Geometric and Topological Data Analysis of Enzyme Kinetics

Explore geometric and topological data analysis techniques applied to enzyme kinetics in this 24-minute talk from the Applied Algebraic Topology Network. Dive into a mathematical study of a differential equation model describing molecular dynamics of Extracellular Signal Regulated Kinase (ERK), linked to cancer and developmental defects. Learn how persistent homology serves as a discriminative feature in the parameter space of reaction rates. Discover how computational algebra and geometry enable interpretable quantification of ERK reaction rates through model reduction. Analyze the topology of data generated by Bayesian inference using super-level-set filtration via Kernel Density Estimation. Examine the significance of bottleneck distance between persistence diagrams and compare various filtration methods. Gain insights into how genetic perturbations affect enzyme kinetics in parameter space and their biological interpretations. Cover topics including signaling pathways, mutations, underlying reactions, law of mass action, model reduction, inference, statistical tools, and bootstrapping.

Introduction
Signaling pathway
Mutations
Underlying reaction
Law of mass action
Model reduction
Inference
Statistical tools
Kernel density estimation
Bootstrapping