Detecting periodic patterns in unevenly spaced gene expression time series using Lomb-Scargle periodograms

MOTIVATION: Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform (FFT) algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spaced gene expression time series has not been well substantiated. METHODS: The Lomb-Scargle periodogram approach is used to search time series of gene expression to quantify the periodic behavior of every gene represented on the DNA array. The Lomb-Scargle periodogram analysis provides a direct method to treat missing values and unevenly spaced time points. We propose the combination of a Lomb-Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene expression patterns. RESULTS: We analyzed the Plasmodium falciparum gene expression dataset. In the Quality Control Dataset of 5080 expression patterns, we found 4112 periodic probes. In addition, we identified 243 probes with periodic expression in the Complete Dataset, which could not be examined in the original study by the FFT analysis due to an excessive number of missing values. While most periodic genes had a period of 48 h, some had a period close to 24 h. Our approach should be applicable for detection and quantification of periodic patterns in any unevenly spaced gene expression time-series data.     

Plasmonic Perfect Absorbers for Biosensing Applications

We present a theoretical modal investigation of plasmonic perfect absorbers (PPAs) based on the localized surface plasmon resonance (LSPR) for biosensing applications. We design the PPA geometry with a layer of periodic metallic nanoparticles on one side of a dielectric substrate and a single metallic layer on the opposite side. The electromagnetic (EM) fields confine partly in the surrounding medium above the substrate and within the substrate itself. We examine the modes of the PPA geometry for a wavelength range of 600–1500 nm. The fundamental mode of the system provides perfect absorption for a wide angle of incidence 0–70°. The second-order mode shows a strong angular dependence with a sharp resonance and exhibits perfect optical absorption when the critical coupling condition for LSPR is achieved. The coupling condition depends on the size, periodicity, dielectric spacer, and the surrounding material of the system. The strong dependence on the surrounding material makes it a promising candidate for biosensing applications. We introduce a novel approach to investigate the angular dependence of the refractive index change for the PPA system. This novel technique contributes the significant attributes of the LSPR sensors, can be used for any required resonance wavelength depending on geometric design, and it also provides sensitivity analogous to the standard surface plasmon resonance (SPR) biosensors.     

Latent periodicity of protein families, identified with the indel-aware algorithm

Latent amino acid repeats seem to be widespread in genetic sequences and to reflect their structure, function, and evolution. We have recently identified latent periodicity in more than 150 protein families including protein kinases and various nucleotide-binding proteins. The latent repeats in these families were correlated to their structure and evolution. However, a majority of known protein families were not identified with our latent periodicity search algorithm. The main presumable reason for this was the inability of our techniques to identify periodicities interspersed with insertions and deletions. We designed the new latent periodicity search algorithm, which is capable of taking into account insertions and deletions. As a result, we identified many novel cases of latent periodicity peculiar to protein families. Possible origins of the periodic structure of these families are discussed. Summarizing, we presume that latent periodicity is present in a substantial portion of known protein families. The latent periodicity matrices and the results of Swiss-Prot scans are available from http://bioinf.narod.ru/del/.     

Multi-Annual Fluctuations in Reconstructed Historical Time-Series of a European Lobster (Homarus gammarus) Population Disappear at Increased Exploitation Levels

Through the history of ecology, fluctuations of populations have been a dominating topic, and endogenous causes of fluctuations and oscillations have been recognized and studied for more than 80 years. Here we analyzed an historical dataset, covering more than 130 years, of European lobster (Homarus gammarus) catches. The data shows periodic fluctuations, which are first dampened and then disappear over time. The disappearance of the periodicity coincided with a substantial increase in fishing effort and the oscillations have not reappeared in the time series. The shifting baseline syndrome has changed our perception of not only the status of the stock, but also the regulating pressures. We describe the transition of a naturally regulated lobster population into a heavily exploited fisheries controlled stock. This is shown by the incorporation of environmental and endogenous processes in generalized additive models, autocorrelation functions and periodicity analyses of time-series.     

