eMB: Collaborative Research: A mathematical theory for the biological concept of modularity

Biological phenomena are often driven by complex dynamic regulatory networks. In natural or engineered systems, complicated structures can be generated from simpler building blocks, or modules. This notion of complex systems built from modules is also prevalent in modern systems biology. However, a clear theoretical foundation of modularity, including useful definitions of basic concepts and mechanisms, is still missing. This research project will fill this gap by defining modular structures in biological systems in a mathematically rigorous way. The research will determine why modularity can be advantageous to an organism and elucidate how modularity can be leveraged to advance our understanding of molecular systems. Studying the modularity of specific gene regulatory networks underlying salamander limb regeneration as well as hormone regulation in plants harbors the potential to reveal novel biological insights. Through involvement of students in all aspects of the research, this project contributes to the interdisciplinary training of STEM workforce. The dissemination of results through a dedicated project website and webinars enables anyone to analyze biological network models. The foundation of this project is a rigorous, structure-based definition of modularity in the context of Boolean networks, a common modeling framework in systems biology. Through computational, experimental, and theoretical studies, it will be shown that this definition of modularity (i) is biologically meaningful, (ii) implies a decomposition of the dynamics of Boolean networks, which can be employed to efficiently compute their dynamics, and (iii) that modular networks can be controlled effectively. The theoretical results, including theorems and implemented algorithms for practical computation, will advance the body of knowledge in the fields of network analysis, systems biology, and developmental biology. The validity of the project will be demonstrated through (1) in vivo analyses in the model plant Arabidopsis, (2) in silico analyses in an emerging animal model, axolotl. This will yield novel biological insights regarding (1) the interplay between phytohormones during Arabidopsis organogenesis, and (2) gene regulatory networks directing fibroblast reprogramming in axolotls. 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.