DMS/NIGMS 1: Data-driven Ricci curvatures and spectral graph for machine learning and adaptive virtual screening

计算机辅助药物设计（CADD），包括基于结构的虚拟筛选大量可用的化合物（配体）为给定的药物靶标，已成为现代药物发现的重要组成部分。虚拟筛选的实际值依赖于靶-配体结合亲和力预测的准确性。如何准确预测目标分子与配体的结合结构（分子几何形状）以及与不同的海量数据集相关的结合亲和力是虚拟筛选面临的巨大挑战。该项目旨在通过引入新的，更有效的分子几何形状的数学表示来解决机器学习（ML）-CADD模型开发中的巨大挑战，该数学表示能够通过Ricci曲率及其相关的光谱信息跟踪分子几何形状的变化。该项目的成果将在计算药物设计，生物分子建模，数据分析，降维和数学生物学的重要领域提供新颖，更可靠的计算方法。此外，该项目将为研究生和本科生提供数据分析，生物建模，算法开发和计算药物设计方面的培训。计划从这个项目中加强课程，作为调查人员教学研究实践的继续。新的数学框架和深度学习架构直接集成到计算机软件包中，以确保药物设计、生物学、计算机科学和数学领域的研究人员广泛使用。此外，该项目还将帮助培养高等数学、数据科学和分子生物学领域的下一代研究人员。该项目将从基于几何学的方法和鲁棒性训练数据中开发用于生物分子数据分析的新型低维表示，以彻底改变目前基于结构的虚拟筛选实践。主要目标是：1）引入分子形状引导的持久Ricci曲率，同时提供局部几何形状和光谱信息以降低结构复杂性，同时仍然保持对生物分子相互作用的充分描述; 2）开发靶-配体自适应深度学习协议，用于对接后姿势选择、结合亲和力预测、排名和其他分子性质的估计; 3）在各种数据集上广泛验证所提出的方法，以优化数学表示和学习网络。具体而言，该项目将专注于开发用于磷酸二酯酶-2（PDE 2）抑制剂虚拟筛选的拟议模型，为治疗各种人类疾病提供有前景的治疗策略的宝贵成果。一个将计算-实验模型相结合的闭环系统将进一步加强所提出的模型的鲁棒性和准确性。4)该奖项旨在为未接受过高等数学或复杂机器学习正式培训的研究人员开发使用并行和GPU架构的用户友好型软件包和Web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价值和更广泛的影响审查标准进行评估，被认为值得支持。

Computer-aided drug design (CADD), including structure-based virtual screening of a large number of available compounds (ligands) for a given drug target, has become an essential component of modern drug discovery. The actual value of the virtual screening relies on the accuracy of the target-ligand binding affinity prediction. It is recognized as a grand challenge for the virtual screening to accurately predict the target-ligand binding structures (molecular geometries) and binding affinities associated with diverse and massive datasets. This project aims to address the grand challenge in development of machine-learning (ML)-CADD models by introducing new, more effective mathematical representations of molecular geometries with the ability to track molecular geometry changes via Ricci curvatures and their associated spectral information. The outcomes of this project will furnish novel, more reliable computational approaches in essential areas of computational drug design, biomolecular modeling, data analysis, dimensionality reduction, and mathematical biology. Moreover, this project will provide graduate and undergraduate students with training in data analysis, biological modeling, algorithm development, and computational drug design. The enhancement of curricula from this project is planned as a continuation of the investigators' teaching-research practice. The new mathematical framework and deep learning architectures are directly integrated into computer software packages to ensure extensive usage by the community of researchers in drug design, biology, computer science, and mathematics. Additionally, the project will help train the next generation of researchers in advanced mathematics, data science, and molecular biology.This project will develop novel low-dimensional representations for biomolecular data analysis from mathematics-based approaches and robustness training data to revolutionize the current practice in structure-based virtual screening. The main objectives are: 1) to introduce molecular shape guided persistent Ricci curvature and, at the same time, to provide local geometry and spectral information to reduce the structural complexity while still maintaining an adequate description of biomolecular interactions; 2) to develop a target-ligand adaptive deep learning protocol for post-docking pose selection, binding affinity prediction, ranking, and estimation of other molecular properties; 3) to extensively validate the proposed methods on a variety of datasets to optimize the mathematical representations and learning networks. Specifically, this project will focus on the development of the proposed models for the virtual screening of phosphodiesterase-2 (PDE2) inhibitors, providing valuable hits of a promising therapeutic strategy for the treatment of various human diseases. A close loop integrating computational-experimental models will further strengthen the robustness and accuracy of the proposed models.; 4) to develop user-friendly software packages and web servers 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.