Case Studies in Modelling Collective Cell Motion in Biology

Philip K MainiWolfson Centre for Mathematical Biology

Mathematical InstOxford

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

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