CIRCADA: Shiny Apps for Exploration of Experimental and Synthetic Circadian Time Series with an Educational Emphasis

Abstract

Circadian rhythms are daily oscillations in physiology and behavior that can be assessed by recording body temperature, locomotor activity, or bioluminescent reporters, among other measures. These different types of data can vary greatly in waveform, noise characteristics, typical sampling rate, and length of recording. We developed 2 Shiny apps for exploration of these data, enabling visualization and analysis of circadian parameters such as period and phase. Methods include the discrete wavelet transform, sine fitting, the Lomb-Scargle periodogram, autocorrelation, and maximum entropy spectral analysis, giving a sense of how well each method works on each type of data. The apps also provide educational overviews and guidance for these methods, supporting the training of those new to this type of analysis. CIRCADA-E (Circadian App for Data Analysis-Experimental Time Series) allows users to explore a large curated experimental data set with mouse body temperature, locomotor activity, and PER2::LUC rhythms recorded from multiple tissues. CIRCADA-S (Circadian App for Data Analysis-Synthetic Time Series) generates and analyzes time series with user-specified parameters, thereby demonstrating how the accuracy of period and phase estimation depends on the type and level of noise, sampling rate, length of recording, and method. We demonstrate the potential uses of the apps through 2 in silico case studies.

Keywords: Shiny app; biological oscillations; circadian rhythms; data analysis; discrete wavelet transform; mathematical analyses; periodogram.

Figure 1.

Partial screenshot of CIRCADA-S Summary tab, comparing results from the five methods for a set of 1,000 generated time series with the user-selected characteristics. The histograms of period errors demonstrate the differences between the methods. The DWT, autocorrelation, and Lomb-Scargle produce discrete estimates with possible values determined by the sampling interval and number of cycles, while sine-fitting and MESA produce finer-grained estimates.

Figure 2.

Errors in estimating period using sine-fitting (left) and Lomb-Scargle (right) methods for 1,000 noisy sinusoids with normally distributed periods (mean 24 h, SD 0.5 h), amplitude 1, noise standard deviation 0.5 with pink noise, and quadratic trend, for indicated number of days and sampling interval.

Figure 3.

Power study using generated time series. Top: example of a 4-day noisy sinusoid. Bottom: Probability of detecting a significant different in sine-fit period between two groups for the indicated number of samples and length of time series (using t.test in R), where the true means are 23.35 and 23.85 h. Periods within each group are normally distributed with standard deviation 0.25h, amplitude is 1, noise is pink with standard deviation is 0.5, trend is quadratic, and a sampling interval is 0.5h. Around 30 samples would be needed to obtain a statistical power of 0.80 using a 3-day duration, while increasing the duration to 4 days substantially decreases the required sample size to just over 20.