Contributions to the mathematical biophysics of the central nervous system

Various neural mechanisms are considered which deal with point to point correspondence between two sets of neural elements with a smaller number of conducting elements between them; the transmission of nerve impulses in a limited range of intensities; movement of the transmission of excitation along a contour; the reaction to the size of an object independent of its distance; and an interpretation of the effect of a warning stimulus and of stimulus intensity upon reaction time. For the latter cases a comparison of the theoretical equations is made with some of the available experimental data, and a general agrement is found.     

Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

Summary In this article, we propose a new generalized index to recover relationships between two sets of random vectors by finding the vector projections that minimize an L ₂ distance between each projected vector and an unknown function of the other. The unknown functions are estimated using the Nadaraya–Watson smoother. Extensions to multiple sets and groups of multiple sets are also discussed, and a bootstrap procedure is developed to detect the number of significant relationships. All the proposed methods are assessed through extensive simulations and real data analyses. In particular, for environmental data from Los Angeles County, we apply our multiple‐set methodology to study relationships between mortality, weather, and pollutants vectors. Here, we detect existence of both linear and nonlinear relationships between the dimension‐reduced vectors, which are then used to build nonlinear time‐series regression models for the dimension‐reduced mortality vector. These findings also illustrate potential use of our method in many other applications. A comprehensive assessment of our methodologies along with their theoretical properties are given in a Web Appendix.     

Beitrag einzelner parameter zum wahrnehumungsgemäßen unterschied von zusammengesetzten reizen bei der honigbiene

The perceptual difference between stimuli can be regarded as distance within the perceptual space of the bee. The author used this assumption to determine the specific distance function, on the basis of which the differences in the individual perceptual parameters constituted the perceptual difference between the complex stimulus and the reference stimulus. The perceptual differences can be deduced only indirectly from the choice frequency. Consequently, it was necessary to establish a “calibration curve”, to deduce quantitatively the perceptual difference from the choice frequency. The resulting hyperbolic curves for the parameters “brightness” and “size” were almost identical (Fig. 2). The perceptual difference between the complex stimulus and the reference stimulus is greater than one would expect in an Euclidean space. Rather it is the sum of the distances along the perceptual parameters which compose the complex stimulus (Fig. 3). Thus, the bee determines the perceived difference of composite stimuli which affect the perceptual parameters “brightness” and “size” in terms of the city-blockmetric.     

Finding the nearest neighbors in biological databases using less distance computations

Modern biological applications usually involve the similarity comparison between two objects, which is often computationally very expensive, such as whole genome pairwise alignment and protein 3D structure alignment. Nevertheless, being able to quickly identify the closest neighboring objects from very large databases for a newly obtained sequence or structure can provide timely hints to its functions and more. This paper presents a substantial speedup technique for the well-studied k-nearest neighbor (k-nn) search, based on novel concepts of virtual pivots and partial pivots, such that a significant number of the expensive distance computations can be avoided. The new method is able to dynamically locate virtual pivots, according to the query, with increasing pruning ability. Using the same or less amount of database preprocessing effort, the new method outperformed the second best method by using no more than 40 percent distance computations per query, on a database of 10,000 gene sequences, compared to several best known k-nn search methods including M-Tree, OMNI, SA-Tree, and LAESA. We demonstrated the use of this method on two biological sequence data sets, one of which is for HIV-1 viral strain computational genotyping.     

A fuzzy-set-theory-based approach to analyse species membership in DNA barcoding

Reliable assignment of an unknown query sequence to its correct species remains a methodological problem for the growing field of DNA barcoding. While great advances have been achieved recently, species identification from barcodes can still be unreliable if the relevant biodiversity has been insufficiently sampled. We here propose a new notion of species membership for DNA barcoding-fuzzy membership, based on fuzzy set theory-and illustrate its successful application to four real data sets (bats, fishes, butterflies and flies) with more than 5000 random simulations. Two of the data sets comprise especially dense species/population-level samples. In comparison with current DNA barcoding methods, the newly proposed minimum distance (MD) plus fuzzy set approach, and another computationally simple method, 'best close match', outperform two computationally sophisticated Bayesian and BootstrapNJ methods. The new method proposed here has great power in reducing false-positive species identification compared with other methods when conspecifics of the query are absent from the reference database.     

