A Hybrid Technique for the Periodicity Characterization of Genomic Sequence Data

Many studies of biological sequence data have examined sequence structure in terms of periodicity, and various methods for measuring periodicity have been suggested for this purpose. This paper compares two such methods, autocorrelation and the Fourier transform, using synthetic periodic sequences, and explains the differences in periodicity estimates produced by each. A hybrid autocorrelation—integer period discrete Fourier transform is proposed that combines the advantages of both techniques. Collectively, this representation and a recently proposed variant on the discrete Fourier transform offer alternatives to the widely used autocorrelation for the periodicity characterization of sequence data. Finally, these methods are compared for various tetramers of interest in C. elegans chromosome I.     

Digital signal processing methods for biosequence comparison.

A method is discussed for DNA or protein sequence comparison using a finite field fast Fourier transform, a digital signal processing technique; and statistical methods are discussed for analyzing the output of this algorithm. This method compares two sequences of length N in computing time proportional to N log N compared to N2 for methods currently used. This method makes it feasible to compare very long sequences. An example is given to show that the method correctly identifies sites of known homology.     

Analysis of EEG signals during epileptic and alcoholic states using AR modeling techniques

Electroencephalogram (EEG) analysis remains problematic due to limited understanding of the signal origin, which leads to the difficulty of designing evaluation methods. In spite of these shortcomings, the EEG is a valuable tool in the evaluation of some neurological disorders as well as in the evaluation of overall cerebral activity. In most studies, which use quantitative EEG analysis, the properties of measured EEG are computed by applying power spectral density (PSD) estimation for selected representative EEG samples. The sample for which the PSD is calculated is assumed to be stationary. This work deals with a comparative study of the PSD obtained from normal, epileptic and alcoholic EEG signals. The power density spectra were calculated using fast Fourier transform (FFT) by Welch's method, auto regressive (AR) method by Yule–Walker and Burg's method. The results are tabulated for these different classes of EEG signals.     

MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform

A multiple sequence alignment program, MAFFT, has been developed. The CPU time is drastically reduced as compared with existing methods. MAFFT includes two novel techniques. (i) Homo logous regions are rapidly identified by the fast Fourier transform (FFT), in which an amino acid sequence is converted to a sequence composed of volume and polarity values of each amino acid residue. (ii) We propose a simplified scoring system that performs well for reducing CPU time and increasing the accuracy of alignments even for sequences having large insertions or extensions as well as distantly related sequences of similar length. Two different heuristics, the progressive method (FFT-NS-2) and the iterative refinement method (FFT-NS-i), are implemented in MAFFT. The performances of FFT-NS-2 and FFT-NS-i were compared with other methods by computer simulations and benchmark tests; the CPU time of FFT-NS-2 is drastically reduced as compared with CLUSTALW with comparable accuracy. FFT-NS-i is over 100 times faster than T-COFFEE, when the number of input sequences exceeds 60, without sacrificing the accuracy.     

The filtered Fourier difference spectrum predicts psychophysical letter discrimination in the peripheral retina

We wished to devise a measure of dissimilarity (D) which could predict psychophysical discrimination performance for Snellen letter pairs in peripheral vision. Threshold size for discriminating 33 pairs of Snellen letters was measured at 30 degrees eccentricity in the nasal retina for two subjects. D was computed for each pair by performing an overlap subtraction in the spatial domain, followed by a Fast Fourier Transform on this difference image, and dividing the total power in the resultant 'difference spectrum' by the sum of the powers of the individual letter spectra. A plot of D vs. psychophysical threshold letter size gave a mean correlation of R = -0.81. When D was calculated for letters that were low-pass filtered at different cut-off frequencies, the correlation with psychophysical performance was greatest when cut-off was between 1.25-1.9 cycles/letter (R = -0.85). Conversely, when the difference spectrum was high-pass filtered at different cut-off frequencies, the correlation decreased continuously as the cut-off increased. These results imply that the band of frequencies between zero and 1.25 cycles/letter are most important for letter discrimination in peripheral vision.     

The effects of motor unit synchronization on the power spectrum of the electromyogram

A realistic model for two synchronized motor unit action potential trains (MUAPT) is presented in which the variability of the time difference between corresponding action potentials (hereafter denoted by delay) is taken into account. Specifically, this delay is modeled as a continuous random variable that may assume both positive and negative values.Expressions are derived for the auto- and cross-power spectra of two such trains using their relations with the auto- and cross-correlation functions, respectively, with which they form Fourier transform pairs.The results show that the auto- and the cross-power spectra of two such synchronized MUAPTs differ from the auto- and the cross-spectra of two independent MUAPTs. The contribution of the statistics of the interpulse intervals to one of the autopower spectra is smaller and the cross-power spectra no longer reduce to a Dirac -function at the origin but are now determined by the other auto-power spectrum and by the Fourier transform of the density function associated with the time difference between corresponding action potentials. As a consequence of this change in the cross-power spectra synchronization leads to an absolute increase of power at low frequencies and to a relative decrease of power at high frequencies.The results are then generalized to electromyograms (EMG) composed of more than just two MUAPTs and illustrated with simulated power spectra with which the theory shows excellent agreement.     