Analysing noisy time-series: describing regional variation in the cyclic dynamics of red grouse

We develop a method for describing the periodicity of noisy 'quasi-cyclic' time-series based on integrals of their power spectra corresponding to different frequency intervals that we use to classify time-series as 'strongly cyclic', 'weakly cyclic' or 'non-cyclic'. We apply this analysis to over 300 time-series of shooting records of red grouse from 289 moors located in 20 regions of the UK. Time-series from 63 of these populations were not distinguishable from white noise, but significant evidence of cyclic behaviour in the 2-15 year range was detected in time-series from 183 other populations. Time-series from the remaining 43 populations, though distinguishable from white noise, did not exhibit consistently recognizable cyclic behaviour in the same period range. Cyclic populations exhibit an average periodicity of 8.3 years, but only 20% of these populations cycle with a period of four to six years. Geographically, grouse populations are remarkable more for their dynamic heterogeneity than for any observable regularity. The relationship between the location of populations and their dynamical behaviour is weak. The prevalence of cyclic time-series within a region did not significantly differ from the overall average value. Moor region explained 22% of the variation in periodicity, differing from the overall mean in three regions. Average periodicity increases significantly from 6.8 to 8.9 years from the most southerly to most northerly populations. However, latitude explains only 5.3% of the variation in periodicity of the cycles.     

Identification of amino acid latent periodicity within 94 protein families.

Here, we have applied information decomposition, cyclic profile alignment, and noise decomposition techniques to search for latent repeats within protein families of various functions. We have identified 94 protein families with a family-specific periodicity. In each case, the periodic element was found in greater than 70% of family members. Latent periodicity profiles with specific length and signature were obtained in each case. The possible relationship between the periodic elements thus identified and the evolutionary development of the protein families are discussed with specific reference to the possibility that there is a correlation between the periodic elements and protein function.     

Functional mixed-effects model for periodic data

Periodic data are frequently collected in biomedical experiments. We consider the underlying periodic curves giving rise to these data, and account for the periodicity in their functional model to improve estimation and inference. We propose to incorporate the periodic constraint in the functional mixed-effects model setting. Both the fixed functional effects and random functional effects are modeled in the same periodic functional space, hence the population-average estimates and subject-specific predictions are all periodic. An efficient algorithm is given to estimate the proposed model by an O(N) modified Kalman filtering and smoothing algorithm. The proposed method is evaluated in different scenarios through simulations. Treatments to none-full period data and missing observations along the period are also given. Analysis of a cortisol data set obtained from a study on fibromyalgia is conducted as illustration.     

The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series

This paper investigates the utility of the Lomb-Scargle periodogram for the analysis of biological rhythms. This method is particularly suited to detect periodic components in unequally sampled time-series and data sets with missing values, but restricts all calculations to actually measured values. The Lomb-Scargle method was tested on both real and simulated time-series with even and uneven sampling, and compared to a standard method in biomedical rhythm research, the Chi-square periodogram. Results indicate that the Lomb-Scargle algorithm shows a clearly better detection efficiency and accuracy in the presence of noise, and avoids possible bias or erroneous results that may arise from replacement of missing data by interpolation techniques. Hence, the Lomb-Scargle periodogram may serve as a useful method for the study of biological rhythms, especially when applied to telemetrical or observational time-series obtained from free-living animals, i.e., data sets that notoriously lack points.     

The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series

This paper investigates the utility of the Lomb–Scargle periodogram for the analysis of biological rhythms. This method is particularly suited to detect periodic components in unequally sampled time-series and data sets with missing values, but restricts all calculations to actually measured values. The Lomb-Scargle method was tested on both real and simulated time-series with even and uneven sampling, and compared to a standard method in biomedical rhythm research, the Chi-square periodogram. Results indicate that the Lomb–Scargle algorithm shows a clearly better detection efficiency and accuracy in the presence of noise, and avoids possible bias or erroneous results that may arise from replacement of missing data by interpolation techniques. Hence, the Lomb–Scargle periodogram may serve as a useful method for the study of biological rhythms, especially when applied to telemetrical or observational time-series obtained from free-living animals, i.e., data sets that notoriously lack points.     

Do mountain hare populations cycle?

