1. Case Studies in Modelling Collective Cell Motion in Biology Philip K Maini Wolfson Centre for Mathematical Biology Mathematical Inst Oxford UK

2. ACID-MEDIATED INVASION HYPOTHESIS

3. Acid-Mediated Invasion Hypothesis A bi-product of the glycolytic pathway is lactic acid – this lowers the extracellular pH so that it favours tumour cell proliferation AND it is toxic to normal cells. R.A. Gatenby and E.T. Gawslinski, A reaction-diffusion model of cancer invasion, Cancer Research, 56, 5745-5753 (1996)

4. Gatenby-Gawlinski Model

5. Travelling waves of invasion

17. Experimental Validation

18. GLUCOSE-LACTATE METABOLIC COOPERATION

22. The alphas GLUT expression is hypoxia-induced, MCT1 expression is hypoxia-repressed. If cell expression of MCT1 is high relative to that for GLUT, then alpha_L > alpha_G etc

23. Results

24. Symbiosis

25. Parameter Space Analysis (glucose comsuption, lactate consumption, preference for lactate)

26. Results Symbiosis is possible but requires metabolic activity several orders of magnitude higher than observed in vitro.

27. Experiments

28. Experimental Results

29. MODELLING DYNAMICS IN THE CRYPT

37. Let q be number density

39. Conclusions Explored effects of metabolism in tumour growth. Used a multiscale model of the crypt to explore the effects of key processes thought to determine cell progression and fixing.

40. ACKNOWLEDGEMENTS Jessica McGillen Philip Murray Eamonn Gaffney Carina Edwards Natasha Martin Marcus Tindall Cat Kelly Alica Martinez-Gonzalez Victor Perez-Garcia