A coding measure scheme employing electron-ion interaction pseudopotential (EIIP)

In this paper, a revision for the existing method of locating exons by genomic signal processing technique employing four binary indicator sequences is presented. The existing method relies on the pronounced period three peaks observed in the Fourier power spectrum of the exon regions which are absent in non-coding regions. The authors have abandoned the four sequences all together and adopted a single 'EIIP indicator sequence' which is formed by substituting the electron-ion interaction pseudopotentials (EIIP) of the nucleotides A, G, C and T in the DNA sequence, reducing the computational overhead by 75%. The power spectrum of this sequence reveals period three peaks for exon regions. Also a number of exons have been identified which exhibit period three peaks when mapped to 'EIIP indicator sequence' and which do not show the same when the binary indicator sequences are employed. We could get better discrimination between exon areas and non-coding areas of a number of genomes when the sequences are mapped to EIIP indicator sequences and the power spectra of the same are taken in a sliding Kaiser window, compared to the existing method using a rectangular window which utilizes binary indicator sequences.     

A computer program for Wiener filtering of evoked potential data.

We have developed a computer program for Wiener filtering of evoked potential data. The basic algorithm involves computation of the difference berween the power spectrum of the sweep sum and the sum of power spectra of individual sweeps. Power spectra are computed by means of the discrete Fourier transform. The program is now being run on a LSI-11 computer in a neurophysiology research laboratory to analyze somatic evoked potential data from monkeys.     

Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Criteria for confirming sequence periodicity identified by Fourier transform analysis: application to GCR2, a candidate plant GPCR?

Methods to determine periodicity in protein sequences are useful for inferring function. Fourier transformation is one approach but care is required to ensure the periodicity is genuine. Here we have shown that empirically-derived statistical tables can be used as a measure of significance. Genuine protein sequences data rather than randomly generated sequences were used as the statistical backdrop. The method has been applied to G-protein coupled receptor (GPCR) sequences, by Fourier transformation of hydrophobicity values, codon frequencies and the extent of over-representation of codon pairs; the latter being related to translational step times. Genuine periodicity was observed in the hydrophobicity whereas the apparent periodicity (as inferred from previously reported measures) in the translation step times was not validated statistically. GCR2 has recently been proposed as the plant GPCR receptor for the hormone abscisic acid. It has homology to the Lanthionine synthetase C-like family of proteins, an observation confirmed by fold recognition. Application of the Fourier transform algorithm to the GCR2 family revealed strongly predicted seven fold periodicity in hydrophobicity, suggesting why GCR2 has been reported to be a GPCR, despite negative indications in most transmembrane prediction algorithms. The underlying multiple sequence alignment, also required for the Fourier transform analysis of periodicity, indicated that the hydrophobic regions around the 7 GXXG motifs commence near the C-terminal end of each of the 7 inner helices of the alpha-toroid and continue to the N-terminal region of the helix. The results clearly explain why GCR2 has been understandably but erroneously predicted to be a GPCR.     

Review and classification of variability analysis techniques with clinical applications

Background

Representation of independent biophysical sources using Fourier analysis can be inefficient because the basis is sinusoidal and general. When complex fractionated atrial electrograms (CFAE) are acquired during atrial fibrillation (AF), the electrogram morphology depends on the mix of distinct nonsinusoidal generators. Identification of these generators using efficient methods of representation and comparison would be useful for targeting catheter ablation sites to prevent arrhythmia reinduction.

Method

A data-driven basis and transform is described which utilizes the ensemble average of signal segments to identify and distinguish CFAE morphologic components and frequencies. Calculation of the dominant frequency (DF) of actual CFAE, and identification of simulated independent generator frequencies and morphologies embedded in CFAE, is done using a total of 216 recordings from 10 paroxysmal and 10 persistent AF patients. The transform is tested versus Fourier analysis to detect spectral components in the presence of phase noise and interference. Correspondence is shown between ensemble basis vectors of highest power and corresponding synthetic drivers embedded in CFAE.

Results

The ensemble basis is orthogonal, and efficient for representation of CFAE components as compared with Fourier analysis (p ≤ 0.002). When three synthetic drivers with additive phase noise and interference were decomposed, the top three peaks in the ensemble power spectrum corresponded to the driver frequencies more closely as compared with top Fourier power spectrum peaks (p ≤ 0.005). The synthesized drivers with phase noise and interference were extractable from their corresponding ensemble basis with a mean error of less than 10%.

