difference in potential energy for both orientations parallel-perpendicular with the thermal agitation energy allows one to interpret the intervals where these orientations occur. The model implies that the conductivity of the cytoplasm is slightly higher than that of the external medium. This assumption is easy to understand taking into account that not all the intracytoplasmic material is released to the exterior during cell death.