The insulin signalling cascade is one of the most important regulatory and signalling pathways in humans. Dysregulation or dysfunction of the insulin signalling pathways often underlies the molecular ætiology of diseases such as diabetes, obesity, and Alzheimer’s. In turn, these diseases are the harbingers of various co-morbidities such as cardio-vascular disease, chronic inflammation, and dementia. The healthcare, economic, personal, and mortality burden of these diseases cannot be overstated. Mathematical modelling of insulin signalling is indispensable in the effort to understand the dynamics of the insulin signalling cascade and how malfunctions therein lead to disease. However, despite the availability and complexity of existing models, few have explicitly connected the signalling cascade, glucose transporter activity, and metabolism with one another. In order to study these interactions, a `three-module’ approach was adopted that defined the signalling cascade, glucose transporter activity, and metabolism as core, `input-output’ modules. The present work is limited to the signalling cascade and glucose transporter activity modules whereas work by Dr. Cobus van Dyk is concerned with the metabolic module. With this in mind, this thesis sets forth three aims. Firstly, to establish standardised culturing conditions which can be used to determine the basal state of insulin signalling and glucose transporter activity. Secondly, to develop a core, mathematical model based on Western blotting and radio-labelled glucose -assay data which is able to describe the concentration- and time-dependence of the signalling cascade and glucose transporter activity in response to insulin. Thirdly, to determine the clustering behaviour of GFP-tagged GLUT4 molecules in response to insulin. The first goal was to standardise culturing conditions. Herein, the ability of high (25mM), medium (15mM), and low (5mM) glucose culturing conditions were evaluated with regards to their ability to sensitise or desensitise the insulin signalling cascade as well as the degree to which they are able to induce the differentiation of C2C12 myoblasts into myocytes. The glucose and lactate concentrations in the external media were used to determine the glucose-lactate flux of the C2C12 cells. This served as a proxy for the induction of insulin-dependent glucose transport and metabolism. A modified Ladd staining protocol was used to assess the degree to which C2C12 cells could differentiate under the culturing protocols. The second goal was to construct a core, mathematical model of insulin signalling and glucose transporter activity. The time-dependent phosphorylation and dephosphorylation of the insulin receptor and the serine 473 and threonine 308 sites of Akt in response to varying insulin concentrations was investigated using Western blotting techniques. The glucose transporter (GLUT4) activity was assayed using radio-carbon glucose. The data were used to optimise parameters for a core, ODE-based model of the signalling and glucose transporter modules. The third goal, to investigate the clustering behaviour of GLUT4 in response to insulin, was investigated by using confocal microscopy to image GFP-tagged GLUT4 molecules before and after being stimulated with insulin. A hierarchical clustering algorithm as well as further geometric and statistical analyses were used to determine the number, size, density, and distribution of GLUT4 clusters pre and post insulin exposure. Of the remaining chapters, Chapter 1 discusses the background, context, scope, and aims of this study as well as further elaborating on the `three module’ approach. The literature review in Chapter 2 provides an overview of the relevant literature as delineated by the scope and aims of this study. The materials and methods are provided in Chapter 3, with specific alterations or methodologies being further discussed in the relevant experimental chapters. The final chapter, Chapter 7, provides the reader with general discussions, limitations, and final thoughts concerning this work.