Conclusions

The new transform is able to efficiently identify CFAE features using DF calculation and by discerning morphologic differences. Unlike the Fourier transform method, it does not distort CFAE signals prior to analysis, and is relatively robust to jitter in periodic events. Thus the ensemble method can provide a useful alternative for quantitative characterization of CFAE during clinical study.     

Infrared spectroscopy as a tool for discrimination between sensitive and multiresistant K562 cells.

Fourier transform infrared spectroscopy was performed on human leukemic daunorubicin-sensitive K562 cells and their multiresistant counterpart derived by selection. Statistical analysis, including variable reduction and linear discriminant analysis was performed on sensitive and multiresistant cells spectra in order to establish a diagnostic tool for multiresistant pattern. For each of the two methods of data reduction tested [genetic algorithm or principal component analysis (PCA)] discrimination between the two cell lines was found to be possible. The best results, obtained with PCA-reduction, showed an accuracy of 93% on a distinct test set of spectra. These results demonstrate the efficiency of Fourier transform infrared spectroscopy for classification. Further analysis of the spectral differences indicated that discrimination between resistant and sensitive cells was based on variations in all cellular contents. Lipid and nucleic acid decreased, relatively, while the protein content increased.     

Stability of the heart rate power spectrum over time in the conscious dog

The purpose of this experiment was to test the stability of the heart rate (HR) power spectrum over time in conscious dogs. HR was recorded for 1 h for each of six animals on 2 days. A Fast Fourier transform was used to derive the HR power spectrum for the 12 contiguous 5-min epochs comprising the 1-h recordings. Changes in frequency and amplitude of the various spectral peaks were quantitatively examined. We confirm the presence of two major concentrations of power centered around 0.02 (low frequency peak) and 0.32 Hz (high frequency peak). However, we observed variations in these spectral peaks, especially their amplitudes, both within each hour and from day 1 to day 2. The amplitudes of these two spectral peaks tended to vary reciprocally. HR power spectra based on 5 min of recorded data were also derived from an additional eight animals in both the lying and standing positions; the power spectra from these short recordings were sufficiently sensitive to detect redistributions in power due to changes in posture in all eight dogs. We conclude that: 1) data should be recorded for relatively long periods (e.g., 1 h) to characterize the HR power spectrum; 2) some variability in frequency and amplitude will persist across spectra even when based on longer data bases; 3) care should be taken to ensure that the subject's behavioral state is stable within the recording period; 4) shorter (e.g., 5 min) data bases are not suitable except for detecting relatively robust changes in the HR power spectrum.     

Hydrophobicity scales and computational techniques for detecting amphipathic structures in proteins

Protein segments that form amphipathic alpha-helices in their native state have periodic variation in the hydrophobicity values of the residues along the segment, with a 3.6 residue per cycle period characteristic of the alpha-helix. The assignment of hydrophobicity values to amino acids (hydrophobicity scale) affects the display of periodicity. Thirty-eight published hydrophobicity scales are compared for their ability to identify the characteristic period of alpha-helices, and an optimum scale for this purpose is computed using a new eigenvector method. Two of the published scales are also characterized by eigenvectors. We compare the usual method for detecting periodicity based on the discrete Fourier transform with a method based on a least-squares fit of a harmonic sequence to a sequence of hydrophobicity values. The two become equivalent for very long sequences, but, for shorter sequences with lengths commonly found in alpha-helices, the least-squares procedure gives a more reliable estimate of the period. The analog to the usual Fourier transform power spectrum is the "least-squares power spectrum", the sum of squares accounted for in fitting a sinusoid of given frequency to a sequence of hydrophobicity values. The sum of the spectra of the alpha-helices in our data base peaks at 97.5 degrees, and approximately 50% of the helices can account for this peak. Thus, approximately 50% of the alpha-helices appear to be amphipathic, and, of those that are, the dominant frequency at 97.5 degrees rather than 100 degrees indicates that the helix is slightly more open than previously thought, with the number of residues per turn closer to 3.7 than 3.6. The extra openness is examined in crystallographic data, and is shown to be associated with the C terminus of the helix. The alpha amphipathic index, the key quantity in our analysis, measures the fraction of the total spectral area that is under the 97.5 degrees peak, and is a characteristic of hydrophobicity scales that is consistent for different sets of helices. Our optimized scale maximizes the amphipathic index and has a correlation of 0.85 or higher with nine previously published scales. The most surprising feature of the optimized scale is that arginine tends to behave as if it were hydrophobic; i.e. in the crystallographic data base it has a tendency to be on the hydrophobic face of teh amphipathic helix. Although the scale is optimal only for predicting alpha-amphipathicity, it also ranks high in identifying beta-amphipathicity and in distinguishing interior from exterior residues in a protein.(ABSTRACT TRUNCATED AT 400 WORDS)     

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.     

