Collaborative Research: A Control Theoretic Framework for Guided Folding and Unfolding of Protein Molecules

这笔资金将用于研究准确预测蛋白质折叠和展开的路径，并应用于计算机辅助抗病毒药物设计、蛋白质纳米机器控制以及与蛋白质错误折叠有关的疾病(如阿尔茨海默氏症)的治疗，从而促进科学进步，促进国家健康和繁荣。基于物理学的方法可靠地捕捉到了支配蛋白质分子构象变化的过程，但通常要付出巨大的计算成本。最近发展的一种建模范式，用在原子间作用力的影响下折叠的大量刚性纳米连接来描述蛋白质分子，可以显著减少计算负担，但在确保预测的折叠和展开路径是真实的而不是由数值算法人为驱动的方面提出了挑战。在这个项目中，这一挑战被克服了，使用基于优化的控制理论框架来指导折叠和展开动力学，同时尊重生物现实的构象熵变化率。从这一框架的开发中获得的知识将使系统地研究蛋白质构象动力学，包括揭示冠状病毒尖峰蛋白的路径，同时还将推进以前未探索的控制工具，这些工具可能有助于机器人在混乱的环境中导航。一种独特的蛋白质途径数据发声方法将使这一知识广泛获得，并将被整合到工程、计算机科学和艺术本科生的课程项目中，以及旨在指导高中生的STEM研究活动中。这项研究旨在通过严格开发和研究计算高效和数值稳定的算法，准确预测蛋白质的折叠和展开，同时避免与人为快速丢失构象熵相关的路径，在基于优化的非线性控制和蛋白质构象动力学这两个看似不相关的领域之间架起一座桥梁。该项目将通过开发一种新的非迭代、大规模、基于二次规划的超椭球上具有大状态空间维度的蛋白质折叠动力学的控制方案；构建一种大规模、变步长的数值积分算法，预计将减少积分步骤的数量，其中每一步都需要非常大的原子间作用力矢量场的繁琐计算；以及开发一种控制理论方法来系统地研究蛋白质展开问题，从而填补使用动静态柔量方法编码熵损失约束方面的关键知识空白。用于验证的基本事实数据将从全原子分子动力学模拟中获得，对于蛋白质谷氨酸酶模型，将从基于光学镊子的机械展开实验中获得公开的实验数据。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。

This grant will fund research that enables accurate prediction of pathways for protein folding and unfolding, with application to computer-aided anti-viral drug design, control of protein-based nano-machines, and treatment of diseases related to protein misfolding such as Alzheimer’s, thereby promoting the progress of science, and advancing the national health and prosperity. Physics-based approaches reliably capture the processes that govern conformational changes of protein molecules, but typically do so at great computational expense. A recently developed modeling paradigm, which describes protein molecules in terms of large numbers of rigid nano-linkages that fold under the influence of interatomic forces, can significantly reduce the computational burden, but presents challenges with ensuring that the predicted folding and unfolding pathways are realistic and not artificially driven by the numerical algorithm. In this project, this challenge is overcome using an optimization-based control theoretic framework to guide both folding and unfolding dynamics while respecting biologically realistic rates of change of conformational entropy. Knowledge gained from the development of this framework will enable systematic investigation of protein conformational dynamics, including unfolding pathways of coronavirus spike proteins, while also advancing previously unexplored control tools that may help robots navigate cluttered environments. A unique approach to sonification of protein pathway data will make this knowledge broadly accessible and will be integrated in course projects for undergraduate students in engineering, computer science, and art, as well as in research activities aiming to mentor high school students in STEM.This research aims to bridge the two seemingly unrelated fields of optimization-based nonlinear control and conformational dynamics of proteins through rigorous development and investigation of computationally efficient and numerically stable algorithms that accurately predict protein folding and unfolding while avoiding pathways associated with artificially rapid loss of conformational entropy. This project will fill the critical gap in knowledge of encoding entropy-loss constraints using the kinetostatic compliance method by developing a novel non-iterative, large-scale, quadratic programming-based control scheme over hyper-ellipsoids for protein folding dynamics with large state-space dimensions; constructing a large-scale, variable-step-size, numerical integration algorithm that is expected to reduce the number of integration steps, where each step requires the burdensome computation of a very large interatomic force vector field; and developing a control theoretic approach for systematically investigating the problem of protein unfolding. Ground truth data for validation will be obtained from all-atom molecular dynamics simulations and, in the case of the model protein barnase, publicly available experimental data from optical tweezer-based mechanical unfolding experiments.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.