Friday April 29th, at 11:00AM Math Conference room

April 25, 2016 by Duan Chen
Categories: Spring 2022
Kelin Xia, Michigan State University
Title: Topological modeling and analysis of complex data in biomolecules
Abstract: Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the most challenging tasks in biological science. We have introduced persistent homology for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification. The multidimensional persistent homology is proposed and further used to quantitatively predict the stability of protein folding configurations generated by steered molecular dynamics. An excellent consistence between my persistent homology prediction and molecular dynamics simulation is found. Further, we introduce multiresolution persistent homology to handle complex biomolecular data. The essential idea is to match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. By appropriately tuning the resolution of a density function, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks and graphs.