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.