Clustering 100,000 protein structure decoys in minutes

Ab initio protein structure prediction methods first generate large sets of structural conformations as candidates (called decoys), and then select the most representative decoys through clustering techniques. Classical clustering methods are inefficient due to the pairwise distance calculation, and thus become infeasible when the number of decoys is large. In addition, the existing clustering approaches suffer from the arbitrariness in determining a distance threshold for proteins within a cluster: a small distance threshold leads to many small clusters, while a large distance threshold results in the merging of several independent clusters into one cluster. In this paper, we propose an efficient clustering method through fast estimating cluster centroids and efficient pruning rotation spaces. The number of clusters is automatically detected by information distance criteria. A package named ONION, which can be downloaded freely, is implemented accordingly. Experimental results on benchmark data sets suggest that ONION is 14 times faster than existing tools, and ONION obtains better selections for 31 targets, and worse selection for 19 targets compared to SPICKER’s selections. On an average PC, ONION can cluster 100,000 decoys in around 12 minutes.     

Hierarchical grid transformation for image warping in the analysis of two-dimensional electrophoresis gels

Two-dimensional electrophoresis is a widely used method for separating a large number of proteins from complex protein mixtures and for revealing differential patterns of protein expressions. In the computer-assisted proteome research, the comparison of protein separation profiles involves several heuristic steps, ranging from protein spot detection to matching of unknown spots. An important prerequisite for efficient protein spot matching is the image warping step, where the geometric relationship between the gel profiles is modeled on the basis of a given set of known corresponding spots, so-called landmarks, and the locations of unknown spots are predicted using the optimized model. Traditionally, polynomial functions together with least squares optimization has been used, even though this approach is known to be incapable of modeling all the complex distortions inherent in electrophoretic data. To satisfy the need of more flexible gel distortion correction, a hierarchical grid transformation method with stochastic optimization is presented. The method provides an adaptive multiresolution model between the gels, and good correction performance in the practical cross-validation tests suggests that automatic warping of gel images could be based on this approach. We believe that the proposed model also has significance in the ultimate comparison of corresponding protein spots since the matching process should benefit from the closeness of the true spot pairs.     

Protein structure alignment

A new method of comparing protein structures is described, based on distance plot analysis. It is relatively insensitive to insertions and deletions in sequence and is tolerant of the displacement of equivalent substructures between the two molecules being compared. When presented with the co-ordinate sets of two structures, the method will produce automatically an alignment of their sequences based on structural criteria. The method uses the dynamic programming optimization technique, which is widely used in the comparison of protein sequences and thus unifies the techniques of protein structure and sequence comparison. Typical structure comparison problems were examined and the results of the new method compared to the published results obtained using conventional methods. In most examples, the new method produced a result that was equivalent, and in some cases superior, to those reported in the literature.     

The role of visual information in numerosity estimation

Mainstream theory suggests that the approximate number system supports our non-symbolic number abilities (e.g. estimating or comparing different sets of items). It is argued that this system can extract number independently of the visual cues present in the stimulus (diameter, aggregate surface, etc.). However, in a recent report we argue that this might not be the case. We showed that participants combined information from different visual cues to derive their answers. While numerosity comparison requires a rough comparison of two sets of items (smaller versus larger), numerosity estimation requires a more precise mechanism. It could therefore be that numerosity estimation, in contrast to numerosity comparison, might rely on the approximate number system. To test this hypothesis, we conducted a numerosity estimation experiment. We controlled for the visual cues according to current standards: each single visual property was not informative about numerosity. Nevertheless, the results reveal that participants were influenced by the visual properties of the dot arrays. They gave a larger estimate when the dot arrays consisted of dots with, on average, a smaller diameter, aggregate surface or density but a larger convex hull. The reliance on visual cues to estimate numerosity suggests that the existence of an approximate number system that can extract numerosity independently of the visual cues is unlikely. Instead, we propose that humans estimate numerosity by weighing the different visual cues present in the stimuli.     