Insight into protein structure and protein-ligand recognition by Fourier transform infrared spectroscopy

An overview of the application of Fourier transform infrared spectroscopy for the analysis of the structure of proteins and protein-ligand recognition is given. The principle of the technique and of the spectra analysis is demonstrated. Spectral signal assignments to vibrational modes of the peptide chromophore, amino acid side chains, cofactors and metal ligands are summarized. Several examples for protein-ligand recognition are discussed. A particular focus is heme proteins and, as an example, studies of cytochrome P450 are reviewed. Fourier transform infrared spectroscopy in combination with the various techniques such as time-resolved and low-temperature methods, site-directed mutagenesis and isotope labeling is a helpful approach to studying protein-ligand recognition.     

Molecular structure and vibrational spectra of 4-nitrobenzylchloride by ab initio Hartree–Fock and density functional methods

The Fourier transform Raman and Fourier transform infrared spectra 4-nitrobenzylchloride of (NBC) were recorded in the solid phase. The Fourier transform gas phase infrared spectrum of NBC was also recorded. The equilibrium geometry, harmonic vibrational frequencies, infrared intensities and Raman scattering activities were calculated by HF/DFT (B3LYP and BLYP) and SVWN methods with the 6-31G(d,p) basis set. The scaled theoretical wave numbers by B3LYP showed very good agreement with the experimental ones. A detailed interpretation of the infrared and Raman spectra of NBC is reported on the basis of the calculated potential energy distribution. The theoretical spectrograms for the IR spectrum of the title molecule have been constructed.     

The specificity in promoter recognition by the Bacillus subtilis RNA polymerase deltaA and deltaH holoenzymes is connected with periodicities in the promoter nucleotide sequences

Promoters recognized by deltaA-RNA and deltaH-RNA polymerase have different periodic patterns their nucleotide disposition. By using the special method of Fourier analysis for symbolic sequences. Fourier spectra of the primary structure of promoters transcribed bv deltaA-RNA and deltaH-RNA polymerase were obtained. For two data sets, a small one and a big one, a stepwise discriminant analysis with jackknife test based on the spectral characteristics of each of the promoters was performed. It was shown that it is possible to classify the data with the accuracy of 100% sets into classes: promoters that are recognized by the deltaA-RNA polymerise and promoters that are recognized by the deltaH-RNA polymerase. Significant correlations between the promoter strength and the characteristics of their Fourier spectra were obtained. Thus, the periodicity in nucleotide distribution along the polynucleotide chain is the attribute sufficient for promoter recognition by RNA polymerase holoenzyme.     

Spectral Analysis of Binary Time Series: Square Waves vs. Sinusoidal Functions

The analysis of signals consisting of discrete and irregular data causes methodological problems for the Fourier spectral Analysis: Since it is based on sinusoidal functions, rectangular signals with unequal periodicities cannot easily be replicated. The Walsh spectral Analysis is based on the so called "Walsh functions", a complete set of orthonormal, rectangular waves and thus seems to be the method of choice for analysing signals consisting of binary or ordinal data. The paper compares the Walsh spectral analysis and the Fourier spectral analysis on the basis of simulated and real binary data sets of various length. Simulated data were derived from signals with defined cyclic patterns that were noised by randomly generated signals of the same length. The Walsh and Fourier spectra of each set were determined and up to 25% of the periodogram coefficients were utilized as input for an inverse transform. Mean square approximation error (MSE) was calculated for each of the series in order to compare the goodness of fit between the original and the reconstructed signal. The same procedure was performed with real data derived from a behavioral observation in pigs. The comparison of the two methods revealed that, in the analysis of discrete and binary time series, Walsh spectral analysis is the more appropriate method, if the time series is rather short. If the length of the signal increases, the difference between the two methods is less substantial.     

Long-Term Heart Rate Fluctuations in Postoperative and Brain-Dead Patients

Long-term heart rate fluctuations in postoperative and brain-dead patients were investigated. Heart rates were monitored continuously, and the data were stored, edited, and interpolated to allow for data lost during calibration and disconnection of the sensors for various treatments. Heart rate power spectra were calculated using the fast Fourier transform method. The power spectra of the patients who recovered showed that the heart rate fluctuated and produced a 1/f relationship, termed 1/f fluctuations, whereas those of patients who died in the intensive care unit (ICU) consisted of white-noise-like signals. The power spectra in brain-dead patients showed a 1/f relationship under steady-state conditions, while the power density and variation of the frequency distribution were lower than those in a normal subject. Therefore, 1/f fluctuations appear to be universal and occur independent of the central nervous system. (Chronobiology International, 15(6), 633-646, 1998)