Writing in 1945 on the role of models in biology, Arturo Rosenblueth and Norbert Wiener (founders of cybernetics, arguably a precursor of today’s systems biology) said, “The best material model for a cat is another, or preferably the same cat”. In a review in BMC Biology, Jeremy Gunawardena revisits the topic and confronts again the thorny issue of how to marry the elegance and precision of mathematical modeling to the messy reality of biology.
Gunawardena, who is a mathematician by training, provides a highly readable historical and personal perspective on how to approach models of biological systems for biologists. Currently, forward or reverse modeling are the two strategies described in the literature.
It is forward modeling that is the focus of Gunawardena’s review –though he stresses that reverse modeling (which provides causalities from existing experimental data) has been useful in suggesting new molecular components or interactors in pathways and will be helpful to interpret very large datasets, especially clinical data. Forward modeling takes known causalities and can predict what else may be expected of such a system. To build such a model however requires a detailed knowledge of the biology of the system to inform the assumptions and parameters on which the model will be built.
If all of biology were based on fundamental laws, for example of physics, then all models would be predictive. However because of the complexity of biological systems, models cannot be built to account for every protein/complex or parameter in a pathway; so to quote pharmacologist James Black, models are “meant to expose assumptions, define expectations and help us devise new tests”. Or as Gunawardena says – “a mathematical model is a logical machine for converting assumptions into conclusions”, with the proviso that – to quote George Box – “All models are wrong, but some of them are useful”.
This is the point that Gunawardena readably and compellingly elaborates – a model must be falsifiable and so encompass phenomology and guesswork, and crucially, be built on a modest number of reasonable assumptions that must be based on a real understanding of the biology.
Taking three favorite examples, and following discussion with the original authors themselves, Gunawardena shows that when Reinhart Heinrich and Tom Rapoport modelled non-identical compartments in trafficking – the coat protein and SNARE decorated vesicles – a parsimonious model revealed the phenomena and provided an example of guessing which parameters were most crucial. Here it was binding affinities and the total amount of protein incorporated.
The second example is from T-cell receptor interactions with the proteins of the major histocompatability complex. Altan-Bonnet’s and Ron Germain’s model takes into account the importance of feedback loops and ‘kinetic proof-reading’ and a detailed model based on known biochemistry – but some parameters were measured. As Germain said: “the model never worked until we actually measured ERK activation at the single cell level and discovered its digital nature”.
A final example was Julian Lewis’s model of the somitogenesis clock that formalized negative auto-regulation of her1/her7 and incorporated time delays (as suggested by Nick Monk) to ensure the model worked.
These examples show how through forward modeling we can gain insight into how phenomena such as feedback, homeostasis, canalization and noise operate in biology. Clearly there is more that quantitative biology can show us – but biologists should have the courage to “stick the model’s neck out after it is fitted and try to falsify it” (to quote Gunawardena).
Modeling is by its nature an interdisciplinary enterprise, drawing on the expertise of mathematicians and informaticists as well as biologists, and as a journal with a breadth of content that encompasses all approaches to the mysteries of biology, we warmly welcome submissions reflecting quantitative and modeling approaches to the fundamental processes of life.
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