Match/X,A Gene Expression Pattern Recognition Algorithm Used to Identify Genes Which May be Related to CDC2 Function and Cell Cycle Regulation

Large-scale microarray gene expression studies can provide insight into complex genetic networks and biological pathways. A comprehensive gene expression database was constructed using Affymetrix GeneChip microarrays and RNA isolated from more than 6,400 distinct normal and diseased human tissues. These individual patient samples were grouped into over 700 sample sets based on common tissue and disease morphologies, and each set contained averaged expression data for over 45,000 gene probe sets representing more than 33,000 known human genes. Sample sets were compared to each other in more than 750 normal vs. disease pairwise comparisons. Relative up or down-regulation patterns of genes across these pairwise comparisons provided unique expression fingerprints that could be compared and matched to a gene of interest using the Match/X algorithm. This algorithm uses the kappa statistic to compute correlations between genes and calculate a distance score between a gene of interest and all other genes in the database. Using cdc2 as a query gene, we identified several hundred genes that had similar expression patterns and highly correlated distance scores. Most of these genes were known components of the cell cycle involved in G2/M progression, spindle function or chromosome arrangement. Some of the identified genes had unknown biological functions but may be related to cdc2 mediated mechanism based on their closely correlated distance scores. This algorithm may provide novel insights into unknown gene function based on correlation to expression profiles of known genes and can identify elements of cellular pathways and gene interactions in a high throughput fashion.     

How good is prediction of protein structural class by the component-coupled method?

Proteins of known structures are usually classified into four structural classes: all-alpha, all-beta, alpha+beta, and alpha/beta type of proteins. A number of methods to predicting the structural class of a protein based on its amino acid composition have been developed during the past few years. Recently, a component-coupled method was developed for predicting protein structural class according to amino acid composition. This method is based on the least Mahalanobis distance principle, and yields much better predicted results in comparison with the previous methods. However, the success rates reported for structural class prediction by different investigators are contradictory. The highest reported accuracies by this method are near 100%, but the lowest one is only about 60%. The goal of this study is to resolve this paradox and to determine the possible upper limit of prediction rate for structural classes. In this paper, based on the normality assumption and the Bayes decision rule for minimum error, a new method is proposed for predicting the structural class of a protein according to its amino acid composition. The detailed theoretical analysis indicates that if the four protein folding classes are governed by the normal distributions, the present method will yield the optimum predictive result in a statistical sense. A non-redundant data set of 1,189 protein domains is used to evaluate the performance of the new method. Our results demonstrate that 60% correctness is the upper limit for a 4-type class prediction from amino acid composition alone for an unknown query protein. The apparent relatively high accuracy level (more than 90%) attained in the previous studies was due to the preselection of test sets, which may not be adequately representative of all unrelated proteins.     

Visual discrimination of objects differing in spatial depth by goldfish

Training experiments were performed to investigate the ability of goldfish to discriminate objects differing in spatial depth. Tests on size constancy should give insight into the mechanisms of distance estimation. Goldfish were successfully trained to discriminate between two black disk stimuli of equal size but different distance from the tank wall. Each stimulus was presented in a white tube so that the fish could see only one stimulus at a time. For each of eight training stimulus distances, the just noticeable difference in distance was determined at a threshold criterion of 70% choice frequency. The ratio of the retinal image sizes between training stimulus and comparison stimulus at threshold was about constant. However, in contrast to Douglas et al. (Behav Brain Res 30:37–42, 1988), goldfish did not show size constancy in tests with stimuli of the same visual angle. This indicates that they did not estimate distance, but simply compared the retinal images under our experimental conditions. We did not find any indication for the use of accommodation as a depth cue. A patterned background at the rear end of the tubes did not have any effect, which, however, does not exclude the possibility that motion parallax is used as a depth cue under natural conditions.     

Extensive distance geometry calculations with different NOE calibrations: New criteria for structure selection applied to Sandostatin and BPTI

Summary To generate structures efficiently, a version of the distance geometry program DIANA for a parallel computer was developed, new objective criteria for the selection of NMR solution structures are presented, and the influence of using different calibrations of NOE intensities on the final structures are described. The methods are applied to the structure determination of Sandostatin, a disulfide-bridge octapeptide, and to model calculations of BPTI. On an Alliant FX2800 computer using 10 processors in parallel, the calculations were done 9.2 times faster than with a single processor. Up to 7000 Sandostatin structures were calculated with distance and angular constraints. The procedure for selecting acceptable structures is based on the maximum values of pairwise RMSDs between structures. Suitable target function cut-offs are defined independent of the number of starting structures. The method allowed for an objective comparison of three groups of Sandostatin structures that were calculated from different sets of upper distance constraints which were derived from the same NOE intensity data using three empirical calibration curves. The number of converged structures and the target function values differed significantly among the three groups, but the structures were qualitatively and quantitatively very similar. The conformation is well determined in the cyclic region Cys²–Cys⁷ and adopts a -turn centered at d-Trp⁴–Lys⁵. The criteria for structure selection were further tested with BPTI. Results obtained from sets of structures calculated with and without using the REDAC strategy are consistent and suggest that the structure selection method is objective and generally applicable.     

