| Summary: | A working internal circadian clock allows a healthy organism to keep time in order to anticipate transitions between night and day, allowing the temporal optimisation and control of internal processes. The internal circadian clock is regulated by a set of core genes that form a tightly coupled oscillator system. These oscillators are autonomous and robust to noise, but can be slowly reset by external signals that are processed by the master clock in the brain. In this thesis we explore the robustness of a tightly coupled oscillator model of the circadian clock, and show that its deterministic and stochastic forms are both significantly robust to noise. Using a simple linear algebra approach to rhythmicity detection, we show that a small set of circadian clock genes are rhythmic and synchronised in mouse tissues, and rhythmic and synchronised in a group of human individuals. These sets of tightly regulated, robust oscillators, are genes that we use to de ne the expected behaviour of a healthy circadian clock. We use these “time fingerprints" to design a model, dubbed “Time-Teller", that can be used to tell the time from single time point samples of mouse or human transcriptome. The dysfunction of the molecular circadian clock is implicated in several major diseases and there is significant evidence that disrupted circadian rhythm is a hallmark of many cancers. Convincing results showing the dysfunction of the circadian clock in solid tumours is lacking due to the difficulties of studying circadian rhythms in tumours within living mammals. Instead of developing biological assays to study this, we take advantage of the design of Time-Teller, using its underlying features to build a metric, Θ, that indicates dysfunction of the circadian clock. We use Time-Teller to explore the clock function of samples from existing, publicly available tumour transcriptome data. Although multiple algorithms have been published with the aims of “time-telling" using transcriptome data, none of them have been reported to be able to tell the times of single samples, or provide metrics of clock dysfunction in single samples. Time-Teller is presented in this thesis as an algorithm that both tells the time of a single time-point sample, and provides a measure of clock function for that sample. In a case study, we use the clock function metric, , as a retrospective prognostic marker for breast cancer using data from a completed clinical trial. Θ is shown to correlate with many prognostic markers of breast cancer, and we show how could also be a predictive marker for treatment efficacy and patient survival.
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