Robust regression for periodicity detection in non-uniformly sampled time-course gene expression data

<p>Abstract</p> <p>Background</p> <p>In practice many biological time series measurements, including gene microarrays, are conducted at time points that seem to be interesting in the biologist's opinion and not necessarily at fixed time intervals. In many circumstances we are interested in finding targets that are expressed periodically. To tackle the problems of uneven sampling and unknown type of noise in periodicity detection, we propose to use robust regression.</p> <p>Methods</p> <p>The aim of this paper is to develop a general framework for robust periodicity detection and review and rank different approaches by means of simulations. We also show the results for some real measurement data.</p> <p>Results</p> <p>The simulation results clearly show that when the sampling of time series gets more and more uneven, the methods that assume even sampling become unusable. We find that M-estimation provides a good compromise between robustness and computational efficiency.</p> <p>Conclusion</p> <p>Since uneven sampling occurs often in biological measurements, the robust methods developed in this paper are expected to have many uses. The regression based formulation of the periodicity detection problem easily adapts to non-uniform sampling. Using robust regression helps to reject inconsistently behaving data points.</p> <p>Availability</p> <p>The implementations are currently available for Matlab and will be made available for the users of R as well. More information can be found in the web-supplement <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

Robust discovery of periodically expressed genes using the laplace periodogram

<p>Abstract</p> <p>Background</p> <p>Time-course gene expression analysis has become important in recent developments due to the increasingly available experimental data. The detection of genes that are periodically expressed is an important step which allows us to study the regulatory mechanisms associated with the cell cycle.</p> <p>Results</p> <p>In this work, we present the Laplace periodogram which employs the least absolute deviation criterion to provide a more robust detection of periodic gene expression in the presence of outliers. The Laplace periodogram is shown to perform comparably to existing methods for the <it>Sacharomyces cerevisiae</it> and <it>Arabidopsis</it> time-course datasets, and to outperform existing methods when outliers are present.</p> <p>Conclusion</p> <p>Time-course gene expression data are often noisy due to the limitations of current technology, and may include outliers. These artifacts corrupt the available data and make the detection of periodicity difficult in many cases. The Laplace periodogram is shown to perform well for both data with and without the presence of outliers, and also for data that are non-uniformly sampled.</p

Detecting Periodic Genes from Irregularly Sampled Gene Expressions: A Comparison Study

Time series microarray measurements of gene expressions have been exploited to discover genes involved in cell cycles. Due to experimental constraints, most microarray observations are obtained through irregular sampling. In this paper three popular spectral analysis schemes, namely, Lomb-Scargle, Capon and missing-data amplitude and phase estimation (MAPES), are compared in terms of their ability and efficiency to recover periodically expressed genes. Based on in silico experiments for microarray measurements of Saccharomyces cerevisiae, Lomb-Scargle is found to be the most efficacious scheme. 149 genes are then identified to be periodically expressed in the Drosophila melanogaster data set

Time-Course Analysis of Cyanobacterium Transcriptome: Detecting Oscillatory Genes

The microarray technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining these data one can identify the dynamics of the gene expression time series. The detection of genes that are periodically expressed is an important step that allows us to study the regulatory mechanisms associated with the circadian cycle. The problem of finding periodicity in biological time series poses many challenges. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, outliers and unevenly sampled time points. Consequently, the method for finding periodicity should preferably be robust against such anomalies in the data. In this paper, we propose a general and robust procedure for identifying genes with a periodic signature at a given significance level. This identification method is based on autoregressive models and the information theory. By using simulated data we show that the suggested method is capable of identifying rhythmic profiles even in the presence of noise and when the number of data points is small. By recourse of our analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a {\it Hes1} promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.Comment: 36 pages, 17 figure

Comparative Performance Analysis of the Algorithms for Detecting Periodically Expressed Genes

Thus far, a plethora of analysis on genome-wide gene expression microarray experiments on the cell cycle have been reported. Time series data from these experiments include gene expression profiles that might be periodically expressed. However, the numbers and actual genes that are periodically expressed have not been reported with consistency, analysis on similar experiments reports disparate numbers of genes that are periodically expressed with scant overlap. This work ultimately compares the performance of five spectral estimation schemes in their ability to recover periodically expressed genes profiles. Lomb-Scargle (LS), Capon, Missing-Data Amplitude and Phase Estimation (MAPES), Real Value Iterative Adaptive Approach (RIAA) and Lomb-Scargle Periodogram Regression (LSPR) are rigorously studied and pitted against each other in various simulated testing conditions. Results obtained using synthetic and microarray data reveals that RIAA is an efficient and robust method for the detection of periodically expressed genes in short time series data that might be characterized with noisy and irregularly sampled data points

RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression

An important task in astroparticle physics is the detection of periodicities in irregularly sampled time series, called light curves. The classic Fourier periodogram cannot deal with irregular sampling and with the measurement accuracies that are typically given for each observation of a light curve. Hence, methods to fit periodic functions using weighted regression were developed in the past to calculate periodograms. We present the R package RobPer which allows to combine different periodic functions and regression techniques to calculate periodograms. Possible regression techniques are least squares, least absolute deviations, least trimmed squares, M-, S- and τ -regression. Measurement accuracies can be taken into account including weights. Our periodogram function covers most of the approaches that have been tried earlier and provides new model-regression-combinations that have not been used before. To detect valid periods, RobPer applies an outlier search on the periodogram instead of using fixed critical values that are theoretically only justified in case of least squares regression, independent periodogram bars and a null hypothesis allowing only normal white noise. Finally, the package also includes a generator to generate artificial light curves

Time-course analysis of cyanobacterium transcriptome: detecting oscillatory genes

The microarray technique allows the simultaneous measurements of the expression levels of thousands of mRNAs. By mining these data one can identify the dynamics of the gene expression time series. The detection of genes that are periodically expressed is an important step that allows us to study the regulatory mechanisms associated with the circadian cycle. The problem of finding periodicity in biological time series poses many challenges. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, outliers and unevenly sampled time points. Consequently, the method for finding periodicity should preferably be robust against such anomalies in the data. In this paper, we propose a general and robust procedure for identifying genes with a periodic signature at a given significance level. This identification method is based on autoregressive models and the information theory. By using simulated data we show that the suggested method is capable of identifying rhythmic profiles even in the presence of noise and when the number of data points is small. By recourse of our analysis, we uncover the circadian rhythmic patterns underlying the gene expression profiles from Cyanobacterium Synechocystis.Facultad de Ciencias Exacta