Mathematical models are of fundamental importance in developing new knowledge of complex biological systems for several reasons: assessing the consistency between hypotheses and experimental data; analysis of large and often heterogeneous data sets; simulations of biological systems; and guiding new experimental design. Since we have a very insufficient conceptual understanding of living organisms, it is challenging to describe complex biological systems mathematically.
In this talk I will discuss a novel mathematical framework for the comparison of mathematical models that can lead to a deeper and simplified conceptual and mathematical understanding of complex biological systems. The methodology for model comparison is based on determining the conceptual similarities of models and allows for the comparison of any models irrespective of their mathematical formalism. Within this framework we consider each model as a data point in a model space and associate measures of distance and equivalence between models. Our model comparison framework can simplify the landscape of mathematical modelling by grouping models into categories of models that are conceptually similar. This categorisation can help to unify models and concepts, as well as reveal the set of design principles underlying all models in the same category.
Dr Dr Sean T. Vittadello
Postdoctoral Research Fellow, The University of Melbourne
Dr Sean Vittadello joined the Theoretical Systems Biology Group at The University of Melbourne as a Postdoctoral Research Fellow in 2020. His research involves both pure and applied mathematics motivated by specific interests in the development and application of new mathematical frameworks to further our understanding of complex biological systems.
Dr Vittadello’s recent research has resulted in a novel and powerful approach for the comparison of mathematical models, in particular providing methodologies for the unification of models and for the discovery of design principles underlying models of biological systems. This research has already led to the discovery of design principles for models of developmental patterning processes that were previously regarded as unrelated and incompatible. Such general and abstract mathematical approaches which form the basis of Dr Vittadello’s research are essential for developing a deeper conceptual understanding of living organisms far beyond that obtainable by reductionist methodologies.