Robust and Reliable Mathematical Models for Biomolecular Data via Differential Geometry and Graph Theory

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This project is jointly funded by Division of Mathematical Sciences/Mathematical Biology Program and the Established Program to Stimulate Competitive Research (EPSCoR).A major trend of biological sciences in the 21st century is their transition from quantitative, phenomenological, and descriptive to quantitative, analytical, and predictive. Fundamental challenges that hinder the current understanding of biomolecular structure-function relationships, which is the central theme of biological sciences, are their tremendous structural complexity and excessively large datasets. The project will address grand challenges in understanding the biomolecular structure-function relationship from massive datasets by introducing new concepts in graph theory and differential geometry. The results from this project will open a new direction and foster similar approaches in biological data analysis. The graduate and undergraduate students will receive training in data analysis, biological modeling, and algorithm development from this project. In addition, novel mathematical frameworks will be available in the software packages to ensure extensive usage by the community of researchers throughout biology, computer science, and mathematics.This project will develop new spectral graph theory and differential geometry-based approaches to revolutionize the current practice in biomolecular data analysis and modeling. First, investigators will introduce multiscale weighted colored algebraic graphs (spectral graphs) to reduce the structural complexity of biomolecular data. These methods will be tailored for various biological systems, such as protein binding to protein, ligand, DNA, and RNA, protein folding stability changes upon mutation, drug toxicity, solvation, solubility, and partition coefficient. Secondly, investigators will construct low-dimensional element interactive manifolds for the first time to properly encode chemical and biological information. These methods will be carefully integrated with advanced machine learning or deep learning algorithms to uncover biomolecular structure-function relationships. Finally, investigators will extensively validate the proposed methods on a variety of datasets, optimize these mathematical learning strategies using parallel and GPU architectures, and develop user-friendly software packages or online servers for researchers who might not have training in mathematics and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.