Algebraic Systems Biology

Heather A. Harrington

Signalling pathways in molecular biology can be modelled by polynomial dynamical systems. I will present models describing two biological systems involved in development and cancer. I will overview approaches to analyse these models with data using computational algebraic geometry, differential algebra and statistics. Finally, I will present how topological data analysis can provide additional information to distinguish wild-type and mutant molecules in one pathway. 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. molecular mutations) result in kinetic differences that are observed as phenotypic changes (e.g.mutations in fruit fly wings).