Algebraic Systems Biology

Heather Harrington, University of Oxford

Signalling pathways can be modelled as a biochemical reaction network. When the kinetics follow mass-action kinetics, the resulting mathematical model is a polynomial dynamical system. 

I will overview approaches to analyse these models with steady-state data using computational algebraic geometry and statistics. Then I will present how to analyse such models with time-course data using differential algebra and geometry for model identifiability.  Finally, I will present how topological data analysis can provide additional information to distinguish these models and experimental data from wild-type and mutant molecules. These case studies showcase how computational geometry, topology and dynamics can provide new insights in the biological systems, specifically how changes at the molecular scale (e.g. MEK WT and mutants) result in phenotypic changes (e.g. fruit fly mutations).