The Certainties and The Consequences of Mathematical Models in Biomedicine

In a Perspective published in Science, entitled “Systems biology (un)certainties”, Dr. Paul Kirk from MRC Biostatistics Unit, Dr. Ann Babtie, and Prof. Michael Stumpf, both from Imperial College, highlight  the opportunities provided by mathematical models in the biomedical sciences, but stress the importance of assessing uncertainty and avoiding over-interpretation.

Mathematical and statistical models have proven themselves time and again to be incredibly useful in biology, providing new insights and allowing novel predictions to be made. Their use is (or should be) uncontroversial.

There are many reasons why biology and medicine are hard. Foremost among these is the complexity of biological systems. At every level – from single cells up to whole populations of people – biology is characterised by interactions between large numbers of different things. For example, the behaviour of cells in the human body depends on interactions between – among other things – different proteins, which are biological molecules for which our genes provide the blueprints. Since humans have somewhere around 20,000 – 25,000 different protein-coding genes, it is perhaps unsurprising that it is incredibly difficult to understand the inner workings of our cells!

Systems biology is the field that tries to make sense of complex biological systems by combining experimental observations with biostatistical, mathematical, and computational modelling. One important part of systems biology is hypothesis generation. This means that we analyse experimental observations using statistical models in order to spot patterns in our data. These patterns can help scientists to come up with new ideas (hypotheses) about how biology works, and to make new predictions. Using statistical techniques to extract useful information from complex, noisy data is a task that occurs throughout the emerging field of data science. For example, providers of online services (such as Netflix and Google) use similar ideas to suggest films or websites that their users might like to view.


As well as using data science approaches to come up with new ideas, systems biologists also use mathematical models to test existing hypotheses. Mathematical models can be very useful for this, because they provide a formal language in which to express current ideas, and allow us to test the possible consequences of these ideas. For example, if we believe that the amount of a particular protein in a cell increases and decreases over time in a regular pattern (i.e. its abundance oscillates), we might be able to test if this has an effect on the behaviour of a cell, compared to an alternative model in which the protein always remains at a constant level (see figure). This can help scientists to target their experiments, in order to try to break (or “falsify”) a current model, which can be a step toward devising new and better models.

Some scientists have previously criticised systems biology, because they think it is trying to do the impossible: using limited experimental data to try to come up with massively complicated models that will explain, for example, the complete workings of a whole cell. However, this is not usually the aim of systems biology, which is typically concerned with more modest hypothesis generation, and targeted model testing, as described above. In their article, Kirk, Babtie and Stumpf contend that the reason for this misunderstanding may be due to scientists presenting mathematical modelling approaches without adequately communicating either the limitations or the uncertainty in the consequences of their models.

Kirk, Babtie and Stumpf assert that the foundation of good mathematical and statistical modelling is to always provide an honest assessment of the limitations of the model and to report the uncertainty in its implied consequences. There are many ways in which the uncertainty associated with mathematical models can be assessed, such as the Topological Sensitivity Analysis (TSA) approach described in Babtie*, Kirk*, and Stumpf, 2014 (PNAS, vol. 111(52), 18507-18512).

The key to ensuring that models continue to be useful is to communicate them effectively, assess uncertainty, and avoid over-interpretation – however tempting it may be.


To read the Perspective published in Science, please click here: Perspective_Kirk_AuthorVersion (This is the author’s version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science on 23 October 2015: Vol. 350 no. 6259 pp. 386-388, DOI: 10.1126/science.aac9505.)