Spatio-temporal inference for circadian gene transcription in the mammalian SCN

Almost all life on earth exhibit circadian rhythms of behaviours that are tied to the natural day and night cycle. In mammals, the suprachiasmatic nucleus (SCN) is responsible for generating and communicating these rhythms to peripheral tissues. The neurons of the SCN function as noisy molecular clocks, expressing circadian genes in an oscillatory fashion over the course of 24 hours through a transcriptional/translational feedback loop (TTFL). The cells synchronise to form a robust clock, capable of exact timekeeping and entrainment to external stimuli, e.g. light, via intercellular signalling. This thesis investigates spatio-temporal inference for stochastic models of the TTFL, motivated by the availability of high-resolution bioimaging data of core circadian genes Period and Cryptochrome from mouse SCN. We begin by introducing the mammalian clock and SCN bioimaging data. We then cover various methodologies for mechanistic and stochastic modelling of gene transcription, including chemical reaction networks, the chemical Langevin equation, and Markov chain Monte Carlo methods for Bayesian inference. We derive stability criteria for a model of the single-cell TTFL that describes transcriptional inhibition through a distributed delay. The model is fitted to imaging data of the gene Cry1, which allows us to infer the dynamics of circadian gene transcription and molecular population sizes. A Bayesian hierarchical framework is developed to model spatial dependencies observed in the parameter estimates of the single-cell model. The methodology is applied to bioimaging data of the Cry1-gene and the analysis tools are developed further by deriving a Bayesian period estimator and an inhibition profile which allow us to study the spatial distribution of key properties of the TTFL across SCN tissue. Finally, the methodology is extended to include an additional molecular species that captures transcriptional activation. This extension confers a mechanistic spatial interpretation to the model by describing the effect of intercellular signalling. By eliciting informative prior distributions for parameters of the circadian Per2 feedback loop, we are able to fit the model to simultaneous recordings of Per2 and calcium. The model fit represents a first step in obtaining a complete model of both single-cell and organ-wide dynamics with empirically estimated parameters