Thesis
Mathematical modelling of the tumour microenvironment : the causes and consequences of tumour acidity
- Creator
- Awarding institution
- University of Strathclyde
- Date of award
- 2012
- Thesis identifier
- T13395
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- Extracellular acidity and high levels of lactate are commonly observed in solid tumours. Some tumours also exhibit a reversed cellular pH gradient with an intracellular pH that is higher than the extracellular. This has been shown to play a crucial part in not only the invasive and metastatic cascade of tumours, but also on their response to therapies. In this thesis, we present four different mathematical models that examine the possible causes of tumour acidity and its effect on cell metabolism and tumour invasion. In the second chapter, we derive an ordinary differential equation model that explicitly focus on the interplay between H+-ions and lactate. We subject the model to qualitative and quantitative analysis and, in particular, we study the effect in the variations of key parameter estimates on the emergence of a reversed transmembrane pH gradient within the tumour. The model predicts that a re- versed pH gradient is attainable under aerobic conditions when sources of H+-ions other than those from glycolysis are decreased and the lactate/H+ cell membrane transporter (MCT) activity is increased - but we find the intra- and extracellular pH values in this case to be too alkaline to be physiological. Under anaerobic conditions, we find that decreasing the sources of H+-ions other than those from glycolysis and also the glycolytic rate gives rise to a reversed cellular pH gradient, but again for intra- and extracellular pH values that are far from realistic biologically. In the third chapter, we present an extension to the first model by including the spatial diffusion of hydrogen ions and lactate. This spatial extension also predicts ii a reversed transmembrane pH gradient but this time for more realistic intra- and extracellular pH values. We find that low levels of blood lactate can give rise to a reversed pH gradient throughout the spatial domain independent of the levels of tissue lactate. Likewise, we have found the existence of a negative pH gradient to be strongly dependent on the combined activity of a lactate/H+ cell membrane transporter and other sources of H+-ion. In the fourth chapter, we study the role of oxygen and pH on early tumour growth using a hybrid cellular automaton model. We examine whether the levels of oxygen, intra- or extracellular pH are the dominating metabolites driving tumour growth and phenotypic transformations. This model predicts that when tumour cells are strongly sensitive to changes in the intracellular pH, a low activity of the Na+/H+ cell membrane transporter (NHE) or a high rate of anaerobic glycolysis can give rise to a "fingering" morphology. Furthermore, we show that as the activity of the MCT transporter increases, all the tumour cells within the spheroid can exhibit a reversed transmembrane pH gradient. In the fifth chapter, we examine the effect of extracellular acidity on tumour invasion focusing, in particular, on cellular adhesion, matrix-degrading enzyme activity and cellular proliferation. Our numerical simulations using a cellular Potts model show that, under acidic extracellular pH, cell-ECM adhesion strength has a comparable effect on tumour invasiveness as the rate at which the ECM is degraded by proteolytic enzymes. We also show that tumour cells cultured under physiological pH tend to be larger and develop a "diffuse" morphology compared to those cultured at acidic pH which display protruding "fingers" at the advancing tumour front.
- Resource Type
- DOI
- Date Created
- 2012
- Former identifier
- 989359
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