## Wednesday, 22 May 2013

### Mathematical biology or Bioinformatics

Conversation overheard in an inter-disciplinary research centre of unknown location.

Molecular Biologist: So, what kind of research do you do?
Mathematical Biologist: I do modelling, mathematical modelling of cancer.
Molecular Biologist: I see, interesting. So you mean bioinformatics?
Mathematical Biologist (trying to be polite): Well, not quite. My work is more about building mechanistic models that help our understanding of different steps of tumour progression.
Molecular Biologist: I never quite understood all those statistical methods and hypothesis testing, but I'm glad someone likes it!
Mathematical Biologist (slowly losing patience): Well actually….I'm not very good with statistics either, my work is more about understanding the mechanisms at work in cancer, using mathematics.
Molecular Biologist: Oh, I think I understand now. By the way, I have some microarray-data that maybe you can have a look at.
Mathematical Biologist (squeezing through the opening elevator doors): Ok…..drop me an email.

This dialogue is fictional but draws inspiration from the many encounters and discussions I've had about my research with biologists. Usually the conversations last a bit longer than the above, and end in some sort of understanding of what my work is really about.

It's not that I'm easily offended when people think that I'm a bioinformatician, but mathematical/theoretical biology and bioinformatics are fundamentally different lines of research, with different methods and goals, and I'll try to explain why I think that is the case.

In order to illustrate my point we need to take a step back from biology and look at science from a broader perspective. The process of doing science and producing new knowledge about the world is usually termed the scientific method and can roughly be divided into: Hypotheses, Experiments, Results and Conclusions/Findings (I'm sure many philosophers of science will disagree on this, but this basic subdivision will do for my argument). The process is circular in that we start with some idea about how a certain system or phenomena is structured (i.e. a hypothesis), we then transform that hypothesis to a statement that is experimentally testable, carry out the experiment, and from the data determine if the hypothesis was true or false. This fact is added to our knowledge of the world and from our extended body of knowledge we produce new hypotheses.

In order to structure our knowledge about a phenomenon we construct theories that in a more or less formal manner codify our knowledge within a coherent framework. Mathematics is such a framework that was applied successfully first in physics, and then later in chemistry and most other natural sciences. In the language of mathematics we can transform statements in a rigorous, truth-preserving manner, moving from things that are certainly true (based on observation) to things that are possibly true (to be decided by experiment).

It is in this part of the scientific method that mathematical biology fits in. In a mathematical model we incorporate known facts, and maybe add some hypothetical ones, analyse the model and produce hypotheses that hopefully are testable in experiments (disclaimer: this is highly idealised. A lot of mathematical biology is far disconnected from experiments and more concerned with mathematical analysis, but where to draw the line between mathematical biology and applied analysis is at least to me a pointless exercise). Another equally important task for mathematical biologists is to form new theoretical constructs, and define new properties that are of relevance. An example of this is R0, the 'basic reproduction number' of a pathogen, that quantifies the number of cases one case generates on average over the course of its infectious period. It was defined by Ronald Ross when studying malaria with the aid of mathematical modelling, work that later was awarded with the Nobel Prize in Medicine in 1902.

If the role of mathematical biology is to define new concepts and generate hypotheses, where does bioinformatics fit into the process of scientific discovery? The role of bioinformatics is to structure and make sense of the other side of the scientific method; to design experiments and aid us in interpreting the outcomes. In molecular biology the days of simple experiments when measuring a single quantity was enough to prove or disprove a hypothesis are almost gone. With todays measurement techniques such as microarray, methylation probes or SNP-analysis, one is presented with quantities of data that are far beyond the reach of the human intellect. In order to decode the data, and draw conclusions we need algorithms developed by bioinformaticians. Apart from this they are also involved in the step between hypotheses and experiments, designing the most efficient and accurate ways of carrying out experiments (e.g. determining how much coverage we get with a given sequencing technique).

In my view mathematical biology and bioinformatics serve as two independent and non-overlapping disciplines that both aid the actual biologists (i.e. the experimentalists) in making the scientific method spin.

The inspiration for this post (and the figure) came from +Jacob Scott who came up with the idea when writing a recent review on mathematical modelling of metastases. Thanks!