JTK_CYCLE: an efficient nonparametric algorithm for detecting rhythmic components in genome-scale data sets

Abstract

Circadian rhythms are oscillations of physiology, behavior, and metabolism that have period lengths near 24 hours. In several model organisms and humans, circadian clock genes have been characterized and found to be transcription factors. Because of this, researchers have used microarrays to characterize global regulation of gene expression and algorithmic approaches to detect cycling. This article presents a new algorithm, JTK_CYCLE, designed to efficiently identify and characterize cycling variables in large data sets. Compared with COSOPT and the Fisher's G test, two commonly used methods for detecting cycling transcripts, JTK_CYCLE distinguishes between rhythmic and nonrhythmic transcripts more reliably and efficiently. JTK_CYCLE's increased resistance to outliers results in considerably greater sensitivity and specificity. Moreover, JTK_CYCLE accurately measures the period, phase, and amplitude of cycling transcripts, facilitating downstream analyses. Finally, JTK_CYCLE is several orders of magnitude faster than COSOPT, making it ideal for large-scale data sets. JTK_CYCLE was used to analyze legacy data sets including NIH3T3 cells, which have comparatively low amplitude oscillations. JTK_CYCLE's improved power led to the identification of a novel cluster of RNA-interacting genes whose abundance is under clear circadian regulation. These data suggest that JTK_CYCLE is an ideal tool for identifying and characterizing oscillations in genome-scale data sets.

Figure 1. JTK_CYCLE reliably detects cycling transcripts

To simulate circadian gene expression, a test set of 1024 ‘transcripts’ was randomly generated with 48 time points per transcript. Half of these transcripts were non-rhythmic with amplitudes equal to zero; the other half consisted of transcripts with amplitudes ranging from one (weakly rhythmic) to six (strongly rhythmic). JTK_CYCLE (A), COSOPT (B), and Fisher’s G-test (C) were used to analyze these data, and −Log 10 p-values were plotted as a function of the true amplitude. JTK_CYCLE reliably distinguished rhythmic from non-rhythmic transcripts; in comparison, COSOPT and Fisher’s G-test showed considerable overlap between the null-distribution and the true-positives.

Figure 2. JTK_Cycle outperforms Fisher’s G-test and COSOPT at both 1-and 4-hour sampling resolutions

Using the results from Figure 1, ROC plots were generated to visualize the sensitivity and specificity of JTK_Cycle (A, B), COSOPT (C, D) and Fisher’s G-test (E, F) at both one (left) and four (right) hour sampling resolutions. Color-coded lines represent −Log 10 p-values.

Figure 3. JTK_CYCLE accurately estimates the period length of cycling transcripts

A test set of 512 rhythmic ‘transcripts’ was generated with period lengths ranging from 20–30 hours. JTK_CYCLE (A), COSOPT (B), and Fisher’s G-test (C) were used to estimate the period length of these transcripts. JTK_CYCLE (R² = 0.926) and COSOPT (R² = 0.732) periods varied linearly with the true period; in contrast, Fisher’s G test (R² = 0.053) was considerably less accurate in estimating period. Dotted lines represent the expected values of these distributions.

Figure 4. JTK_CYCLE reliably estimates phase and amplitude of cycling transcripts

A test set of 512 rhythmic ‘transcripts’ was generated with phases varying uniformly across the period length and amplitudes ranging from one (essentially non-rhythmic) to six (strongly rhythmic). JTK_CYCLE was used to estimate the phase of these transcripts. In (A), JTK_CYCLE phase is plotted as a function of the true phase showing a strong linear correlation (R² = 0.766). Note that phase is defined as the time point at which the underlying curve reaches its maximum value; consequently, given the cyclical nature of the circadian clock, the outliers observed on both the x-and y-axes are in much closer agreement with their expected values than they appear. In (B), JTK_CYCLE amplitude is plotted as a function of true amplitude, revealing a strong linear correlation (R² = 0.912). Dotted lines represent the expected values of these distributions.

Figure 5. DAVID analysis of cycling genes detected by JTK_CYCLE in NIH3T3 cells reveals a cluster of RNA-binding genes with similar phases

JTK_CYCLE was used to re-analyze cycling transcripts in synchronized NIH3T3 cells (Hughes et al. 2009). JTK_CYCLE detected more than twice as many cycling transcripts (N=30) as previously reported. DAVID analysis was performed on these 30 transcripts to detect enriched functional classes. Among the most enriched groups was a cluster of eight genes involved in RNA binding and recognition (A). Green blocks indicate that the annotations on the x-axis are present in the genes on the y-axis. Of these eight genes, six show similar phases of their oscillations (B), suggesting a common underlying mechanism (the dotted line represents a moving average of the median-normalized expression patterns of all six transcripts).