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Case Studies in Modelling
Collective Cell Motion in Biology
Philip K Maini
Wolfson Centre for Mathematical Biology
Mathematical Inst
Oxford
UK
ACID-MEDIATED INVASION
HYPOTHESIS
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)
Gatenby-Gawlinski Model
Travelling waves of invasion
Experimental Validation
GLUCOSE-LACTATE METABOLIC
COOPERATION
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
Results
Symbiosis
Parameter Space Analysis (glucose comsuption, lactate
consumption, preference for lactate)
Results
• Symbiosis is possible but requires metabolic
activity several orders of magnitude higher
than observed in vitro.
Experiments
Experimental Results
MODELLING DYNAMICS IN THE
CRYPT
Let q be number density
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.
ACKNOWLEDGEMENTS
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Jessica McGillen
Eamonn Gaffney
Natasha Martin
Cat Kelly
Alica Martinez-Gonzalez
Victor Perez-Garcia
Philip Murray
Carina Edwards
Marcus Tindall