eMB: Collaborative Research: Discovery and calibration of stochastic chemical reaction network models

数学模型是一种广泛使用的工具，用于提高我们对生物系统的理解、预测和控制能力。这些模型通常被编码为化学反应网络（CRN），涉及大量反应，这些反应描述了系统的成分（如蛋白质）如何随时间改变其状态。CRN模型组件通常仅部分已知，因此将已知组件的理论物理模型与从实验数据估计未知组件及其动态的技术相结合的方法可以提高其预测能力。这是科学机器学习（SciML）的领域。该项目将开发新的SciML方法，用于构建、模拟和分析CRN模型，其中包括蛋白质状态演化中的随机性，这是准确预测单个生物细胞内化学系统行为的重要特征。新方法将应用于系统和合成生物学中的问题（对天然系统的理解以及新型细胞系统的开发），但也将适用于涉及CRN的广泛领域（包括流行病学、物理化学和药理学）。通过将其纳入SciML组织广泛使用的开源软件库，这些方法将免费提供给任何研究科学和工程问题的研究人员使用。将为博士后学者和本科生研究人员提供培训机会，他们将获得在跨学科团队中工作的经验，开发SciML方法，将这些方法集成到开源软件中，并将新软件应用于研究生物系统。该项目扩展了对离散随机导数估计的数学理解，以促进扩展科学机器学习（SciML）化学反应网络（CRN）的训练技术。将SciML扩展到细胞系统的一个明显困难是它们倾向于噪声行为，因为它们通过随机模拟算法（如吉莱斯皮方法）建模为离散随机跳跃过程。这样的过程对于许多SciML工作流来说是有问题的，这些工作流严重依赖于自动微分（AD）来扩展训练技术。这是因为以前没有一般的方法，适用于AD他们在一个无偏的方式与低方差估计。这个项目建立在最近扩展的AD离散随机过程，这是能够产生无偏的低方差导数估计。衍生估计和衍生概率演化的敏感性方程所产生的随机过程之间的严格连接将被证明，从而建立一个坚实的理论基础的无偏性和方差的衍生估计的背景下CRNs。将证明在细胞模型上部署离散随机AD（DSAD）进行模型校准的可行性，并将用于模型发现的SciML通用微分方程方法推广到基于理论的数据驱动的CRN中缺失反应的发现。最后，这些方法的适用性将在一系列细胞系统（包括B细胞抗原受体信号系统，σV溶菌酶应激反应系统和混合反馈振荡器）上得到证明。该奖项反映了NSF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。

Mathematical models are a widely used tool for improving our understanding, ability to predict, and ability to control the behavior of biological systems. Such models are often encoded as chemical reaction networks (CRNs), involving large collections of reactions that describe how constituents of the system, such as proteins, change their states over time. CRN model components are often only partially known, and thus methods which mix theoretical physics-based models for known components, with techniques that estimate unknown components and their dynamics from experimental data, can improve their predictive capabilities. This is the domain of Scientific Machine Learning (SciML). This project will develop new SciML methods for constructing, simulating, and analyzing CRN models that include randomness in the evolution of protein states, an important feature to accurately predict the behavior of chemical systems within individual biological cells. The new methods will be applied to problems in systems and synthetic biology (the understanding of native, and the development of novel, cellular systems), but will also be applicable across a wide range of fields involving CRNs (including epidemiology, physical chemistry, and pharmacology). Via their incorporation into widely used open source software libraries of the SciML organization, the methods will be freely available for use by any researcher studying problems across science and engineering. Training opportunities will be provided for a postdoctoral scholar and an undergraduate researcher, who will gain experience working in interdisciplinary teams, developing SciML methods, integrating these methods into open source software, and applying the new software to study biological systems.This project extends the mathematical understanding of discrete stochastic derivative estimators to facilitate scaling Scientific Machine Learning (SciML) training techniques to chemical reaction networks (CRNs). One distinct difficulty in extending SciML to cellular systems is their proneness to noisy behaviors, as they are modeled as discrete stochastic jump processes via stochastic simulation algorithms such as the Gillespie method. Such processes are problematic for many SciML workflows which critically depend on automatic differentiation (AD) to scale training techniques. This is because there previously existed no general method for applying AD to them in an unbiased manner with low variance estimators. This project builds on a recent extension of AD to discrete stochastic processes which is capable of generating unbiased low variance derivative estimators. The rigorous connection between the generated stochastic process for the derivative estimator and the derivative probability evolution given by the sensitivity equations will be proven, thus establishing a firm theoretical underpinning for the unbiasedness and variance of the derivative estimator in the context of CRNs. The feasibility to deploy discrete stochastic AD (DSAD) on cellular models to perform model calibration will be demonstrated, and SciML universal differential equation methods for model discovery will be generalized to the theory-based data-driven discovery of missing reactions in CRNs. Finally, the applicability of these methods will be demonstrated on a range of cellular systems (including the B-cell antigen receptor signaling system, the σV lysozyme stress response system, and a mixed feedback oscillator).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.