We investigated the occurrence and distribution of multi-annual cycles in abundance of mountain hare populations across a wide area of their range in northern Europe. We analysed 125 time-series of mountain hare abundance indexed from hunting bag records and questionnaire responses from Scotland, Sweden, Finland and Switzerland. We also reanalysed 17 previously published time-series based on hunting bag records and snow track indices from mountain hare populations in Scotland, Norway, Sweden, Finland, Russia and Italy. Autocorrelation analysis showed that 45% of mountain hare populations showed evidence of cycles, characterised by significant negative autocorrelations at half or the whole cycle period. The amplitude and periodicity of cycles varied between and within countries. Time-series in Scotland were characterised by high-amplitude weak cycles with a mean periodicity of nine years but with a range of 4–15 years. Norwegian and Swedish time-series revealed low amplitude weak cycles with a 3–7 year period. Finnish time-series showed low amplitude cycles with a 4–11 year period. Alpine time-series were predominantly non-cyclic, while the limited number of series from Russia showed high amplitude weak cycles with an 8–11 year period. The results reveal that mountain hare populations show a wide range of population dynamics with distinct regional differences in periodicity, amplitude and density dependent structure of cycles. These findings suggest that different factors may limit or regulate mountain hare populations in different regions of Europe thus supporting the results of recent field studies.     

Sequence periodic pattern of HERV LTRs: A matrix simulation algorithm

Flanking regulatory long terminal repeats (LTRs) in Human endogenous retrovirus (HERV) is a kind of typical DNA repeat that is widespread in the human genome. Currently, many algorithms have been developed to detect the latent periodicity of a wide range of DNA repeats. However, no such attempt was made for HERV LTRs. The present study focused on the investigation of the possible sequence periodic patterns in the HERV LTRs and their regulatory mechanisms. We calculated the sequence periods of 5′, 3′ and combined LTRs in HERVs with our devised matrix simulation algorithm. It is interesting that 5′ and 3′ LTRs have the same period of 7, and combined LTRs have a period of 9. These results indicated that HERV LTRs have predominant periodic patterns. Based on the obtained sequence periodicity, we constructed periodic consensus sequences of 5′, 3′ and combined LTRs. As to 5′ and 3′ LTRs with the same period – 7, we manually scanned the nucleotide bases in the corresponding positions of their periodic consensus sequences, and found some positions have the nucleotide base unchanged, such as the 1st, 5th and 7th positions. These conservative nucleotide base positions represent critical binding sites of regulatory LTRs, and may be indicative of conserved regulatory mechanisms in LRT-participating regulatory networks.     

Behavioral discrimination and time-series phenotyping of birdsong performance

Variation in the acoustic structure of vocal signals is important to communicate social information. However, relatively little is known about the features that receivers extract to decipher relevant social information. Here, we took an expansive, bottom-up approach to delineate the feature space that could be important for processing social information in zebra finch song. Using operant techniques, we discovered that female zebra finches can consistently discriminate brief song phrases (“motifs”) from different social contexts. We then applied machine learning algorithms to classify motifs based on thousands of time-series features and to uncover acoustic features for motif discrimination. In addition to highlighting classic acoustic features, the resulting algorithm revealed novel features for song discrimination, for example, measures of time irreversibility (i.e., the degree to which the statistical properties of the actual and time-reversed signal differ). Moreover, the algorithm accurately predicted female performance on individual motif exemplars. These data underscore and expand the promise of broad time-series phenotyping to acoustic analyses and social decision-making.     

Species detection and delineation in the marine planktonic diatoms Chaetoceros and Bacteriastrum through metabarcoding: making biological sense of haplotype diversity

High-throughput sequencing (HTS) metabarcoding is commonly applied to assess phytoplankton diversity. Usually, haplotypes are grouped into operational taxonomic units (OTUs) through clustering, whereby the resulting number of OTUs depends on chosen similarity thresholds. We applied, instead, a phylogenetic approach to infer taxa among 18S rDNA V4-metabarcode haplotypes gathered from 48 time-series samples using the marine planktonic diatoms Chaetoceros and Bacteriastrum as test case. The 73 recovered taxa comprised both solitary haplotypes and polytomies, the latter composed each of a highly abundant, dominant haplotype and one to several minor, peripheral haplotypes. The solitary and dominant haplotypes usually matched reference sequences, enabling species assignation of taxa. We hypothesise that the super-abundance of reads in dominant haplotypes results from the homogenization effect of concerted evolution. Reads of populous peripheral haplotypes and dominant haplotypes show comparable distribution patterns over the sample dates, suggesting that they are part of the same population. Many taxa revealed marked seasonality, with closely related ones generally showing distinct periodicity, whereas others occur year-round. Phylogenies inferred from metabarcode haplotypes enable delineation of biologically meaningful taxa, whereas OTUs resulting from clustering algorithms often deviate markedly from such taxa.     

