CAREER: experimental design and model reduction in systems biology

数学建模是理解复杂生物系统行为的重要工具。在系统生物学中，数学模型通常非常复杂，考虑了系统中基因和蛋白质之间的相互作用。相比之下，实验数据的数量几乎总是有限的。复杂模型和有限数据之间的这种信息鸿沟给模型分析带来了挑战，并模糊了对复杂生物系统背后的关键控制机制的洞察。缩小信息差距的两个直观策略是获取更多数据和简化模型。为了获得更多的数据，实验设计需要回答以下问题：在所有可能的新实验中，哪个会带来最多的新信息量？要简化模型，需要回答这样一个问题：在所有可能的简化(例如，删除或组合参数或变量)中，哪一个是最合适的？该项目旨在开发新的计算算法来回答这两个问题。实验设计是生物学家每天都在考虑的问题。模型简化回答了一个基本的生物学问题，即如何识别复杂生物系统背后的关键机制。这两个问题的严密计算算法有望极大地有利于复杂生物系统的实验研究，为生物学家的专家直觉提供补充，并为该领域带来新的知识，这正是本项目的研究重点。拟议的研究还将导致教育活动，如为生物学家编写计算教程和讲习班，在本科生和研究生一级开发新的跨学科课程，以及研究监督和面向高中生、本科生和研究生的社区外联。虽然实验设计和模型简化是两个完全不同的问题，但这个项目将开发一个统一的计算框架和几何解释来系统地解决这两个问题。其核心思想是将数学模型看作一个流形，并利用其几何特征来指导实验设计和模型简化。这项拟议的研究被组织成两个推进。推力1号的目标是开发计算算法，以识别将参数不确定性降至最低的实验，建立几何解释。拟议的算法将在开源软件中实现，这些软件将提供给来自不同学科的研究人员，并将作为教育工具。推力2旨在开发基于流形学习的模型简化算法，探索它们识别适应行为的机制的能力，并将所提出的算法应用于蛋白质信号通路和细胞分化过程的研究。研究成果将通过同行评议的出版物、会议、研讨会和研讨会教程向广大受众传播。

Mathematical modeling is a crucial tool for understanding behaviors of complex biological systems. In systems biology, mathematical models are often highly complex, accounting for interactions among genes and proteins in the system. In contrast, the amount of experimental data is almost always limited. This information gap between complex model and limited data presents challenges to model analysis, and obscures the insights into the key controlling mechanisms underlying complex biological systems. Two intuitive strategies to close the information gap are to obtain more data and to simplify the model. To obtain more data, experimental design is needed to answer the following question: among all possible new experiments, which one will bring in the maximal amount of new information? To reduce the model, one needs to answer the question: among all possible simplifications (e.g., remove or combine parameters or variables), which one is the most appropriate? This project aims to develop novel computational algorithms to answer both questions. Experimental design is a question that biologists consider on a daily basis. Model reduction answers a fundamental biology question of how to identify key mechanisms underlying complex biological systems. Rigorous computational algorithms for these two questions are expected to greatly benefit experimental studies of complex biological systems, provide insights that are complementary to biologists' expert intuitions, and bring new knowledge to the field, which is exactly the research focus of this project. The proposed research will also lead to educational activities, such as development of computational tutorials and workshops for biologists, development of novel interdisciplinary courses at both undergraduate and graduate levels, as well as research supervision and community outreach to high-school, undergraduate and graduate students. Although experimental design and model reduction are two quite different problems, this project will develop a unified computational framework and geometric interpretation to tackle both problems in a systematic way. The key idea is to consider a mathematical model as a manifold, and use its geometric features to guide experimental designs and model reduction. The proposed research is organized into two thrusts. Thrust 1 aims to develop computational algorithms to identify experiments that minimizes parameter uncertainty, establish geometric interpretations. The proposed algorithms will be implemented in open-source software, which will be offered to researcher from diverse disciplines and will also serve as education tools. Thrust 2 aims to develop model reduction algorithms based on manifold learning, explore their ability to identify mechanisms for the adaptation behavior, and apply the proposed algorithms to study protein signaling pathways and cell differentiation processes. The research results will be disseminated to the broad audience via peer reviewed publications, conference, seminars, and workshop tutorials.