Functional Data Analysis and QTL Detection Across Time within the Circadian Clock

Circadian data are typically analysed using the Fast Fourier Transform Non- Linear Least Squared method. The purpose of my project was to develop a new approach and to apply this to the analysis of rhythms for Quantitative Trait Locus (QTL) mapping over a time domain. This was achieved by examining the rhythms as functional data. The data used for this process came from what is known as the W9W recombinant inbred line population of Arabidopsis thaliana plant. Contrasting conditions of light and dark were also examined. The data consisted of circadian rhythm measurements that were expressed through the CCR2 gene measured by luciferase imaging of living plants. In order to facilitate exploratory analysis of the way in which the curves behaved, they were smoothed and fitted using basis functions. Through this process the circadian rhythms were transformed from discrete observations to clearly defined functions. From there, derivatives were taken and both velocity and acceleration were examined. This led to the identification of changes in length of period between wild-type and mutant plants, as well as allowing direct comparisons of the curves behaviour between differing light and dark conditions. Having examined the correlation functions of the population free-running in darkness, further exploration was carried out by conducting principal-component analysis. This enabled the main types of variability in the wild type and mutant to be identified and analysed. QTL mapping analysis was then performed in the time domain measuring velocity with plants free-running in darkness. Viewing these data as functions allowed for a thorough and detailed exploration. This led to the discovery of new genetic information that would have otherwise have been overlooked. Overall, the techniques used in this project have opened the door to further study and investigation of the quantitative basis of circadian rhythms.