Speaker
Description
Mathematical models provide a powerful framework for analysing the dynamics of biochemical reaction networks (BCRNs); however, effective modelling of complex biological systems requires balancing complexity and accuracy. As such, the rigorous and principled reduction of BCRNs via systematic, model-independent methods, while ensuring that key dynamics are preserved, is of vital importance.
In this talk, we discuss how to automate the fast yet rigorous non-dimensionalisation, preprocessing, and reduction of BCRNs, without being limited to low-dimensional models, as many current approaches are. Using the parametrisation method, the constructive counterpart to Tikhonov–Fenichel theory, together with techniques from algebraic geometry and linear algebra, we automate the end-to-end, principled reduction of a wide class of BCRNs without dimensional constraints. Importantly, the true power of the parametrisation method lies in its ability to deal with systems exhibiting multiple timescales, where standard geometric singular perturbation theory approaches can fail. We demonstrate the approach by rigorously reducing numerous well-known and real-world BCRNs, many of which we reduce for the first time, establishing its utility and showing that even low-order reduced models can achieve high fidelity and accuracy.
