Unexpected network dynamics

Cells respond to external challenges and internal disruption by expressing genes that produce new proteins, or by modulation of the function of existing proteins. These processes are regulated by other proteins, forming a web of interactions from which the cell’s behavior emerges. The web of interaction responsible for these decisions is called a gene regulatory network, and understanding its behavior can allow the prediction of cellular responses to important conditions, such as cancer-causing perturbations and medical interventions. Mathematical models are crucial in this effort, but finding an accurate model from experimental data is very difficult. The proposed work investigates gene regulatory network models using mathematical methods together with machine learning to identify more common and less common predicted cellular behaviors. This blend of traditional mathematics with AI tools leverages the known behavior of small networks to predict the behavior of large networks, currently a challenging task. The work will allow the discovery of surprising and unexpected network behavior which may be detrimental to cellular health, and will advance the ability to study gene networks of clinical interest, such as the cellular machinery of the deadly fungus C. neoformans. This project will also train student researchers in theory, computation, and scientific communication, which are skills that translate well into the private research sector of the economy. Additionally, the proposed work will be the basis of lesson plans for middle- and high-school teachers. Modeling the dynamics of gene regulatory networks is a very important problem in systems biology. The precise parameterization of gene regulatory network models is an extremely challenging problem, severely taxing experimental methodologies and limiting predictive power. The proposed work changes this paradigm by interrogating the entire class of models compatible with a regulatory network structure. This is only possible since the class of monotone Boolean models (MBM) is finite, and each model has a finite state space, allowing the enumeration of all attractors. Importantly, the lattice structure of MBM allows theoretical, rather than just numerical, understanding of the structure of the attractors across all MBMs. The proposed work combines deep mathematical understanding of the lattice structure of MBM and their continuation structure to enable, for the first time, an inductive description of attractors of larger networks from the attractors of their subnetworks. Hypothesis generation will be aided by machine learning and AI. These computational tools will be used to scale up the proposed approach to larger networks. The mathematical and data science tools developed in this proposal will be used to study the titanization phenotype of the pathogenic yeast C. neoformans, and the number of intermediate states in the epithelial-mesenchymal transition network implicated in cancer. Both graduate and undergraduate students will be provided with professional and research mentorship, and middle- and high-school teachers will be provided with classroom exercises in modeling genetic networks that support the Common Core mathematics guidelines. 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.