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Topological fingerprints of an alpha helix
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How Math and AI Are Revolutionizing Biosciences
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- 1 Intro
- 2 COVID-19 demonstrates the importance of biosciences
- 3 Challenges of AI in biomolecular systems Geometric dimensionality where N-5000 for a protein.
- 4 Two schools of thinking
- 5 Our Strategy
- 6 Classical Topology Mobius Strips (1858) Klein Bottle (1882)
- 7 Topological invariants: Betti numbers
- 8 Vietoris-Rips complexes of planar point sets
- 9 Algebraic Topology Vietoris-Rips complexes, persistent homology and topological fingerprint
- 10 Topological fingerprints of an alpha helix
- 11 Persistent cohomology incorporating non-geometric information in topology
- 12 Differential geometry based minimal surface model
- 13 Differential Geometry (Connections & curvature forms) Gauss Mean
- 14 De Rham-Hodge theory and discrete exterior calculus Hodge decomposition
- 15 Evolutionary de Rham-Hodge Filtration of a manifold
- 16 Algebraic Graph Theory for Biomolecules
- 17 Persistent Spectral Graph (Persistent Laplacian)
- 18 Mathematical deep learning
- 19 Drug Design Data Resource (D3R) Grand Challenges
- 20 Life cycle of SARS-CoV-2 in host cells
- 21 Mutation Tracker
- 22 Mutations Strengthened SARS
- 23 We predicted key mutation sites in prevailing variants Mutations at 501 and 452 in prevailing SARS-CoV-2 variants
- 24 We discovered the mechanism of viral transmission and evolution
- 25 Mutation-induced binding free energy changes for spike protein-ACE-2 complex (more infectious)
- 26 Genome-Math-Al modeling of protein-protein binding affinity changes following mutations
- 27 Atlas of emerging variants
- 28 Geometric Differential topology topology
