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

该项目由数学科学部/数学生物学计划和促进竞争研究的既定计划（EPSCoR）共同资助。21世纪生物科学的一个主要趋势是从定量、现象学和描述性向定量、分析性和预测性转变。生物分子结构-功能关系是生物科学的中心主题，阻碍当前对生物分子结构-功能关系理解的根本挑战是它们巨大的结构复杂性和过大的数据集。该项目将通过引入图论和微分几何中的新概念，解决从海量数据集中理解生物分子结构-功能关系的重大挑战。该项目的结果将为生物数据分析开辟一个新的方向，并促进类似的方法。研究生和本科生将从这个项目中接受数据分析、生物建模和算法开发方面的培训。此外，新的数学框架将在软件包中提供，以确保整个生物学，计算机科学和数学的研究人员社区的广泛使用。该项目将发展新的光谱图理论和基于微分几何的方法，以彻底改变当前生物分子数据分析和建模的实践。首先，研究人员将引入多尺度加权彩色代数图（谱图）来降低生物分子数据的结构复杂性。这些方法将适用于各种生物系统，如蛋白质与蛋白质的结合、配体、DNA和RNA、突变时蛋白质折叠稳定性的变化、药物毒性、溶剂化、溶解度和分配系数。其次，研究人员将首次构建低维元素交互流形，对化学和生物信息进行适当编码。这些方法将与先进的机器学习或深度学习算法相结合，以揭示生物分子结构-功能关系。最后，研究人员将在各种数据集上广泛验证所提出的方法，使用并行和GPU架构优化这些数学学习策略，并为可能没有接受过数学和机器学习培训的研究人员开发用户友好的软件包或在线服务器。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.