easyClock: a simple desktop app for analyzing and showing daily biological rhythms

Following data input and preview, users can select a file for analysis (Fig. 1D & E). All time-series within the selected file are analyzed, with users prompted to specify the period of interest; a minimum of 48 h is recommended. The current version of easyClock includes four analytical regression methods: Cosinor, Cosine-Kendall, Python-JTK, and Harmonic-Cosinor. To handle autoregressive (AR) noise [19, 20] or non-stationary oscillations [21] often present in real biological data, easyClock also integrates modules that correct for or characterize these effects. Besides, inter-individual variability and group differences can be efficiently assessed using linear mixed-effects modeling [22].

Both the Cosinor and Cosine-Kendall are designed for analyzing cosine-like rhythmic data. In easyClock, the Cosinor method applies ordinary least squares regression to fit a linearized cosine model to the data [11]: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y = M + \beta_{{1}} {\mathrm{cos}}\left( {wx} \right) \, + \, \beta_{{2}} {\mathrm{sin}}\left( {wx} \right) + \varepsilon$$\end{document}. Rhythmicity is assessed using an F-test for the null hypothesis: β₁ = β₂ = 0. To control for false positives across multiple comparisons within each time series (i.e., across different periods), p-values are adjusted using the Bonferroni correction. The Cosine-Kendall method extends the Cosinor approach by ranking the data to reduce the influence of outliers or non-Gaussian noises. It measures concordance between the ranked input and each ranked cosine reference using the non-parametric test–Kendall's tau rank correlation [23]. The lowest p value from the best-fitting model is selected, and Bonferroni correction is applied for multiple period and lag tests within each time series.

The easyClock package also features a non-parametric test, Python-JTK, which is a modified reimplementation of the original JTK_CYCLE algorithm. Originally developed for R, JTK_CYCLE is widely used for detecting circadian rhythms [10]. It operates by performing rank-based comparisons between the input data and a library of discrete, triangle-shaped templates that may be either symmetric or asymmetric. In easyClock, Python-JTK uses Kendall's tau both to measure similarity and assess statistical significance, bypassing the Jonckheere–Terpstra (JT) test employed in the original algorithm. A key advantage of Python-JTK in easyClock is its ability to automatically accommodate both regular and irregular time intervals, making it suitable for a wide range of experimental designs. To improve computational efficiency, easyClock allows users to customize parameters such as expected period, acrophase, and asymmetry, thereby reducing the number of template comparisons and accelerating the analysis. The Benjamini–Hochberg procedure is applied to adjust raw p-values (reported as BH.Q) when group sizes are large, while the Bonferroni correction is applied within each time series when analyzing smaller group sizes (reported as ADJ.P). To handle the AR noise commonly present in real biological data, easyClock also integrates an AR-JTK module that automatically detects and removes this noise before re-analysis.

Drosophila behaviors, such as sleep and locomotor activity, frequently display bimodal patterns under 12-/12-h light/dark cycles [24]. Traditional unimodal analysis methods are inadequate for capturing these complex rhythms. To address this, easyClock incorporates Harmonic-Cosinor analysis (also known as multiple-component cosinor [25]), which enables the fitting of bimodal waveforms by combining multiple sine and cosine components within each cycle (two components in the current version). The concordance between input data and each composite waveform reference is assessed using Kendall's tau rank correlation, as demonstrated in the Cosinor-Kendall and Python-JTK methods.

In addition to data preview (Fig. 3A), easyClock enables automatic generation of various graphs (Fig. 1F). Actograms are widely used in circadian rhythm research for visualizing rhythmic patterns and phase shifts in time-series data. Users can quickly export double-plotted actograms (Fig. 3B) for any selected group with a few intuitive clicks, without the need to adjust parameters.

Furthermore, easyClock provides visualization of fitted models following analysis. For each dataset, it displays the best fit of the selected model on the original or group-averaged time series, allowing users to visually assess the quality of rhythmicity detection. Depending on the selected method, users can visualize the fitting results of Cosinor analysis, Cosine-Kendall, Python-JTK, and Harmonic-Cosinor (Fig. 3C–F). Additionally, easyClock can provide visualization of the optimal Python-JTK fit with AR correction (Fig. 3G, H).

Omics approaches are widely used to screen for cycling genes or proteins, but their scale and complexity pose challenges for rhythmicity analysis. For example, a time-series transcriptome in Drosophila typically comprises thousands of genes, leading to millions of statistical comparisons. To demonstrate how easyClock simplifies these procedures, we re-analyzed a previously published transcriptomic dataset.

We identified 272 genes with BH.Q < 0.05 in both replicates, including core clock genes such as per, tim, vri, Pdp1, and cry [26, 27] (Fig. 4C). This approach may increase the FDR since replicate-specific noise (e.g., phase-inverted fluctuations) could meet the significance threshold in both replicates without representing reproducible cycling patterns. To address this, we subsequently determined Spearman correlations between replicates for these 272 candidate genes. Sixty genes showed significant positive correlations between replicates (p < 0.05, r > 0), including per, tim, vri, and cry (Fig. 4D). Of these, 52 genes were previously reported as cyclic [7], while 8 genes—including lolal, CG3940, CdsA, alpha-Est10, Ost48, Dh44-R2, CG11241, CG30493—were newly identified and displayed weak cycling patterns (Fig. 4E; Supplementary Fig. 1).

Previous studies combined the replicates for analysis [7], differing from our hybrid approach (intersection + correlation). Nonetheless, easyClock supports both independent and grouped replicate workflows; grouping reduces analysis time but increases file loading duration. Using grouped replicates in easyClock, we identified 1,726 genes with BH.Q < 0.05. Among the 268 previously recognized cycling genes [7], 232 were detected in our grouped analysis, including per,tim, vri, Pdp1, and cry. The Clk gene was newly detected with easyClock in the grouped analysis (Fig. 4F), highlighting the tool's high sensitivity for detecting low-amplitude cycling patterns (Fig. 4G). Overall, easyClock offers an efficient, user-friendly platform for rapid analysis of time-series omics data.