Clustering Nonstationary Circadian Rhythms using Locally Stationary Wavelet Representations

Abstract

ArticleAbstract. Rhythmic processes are found at all biological and ecological scales, and are fun-5 damental to the efficient functioning of living systems in changing environments. The biochemical 6 mechanisms underpinning these rhythms are therefore of importance, especially in the context of 7 anthropogenic challenges such as pollution or changes in climate and land use. Here we develop and 8 test a new method for clustering rhythmic biological data with a focus on circadian oscillations. The 9 method combines locally stationary wavelet time series modelling with functional principal compo-10 nents analysis and thus extracts the time-scale patterns arising in a range of rhythmic data. We 11 demonstrate the advantages of our methodology over alternative approaches, by means of a simula-12 tion study and real data applications, using both a published circadian dataset and a newly generated 13 one. The new dataset records plant response to various levels of stress induced by a soil pollutant, a 14 biological system where existing methods which assume stationarity are shown to be inappropriate. 15Our method successfully clusters the circadian data in an interesting way, thereby facilitating wider 16 ranging analyses of the response of biological rhythms to environmental changes. 17Key words. evolutionary wavelet spectrum, nondecimated wavelet transform, nonstationary 18 processes, unsupervised learning, plant circadian clock 19

Physiological and Genetic Dissection of Sucrose Inputs to the Arabidopsis thaliana Circadian System

“…It has been recently proposed that the Arabidopsis oscillator is not fixed but dynamically responds to both external and internal stimuli [23,42]. Our work here further supports such a fluid nature.…”

Multiple metals influence distinct properties of the Arabidopsis circadian clock

“…Traditionally, the analysis of (rhythmic) circadian data has centred around the investigation of how certain circadian clock parameters (periodicity, phase, amplitude and clock precision) are affected (supplementary Fig S1 provides a brief introduction into the nature of these parameters [20,23,55]).…”

Wavelet spectral testing: Application to nonstationary circadian rhythms

“…If the changes are limited to period and/or phase then existing Fourier-based theory may be adequate. However, when the changes to the circadian clock are less straightforward, for example involving non-stationarity or changes at multiple scales (Hargreaves et al, 2018), the application of these established methods may be conducive to misleading conclusions. The potential value of our approach is illustrated by three complementary examples, encompassing the effect of various salt stresses on plants, the identification of mutations inducing rapid rhythms, and the response of nematode clocks to pharmacological treatment, as described in the following sections.…”

“…The primary contribution of this work is the development of novel wavelet-based hypothesis tests that allow for circadian behaviour comparison while accounting for data nonstationarity. A substantial body of circadian literature advocates the use of wavelet (Price et al, 2008;Harang et al, 2012;Leise et al, 2013) and in particular spectral representations (Hargreaves et al, 2018) of circadian rhythms. This motivates our choice to formally compare circadian signals in the wavelet spectral domain by using their time-scale signature patterns and thus accounting for their proven nonstationary features.…”

“…However, for many real time series, including our circadian datasets, this is unrealistic (Price et al, 2008) and a model where the frequency behaviour can vary with time is needed. Motivated by literature advocating wavelets as analysis tools for circadian rhythms (Leise et al, 2013), we adopt the locally stationary wavelet (LSW) process model of Nason et al (2000) with previously demonstrated utility for circadian analysis (Hargreaves et al, 2018). In a nutshell, the Fourier building blocks in equation (2.1) are replaced by families of discrete nondecimated wavelets and an LSW process {X t ;T } T −1 t =0 , T = 2 J ≥ 1 is represented as follows…”