Block alignment: New representation and comparison method to study evolution of genomes

Genomes are not random sequences because natural selection has injected information in biological sequences for billions of years. Inspired by this idea, we developed a simple method to compare genomes considering nucleotide counts in subsequences (blocks) instead of their exact sequences.We introduce the Block Alignment method for comparing two genomes and based on this comparison method, define a similarity score and a distance. The presented model ignores nucleotide order in the sequence. On the other hand, in this block comparison method, due to exclusion of point mutations and small size variations, there is no need for high coverage sequencing which is responsible for the high costs of data production and storage; moreover, the sequence comparisons could be performed with higher speed.Phylogenetic trees of two sets of bacterial genomes were constructed and the results were in full agreement with their already constructed phylogenetic trees. Furthermore, a weighted and directed similarity network of each set of bacterial genomes was inferred ab initio by this model. Remarkably, the communities of these networks are in agreement with the clades of the corresponding phylogenetic trees which means these similarity networks also contain phylogenetic information about the genomes. Moreover, the block comparison method was used to distinguish rob(15;21)c-associated iAMP21 and sporadic iAMP21 rearrangements in subgroups of chromosome 21 in acute lymphoblastic leukemia. Our results show a meaningful difference between the number of contigs that mapped to chromosomes 15 and 21 in these cases. Furthermore, the presented block alignment model can select the candidate blocks to perform more accurate analysis and it is capable to find conserved blocks on a set of genomes.     

On visual orientation of dot patterns

Two-dimensional normally distributed random dot patterns were used in two experiments on visual orientation estimation. In the first experiment the patterns differed in their sample correlation and in dot number. In the second one the number of dots was maintained constant but the patterns were generated as a superposition of two normally distributed orthogonal sets composed of different number of dots. In both experiments the estimated orientation depended on stimuli correlation-with increasing correlation the estimated orientation gets closer to the orientation of the least square distance axis of the pattern. Even at very low unsignificant correlations there still remained a hint about stimulus orientation which was not estimated at random. Equalizing consecutively the number of dots in the two orthogonal dot patterns during the second experiment did not result in chance performance either. The bimodal angular distributions of the obtained responses permitted to approach the problem of orientation ambiguity. The results are discussed in terms of optimization processes taking place in the visual system.     

Selecting oligonucleotide probes for whole-genome tiling arrays with a cross-hybridization potential

For designing oligonucleotide tiling arrays popular, current methods still rely on simple criteria like Hamming distance or longest common factors, neglecting base stacking effects which strongly contribute to binding energies. Consequently, probes are often prone to cross-hybridization which reduces the signal-to-noise ratio and complicates downstream analysis. We propose the first computationally efficient method using hybridization energy to identify specific oligonucleotide probes. Our Cross-Hybridization Potential (CHP) is computed with a Nearest Neighbor Alignment, which efficiently estimates a lower bound for the Gibbs free energy of the duplex formed by two DNA sequences of bounded length. It is derived from our simplified reformulation of t-gap insertion-deletion-like metrics. The computations are accelerated by a filter using weighted ungapped q-grams to arrive at seeds. The computation of the CHP is implemented in our software OSProbes, available under the GPL, which computes sets of viable probe candidates. The user can choose a trade-off between running time and quality of probes selected. We obtain very favorable results in comparison with prior approaches with respect to specificity and sensitivity for cross-hybridization and genome coverage with high-specificity probes. The combination of OSProbes and our Tileomatic method, which computes optimal tiling paths from candidate sets, yields globally optimal tiling arrays, balancing probe distance, hybridization conditions, and uniqueness of hybridization.     

