III: Medium: De Rham-Hodge theory modeling and learning of biomolecular data

理解生命规律是21世纪生物科学的主要使命。大量生物学数据的可获得性和计算算法的最新进展为生物科学从定性、现象学和描述性方法过渡到定量、分析和预测方法铺平了道路。然而，巨大的结构复杂性和过大的数据集阻碍了这种转变。例如，即使是世界上所有的计算机放在一起也没有足够的能力来自动设计药物，因为蛋白质-药物相互作用的结构复杂性，与药物构型相关的过大的数据集，以及涉及的分子模拟和/或机器学习的高维度。在本项目中，这些挑战将通过创新的数学战略加以解决。来自密歇根州立大学数学和计算机科学的一个团队将把复杂的数学转化为计算算法，以创建复杂生物分子或它们之间相互作用的简化表示。因此，深度学习和其他类型的机器学习可以有效地从海量和多样化的生物分子数据集中提取结构-功能关系。这些信息对于揭示生命规律和设计新的生物分子，包括生物医学，将是极其有价值的，最终将考验我们对生物分子世界的理解，并为人类健康带来直接好处。此外，该项目将支持密歇根州立大学开发计算生物物理学和机器学习的本科生和研究生课程。最后，这项研究将促进下一代研究人员的跨学科培训，他们是高等数学、计算机算法和分子水平生物学的专家。本项目的目标是开发基于德罗姆-霍奇理论的新方法，以彻底改变目前生物分子数据分析和建模的实践。德罗姆-霍奇理论是20世纪S数学的标志，对现代数学、量子物理和计算机科学产生了重大影响。研究人员将首次引入德罗姆-霍奇理论，以降低生物分子的结构复杂性。此外，研究小组将首次提出持久的德罗姆-霍奇理论和元素特定的德罗姆-霍奇理论，以适当地编码生物分子数据表示中的化学和生物信息。这些方法将与先进的机器学习或深度学习算法小心地结合在一起，以揭示生物分子结构-功能关系。此外，研究人员将在各种数据集上广泛验证所提出的方法，例如蛋白质与蛋白质、配体、DNA和RNA的结合、蛋白质折叠稳定性在突变时的变化、药物毒性、溶剂化、溶解度和分配系数。最后，将使用并行和GPU架构为未受过高级数学或复杂机器学习正式培训的研究人员开发用户友好的软件包和在线服务器。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding the rules of life is the major mission of biological sciences in the 21st Century. The availability of massive biological data and the recent advances in computational algorithms have paved the way for biological sciences to transition from a qualitative, phenomenological and descriptive to a quantitative, analytical and predictive approach. However, this transition is hindered by tremendous structural complexity and excessively large datasets. For example, even all the world's computers put together do not have enough power to design drugs automatically because of the structural complexity of protein-drug interactions, excessively large datasets associated with drug configurations, and the high dimensionality of involved molecular simulation and/or machine learning. These challenges will be addressed by innovative mathematical strategies in the present project. A team from mathematics and computer science at Michigan State University will turn sophisticated mathematics into computational algorithms that create simplified representations of complex biomolecules or their interactions. As a result, deep learning and other types of machine learning can be efficiently carried out to extract the structure-function relationship from massive and diverse biomolecular datasets. This information will be extremely valuable for revealing the rules of life and for design new biomolecules, including biomedicine, which ultimately tests our understanding of the biomolecular world and brings a direct benefit to human health. Additionally, this project will support the development of undergraduate and graduate-level courses on computational biophysics and machine learning at Michigan State University. Finally, this research will facilitate the cross-disciplinary training of the next generation researchers who are experts on advanced mathematics, computer algorithms, and molecular-level biology.The objective of the present project is to develop novel de Rham-Hodge theory-based approaches to revolutionize the current practice in biomolecular data analysis and modeling. The de Rham-Hodge theory is a hallmark of the 20th Century?s mathematics that has had a great impact in modern mathematics, quantum physics, and computer science. The investigators will introduce for the first time the de Rham-Hodge theory to reduce the structural complexity of biomolecules. Additionally, the research team will propose the persistent de Rham-Hodge theory and element-specific de Rham-Hodge theory for the first time to properly encode chemical and biological information in biomolecular data representation. These methods will be carefully integrated with advanced machine learning or deep learning algorithms to reveal biomolecular structure-function relationships. Moreover, the investigators will extensively validate the proposed methods on a variety of datasets, such as protein binding to the proteins, ligands, DNA and RNA, protein folding stability changes upon mutation, drug toxicity, solvation, solubility, and partition coefficient. Finally, user-friendly software packages and online servers will be developed using parallel and GPU architectures for researchers who are not formally trained in advanced mathematics or sophisticated 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.