Mathematical modelling of insulin signalling : Effects on glucose metabolism in skeletal muscle

Sammanfattning: The use of models to understand complex phenomena is indispensable to the scientific community. The advantage of a model is that it simplifies the phenomena under study. However, a model should be only as complex as required, no more, no less. Furthermore, a model should avoid known or unknown confounding variables that might obscure the interpretations of observations. Within biology, models can be set up in many different ways, such as mathematical, graphical or verbal descriptions of the system under study. In physiology, the systems under study can be the entire animal or organs or cell cultures from it. To study some aspects of the regulation of glucose and energy homeostasis, skeletal muscles is a preferable model, as it is the main consumer of post-prandial glucose, and thus, important for maintaining whole body glucose and energy homeostasis. Incubation of skeletal muscle specimens in a suitable solution is a model-system that has been used during the last century. The availability of oxygen for energy transformation has been of major concern. Therefore, the experimental system has been validated several times with different methods, both experimentally and mathematically. The result from experimental validations indicates that glycogen content is unequally distributed within the incubated muscle specimens, with the core depleted of glycogen. Furthermore, validation done with the mathematical models describing the experimental systems indicates that oxygen diffusion is sufficient if the following assumptions are valid; homogeneous structure and that the critical value of oxygen pressure is above zero throughout the entire muscle. However, if those assumptions are invalid, the observations of some metabolic and/or signalling data might be invalid. In this thesis, those assumption are validated, with the specific aim to derive mathematical models that can be used to further analyse the metabolic data generated. Set of ordinary differential equation was used to describe the metabolic data derived from incubation of mouse extensor digitorum longus skeletal muscles preparations, paper 1. The parameters and constants were identified within the mathematical model, which then, was further analysed. The results indicated that the experimental system suffered from anoxia and that glycogen was depleted during the incubation time. An immunohistochemical approach was used to verify the predictions from the mathematical model on glycogen depletion, paper 2. A statistical approach was developed herein that made quantitative studies possible and the results verified the prediction from the mathematical model in paper 1. Furthermore, a correlation between fibre type distribution and glycogen depletion was observed, indicating that the assumption on homogeneous glucose handling might be too hard. The existence of anoxia within the incubated muscle specimens was revealed. A novel hypothesis regarding deficient insulin diffusion into the centre of the incubated muscle preparation as the cause for quasi-depletion of glycogen was tested, paper 3. The hypothesis was falsified; instead increased insulin signalling was observed in the core of the muscle, correlating with fibre types on the single-cell-level. In conclusion, the studies presented in this thesis provide evidence that muscle preparations are suffering of anoxia after incubation leading to depletion of glycogen. Furthermore, the assumption on homogeneous glucose handling is falsified. Finally, a mathematical model is provided that can be used to estimate the un-measurable glycogen concentrations and estimate the glucose uptake rate in the superficial fibres.