Regular Seminar Heather Harrington (Oxford)
Systems biology aims to understand the molecular interactions that turn genes on/off, ultimately regulating cellular decisions. These interactions may be described by a mathematical model that is a polynomial dynamical system. Generally these interactions are unknown, leading to multiple models; therefore it is desirable to compare models with experimental data (e.g., steady-state concentrations of proteins). Often model parameter values are unknown, and data is limited (subset of measurable variables, often with noise). An emerging field, `algebraic systems biology', offers algebraic approaches to study problems systems biology. We present an algebro-geometric method for ruling out models with limited information and apply it to a biological system known to dysfunction in many colorectal cancers. We are currently extending the framework to include dynamics (i.e. time course data) using differential algebra elimination and will present preliminary results.