Explore how mathematics and artificial intelligence are revolutionizing biosciences in this 47-minute lecture by Guo-Wei Wei. Delve into the challenges of applying AI to biological discovery, including the structural complexity of macromolecules and high dimensionality of biological variability. Learn about innovative mathematical approaches such as evolutionary de Rham-Hodge theory, persistent cohomology, and persistent spectral graph theory, which enhance AI's ability to handle large biological datasets. Discover how these techniques have been successfully applied to computer-aided drug design, predicting SARS-CoV-2 variants, and understanding viral mutations. Gain insights into the intersection of classical topology, algebraic topology, differential geometry, and graph theory with modern biological problems. Understand the importance of reducing complexity in biological data and how mathematical AI approaches are advancing our understanding of life sciences, from molecular structures to viral evolution.
Overview
Syllabus
Intro
COVID-19 demonstrates the importance of biosciences
Challenges of AI in biomolecular systems Geometric dimensionality where N-5000 for a protein.
Two schools of thinking
Our Strategy
Classical Topology Mobius Strips (1858) Klein Bottle (1882)
Topological invariants: Betti numbers
Vietoris-Rips complexes of planar point sets
Algebraic Topology Vietoris-Rips complexes, persistent homology and topological fingerprint
Topological fingerprints of an alpha helix
Persistent cohomology incorporating non-geometric information in topology
Differential geometry based minimal surface model
Differential Geometry (Connections & curvature forms) Gauss Mean
De Rham-Hodge theory and discrete exterior calculus Hodge decomposition
Evolutionary de Rham-Hodge Filtration of a manifold
Algebraic Graph Theory for Biomolecules
Persistent Spectral Graph (Persistent Laplacian)
Mathematical deep learning
Drug Design Data Resource (D3R) Grand Challenges
Life cycle of SARS-CoV-2 in host cells
Mutation Tracker
Mutations Strengthened SARS
We predicted key mutation sites in prevailing variants Mutations at 501 and 452 in prevailing SARS-CoV-2 variants
We discovered the mechanism of viral transmission and evolution
Mutation-induced binding free energy changes for spike protein-ACE-2 complex (more infectious)
Genome-Math-Al modeling of protein-protein binding affinity changes following mutations
Atlas of emerging variants
Geometric Differential topology topology
Taught by
Applied Algebraic Topology Network
