Competition and evolutionary-enlightened treatments: competition (part 1)

Here at Moffitt we are privileged to work with physician-scientists like Bob Gatenby that understands and encourages the use of mathematical modeling in cancer. It is his effort, after all, that made our department of Integrated Mathematical Oncology possible in the first place.

One of the ideas that Bob has been championing is called Adaptive Therapies (AT). This approach (explained in Gatenby et al CR 2009 and Silva et al CR 2012) means that instead of trying to kill all the tumor cells we can with standard treatments like chemotherapy, we should instead aim to just kill as many as we can get away with without selecting too strongly for resistant cells. The basic facts are that in a heterogeneous tumor (like most are), resistance is likely present before the application of the treatment. Also, in the case of chemotherapy, resistance comes at a cost to the resistant cell: the energy required to produce the pumps to discard the drug before it causes any harm would impact the cell’s proliferation.

With these two pieces of information, the idea is that ATs work by letting the tumor susceptible population recover from the treatment and limit the proliferation of the chemo-resistant cells. Basically you give up on the dream of completely eradicating the cancer in a patient for the more solid possibility of being able to control its growth and manage resistance.

During my meeting in Barcelona, a few days ago, I met with researchers working on managing the emergence of resistance in a variety of fields including bacteria and agriculture. One of the atendees was Andrew Read, a biologist from Penn State with a distinctive Kiwi accent, working on infectious diseases. My understanding of the conversation was that he was not convinced that there was enough evidence that susceptible cells supress the growth of resistant ones. He (together with Silvie Huijben and Troy Day) posits that in managing diseases like malaria with existing drugs, relative fitness is not as important as absolute fitness.

Here is the logic, which feels rather intuitive: resistant cells may grow at a slower pace but if there are abundant resources and space and all the relevant action happens on the growing edge of the tumour then where’s the competition that will make sure resistance cells are kept in check?

The image that heads this post corresponds to a simulation image of a very simple agent-based model where every pixel represents a cell. The colours (mostly shades of grey) represent the degree of resistance (1-100) so that darker shades are less resistant and tad faster proliferators. As the tumour grows from the middle it becomes easy to see that:

  1. Heterogeneity appears and given the weakness of selection is, to some extent, maintained.
  2. The tumour gets darker as it grows showing that, over time, the faster proliferating/less resistant cells increase their proportion of the tumour burden.

The simulation can be seen more clearly here:

Untitled.001
Average # of receptors over time as the tumor grows

As the above figure shows, our interpretation of the head figure is not misleading: as the tumor grows the average cell decreases in resistance potential and increases in proliferative potential.

Certainly not groundbreaking results but they help define our intuition of how even small differences in proliferation can lead to dominance of certain clones on the growing edge of a tumour. As we start with a cell with moderate amounts of resistance/growth (30/100), we see how faster proliferators (with values that quickly reach the low 10s and then 1) start occupying increasingly more of the space on the edge of the tumour. Thus limiting the proliferation of cells that have more resistance. This is taking into consideration that mutations are relatively rare (1%) and very incremental (they change resistance/growth by 1 unit). Why is this important? without that dominance in the tumour’s growing edge, ATs are a non-starter. We will see soon why this is important.

Code for this quick and dirty model can be found in my github.

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