Sensitivity analysis in systems biology modelling and its application to a multi-scale model of blood glucose homeostasis

Biological systems typically consist of large numbers of interacting components and involve processes at a variety of spatial, temporal and biological scales. Systems biology aims to understand such systems by integrating information from all functional levels into a single cohesive model. Mathematical and computational modelling is a key part of the systems biology approach and can be used to produce composite models which describe systems across multiple scales. One of the major diculties in constructing models of biological systems is the lack of precise parameter values which are often associated with a high degree of uncertainty. This uncertainty in parameter values can be incorporated into the modelling process using sensitivity analysis, the systematic investigation of the relationship between uncertain model inputs and the resulting variation in the model outputs. This thesis discusses the use of global sensitivity analysis in systems biology modelling and addresses two main problem areas: the application of sensitivity analysis to time dependent model outputs and the analysis of multi-scale models. An approach to the analysis of time dependent model outputs which makes use of principal component analysis to extract the key modes of variation from the data, is presented. The analysis of multi-scale models is addressed using group-based sensitivity analysis which enables the identication of the most important sub-processes in the model. Together these methods provide a new methodology for sensitivity analysis in multi-scale systems biology modelling. The methodology is applied to a composite model of blood glucose homeostasis that combines models of processes at the sub-cellular, cellular and organ level to describe the physiological system. The results of the analysis suggest three main points about the system: the mobilisation of calcium by glucagon plays a minor role in the regulation of glycogen metabolism; auto-regulation of hepatic glucose production by glucose is important in regulating blood glucose levels; time-delays between changes in blood glucose levels, the release of insulin by the pancreas and the eect of the hormone on hepatic glucose production are important in the possible onset of ultradian glucose oscillations. These results suggest possible directions for further study into the regulation of blood glucose