The mathematics of cancer

Most papers, even if they show interesting results, have a limited impact on my work. Papers can yield interesting or relevant methods or results that I will aim to incorporate in my work, or they can present a new perspective on an existing problem that challenges the way I used to think before.

In the last 2-3 of years I found papers that sit somewhere between these two cathegories. For instance, I refer to Gerlinger’s paper with Swanton as the second best kind of paper you can find: one that may not change the way I see things but presents the worldview that the authors and I share to a wider audience.

Today’s paper, the one by Philipp Altrock, Lin Liu and Franziska Michor falls in the cathegory of papers that are just incredibly useful even if none of the material is particularly new to me. The reason is, of course, that this is a review paper. One of the few that Nature Reviews Cancer has published on mathematical modelling in cancer (the other two I know are the one by Sandy Anderson and the one by Helen Byrne). And it is a great summary, covering a good deal of mathematical oncology literature from recent years and highlighting some of the strengths but also weaknesses of that work.

It does not cover all the of it though. It highlights mathematical approaches such as branching and Moran processes, (ordinary and partial) diferential equations, agent-based models as well as one of my favourite tools: evolutionary game theory. Some approaches are neglected. One that comes to mind is Reniak’s Inmerse Boundary as well as other more biophysically realistic models. That is understandable given the emphasis of the review on aspects that are likely to drive evolutionary dynamics in cancer like mutations and interactions with the microenvironment.

In conclusion it is a good read that covers most of the relevant literature for those of us concerned on the evolutionary aspects of mathematical oncology. There are some things that a review like this could have covered and that might be material for a follow-up review. One (and I have taken the liberty of using a design by Arturo Araujo to illustrate the point) is that mathematical models of cancer can be used to integrate data and hypotetheses coming from different scales, experimental systems and approaches.

BD2K figure v7

This view of mathematical modelling as a multi-scale glue is what makes it such a great tool  to translate biological discoveries into clinical practice. Individual experiments and results alone are unlikely to be substantial enough to change how cancer is treated  but through the glue of mathematical modelling, a lot of these results can flesh out a bigger idea.

Another one is about how mathematical models of cancer are built, and even more relevant, how do they integrate data. You can either start with some experimental/clinical data and then build a mathematical model onto which to fit such data or… you can start from first principles and see where they take you and then experimentally validate the results. The former uses hypotheses whereas the second generates them.

I guess I should convince somebody to write a complementary review article to follow this one.
Altrock, P., Liu, L., & Michor, F. (2015). The mathematics of cancer: integrating quantitative models Nature Reviews Cancer, 15 (12), 730-745 DOI: 10.1038/nrc4029


The tools for a modern lab

Many of the faculty at the Integrated Mathematical Oncology department refer to their groups as labs (Jacob Scott’s Theory Division is one of the exceptions). This is not strange since we work in a research institute in which the vast majority of the researchers are experimentalists and where the term lab is the standard way to refer to the space/equipment as well as the people working with them. As mathematical oncologists though, and as corny as this will sound, the only strength we have is the people in the group and not the fancy machines or sophisticated techniques we might have.

But that does not mean that we do not use tools and that these tools are not very important for our work. An interdisciplinary multi-site group is a possibility nowadays but only when certain types of tools are used which is why our group is now using:

  1. Slack for internal communication: prettier than IRC, faster than email, fancier than a messenger and more multiplatform that Apple Messages or Google Hangouts would be. Perfect? not entirely: we would be more comfortable with a less propietary system, maybe a Telegram with more group collaboration options.
  2. Dropbox/OneDrive/GoogleDrive (yes, 3 of them): because that is where our grants/papers/simulation results live.
  3. Github for code: just trying to get more used to this. Usually code is developed by one person per project so we do not have the same incentives to use Github as larger groups where code is owned by more than one person. But in the interest of transparency and being open acess this is how we intend to share work with the rest of the community.
  4. Python: to play with the data coming from our models. A lot of us are still more comfortable using Mathematica or Matlab but these are not opensource so that even if we shared the code many people would not be able to do much with it.
  5. Twitter: the social network of choice for many scientists. You will find many of us on Google’s G+ too.
  6. Skype for when not all the clever people can be in the same room.
  7. Blackboards. Old school but invaluable if all the clever people are in the same room.

Other important but not mandatory tools include:

  1. Evernote: Because not everything we produce is code, a grant or paper draft.
  2. Overleaf: The best way to work on a manuscript those times in which we can get away not using MS Word.

Things we tend not to use? Phone/Fax/Pony express/Carrier pigeons.

Suggestions? The idea is to have a core set of tools that allow us to collaborate and that everybody is happy using. The last is an important point: we are reaching a stage in which people are constantly asked to create more accounts and install new applications that do not talk to each other.

Update (13th Dec 2015): Following Jacob Scott’s advice I have added the links to the various services we use.