An exactly solvable, spatial model of mutation accumulation in cancer

Developers

Chay Paterson, Martin A. Nowak, Bartlomiej Waclaw.

Description of the technology

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate large and clinically detectable solid tumours.

This technology proposes an exactly solvable mathematical model of a tumour featuring replication of cancer cells, mutations endowing cells with fitness advantage, and migration that causes cells to disperse. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. It was also shown that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time.

Practical application

The technology is highly applicable for prognosis of cancer development. These predictions can be made for two aspects of cancer: growth laws, and genetic heterogeneity of tumours.

Analytical solubility (the possibility to get exact analytical solutions) means that the model works for tumours of any size, including large masses that need to be surgically removed, and it can be thus used to model cancer progression in humans.

The model can be used for computer simulation of tumors with the purpose of the drug discovery, the creation of the anti-cancer therapies and others.

Laboratories

• SUPA, School of Physics and Astronomy, The University of Edinburgh, Edinburgh (United Kingdom)
• Program for Evolutionary Dynamics, Harvard University, Cambridge (USA)
• SynthSys-Synthetic & Systems Biology, The University of Edinburgh, Edinburgh (United Kingdom)

Links

Publications

• Paterson, C., Nowak, M.A., Waclaw, B. «An exactly solvable, spatial model of mutation accumulation in cancer." 6 Scientific Reports, (2016): 39511.
• Waclaw, B. et al. «A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity." 526 Nature, (2015): 261–264.
• Antal, T., Krapivsky, P. L. & Nowak, M. A. «Spatial evolution of tumors with successive driver mutations." Physical Review E 92 (2015).