Determining the three-dimensional fold of a protein from approximate constraints

We propose a new approach for calculating the three-dimensional (3D) structure of a protein from distance and dihedral angle constraints derived from experimental data. We suggest that such constraints can be obtained from experiments such as tritium planigraphy, chemical or enzymatic cleavage of the polypeptide chain, paramagnetic perturbation of nuclear magnetic resonance (NMR) spectra, measurement of hydrogen-exchange rates, mutational studies, mass spectrometry, and electron paramagnetic resonance. These can be supplemented with constraints from theoretical prediction of secondary structures and of buried/exposed residues. We report here distance geometry calculations to generate the structures of a test protein Staphylococcal nuclease (STN), and the HIV-1 rev protein (REV) of unknown structure. From the available 3D atomic coordinates of STN, we set up simulated data sets consisting of varying number and quality of constraints, and used our group's Self Correcting Distance Geometry (SECODG) program DIAMOD to generate structures. We could generate the correct tertiary fold from qualitative (approximate) as well as precise distance constraints. The root mean square deviations of backbone atoms from the native structure were in the range of 2.0 A to 8.3 A, depending on the number of constraints used. We could also generate the correct fold starting from a subset of atoms that are on the surface and those that are buried. When we used data sets containing a small fraction of incorrect distance constraints, the SECODG technique was able to detect and correct them. In the case of REV, we used a combination of constraints obtained from mutagenic data and structure predictions. DIAMOD generated helix-loop-helix models, which, after four self-correcting cycles, populated one family exclusively. The features of the energy-minimized model are consistent with the available data on REV-RNA interaction. Our method could thus be an attractive alternative for calculating protein 3D structures, especially in cases where the traditional methods of X-ray crystallography and multidimensional NMR spectroscopy have been unsuccessful.     

VDA, a method of choosing a better algorithm with fewer validations

The multitude of bioinformatics algorithms designed for performing a particular computational task presents end-users with the problem of selecting the most appropriate computational tool for analyzing their biological data. The choice of the best available method is often based on expensive experimental validation of the results. We propose an approach to design validation sets for method comparison and performance assessment that are effective in terms of cost and discrimination power.Validation Discriminant Analysis (VDA) is a method for designing a minimal validation dataset to allow reliable comparisons between the performances of different algorithms. Implementation of our VDA approach achieves this reduction by selecting predictions that maximize the minimum Hamming distance between algorithmic predictions in the validation set. We show that VDA can be used to correctly rank algorithms according to their performances. These results are further supported by simulations and by realistic algorithmic comparisons in silico.VDA is a novel, cost-efficient method for minimizing the number of validation experiments necessary for reliable performance estimation and fair comparison between algorithms.Our VDA software is available at http://sourceforge.net/projects/klugerlab/files/VDA/     

A quantitative assessment of congruence between molecular and nonmolecular estimates of phylogeny

Summary An important means of assessing the validity of phylogenetic hypotheses is to measure congruence between different studies of the same group. We applied statistical methods to assess patterns of congruence among phylogenies taken from the literature, using strict-consensus and quartet statistics to measure congruence for 48 pairs of phylogenies of various groups of birds and mammals. The strict-consensus measures were higher on average for distance-distance comparisons than for distance-parsimony or parsimony-parsimony comparisons, and for molecular-molecular comparisons than for molecular-morphological or morphological-morphological comparisons. However, the only factor that was consistently important statistically was the number of taxa involved in the comparison, with congruence decreasing as the number of taxa increased. Quartet indices, which measure network similarity regardless of root position, also showed an effect based on number of taxa but exhibited no trend toward higher congruence in molecular-molecular and distance-distance comparisons. The number of studies with jointly unresolved quartets was small, indicating that data sets varied in the degree to which they could resolve relationships at different phylogenetic levels.The levels of congruence between phylogenies, including those employing single-copy nuclear DNA hybridization data, appear to be higher than expected in random sets of trees, cannot be explained by nonindependence of data sets, and thus provide empirical support for the validity of both distance and parsimony methods of phylogenetic inference. In specific instances, low congruence pointed to mistakes in the application of certain methods, and to the existence of problem taxa in need of additional study.     

Behavioural elements of the paradise fish (Macropodus opercularis). II. A functional analysis

The effects of various environmental influences, such as presence of a living predator, dominant conspecific or frightening artificial stimulus, on particular behavioural elements of the paradise fish (Macropodus opercularis) were studied. It has been found that certain sets of the elements are manifested as organizational complexes which characterize a certain mood or form of defensive behaviour. The compound elements of these complexes seemed to be partly interchangeable, partly under environmental control. The main behavioural complexes of the paradise fish were the Territorial complex characterizing the peaceful, home-living animal, Emotionality complex appearing in case of immediate and past danger, Active and Passive defense complexes which represent alternatives in defense, depending on particular stimulus settings. Some supporting evidence for these behavioural complexes are presented and discussed.