Using Algebraic Geometry to Detect Robustness in Reaction Networks

Explore the application of algebraic geometry in detecting robustness within reaction networks through this insightful lecture. Delve into the fascinating property of biological systems to maintain certain features despite environmental changes, focusing on reaction networks and the temporal evolution of species concentrations. Examine the concept of absolute concentration robustness (ACR) and its significance in preserving species concentrations across different equilibria. Investigate local and global notions of robustness in polynomial equation solutions, aiming to develop a practical test for ACR using algebraic-geometric techniques. Learn about the challenges in identifying networks with ACR properties and the ongoing research in this field. Gain valuable insights into the intersection of algebraic geometry and biological systems modeling, including an exploration of zero sensitivity as a necessary condition for ACR and a discussion of the IDH example.

Intro
Setting and Goal
Reaction Networks
Motivation
Absolute concentration robustness
Searching for ACR
Zero sensitivity as a necessary condition
Local ACR
Results
IDH example