Optical Absorption Modeling of Plasmonic Organic Solar Cells Embedding Silica-Coated Silver Nanospheres

We numerically study plasmonic solar cells in which a square periodic array of core–shell Ag@SiO₂ nanospheres (NSs) are placed on top of the indium tin oxide (ITO) layer using a 3D finite-difference time-domain (FDTD) method. We investigate the influence of various parameters such as the periodicity of the array, the Ag core diameter, the active layer thickness, the shell thickness, and the refractive index of the shell materials on the optical performance of the organic solar cells (OSC). Our results show that the optimal periodicity of the array of NSs is dependent on the size of Ag core NSs in order to maximize optical absorption in the active layer. A very thin active layer (<70 nm) and an ultrathin (<5 nm) SiO₂ shell are needed in order to obtain the highest optical absorption enhancement. Strong electric field localization is observed around the plasmonic core–shell nanoparticles as a result of localized surface plasmon resonance (LSPR) excited by Ag NSs with and without silica shell. Embedding 50 nm Ag NSs with 1-nm-thick SiO₂ shell thickness on top of ITO leads to an enhanced intrinsic optical absorption in a 40-nm-thick poly(3-hexylthiophene):phenyl-C₆₁-butyric acid methyl ester (P3HT:PCBM) active layer by 24.7% relative to that without the NSs. The use of 1-nm-thick ZnO shell instead of SiO₂ leads to an enhanced intrinsic absorption in a 40-nm-thick P3HT:PCBM active layer by 27%.

     

Quantitative molecular assessment of chimerism across tissues in marmosets and tamarins

Background

Periodic spacing of A-tracts (short runs of A or T) with the DNA helical period of ~10?C11?bp is characteristic of intrinsically bent DNA. In eukaryotes, the DNA bending is related to chromatin structure and nucleosome positioning. However, the physiological role of strong sequence periodicity detected in many prokaryotic genomes is not clear.

Results

We developed measures of intensity and persistency of DNA curvature-related sequence periodicity and applied them to prokaryotic chromosomes and phages. The results indicate that strong periodic signals present in chromosomes are generally absent in phage genomes. Moreover, chromosomes containing prophages are less likely to possess a persistent periodic signal than chromosomes with no prophages.

Conclusions

Absence of DNA curvature-related sequence periodicity in phages could arise from constraints associated with DNA packaging in the viral capsid. Lack of prophages in chromosomes with persistent periodic signal suggests that the sequence periodicity and concomitant DNA curvature could play a role in protecting the chromosomes from integration of phage DNA.     

Continuous representations of time-series gene expression data.

We present algorithms for time-series gene expression analysis that permit the principled estimation of unobserved time points, clustering, and dataset alignment. Each expression profile is modeled as a cubic spline (piecewise polynomial) that is estimated from the observed data and every time point influences the overall smooth expression curve. We constrain the spline coefficients of genes in the same class to have similar expression patterns, while also allowing for gene specific parameters. We show that unobserved time points can be reconstructed using our method with 10-15% less error when compared to previous best methods. Our clustering algorithm operates directly on the continuous representations of gene expression profiles, and we demonstrate that this is particularly effective when applied to nonuniformly sampled data. Our continuous alignment algorithm also avoids difficulties encountered by discrete approaches. In particular, our method allows for control of the number of degrees of freedom of the warp through the specification of parameterized functions, which helps to avoid overfitting. We demonstrate that our algorithm produces stable low-error alignments on real expression data and further show a specific application to yeast knock-out data that produces biologically meaningful results.