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，用来提高我们对生物系统行为的理解、预测和控制能力。这类模型通常被编码为化学反应网络(CRN)，涉及描述系统成分(如蛋白质)如何随着时间的推移而改变其状态的大量反应集合。CRN模型组件通常只有部分已知，因此，将已知组件的基于理论物理的模型与从实验数据估计未知组件及其动力学的技术相结合的方法可以提高它们的预测能力。这就是科学机器学习(SciML)的领域。该项目将开发新的SciML方法来构建、模拟和分析CRN模型，该模型包括蛋白质状态演变的随机性，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(对天然细胞系统的理解和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)。通过将这些方法整合到本组织广泛使用的开源软件库中，这些方法将免费供任何研究科学和工程问题的研究人员使用。将为一名博士后学者和一名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，并将新软件应用于生物系统研究。该项目扩展了对离散随机导数估计器的数学理解，以促进将科学机器学习(SciML)培训技术扩展到化学反应网络(CRN)。将SciML扩展到蜂窝系统的一个明显的困难是它们容易受到噪声行为的影响，因为它们通过随机模拟算法被建模为离散的随机跳跃过程，例如吉列斯皮方法。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自动区分(AD)来扩展训练技术。这是因为以前不存在以低方差估计器以无偏的方式将AD应用于它们的通用方法。这个项目建立在AD最近扩展到离散随机过程的基础上，它能够产生无偏的低方差导数估计量。证明了导数估计生成的随机过程与灵敏度方程给出的导数概率演化之间的严格联系，从而为导数估计在CRN中的无偏性和方差性奠定了坚实的理论基础。论证了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SciML通用微分方程模型发现方法推广到基于理论的CRN中缺失反应的数据驱动发现。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。该奖项反映了美国国家科学基金会的法定使命，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。

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.